Aramid Conveyor Belts

Energy-saving potential of Aramid-based conveyor belts

S. Drenkelford Master of Science Thesis

Department of Maritime and Transportation Technology Energy-saving potential of Aramid-based conveyor belts

Master of Science Thesis

For the degree of Master of Science in Mechanical Engineering at Delft University of Technology

S. Drenkelford

February 23, 2015

Faculty of Mechanical, Maritime and Materials Engineering (3mE) · Delft University of Technology FACULTY MECHANICAL, MARITIME AND MATERIALS ENGINEERING Delft University of Technology Department Marine and Transport Technology

Mekelweg 2 2628 CD Delft the Netherlands Phone +31 (0)15-2782889 Fax +31 (0)15-2781397 www.mtt.tudelft.nl

Specialization: Transport Engineering and Logistics

Report number: 2014.TEL.7928

Title: Energy-saving potential of aramid-based conveyor belts

Author: S. Drenkelford

Title (in Dutch) Energie besparende potentie van aramide transportbanden

Assignment: Graduation

Confidential: Yes

Initiator (university): prof.dr.ir. G. Lodewijks

Initiator (company): - H. Van De Ven

- Drs. A.M. Beers

Supervisor: MSc M. Zamiralova

Date: January 23, 2015

This report consists of 90 pages and 3 appendices. It may only be reproduced literally and as a whole. For commercial purposes only with written authorization of Delft University of Technology. Requests for consult are only taken into consideration under the condition that the applicant denies all legal rights on liabilities concerning the contents of the advice.

FACULTY OF MECHANICAL, MARITIME AND MATERIALS ENGINEERING Delft University of Technology Department of Marine and Transport Technology

Mekelweg 2 2628 CD Delft the Netherlands Phone +31 (0)15-2782889 Fax +31 (0)15-2781397 www.mtt.tudelft.nl

Student: Assignment type: Graduation Mentor: Prof. dr. ir. G. Lodewijks Report number: 2014.TEL.xxxx Specialization: TEL Confidential: Creditpoints (EC): 35

Subject: Energy consumption of aramid conveyor belts

The bulk material handling industry uses mile after mile of rubber conveyor belts to transport ore and minerals around dry bulk material processing facilities. Research has shown that using aramid materials in conjunction with an NR/BR rubber drastically reduces the energy consumption of conveyor belts. In particular, the overall maximum energy saving could be as much as 60% depending on the conveyor belt system used.

Currently, data are available to estimate the energy consumption of aramid conveyor belts. However, the estimation is based on specific conveyor belt applications. In order to predict the energy saving more generally, this assignment will improve currently available datasheets and establish the fundamental estimation of energy consumption towards general conveyor belt applications, when aramid conveyor belts are in use. The study and analysis will be based on the norm of DIN 22101. One of the outputs of the assignment will be a GUI application allows users to investigate the energy consumption with respect to general belt conveyor configurations.

The report should comply with the guidelines of the section. Details can be found on blackboard.

The professor,

Prof. dr. ir. G. Lodewijks

Summary

Belt conveyor systems are globally responsible for the transportation of vast amounts of bulk solid materials. They are the most efficient solution where large quantities of iron ore, coal, limestone or rocks need to be moved from one place to another. Despite of their efficiency, they still consume large amounts of energy to perform their function. This energy consumption can be significantly reduced by applying Aramid products in conveyor belts. The industry however, is not keen on using these products, since they have not yet proven themselves. The Customer Benefit Model was created by Teijin Aramid to quantify the potential cost savings that can be achieved by the application of Aramid products in conveyor belts and by doing so, convincing potential customers of the benefits. For this purpose, there is a need for a prediction of the possible energy savings that can be achieved by Aramid-based conveyor belts. In this research, a method is developed for the determination of this prediction. A literature survey was done to investigate the current possibilities for the determination of the energy consumption of a belt conveyor. As a primary method of calculation the German belt conveyor standard DIN 22 101 will be used. The energy consuming components of a belt conveyor system are identified and the largest contributor, the indentation rolling resistance, is found to be the most important component that should be determined. Several methods were found to do this, based on viscoelastic half spaces and viscoelastic Winkler foundations. The models that are based on half spaces were found unsuited for this purpose, since a conveyor belt typically consists of a thin layer of rubber material that performs the viscoelastic function. Of the remaining methods, the method of Jonkers and the method of Lodewijks were preferred. To be able to use the method of Lodewijks, Maxwell model parameters need to be determined by approximating the master curves, that were created from measured rubber data from Dynamic Mechanical Analysis, with Prony Series approximations. For the three parameter model that was used and found accurate in literature, the Maxwell model parameters were found to give false results. This was proven by determining the trend of the five parameter model and the trend that was observed for the method of Jonkers, which uses raw data to obtain indentation rolling resistances. It was found that by cutting the master curves at a certain cut-off frequency, the method of Lodewijks can yield quite accurate power requirements for loaded belt conveyors, but underestimates the power requirements for empty conveyors. Due to the complexity of the steps that are required to setup the method of Lodewijks, it is considered not practical and will therefore not be used. The method of Jonkers can be used, although it is known to overestimate the indentation rolling resistance. To reduce this overestimation a modified method of Jonkers is proposed.

Master of Science Thesis v The performance of the proposed method and that of the original Jonkers method were assessed in a case study in which the energy consumptions of four belt conveyor systems were evaluated and compared against the results from external research. The modified method of Jonkers gives a better approximation of the power requirements for loaded conveyor belts, but underestimates the power requirements of empty conveyor belts. It is concluded that the modified method of Jonkers should be used to estimate the power requirements for loaded conveyor belts and the original method of Jonkers for the empty conveyor belts. Since the proposed methods and the generated results are all based on theoretical models, it is recommended that a pilot belt is installed, on which actual measurements can be done. These measurements can then be used to improve the proposed modification to Jonkers method. To make this method usable for employees of Teijin Aramid, a software application has been developed that incorporates both the original and the modified Jonkers method. The software application was tested and is able to perform the analysis that is shown in this study.

vi Master of Science Thesis Samenvatting

Transportbanden zijn wereldwijd verantwoordelijk voor het transport van grote hoeveelheden stortgoederen. Ze zijn de meest efficiÃńnte oplossing op plaatsen waar grote hoeveelheden ijz- ererts, kolen, kalksteen of steen verplaatst moet worden. Ondanks hun efficiÃńntie verbruiken deze installaties toch grote hoeveelheden energie. Deze energieconsumptie kan significant worden verminderd door het toepassen van Aramide producten in de transportbanden. Deze technolo- gie wordt echter niet met open armen ontvangen door de bestaande industrie, doordat deze nieuwe types transportbanden zichzelf nog niet bewezen hebben. Het Customer Benefit Model is gemaakt door Teijin Aramid om de potentiÃńle kostenbesparing te kwantificeren die mogelijk zijn door de toepassing van deze transportbanden en hiermee klanten te overtuigen van de vo- ordelen. De input van dit model zijn de energieverbruiken van de verschillende types Aramide transportbanden. Dit rapport beschrijft de bepaling en de ontwikkeling van een methode om deze energieverbruiken te berekenen. Deze methode moet precies genoeg zijn om betrouwbare resultaten te leveren die de ordergrootte van de potentiÃńle energiebesparingen tonen die door het toepassen van Aramide producten mogelijk zijn. De huidige bestaande methodes voor het bepalen van de energieconsumptie van transportbanden zijn onderzocht door middel van een literatuuronderzoek. De Duitse norm DIN 22 101 zal worden gebruikt als basis voor de energieberekeningen. De componenten van het totale energieverbruik van een transportband zijn geÃŕdentificeerd en de indrukrolweerstand, die het grootste aandeel heeft in het totale energieverbruik, is het belangrijkste component om te berekenen. De literatuur beschrijft verscheidene methoden om de indrukrolweerstand te bepalen, gebaseerd op viscoelastische half-ruimten en viscoelastische Winkler matrasmodellen. De methoden die zijn gebaseerd op een half-ruimtemodel blijken minder bruikbaar, aangezien een transportband gebruikelijk bestaat uit dunne lagen viscoelastisch materiaal. Van de overgebleven methoden zijn de methode van Lodewijks en de methode van Jonkers geselecteerd voor dit onderzoek. Om de methode van Lodewijks te kunnen gebruiken moeten eerst de Maxwell model parameters bepaald worden door met Prony series de master curves te benaderen. Deze master curves zijn gebaseerd op gemeten materiaaleigenschappen die zijn bepaald met Dynamic Mechanical Analysis. Met deze Maxwell model parameters is de methode van Lodewijks doorgerekend en de resultaten bleken het tegenovergestelde te vertonen dan was verwacht, namelijk dat de toevoeg- ing van Sulfron een negatieve invloed zou hebben op de roleigenschappen van het rubber. De hypothese dat het drie-parameter model onjuiste resultaten geeft is bevestigd door de berekening van het vijf-parameter model en de berekening van de methode van Jonkers. Het drie-parameter model kan wel gebruikt worden door de master curves af te snijden boven een bepaalde frequen-

Master of Science Thesis vii tie. De op deze manier behaalde resultaten zijn vrij accuraat voor de beladen transportbanden, maar onderschatten het benodigde vermogen voor de lege transportband. Doordat deze methode erg complex is om op te zetten, wat niet gewenst is voor de industriÃńle toepassing waar dit rapport op doelt, is besloten om de methode van Jonkers verder te gebruiken. Het is echter bekend dat deze methode de vermogensbehoeftes overschat, dus een aangepaste methode van Jonkers is voorgesteld om dit gedrag tegen te gaan. De prestaties van de aangepaste methode van Jonkers en die van de originele methode van Jonkers zijn getoetst aan de resultaten die zijn gepresenteerd door Lodewijks voor een casus betreﬀende de Optimum Collieries in Zuid-Afrika. Voor beladen transportbanden geldt dat de aangepaste methode van Jonkers een betere benadering van de vermogensbehoeften geeft dan de originele methode van Jonkers. Voor lege transportbanden is dit niet het geval en zorgt de aanpassing van de methode voor een onderschatting van de vermogensbehoeften. De conclusie is dat de vermogensbehoeften voor de beladen transportbanden dus het beste berekend kunnen worden met de aangepaste methode van Jonkers en de vermogensbehoeften van de lege transportbanden met de originele methode van Jonkers. Gezien de voorgestelde aangepaste methode van Jonkers en de gegenereerde resultaten enkel zijn gebaseerd op theorie, is het van belang dat er metingen worden gedaan aan een echte transportband, zodat de aangepaste methode van Jonkers indien nodig bijgesteld kan worden. Een software applicatie is ontwikkeld, tegelijkertijd met dit rapport, zodat de medewerkers van Teijin Aramid de originele en de aangepaste methode van Jonkers kunnen gebruiken om vermogensbehoeften en dus energieverbruiken van transportbanden te kunnen bepalen. Deze applicatie is getest en is in staat om de analyse naar behoren uit te voeren.

viii Master of Science Thesis List of symbols

Capital letters A First part contact length of idler and belt m C Secondary resistance factor - C’ Last part contact length of idler and belt m CV Correction factor for the Jonkers method - D Diameter idler roll m E’ Storage modulus Pa E” Loss modulus Pa E* Complex modulus Pa E1 First Maxwell model parameter Pa E2 Second Maxwell model parameter Pa F Total motional resistance N FAuf Load/belt friction in loading zone N FGr Belt/belt cleaner resistance N FGb Belt bending resistance at pulley N FH Main resistance N FHi Main resistance of section i N FN Secondary resistances N FS Special resistances N FSchb Load/chute resistance in loading zone N FSt Gradient resistance N FT ri Pulley bearing resistance N Fz Gravitational force of mass N H Conveyor lifting height m L Conveying lenght m Li Conveying length section i m P Required drive power W U’ Idler bearing resistance N 00 UB Belt flexure resistance N 00 UE Indentation rolling resistance N 00 UF Bulk flexure resistance N Small letters f Friction factor carry strand and return strand combined - fi Friction factor indentation rolling resistance - fb Friction factor idler bearing resistance - fbe Friction factor belt flexure resistance - fbu Friction factor bulk flexure resistance - fij Friction factor Jonkers method - 0 fij Friction factor modified Jonkers method - fo Friction factor carry strand - fu Friction factor return strand - g Gravitational acceleration m/s2 h Cover layer thickness m 0 mG Mass belt kg/m 0 mL Mass load kg/m 0 mR Mass rotating parts kg/m 0 mRo Mass rotating parts (Carry strand) kg/m 0 mRu Mass rotating parts (Return strand) kg/m qR Distributed load on an idler roll N/m v Belt speed m/s

Greek letters α Wrap angle radians δ Phase loss angle o or radians 0 Maximum strain - η Damping coeﬃcient Pa s θ Inclination angle (total system) o o θi Inclination angle of section i λ Trough angle o µ Friction factor pulley/belt - σ Applied stress Pa σ0 Maximum applied stress Pa ω Harmonic excitation frequency of indentation Hz

x Master of Science Thesis List of abbreviations

BEM Boundary Element Model BR Butadiene Rubber CEMA Conveyor Equipment Manufacturers Association DIN Deutsche Institut fÃĳr Normung FEM Finite Element Model MRC Maximum Rolling Coeﬃcient MTPH Metric Tonnes Per Hour NR Natural Rubber phr Parts per Hundred Rubber SBR Styrene-Butadiene Rubber SLS Standard Lineair Solid (model) tan-delta Tangent Delta

Master of Science Thesis xi

Contents

List of symbols ix

List of abbreviations xi

1 Introduction 1 1.1 Energy reduction in belt conveyors ...... 2 1.2 Research goal and scope ...... 3 1.3 Report structure ...... 3

2 Aramid conveyor belts 5 2.1 Twaron ...... 5 2.2 Sulfron ...... 8

3 The energy consumption of belt conveyors 9 3.1 Belt conveyor basics ...... 9 3.1.1 Basic setup of a generic belt conveyor ...... 9 3.1.2 Conveyor belt composition ...... 10 3.1.3 Other components of a belt conveyor system ...... 11 3.2 Energy calculations of DIN 22 101 ...... 13 3.2.1 Total motional resistance ...... 13 3.2.2 Resulting power consumption ...... 16 3.3 Energy consumption distribution ...... 16

4 Indentation rolling resistance 21

Master of Science Thesis xiii 4.1 General theory ...... 21 4.1.1 Viscoelasticity ...... 21 4.1.2 Dynamic Mechanical Analysis ...... 22 4.1.3 Material models ...... 23 4.1.4 Modelling the belt backing layer ...... 24 4.2 Theoretical methods ...... 26 4.2.1 May et al...... 26 4.2.2 Hunter ...... 27 4.2.3 Jonkers ...... 28 4.2.4 Spaans ...... 28 4.2.5 Lodewijks ...... 29 4.3 Numerical methods ...... 32 4.3.1 Wheeler ...... 32 4.3.2 Qui ...... 32 4.4 Selected method ...... 33

5 Rubber rheology 35 5.1 Experimental setup ...... 35 5.2 Creating master curves ...... 36 5.3 Maxwell model parameters ...... 38 5.4 Cutting the master curves ...... 44 5.5 Jonkers method ...... 47 5.5.1 Jonkers method with master curve data ...... 47 5.5.2 Jonkers method without master curve data ...... 48

6 Proposed method 49 6.1 Analysis ...... 49 6.2 Set-up ...... 51

7 Verification 57 7.1 Optimum Collieries ...... 57 7.2 Results ...... 59 7.2.1 Verification power requirements for loaded conveyors ...... 59 7.2.2 Verification power requirements for empty conveyors ...... 62 xiv Master of Science Thesis 7.2.3 Discussion results Optimum Collieries verification ...... 65

8 Case study 67 8.1 Case study: stockpile conveyor ...... 67 8.2 Calculation of the energy consumptions with master curve data ...... 69 8.3 Calculation of the energy consumptions without master curve data ...... 74

9 Software application 77 9.1 System of requirements ...... 77 9.2 System architecture ...... 78 9.2.1 Calculation ...... 78 9.2.2 Calculation of a conveyor belt ...... 79 9.3 Recalculation of the case study ...... 81 9.4 Extra options ...... 85

10 Conclusions 87

11 Recommendations 89

Appendix A: research paper 91

Appendix B: draft of research paper for BeltCon 2015 97

Appendix C: results DMA tests 107 11.1 Control sample, 3Hz ...... 107 11.2 Sulfron sample, 3Hz ...... 109 11.3 Control sample, 6Hz ...... 111 11.4 Sulfron sample, 6Hz ...... 114 11.5 Control sample, 10Hz ...... 116 11.6 Sulfron sample, 10Hz ...... 119 11.7 Control sample, 20Hz ...... 122 11.8 Sulfron sample, 20Hz ...... 125

Bibliography 129

Master of Science Thesis xv xvi Master of Science Thesis Chapter 1

Introduction

Since the industrial revolution, mankind has had an ever-growing need for raw materials, such as iron ore and coal. To fulfil this need, large logistical networks have grown all over the world to move these materials from one place to another. One of the backbones of these networks is the belt conveyor, which can move large quantities of bulk solid material, often with a greater efficiency than for instance trucks or trains. Despite of this great efficiency, they still consume vast amounts of energy. Due to the rapid depletion of fossil fuels around the world and the implied impact on the environment, the urge to reduce this energy consumption keeps increasing.

Figure 1.1 Example of a belt conveyor system in a mining environment [1].

Master of Science Thesis 1 1.1 Energy reduction in belt conveyors

In the past twenty to thirty years there has been an increasing amount of research done on the subject of reducing the energy consumption of conveyor belts. A German study indicated that the largest part of the energy consumption is due to the indentation of the rubber covers when the belt passes an idler roll [2]. This has resulted in the development of the so-called Low Rolling Resistance (LRR) conveyor belts. These belts were designed to reduce the amount of energy that is lost during the conveying operation by reducing the rubber hysteresis losses of the running cover compounds (see Figure 1.2). Work done by researchers like Nordell [3], Gallagher [4] and Zhang [5] have shown the potential of LLR conveyor belts to reduce the energy consumption of both troughed belt conveyors and pipe conveyors.

Figure 1.2 The energy that is required to indent the belt cover material is not all recovered when the material is released. Hence, the loss is the grey area.

Teijin Aramid BV, a former branch of AkzoNobel that is now owned by the Teijin Group, produces products that can also substantially reduce the energy consumption of belt conveyor systems, which are called Aramids. Aramid is an acronym for Aromatic Polyamide and it is a high-performance fibre material. These materials can be used in the carcass of a conveyor belt and in its rubber compounds to reduce the hysteresis losses. In Chapter 2 these materials and their application in conveyor belts are explained elaborately. A study performed by Lodewijks suggests that the savings that can be achieved by these Aramid products in belt conveyor systems can be as high as 60% [6]. Despite of these motivating numbers, the industry is very conservative in the adoption of these new products, due to the large financial risks that are involved with the failure of large belt conveyor systems and failures that have happened with early versions of Aramid-based conveyor belts in the 1990’s. Since that time, Aramid conveyor belts have been improved to a level where they can compete with the conventional steel cord belts. To convince potential clients that these conveyor belts can be a good alternative that can save energy and costs, the Customer Benefit Model (CBM) was created by Teijin Aramid. This model uses the potential energy savings and emission data to provide clients with an overview of the reduced environmental impact and the cost reductions that can be achieved by applying Aramids in conveyor belts. The energy savings are currently determined with fixed proportional factors which are used to scale the potential energy consumptions of the different Aramid-based

2 Master of Science Thesis conveyor belt types in comparison with a conventional steel cord conveyor belt.

1.2 Research goal and scope

The scaling factors for the energy consumption that are used in the CBM are based on a single case study, which can result in varying results when applied to generic belt conveyor systems. In this research, a method is developed to estimate the energy consumption of a generic belt conveyor system under steady state operating conditions that is more accurate than the current solution and therefore yields a more realistic result. With the focus on its usability in a non- technical environment, this study is about ﬁnding the balance between the ease-of-use and the technical accuracy. To reach this goal, the following research questions will be answered:

- Which factors are responsible for the energy consumption of a conveyor belt and to what extent?

- What methods to determine the energy consumption of belt conveyors are available in literature and how are they applicable for this topic?

- What is the desired accuracy of this estimation?

- What should be used as comparison to quantify these energy savings?

To make this method usable with the CBM, a user-friendly software application will be developed alongside of this method, that will allow Teijin employees to calculate the first approximation of the energy consumption of a generic belt conveyor system, in order to use it in the Customer Benefit Model to determine the potential cost savings and reductions in emissions. By comparison with field test results and calculations by consultancy firms, the results of this method can be verified. This study is done as a graduation project at the Delft University of Technology for the faculty of Mechanical, Maritime and Materials Engineering (3me) and Teijin Aramid BV. As stated by the assignment (as showed at the start of this report) this research will be based on the German standard DIN 22 101, in which a methodology is stated for the calculation and design of belt conveyor systems.

1.3 Report structure

In Chapter 2 the Aramid products are explained that are used by Teijin to reduce the energy consumption of conveyor belts. Chapter 3 will show how belt conveyors in general consume energy and how this energy consumption is distributed. In Chapter 4 the details of the indentation rolling resistance are explained, along with the methods that were found in literature to determine this resistance. The limitations of the rubber data that is used in this report is shown in Chapter 5, after which a proposal is done to modify the only remaining method in Chapter 6. Chapter 7 shows the verification of this modified method by comparing it with a case study from public literature. Chapter 8 shows a case study of a fictive belt conveyor system that illustrates the function of this method and the performance of the Aramid-based conveyor belts.

Master of Science Thesis 3 In Chapter 9 the software application that has been developed alongside of this method is shown, which will be able to estimate the energy consumption of a generic belt conveyor system. Finally, conclusions and recommendations are stated in Chapters 10 and 11.

4 Master of Science Thesis Chapter 2

Aramid conveyor belts

Teijin Aramid produces two types of aramid that can reduce the energy consumption of belt conveyors: Twaron and Sulfron. They are engineered to focus on two diﬀerent aspects of energy losses in belt conveyors, respectively the reduction of belt weight and the reduction of the running resistance.

2.1 Twaron

Twaron is a high-strength ﬁbre material with molecules that are characterized by rigid polymer chains. These molecules are linked by strong hydrogen bonds that transfer mechanical stress very eﬃciently, making it possible to use chains of a low molecular weight. A picture of their general molecular structure is shown in Figure 2.2. Figure 2.1 shows the various shapes in which this material is produced.

Figure 2.1 The various shapes in which Twaron is produced. The spool of ﬁbre in the middle can be used to create a carcass of a conveyor belt.

Master of Science Thesis 5 Figure 2.2 Molecular structure of an aromatic polyamide.

In general, the carcass of a belt conveyor for heavy duty applications is made out of steel cords that are embedded in the rubber of the conveyor belt. The function of this carcass, which is transmitting the tensional force, can also be fulfilled by a Twaron fabric carcass. Such a carcass with a similar strength class is a lot lighter than a steel cord carcass, since Twaron is five times stronger that steel on a weight-for-weight basis. Twaron fibres can be woven in two carcass shapes (see Figure 2.3). For long overland conveyors the straight warp fabric is most commonly used, since it gives a more sturdy carcass. Figure 2.4 shows a chart in which the strengths of different materials are shown. It is clear that steel and polyester, which are very common materials in carcasses of conveyor belts, do not even come near the strength per mass of Twaron.

Figure 2.3 The two general carcass shapes that can be woven from Twaron yarns. [7]

6 Master of Science Thesis Figure 2.4 Strength comparison of various carcass materials. [7]

Due to the lower weight of Twaron in comparison with steel, the weight of the belt decreases when a Twaron carcass is used. The weight reduction is even further enhanced by the fact that less rubber is required to encase the carcass, since there are no signiﬁcant gaps between the tension members of a Twaron fabric carcass, as is the case with a steel cord carcass. Figure 2.5a shows the composition of a generic steel cord conveyor belt, in which can be seen that there is a lot of rubber between the steel cords. In a Twaron straight warp fabric carcass, as shown in Figure 2.5b, the Twaron cords are very close to each other, forming an approximately ﬂat surface.

(a) Steel cord carcass. [8] (b) Twaron fabric carcass. [7]

Figure 2.5 Carcass types in conveyor belts

Master of Science Thesis 7 2.2 Sulfron

The running resistance that a conveyor belt needs to conquer to maintain its operation is largely due to indentation losses [2]. The second product of Teijin Aramid, Sulfron, is a rubber compound ingredient that can reduce the energy that is consumed by the conveyor belt when it passes over each idler roll that support it. During these indentations, the carbon black particles within the material break up. When the rubber is released into its original shape as it passes the idler rolls, these particles bond again, which consumes energy. This is where Sulfron comes in, since it comes in between the formation of the new chemical bonds and thus reducing the consumed energy. Besides this advantage, the addition of Sulfron is also beneﬁcial for the resistance to abrasion and the ﬂexibility of the belt. Figure 2.6 shows pellets of Sulfron that can be added to the rubber compounds.

Figure 2.6 Pellets of Sulfron that can be added to a rubber compound to reduce the running resistance of a conveyor belt.

By using Twaron and Sulfron in a conveyor belt, the operational energy consumption can be reduced. Also, if the running resistances are reduced far enough, it could even result in lower requirements for other components in the belt conveyor system, like the drives, the take-up system and the idlers. To determine these possibilities, the energy and tension requirements need to be determined. In the next chapter, the methodology of DIN 22 101 is explained, which will be used as the primal method of calculation.

8 Master of Science Thesis Chapter 3

The energy consumption of belt conveyors

in 1982, the Deutsches Institut für Normung (DIN) published a standard that contained a basic guide for the calculation of the various aspects of belt conveyors. It is called DIN 22 101, “Belt conveyors for bulk materials; bases for calculation and design” [9] and it has been one of the most important tools that engineers can use to predict, amongst others, the energy requirements of a belt conveyor system. For the estimation of the energy consumption this standard determines the resistance to motion of the combination of the belt, the load and the elevation. In this chapter the basic setup of a belt conveyor system and the accompanying components are explained, after which the procedure of DIN 22 101 to determine the energy consumption of belt conveyors is presented. Finally, the relation of this procedure to experimental results found in literature is shown.

3.1 Belt conveyor basics

It is important to understand the composition of belt conveyor systems in general to be able to perform a good calculation of its energy consumption. In this section this general composition is presented and examples of the components are shown.

3.1.1 Basic setup of a generic belt conveyor

Independent of the exact shape and size, any belt conveyor system contains a number of key components. A schematic picture of a generic belt conveyor system is shown in Figure 3.1, in which these components can be seen. Material is loaded at the tail of the conveyor by either a feeding chute or a feeder belt. It is then transported by the belt to the head of the conveyor, where the material is discharged. For overland belt conveyors the carry side of the conveyor generally has a trough shape, as depicted in Figure 3.2. This configuration allows a much greater capacity than a flat belt. Other configurations are possible, like a two roll trough or a five roll trough, but this study focusses on three roll troughs, since it is the most commonly used configuration.

Master of Science Thesis 9 Figure 3.1 Setup and key components of a generic belt conveyor system.

Two angles are of importance in the cross section of the transported material (see Figure 3.2): the trough angle λ, which is the angle of the side rolls with the horizontal axis and the angle of surcharge β, which is the angle under which the bulk solid material rests on the belt. The angle of surcharge depends on the material and the size of the lumps. In general, an angle of 20 to 25 degrees is used for materials like coal and ore.

Figure 3.2 Cross section area of a conveyor belt in a three roll trough conﬁguration.

3.1.2 Conveyor belt composition

Conveyor belts for long overland belt conveyors can be divided into two general categories. The ﬁrst are conveyor belts with a steel cord carcass. Long steel cords run in the direction of the conveyor belt to deal with the tensile forces that the conveyor belt experiences along its track. Figure 3.3a shows a schematic representation of such a conveyor belt. The tensile members are encased in the core of the belt, in the rubber of the carcass layer. The top cover layer is generally made of an abrasive-resistant rubber, since it has to deal with the impact and the grinding of

10 Master of Science Thesis the transported material. The bottom cover is often made of another type of rubber that is designed to reduce the rolling resistance. Figure 3.3b shows a schematic representation of the second belt category: conveyor belts with a fabric carcass. There are a couple of materials that are frequently used to create these fabric carcasses, like polyester, Nylon and Aramid. For long overland conveyors, only Aramid is a worthy material, since it can withstand far greater tensile forces and its elongation under tension is considerably smaller. Similar as with a steel cord belt, a fabric belt also has an abrasive-resistant top cover and a less-rolling resistant bottom cover. It is however often found that the carcass layer that embeds the fabric is thinner than the carcass layer of a steel cord belt, since the surface pressure is better distributed due to the approximately ﬂat surface of such a fabric layer.

(a) Steel cord carcass. (b) Twaron fabric carcass.

Figure 3.3 Carcass types in conveyor belts.

3.1.3 Other components of a belt conveyor system

As shown in Figure 3.1, a belt conveyor system has at least seven important components besides the conveyor belt itself and the static structures that are required to support the whole system. In this study only the belt and the components that directly inﬂuence the belt’s performance are looked into, which are the pulleys, the idlers and the take-up system. The pulleys are located at the begin and the end of a belt conveyor system and their function is to reverse the direction of the belt. In many belt conveyor systems the head pulley is also the drive pulley that powers the belt conveyor. It transfers the rotational power of a drive motor to the pulling force that moves the conveyor belt. An example of a head pulley is shown in Figure 3.4. The idlers support the conveyor belt along the entire track. The combination of the idler rolls that support the total width of the belts in one frame is called an idler set and they are located along the entire conveyor path, standing at distances of one to several meters from each other. In Figure 3.5 four of these sets are shown.

Master of Science Thesis 11 Figure 3.4 Example of a head pulley. [10]

Figure 3.5 Example of idler sets. [11]

Figure 3.6 Example of a (gravity) take-up system. [12]

The take-up system provides the force that is required to keep the belt tension above a certain level. This belt tension is required to be able to transfer the drive power onto the conveyor belt and to prevent belt sag between the idler sets, which would result in an increasing energy consumption. Figure 3.6 shows a take-up system that is powered by gravity. There are also systems that increase the belt tension by tensioning one of the pulleys with the help of winches or threaded axles. The energy that is consumed by a belt conveyor system depends on these components and the circumstances under which the system is operating. To calculate the magnitude of this energy consumption the methodology of DIN 22 101 can be used, which is explained in the next section.

12 Master of Science Thesis 3.2 Energy calculations of DIN 22 101

DIN 22 101 determines the energy consumption of belt conveyors based on the motional resistances of the belt, the material and the surrounding moving equipment. It states that the power consumption of a belt conveyor system during steady state operating conditions can be determined by the following equation:

F · v P = (3.1) η in which: P Required power [W] F Total motional resistance force [N] v Belt speed [m/s] η Eﬃciency of the drive The power consumption of a belt conveyor that is starting or stopping varies from the power consumption during steady state conditions. Due to the fact that these actions generally consume only a fraction of the time that the conveyor runs in a steady state condition, the choice was made to neglect these starting and stopping states. Therefore, the method presented in this report only considers the belt conveyor system during steady state conditions.

3.2.1 Total motional resistance

The total motional resistance force used in Equation 3.1 is the sum of four resistance forces:

F = FH + FN + FSt + FS (3.2)

These four resistance forces are explained below:

Main resistance, FH The main resistance covers the force that is required to move the load an to keep the moving parts of the conveying system in motion. This resistance occurs along the entire length of the conveyor. The main resistance of a belt conveyor can be determined by equation 3.3. One has to note that this equation considers the combination of the carrying strand and the return strand of a belt conveyor by the usage of one combined resistance factor, f.

0 0 0 FH = L · f · g · [mR + (2mG + mL) · cos(θ)] (3.3) in which:

FH Main resistance [N] L Conveyor length [m] f hypothetical friction coeﬃcient for the upper and the lower strand jointly [-] g Gravitational acceleration [m/s2] 0 mR Mass of the rolls per meter of belt length [kg/m] 0 mG Mass of the belt per meter of belt length [kg/m] 0 mL Mass of the load per meter of belt length [kg/m] θ Mean angle of inclination [o]

Master of Science Thesis 13 In DIN 22 101, the friction coefficient f is chosen from a table for belt filling ratios in the range from 0.7 to 1.1, based on the operating and installation conditions and the experience of the engineer. According to this method, the value of f is between 0.012 and 0.035. A concise version of this table can be seen in Table 3.1. If the different values of the friction factors of the upper and the lower strand are known, the calculation is done in twofold, where the weight of the carried material is only accounted for in the calculation of the upper strand.

Table 3.1 Standard values for the average coeﬃcient of friction f for the combination of the carry strand and the return strand of belt conveyors. [9]

Situation f Horizontal conveyors, inclined conveyors, gently declined conveyors - Favourable operating conditions 0.017 - Normally constructed and operated installations 0.020 - Unfavourable operating conditions 0.023 to 0.027 - Normally constructed and operated installations up to 0.035 in extremely low temperatures Declined conveyors (drives operate as dynamos) 0.012 to 0.016

Secondary resistances, FN The secondary resistances that are experienced by the belt conveyor are those that are caused by friction of components at the head an the tail of a belt conveyor. They consist of the resistance due to belt scrapers, loading of the belt and the resistance of the belt when passing pulleys. Stated otherwise, they are resistances that occur only locally and are therefore not dependent on the length of the conveyor. Equation 3.4 represents these secondary resistances.

FN = FAuf + FSchb + FGr + FGb + FT ri (3.4)

With:

FN Secondary resistances [N] FAuf Frictional resistance between the load and the belt in the loading zone [N] FSchb Frictional resistance between the load and the lateral chutes in the loading zone [N] FGr Frictional resistance caused by belt cleaner [N] FGb Belt resistance to bending at the pulleys [N] FT ri Pulley bearing resistance [N] Since these resistances are independent of the length of the belt, their contribution becomes smaller as the length of the conveyor increases. The secondary resistances are generally accounted for by multiplying the main resistance by a factor C, according to the following relation:

14 Master of Science Thesis F C = 1 + N (3.5) FH

The 1982 version of DIN 22 101 contains a table in which the magnitude of the factor C can be determined, based on the length of the belt conveyor. A copy of this table is shown in Table 3.2. It can be seen that only conveyors with a length of 80 meters or higher are considered.

Table 3.2 Standard values for the coeﬃcient C for belt conveyors. [9]

L [m] C L [m] C 80 1.92 600 1.17 100 1.78 700 1.14 150 1.58 800 1.12 200 1.45 900 1.10 300 1.31 1000 1.09 400 1.25 1500 1.06 500 1.20 ≥ 2000 1.05

For conveyors that are shorter than 80 meters, or those that have multiple feeding points, the secondary resistances need to be determined more speciﬁcally by using Equation 3.4. These special conveyors will not be taken into account in this study, since short conveyors do not beneﬁt enough from the application of Aramids in their conveyor belts to justify the required capital investment and conveyors with multiple feeding points are outside the scope of this research.

Gradient resistance, FSt For conveying systems of which the head and the tail are situated on diﬀerent height levels, the gradient resistance FSt describes the required energy to lift the material over this height diﬀerence. This is done by simply using the physical law of potential energy and is shown in the following equation:

0 FSt = H · g · mL (3.6)

0 Where H is the height diﬀerence in meters and mL the mass of the load per meter of belt length, in kilograms per meter.

Special resistances, FS Special resistances FS occur when a conveying system is badly aligned or when special devices are placed to unload the belt at another point than the head of the conveyor. In this research, these circumstances will not be looked into, so the Special resistances will be neglected throughout this report.

Master of Science Thesis 15 3.2.2 Resulting power consumption

The sum of the four resistances can be reduced to a more tidy formula (Equation 3.7), in which the secondary resistances are taken into account by the earlier mentioned factor C and the special resistances are neglected. This formula can then be inserted into Equation 3.1, which yields the equation of the power consumption of a belt conveyor during steady state operating conditions (Equation 3.8).

0 0 0 0 F = C · L · f · g · [mR + (2mG + mL)cos(θ)] + H · g · mL (3.7)

v · (C · L · f · g · [m0 + (2m0 + m0 )cos(θ)] + H · g · m0 ) P = R G L L (3.8) η

It is clear that DIN 22 101 does not contain explicit information about the belt’s material properties. These properties can be accounted for by the friction factor f, which is also known as the rolling resistance factor. As stated earlier, this rolling resistance factor is a fictional factor of the upper and the lower strand of the belt conveyor combined and is derived from empirically filled tables. In the next section, the most important components of this rolling resistance factor are identified, which give insight in the possibilities reducing the energy consumption of conveyor belt systems.

3.3 Energy consumption distribution

In 1993 two German researchers, Hager and Hintz, did an extensive study to determine the energy consumption of belt conveyors and the distribution of its components. They identiﬁed seven components that together form the total motional resistance of belt conveyor systems [2]:

00 Indentation rolling resistance, UE The resistance of the conveyor belt rolling over the idler rolls. (see Figure 3.7). When the belt passes over an idler roll, a part of the rubber is indented. A part of the energy that is required for this indentation is transformed into heat and is lost.

Figure 3.7 Indentation Rolling Resistance

16 Master of Science Thesis 00 Belt ﬂexure resistance, UB The internal friction in the conveyor belt due to the deformation of the belt in between idler sets, which is shown in Figure 3.8. Energy is required to reform the belt into its original shape when it approaches the next idler set.

00 Bulk flexure resistance, UF The friction in the bulk material caused by the deformation of the bulk solid material in between idler sets (see Figure 3.8). Between these sets the belt deflects downward and the edges deflect to the outside. When the belt is forced into its original shape at the next idler set, the bulk solid material is forced into its original shape too, consuming energy to overcome the internal frictional forces.

Figure 3.8 Bulk ﬂexure resistance

Idler bearing resistance, U 0 Frictional resistance in the bearings that support each idler roll.

Secondary resistances, FN The resistances that are caused by belt cleaners and friction in loading zones.

Extraordinary resistances, FS The resistances caused by misalignment of components (called the Special resistances in DIN 22 101)

Gradient resistance FSt The energy that is required to lift the material if the head and the tail of the belt conveyor are located on diﬀerent altitudes.

Master of Science Thesis 17 After experiments on different configurations of belt conveyor systems Hager and Hintz concluded that the largest part of the energy consumption of long horizontal belt conveyors for bulk solid materials is due to the indentation rolling resistance [2]. For a 1000 meter long horizontal conveyor, they calculated that the indentation rolling resistance consumed as much as 61% of the total energy consumption of the belt conveying system. A chart of their findings is shown in Figure 3.9. For inclined or declined conveyors, the distribution is different since the gradient resistance is in these cases identified as the largest factor [2] and can be as high as 66% for a belt conveyor with an ascending angle as small as 5%. Of the remaining energy consuming components, the largest one is again the indentation rolling resistance, which contributes 22% to the total rolling resistance. Since there is no way to reduce the amount of energy that is required to lift the material, the indentation rolling resistance is the primary focus to reduce the energy consumption of belt conveyors.

Figure 3.9 The distribution of the consumed energy of a horizontal overland belt conveyor with a length of approximately 1000 meter [2].

Slightly varying results were found by Alspaugh in 2004, who also identiﬁed the indentation rolling resistance as the dominant energy consumer for long overland belt conveyors and the lifting of the material as greatest consumer for inclined or declined conveyors [13].

18 Master of Science Thesis Since the indentation rolling resistance is identified as the largest contributor to the rolling resistance it will be the main focal point of the determination of the energy consumption in this study. Nonetheless, the other main resistances also contribute to the total energy consumption of a belt conveyor system and can therefore not be neglected. To account for these contributions, the results of Hager and Hintz were examined again. These results show that the indentation rolling resistance accounts for 61% of the total resistance in a flat overland conveyor. Within the total main resistance that occurs for this flat conveyor the indentation rolling resistance accounts for 68%. For an ascending conveyor the contribution of the indentation rolling resistance to the total resistance is much lower, but its contribution to the main resistances is found to be 67% (see Figure 3.10). Since these two values are very close to each other, it will be assumed that the indentation rolling resistance always accounts for 68% of the main resistances.

Figure 3.10 The distribution of the consumed energy of a belt conveyor with an inclination angle of 5% [2].

Based on the ﬁndings in this chapter, this study will focus on the determination of the indentation rolling resistance. The ratio of this indentation rolling resistance and the main resistances will be used to scale the obtained results and in that way account for the other main resistances, which will not be calculated themselves. To determine the indentation rolling resistance several methods were found in literature. In the next chapter these methods are explained and the suitable methods will be selected.

Master of Science Thesis 19 20 Master of Science Thesis Chapter 4

Indentation rolling resistance

Chapter 3 concluded that the largest part of the energy consumption of a belt conveyor system is consumed by the indentation rolling resistance. To be able to make a decent prediction of the energy consumption of a conveyor belt, the indentation rolling resistance factor needs to be determined. In literature, several methods were found that determine the indentation rolling resistance. In this chapter the most inﬂuencing methods are explained. The ﬁrst section of this chapter provides general theory that is required to use the theoretical models that are shown in Section 2. In Section 3 the numerical methods to determine the indentation rolling resistance are explained, after which the methods are selected that will be used in this study.

4.1 General theory

In this section the general theory is presented that will be the basis for the determination of the indentation rolling resistance. It will show the fundamental basis of the material and a number of material models that will be used to describe the material and its behaviour.

4.1.1 Viscoelasticity

The indentation of the rubber bottom cover consumes energy since not all of the energy that is absorbed by the indentation is released back into the system as the rubber is relaxed. This is due to the fact that rubber is a so-called viscoelastic material, by which a material is described that is both elastic and viscous at the same time. The material therefore reacts in an interme- diate way to applied stresses or deformations than normal elastic or viscous materials. Where elastic materials are characterised by Hooke’s law and viscous materials by Newton’s law, the behaviour of a viscoelastic materials is somewhere in between. For a harmonically applied load, the deformation also acts harmonically, but due to the viscous part of the material, its reaction is slower than the applied load: it lags by a certain phase angle that is anywhere between 0 (pure elastic material) and 90 degrees (pure viscous material). The responses of these three materials are shown in Figure 4.1. A viscoelastic material can be described by a complex modulus of elasticity, which is a combination of an elastic modulus (the storage modulus, E0) and a viscous modulus (the loss modulus, E00). The relation between these moduli is graphically shown in Figure 4.2, with E* being the complex modulus and δ the phase lag angle, that relates the time lag in the response of the strain on an applied load.

Master of Science Thesis 21 Figure 4.1 Response to strain of an elastic material, a viscous material and a viscoelastic material.

From Figure 4.2 it can be seen that the storage modulus and the loss modulus are related by the following equation:

E00 = tan(δ) (4.1) E0 The tangent of the phase loss angle δ (tan-delta) is a frequently used parameter to describe the performance of a viscoelastic material, since it relates the stored energy to the lost energy in a load cycle. In general: a lower tan-delta represents a material with lower energy losses.

4.1.2 Dynamic Mechanical Analysis

The exact properties of a viscoelastic material are dependent on its composition and the circumstances in which it operates. To determine these properties a technique called Dynamic Mechanical Analysis (DMA) is used. In this technique, a sample of the material is exposed to a

22 Master of Science Thesis Figure 4.2 Relation between the moduli within a viscoelastic material. harmonic deformation, while the stress response is measured. This yields the complex modulus, the storage modulus, the loss modulus and the tan-delta of the material. These properties are dependent on the frequency of the load cycle and the temperature, so the output of a DMA is a temperature sweep, in which the loading frequency is constant, or a frequency sweep in which the temperature is constant. The results of a DMA can be used to create the master curves of a material. These master curves are built up from many small curves, that represent DMA measurements of a single temperature and multiple loading frequencies. These temperature curves can be shifted in the frequency spectrum by using a time-temperature superposition technique called the Williams- Landel-Ferry (WLF) equation, which is given by equation 4.2 [14]. This technique states that for a given temperature and frequency, there is another combination of temperature and frequency for which the same material properties are valid. The frequency shift that is required to reach this new combination is the shift factor aT . This shift factor can be determined by entering the temperature of the individual temperature curves, a reference temperature and the WLF parameters C1 and C2.

C1(T − TG) log(aT ) = (4.2) C2 + (T − TG)

4.1.3 Material models

To be able to use these material properties to determine the indentation rolling resistance, the bottom cover layer of a conveyor belt needs to be modelled in two ways: the material itself and the layer of material. In literature two models are frequently used to describe the viscoelastic material of conveyor belt materials: the Standard Linear Solid (SLS) model and the generalised Maxwell model. The SLS model is a three parameter model and it is the simplest model that can describe the relaxation behaviour that can be identiﬁed in viscoelastic materials. Figure 4.3 shows this model. The spring E1 represents the elastic part of the material and the combination of spring E2 and the damper η represent the viscous part. The relaxation time of this model, τ, is deﬁned as:

η τ = (4.3) E2

This implicates that this model has a single relaxation time, which is not very accurate for real viscoelastic materials. However, it was found by Lodewijks that a single relaxation time can be suﬃcient for belt speeds between 0.1 and 10 m/s [15]. The second model that is used in literature is the expansion of this model, called the generalised

Master of Science Thesis 23 Maxwell model. In this model n branches of a spring and a damper can be added, creating a (2n+1)-parameter model (see Figure 4.4). This provides the potential for a more accurate model, but also implies a more complex model.

Figure 4.3 Standard Linear Solid model.

Figure 4.4 Generalised Maxwell model.

4.1.4 Modelling the belt backing layer

The material models presented above need to be modelled as a layer of material before the indentation rolling resistance can be determined. Two methods were found in literature.

24 Master of Science Thesis The ﬁrst method is the viscoelastic half space, in which a layer of material is assumed of an inﬁnite thickness, as is displayed in Figure 4.5. This method provides a two-dimensional stress model that can handle the most important stresses within such a material: compression stress and shear stress.

Figure 4.5 Graphic representation of a viscoelastic half space.

The second method that was found is to describe the layer as a Winkler viscoelastic foundation model. In this model, the material is assumed to consist of many separate viscoelastic elements on a rigid base, without interaction between these elements (see Figure 4.6). This model implies that the shear stress and the inertia of the material itself is neglected [15]. The advantage of the Winkler foundation model is that the problem is reduced to a one-dimensional problem, which results in simpler equations.

Figure 4.6 Graphic representation of a Winkler foundation model.

Master of Science Thesis 25 4.2 Theoretical methods

The following researchers have made use of the above material models to derive the indentation rolling resistance forces.

4.2.1 May et al.

In 1959, May et al. laid out the first brick in this field of research with a paper called “Rolling friction of a hard cylinder over a visco-elastic material" [16]. They defined the viscoelastic layer as a two-dimensional viscoelastic half space. To describe the behaviour of the material, the SLS model was chosen. The rolling resistance force was determined through the asymmetrical stress pattern that is caused by the stress relaxation within the viscoelastic material. This stress pattern causes a moment around the cylinder’s axis. The rolling resistance force that counteracts this moment was found to be dependent on the belt speed and has a maximum for a certain belt speed. This specific speed corresponded to a peak in the relaxation time distribution, which is material-dependent. The analysis was performed by keeping the indentation depth at a constant level by increasing the load. They concluded that the load to maintain this depth was also dependent on the belt speed, where the load was required to increase for an increasing velocity. In 1995 Lodewijks rearranged this method so that the vertical load was pre-described, instead of the indentation depth, which is more convenient for evaluating belt conveyor systems. He arrived at the following indentation rolling resistance factor [15]:

∗ ∗ Fi fim = ∗ (4.4) Fz

∗ ∗ In which Fz is the pre-described vertical load and Fi the resulting rolling resistance force, which are deﬁned by:

3 " 3 # 3 " 2# ∗ E1a0 b b 2E2ka0 b Fz = 2 − + 3 + 1 − (4.5) 6Rh a0 a0 Rh a0

4 " 2 4# ∗ E1a0 b b Fi = 2 1 − 2 + 8R h a0 a0   4 2! 3! −1 a0 + b E2a0k 3 k b 1 b b k a0 + 2 k − 1 + + 1 + − k(1 + k) k + e  (4.6) R h 2 a0 3 a0 a0

E1, E2 are the Maxwell model parameters that follow from the SLS model. R is the radius of the roll in meters, h is the thickness of the belt’s bottom cover layer and b is the length of the second part of the contact zone between the belt and the roll. k is the Deborah number, which is deﬁned by:

V τ k = (4.7) a0 a0 is the ﬁrst part of the contact length between the belt and the roll and is given by:

26 Master of Science Thesis 3 3FzDh a0 = (4.8) 4E1

Where D is equal to 2R. Due to the pre-description of the indentation depth, which is generally not the case in the situation of a belt conveyor, this method is not directly applicable in this study.

4.2.2 Hunter

Hunter followed in 1961 with “The rolling contact of a rigid cylinder with a viscoelastic half space" [17]. Like May et al, he models the belt backing material as a viscoelastic half space and the material itself conform the SLS model. He uses a more analytical approach than May et al by using integral equations that allow shear stresses. Hunter also relates the rolling resistance force to the asymmetrical stress distribution within the rolling contact. He approaches the problem from another angle: the retardation instead of the relaxation. For the three parameter Maxwell model the following equations can be stated [15]:

E f = 2 (4.9) E1

µD = E1 + E2 (4.10)

Which represent the retardation coeﬃcient and the dynamic shear modulus. The semi-contact length of the indentation at zero velocity, a0, is deﬁned by Hunter as:

2 2(1 − ν)(1 + f)RFz a0 = (4.11) πµD

The ratio between a and a0, the contact length when the belt has a non-zero speed, can be determined by:

2f ∗ a 2 ∗ 0 = 1 + h (4.12) K (k) I (h) a 0 + 0 K1(k) I1(h)

With k = a/V τ and h = (1 + f)k. K0, K1, I0 and I1 are modified Bessel functions of the zeroth and first order. Through the entering pressure distribution function Hunter finally reaches the indentation rolling resistance factor:

" 2 # ! 1 1 a0 I0(h) Γ1 = a − − − 1 (4.13) h 2 a I1(h)

b = V τ − Γ1 (4.14)

2! ∗ 1 V τ a fih = b − − Γ1 (4.15) R 1 + f a0

Master of Science Thesis 27 Like May et al, Hunter too reaches the conclusion that the rolling friction coeﬃcient is dependent on the belt speed and that it reaches a certain maximum value for a belt speed that corresponds with the relaxation time of the belt material. The usability of the method of Hunter is questionable, since he assumes that the indentation depth is independent of the belt speed [15].

4.2.3 Jonkers

In 1980, Jonkers used a different approach to model the indentation rolling resistance [18]. Instead of using the asymmetrical stress distribution, he uses the rubber hysteresis losses that are caused by the indentation of the viscoelastic material. Jonkers also models the belt’s backing material with the SLS model, but he uses a Winkler model to describe the material layer with a finite thickness [15]. It is assumed that the indentation can be described as half a sinusoidal curve and that the pressure distribution also follows this geometry, with the maximum pressure at the centreline of the roll. Although not correct for typical belt conveying speeds [19], this choice of geometry allowed Jonkers to express the indentation rolling resistance force as a concise equation that is quick and easy in use. The implication is that it overestimates the indentation rolling resistance, which has been shown by, among others, Wheeler [19]. Also, the method of Jonkers does not take the influence of the belt speed on the contact length into account [15]. Despite these downsides, the Jonkers method is still widely used to make a quick comparison of two different belt materials, since it requires very little parameters. Jonkers defines the indentation rolling resistance force of a single roll as:

1 h 3 4 F = f(δ) F 3 (4.16) ij E0D2 Z

In which h and D are respectively the thickness of the bottom cover layer and the diameter of the idler roll and f(δ) is:

" # 4 1 (π + 2δ)cos(δ) 3 fδ = πtan(δ) (4.17) 2 4p1 + sin(δ)

If the friction factor is deﬁned as in DIN 22 101 - like a Coulomb friction, the method of Jonkers yields the following equation:

4 1 " # 3 0 FW 1 (π + 2δ)cos(δ) FZ h 3 fij = = πtan(δ) p 0 2 (4.18) FZ 2 4 1 + sin(δ) E D

An adaptation of the method of Jonkers was used by Lodewijks to be able to compare it with other methods. This adaptation uses the contact length as determined by Lodewijks’ adaptation of the method of May (which will be shown in Section 4.2.5). In this adaptation, the inﬂuence of the belt speed on the contact length is taken into account.

4.2.4 Spaans

Spaans also used the Winkler foundation model for the belt’s backing layer and the SLS model for the material itself. He therefore also neglects the shear forces within the material. Similar

28 Master of Science Thesis to the approach of Jonkers, he established the indentation rolling resistance by determining the hysteresis losses for the belt travelling over a roll and assumes the maximum pressure at the centre line of the roll. The indentation friction factor was determined by Spaans to be [15]:

1/3 Fz fis = 0.5ηi (4.19) 4/3 ∗1/3 2/3 3/4 4/3 (2/3) E D0 (1 + (1 − ηi) )

∗ The indentation damping factor ηi and the lateral stiffness E need to be determined from a harmonic deformation test that is performed on a sample of the total belt [15]. D0 is a diameter in which both the diameter of the roll and the curvature of the belt at the roll are accounted for. The method of Spaans is less useful than methods presented earlier, since he uses the lateral stiffness and the indentation damping coefficient of the total belt, which cannot be determined properly without fabricating a piece of the total belt. More drawbacks to use this model are that it neglects the belt speed dependence of the contact length and that the hysteresis loss factor δ is assumed to be a material constant, which is generally not a valid assumption [15]. To still be able to compare this method with those of Hunter, May and Jonkers, an adaptation was provided by Lodewijks through which only the belt’s backing layer is modelled [15].

By using the three parameter Maxwell model, the damping factor ηi of the damping layer is given as a function of the loss factor tan-delta by [15]:

2πtan(δ) η (δ) = (4.20) i 2 + (π + 2δ)tan(δ)

In which the loss factor tan-delta is given by [15]:

2 ωηE2 tan(δ) = 2 2 2 (4.21) E1E2 + ω η (E1 + E2)

If the assumption is made that the lateral stiﬀness is only caused by the belt’s backing layer, the Winkler model provides the following expression for this stiﬀness [15]:

E E∗ = 1 (4.22) h

The adapted indentation rolling resistance factor of Spaans’ methods can now be expressed:

1/3 1/3 ∗ Fz h fis = 0.5ηi(δ) (4.23) 4/3 1/3 2/3 3/4 4/3 (2/3) E1 D0 (1 + (1 − ηi(δ)) )

A ﬁnal assumption needs to be made in order to compare this method with those of Hunter, May and Jonkers, which is that under normal circumstances, D0 will practically be the same as the idler roll diameter D.

4.2.5 Lodewijks

In 1995 Lodewijks created a method for the calculation of the indentation rolling resistance in which he partly follows the method of May et al [19]. The material is modelled by using the

Master of Science Thesis 29 SLS model, but diﬀerent from May et al., the Winkler foundation model is used to describe the backing layer. An iterative process was established to determine the contact length and the SLS model parameters, by beginning with a simple predictor for the contact length that follows from the Winkler foundation model [15] and is given by equation 4.8. With these SLS model parameters the indentation resistance force is determined and with that, the indentation rolling resistance factor. The stress distribution for the SLS model can be written as:

2 E1 a − x a + x E2k ( −1(a−x) ) a − x σ(x) = a + (1 + k) 1 − e ka − (4.24) 2Rh a a Rh a

In which k is deﬁned as in equation 4.7.

F 1/3 a = z (4.25) 3 2(1/3) E1 b b 2E2k b 6Rh 2 − a + 3 a + Rh 1 − a

The formula for the rolling resistance force Fi is almost equal to that of May et al., but the contact length is diﬀerent.

" # E a4 b 2 b 4 F = 1 1 − 2 + i 8R2h a a 4 " 2! 3! # E2a k 3 k b 1 b b −1 a+b + k − 1 + + 1 + − k(1 + k) k + e k ( a ) (4.26) R2h 2 a 3 a a

For the use in the procedure of DIN 22 101, the following relation can be used:

Fi fim = (4.27) Fz

To compensate for the neglecting of the shear forces by the Winkler foundation, Lodewijks determined a correction factor fs, based on the method of Hunter, which does incorporate the shear forces, and the method of May, which also neglects them.

∗ fih fs = ∗ (4.28) fim

Which allows the calculation of the corrected indentation rolling resistance:

fi = fsfim (4.29)

The graphical relation between the method of May et al., Hunter and the modiﬁed method of May et al. can be seen in Figure 4.7, which were generated for the parameters from Table 4.1. As can be seen, the modiﬁed method of May et al. proposed by Lodewijks yields a lower value for the indentation rolling resistance than its original method and the method of Hunter. The correction factor fs shifts the results in the direction of those of May et al.

30 Master of Science Thesis Figure 4.7 Comparison of the methods of Hunter, May et al. and the adjustment of May et al. as pro- poseds by Lodewijks [15].

Table 4.1 Input parameters used by Lodewi- jks to compare the methods of Hunter, May and his modiﬁcation of May. [15]

R 0.0795 m E1 7 MPa h 0.008 m E2 250 MPa Fz 2000 N η 1875 Pa s V 0.1 - 10 m/s

The accuracy of this method was conﬁrmed by Wheeler in 2003, who compared the results of this method with experimental results [19]. A generalisation of this model was created by Rudolphi and Reicks in 2006, in which they expand the SLS model to the generalised Maxwell material model [20]. This generalised model uses multiple relaxation times, which allows for a more accurate description of rubber behaviour. The methods of Jonkers (both original and the adaptation of Lodewijks) and Spaans show friction factors as shown in Figure 4.8 for input variables of Table 4.1. It is clear that they yield much higher results than the methods of Hunter, May et al. and Lodewijks.

Figure 4.8 Comparison of the methods of Jonkers and Spaans [15].

Master of Science Thesis 31 4.3 Numerical methods

The growing calculating power and speed of computers provide the opportunity to establish numerical approaches to the rolling resistance problem by describing the problem with numerical methods. This allows for the replacement or reduction of complicated diﬀerential equations into simpler equations that can be solved for small fractions of the total system. Two contributing researchers and their methods are explained below.

4.3.1 Wheeler

A finite element method (FEM) model was created by Wheeler to study the indentation rolling resistance of belt conveyors. In the Finite Element Method, a system of various objects and their surroundings are modelled and divided into small sections: the finite elements (see Figure 4.9). For these elements, assumptions can be stated to simplify the required equations to solve the problem for each element. The solutions of each of these elements is put together as the approximation of the total system. Wheeler’s model is based on FEM models of Lynch [21] and Batra et al. [22], in which the indentation depth was specified. Wheeler removed this fixed depth by using an iterative process to vary this indentation depth until the correct vertical load is reached [19]. The model is based on the asymmetrical stress profile of the indentation around the roll axis. By comparing the results of this FEM model to experimental results Wheeler confirmed the accuracy of his model.

Figure 4.9 Finite Element Model used by Wheeler to calculate the indentation rolling resistance. [19]

4.3.2 Qui

A diﬀerent numerical approach was established by Qui in 2006 [23]. He used a method called the Boundary Element Method (BEM). Similar as with the Finite Element Method, this method divides the total problem into small fractions. However, this method only considers the interfaces of the objects within the system, which results in a far smaller number of elements and thus a faster calculation time, but without the ability to handle transient problems. Qui chooses this problem since belt conveyor systems often consist of many rollers, which would make a FEM calculation very time-consuming. A special boundary element was created in order to match the contact boundary conditions of a hard cylinder into a viscoelastic layer. The method is veriﬁed by comparing it to the method of Hunter and is found to give similar results [23].

32 Master of Science Thesis 4.4 Selected method

The goal of this research is to create a method to make a first estimation of the energy-saving potential of aramid products in conveyor belts. This will require a method that is accurate enough to determine an acceptable prediction that does not deviate too much from the reality, but the method does not have to be over-complicated. For this purpose, the use of the two presented numerical approaches is not preferable due to their complexity. The approaches of May et al and Hunter for the application in conveyor belts are limited by their use of the half space model, since the relatively thin backing layer of a conveyor belt cannot be modelled accurately by it [15]. Also, they pre-describe the indentation depth, which is not realistic for belt conveyor applications. These two methods have therefore not been chosen for this study. The method of Spaans requires a sample of the entire belt to determine the lateral stiffness and is therefore excluded from the assessment. This leaves the methods of Jonkers and Lodewijks. The preferred method is that of Lodewijks, due to its confirmed accuracy and the confirmed overestimation of the method of Jonkers. It might however occur that the amount of material data is not available to be able to use this method. To be able to cope with these situations, both models will be examined further in this study. The next chapter will show how the rubber data that is required to use both methods is acquired and transformed.

Master of Science Thesis 33 34 Master of Science Thesis Chapter 5

Rubber rheology

Before the selected methods can be used to evaluate the performance of the aramid-based conveyor belts, the properties of the belt cover materials need to be examined. In the ﬁrst section of this chapter the experiments that were performed to measure these properties are described. In Section 5.2 the procedure to transform these measurements into the so-called master curves is explained, after which the model parameters are determined from these master curves in Section 5.3. Finally, an alternative way to use the master curves for the method of Jonkers is presented in Section 5.5

5.1 Experimental setup

For this study two rubber compound types were prepared at the Teijin Aramid rubber laboratory: a control sample of NR/BR rubber and a sample of the same rubber but with the addition of 2 phr Sulfron D3515. Phr stands for parts per hundred rubber and this is evaluated on a weight-base, D3515 is the Sulfron type that was used. The rubber compound formulations of both rubbers is shown in Table 5.1.

Table 5.1 Rubber compound formulations for both rubber samples produced by the Teijin Aramid rubber laboratory. All values in Parts per Hundred Rubber (phr).

Control sample Sulfron sample Natural rubber (NR) 86 86 Polybutadiene rubber (BR) 14 14 Carbon black 49 49 Sulfron D3515 0 2

Cylindrical samples were taken from both rubber compounds with a height of 18 mm and a diameter of 12 mm. A GABO Eplexor 500N machine was used to perform compression DMA on all samples, which is shown in Figure 5.1.

Master of Science Thesis 35 Figure 5.1 The GABO Eplexor 500N machine that was used to perform DMA on the rubber samples.

The samples were exposed to a pre-ageing process that simulates the running-in of a conveyor belt before the actual analyses were performed. The samples were excited for this purpose with a frequency of 5 kHz at a static pre-strain of 20% and a dynamic strain of 5% for 5 minutes. For the actual DMA each sample was exposed to a temperature of -50 oC to 80 oC, while being excited at a static strain of 3% and a dynamic strain of 2%. For both rubber compounds these temperature sweeps were conducted on 4 samples at 3 Hz, 6 Hz, 10 Hz and 20 Hz. The storage modulus, loss modulus, complex modulus and tan-delta were measured. Appendix 11 shows the results of these temperature sweeps. To be able to use the obtained data to calculate the indentation rolling resistance, master curves need to be created from it. This procedure will be shown in the next section.

5.2 Creating master curves

From the temperature sweeps that follow from the DMA the so-called master curves can be derived by the time-temperature superposition principle. This principle states that a change in temperature shifts the material properties in terms of frequency. This implies that a curve of a material property (e.g. the storage modulus) can be shifted along the frequency axis to simulate a curve of another temperature at another frequency. The method of Williams, Landel and Ferry can be used to shift the various temperature curves in such a way that they form the master curves of any desired temperature. Their method follows the following equation, known as the WLF equation [14]. Recapitalising from Section 4.1:

−C1(T − Tref ) log(aT ) = (5.1) C2 + T − Tref

Where Tref is the desired temperature, T the temperature of the curve that will be shifted and log(aT ) the shift factor. C1and C2 are WLF parameters that are found from experimental data.

36 Master of Science Thesis In this study the frequency shift of each curve is determined by shifting the frequency until an accurate overlay with the surrounding curves was found. The original temperature curves and the shifted temperatures that form the resulting master curves can be seen in Figures 5.2 and 5.3 for respectively the control sample and the Sulfron sample.

Figure 5.2 The original temperature curves and the shifted temperature curves that form the o master curve of the control sample. Tref = 35 C.

Master of Science Thesis 37 Figure 5.3 The original temperature curves and the shifted temperature curves that form the o master curve of the Sulfron sample. Tref = 35 C.

5.3 Maxwell model parameters

From these master curves the Maxwell model parameters can be determined by evaluating the Prony Series that expresses the storage modulus. For the three parameter model this expression is stated by the following equation:

ω2τ 2 E0(ω) = E + E (5.2) 1 2 1 + ω2τ 2

The Maxwell model parameters were found by minimising the least squared error that occurs in the comparison of the Prony Series approximation and the master curve. Figures 5.4 and 5.5 show these approximations for both rubber samples. The obtained Maxwell model parameters are shown in Table 5.2.

38 Master of Science Thesis Figure 5.4 Prony Series approximation to the control sample master curve of the storage modulus.

Figure 5.5 Prony Series approximation to the Sulfron sample master curve of the storage modulus.

Master of Science Thesis 39 Table 5.2 Resulting Maxwell model parameters from the Prony series approximations.

Control sample Sulfron sample

E1 [MPa] 9.7 8.0 E2 [MPa] 81.7 52.3 η [Pa s] 42.6 42.4

The obtained Maxwell model parameters were used to evaluate the case from the paper of Lodewijks from 1995 by using the method of Lodewijks to get an impression of their performance (see Figure 5.6). The third curve is the friction factor curve based on the Maxwell model parameters that are used by Lodewijks [15]. Two unexpected trends are observed that raise suspicion about their usability. The ﬁrst is the substantially lower results than those that were obtained with the Maxwell model parameters of Lodewijks. Figure 5.7 only shows the curves of the control sample and the Sulfron sample, in which the second unexpected trend is shown: the Sulfron sample yields higher friction factors than the control sample. This leads to the hypothesis that the three parameter model does not deliver an accurate description of these two rubber compounds.

Figure 5.6 Resulting friction factor curves of the measured rubber samples and that from Lodewijks [15].

40 Master of Science Thesis Figure 5.7 Friction factor curves of the control sample and the Sulfron sample.

To check whether the fault is not originated in the data itself, the Maximum Rolling Coefficients (MRC) were derived of both samples by using the theory of Jonkers, which is shown in equation 5.3. The MRC is a coefficient that is proportional to the indentation rolling resistance and it can be used to compare the material properties of different materials while neglecting geometric properties that are involved in evaluating friction coefficients.

" #4/3 0.5πtan(δ) (π + 2δ)cos(δ) MRC = (5.3) E01/3 4p1 + sin(δ)

Figure 5.8 shows the MRC’s of both rubber samples on the entire frequency range that is covered by the master curves. It can be seen that for the range of frequencies that is involved with belt conveyor systems, 100 to 1,000 Hz, the Sulfron sample’s MRC is lower, which indicates a lower rolling resistance than the control sample. From this it can be concluded that the experimental data is plausible.

Figure 5.8 Maximum Rolling Coeﬃcients of both the control sample and the Sulfron sample.

Master of Science Thesis 41 An explanation of the results that were obtained with the Prony Series approximation can be found by looking at the master curves of the storage moduli (Figure 5.9). The modulus of the Sulfron sample is lower than that of the control sample, which leads to the better performance of the control sample in terms of the calculated indentation rolling resistances. Although this may appear to conclude that the control sample is less rolling resistant than the Sulfron sample, this conclusion is false. The performance of the rubbers can only be judged by looking at the complete picture, which also includes the loss moduli and, as a result, the tan-delta’s. Figure 5.10 shows the tan-delta master curves of both rubber samples which shows that the tan-delta of the Sulfron sample is considerably lower in the range of 100 to 1,000 Hz.

Figure 5.9 Storage moduli of both the control sample and the Sulfron sample.

Figure 5.10 Tan-delta master curves of both the control sample and the Sulfron sample.

It can be concluded that in the Sulfron sample less energy is stored in one load cycle, but that the amount of energy that is lost in one cycle decreases even more, resulting in a better performance overall.

42 Master of Science Thesis To support the hypothesis that the three parameter model is not sufficient for these materials a five parameter model was evaluated, following the expansion of the method of May that was created by Rudolphi and Reicks [20]. Figures 5.11 and 5.12 show the Prony series approximations for the five parameter models. In Table 5.3 the obtained Maxwell model parameters are shown.

Figure 5.11 Prony Series approximation of the ﬁve parameter model for the control sample.

Figure 5.12 Prony Series approximation of the ﬁve parameter model of the Sulfron sample.

Master of Science Thesis 43 Table 5.3 Resulting Maxwell model parameters from the Prony series approximations.

Control sample Sulfron sample

E1 [MPa] 7.6 6.8 E2 [MPa] 20.2 16.8 E3 [MPa] 82.7 51.9 η2 [Pa s] 221.4 149.6 η3 [Pa s] 20.1 14.4

These resulting sets of Maxwell model parameters were used to evaluate the expansion of the method of May for the same case study parameters as was done for the three parameter model. The results can be seen in Figure 5.13. It is clear that the Sulfron sample yields lower friction factors than the control sample. This proves that the three parameter model is not suﬃcient to describe these rubber compounds.

Figure 5.13 Results of the ﬁve parameter model evaluated for the generalised method of Lodewijks.

The expansion of Rudolphi and Reicks was only done for the method of May with the Winkler foundation as an input. The method of Hunter and the original method of May do not have this expansion, so an expanded version of the method of Lodewijks is not possible in this case.

5.4 Cutting the master curves

From Figures 5.4 and 5.5 it can be seen that the Prony series approximations of the master curves deviates quite a lot in the range of 100 to 1,000 Hz. This might be the cause of the bad performance of the three parameter model. To investigate this possibility, the master curves have been cut off above a certain cut-off frequency. Since we are interested in the frequency range up to 1,000, the choice was made to let the cut-off frequency vary from 10,000 Hz to the end of the master curves range. For every cut off master curve the Prony series approximation was done to find the appropriate Maxwell model parameters. The method of May with the Winkler foundation input was evaluated for each of these sets of Maxwell model parameters to indicate the performance of the SLS model. Figures 5.14 to 5.17 show four of these results.

44 Master of Science Thesis Figure 5.14 Results of the May model for shorter master curves. Cut-oﬀ frequency = 10,000 Hz.

Figure 5.15 Results of the May model for shorter master curves. Cut-oﬀ frequency = 40,000 Hz.

Figure 5.16 Results of the May model for shorter master curves. Cut-oﬀ frequency = 80,000 Hz.

Master of Science Thesis 45 Figure 5.17 Results of the May model for shorter master curves. Cut-oﬀ frequency = 500,000 Hz.

These four figures show the trend that was discovered for cutting of the master curves. There is a certain range of cut-off frequencies for which the Sulfron sample performs better than the control sample. This range was found to be from 70,000 Hz to 500,000 Hz. Outside of this range, the Sulfron sample actually results in higher energy consumptions. A second trend can be spotted from Figures 5.14 to 5.17 and that is that if the cut-off frequency increases, the resulting indentation rolling resistance factors decrease. Since the SLS model has earlier resulted in indentation rolling resistances that are too low, a cut-off frequency of 80,000 Hz was chosen to test the same model with shorter master curves. By evaluating one of the belt conveyors of the Optimum Collieries case study, which will be used for verification purposes in Chapter 7, it was found to yield quite accurate results for loaded conveyor belts. The specifications of this belt conveyor system are stated in Chapter 7. For the empty conveyor belts, the yielded results are significantly lower than those that were presented by Lodewijks. Figures 5.18 and 5.19 show these results (denoted by SLS model) and the results that were calculated by Lodewijks.

Figure 5.18 Results of the evaluation of the loaded belt conveyor KW-01 of the Optimum Collieries for a master curve that is cut-oﬀ at a frequency of 80,000 Hz.

Although this method is seemingly able to yield nice results for the loaded conveyor belts, the total process that is required to calculate the power requirements is quite complex and therefore

46 Master of Science Thesis Figure 5.19 Results of the evaluation of the empty belt conveyor KW-01 of the Optimum Collieries for a master curve that is cut-oﬀ at a frequency of 80,000 Hz. therefore not practical for industrial application. Due to this decision, the method of Jonkers is now the only remaining method for the determination of the indentation rolling resistances of the diﬀerent types of conveyor belts. The next sections explain how this method can be used.

5.5 Jonkers method

As was stated by Lodewijks, the method of Jonkers does not account for the influence of the belt speed on the contact length [15]. It does however account for the influence of the belt speed on the loading frequency. This frequency is the key input for the determination of the correct storage modulus and tan-delta. In this section the procedure to use master curve data for the determination of the storage modulus and the tan-delta is presented first, after which the use of single values for these entities is handled.

5.5.1 Jonkers method with master curve data

In the study of Jonkers it is identiﬁed that the storage modulus and tan-delta are dependent on the loading frequency [18]. The loading frequency can be determined by acknowledging that the belt moves over a distance a + b in a timespan of:

π t = (5.4) ω

When this is combined with the fact that Vbt = a + b, this gives the following relation:

πV ω = (5.5) a + b

Jonkers provides an equation to calculate the contact length in a given loading situation, which is:

2π (π + 2δ)cos(δ)(1 + sin(δ))1/3 a + b = · [hDF ]1/3 (5.6) π + 2δ 4E0 z

Master of Science Thesis 47 So the contact length that is required to determine the loading frequency depends on the loading frequency. Thus, these equations form a loop that can be solved by using an iterative procedure, for which an initial guess for one of the entities is required. In this study an initial guess of the loading frequency will be used. It was found that only two or three steps were required to obtain a converged solution. The master curves that were created in the previous sections are used here to determine the values of the storage modulus and tan-delta for the calculated loading frequencies. It is also possible that master curve data is not present. The following section describes the possibilities and pitfalls that arise in those occasions.

5.5.2 Jonkers method without master curve data

An advantage of the method of Jonkers is that it works with single values of the storage modulus and tan-delta. This allows for the comparison of two different rubbers even when no complete master curves are available. A common test to compare two different viscoelastic materials is a temperature sweep at 10 Hz and 2% strain for both materials [24]. It has to be noted that the indentation rolling resistance and thus the energy consumption of a conveyor belt based on such test results can deviate from realistic values. This is due to the fact that the loading frequencies that are found in belt conveyor applications are generally between 100 and 1,000 Hz. This results in deviations in the values of the storage modulus and tan-delta. The variation of the indentation rolling resistance that are caused by the different material properties at the incorrect loading frequency can be determined by evaluating the MRC at the given frequencies. The deviations were determined for both the control sample and the Sulfron sample by looking up the values of the storage modulus and tan-delta for 10 Hz, 100 Hz and 1,000 Hz. By using equation 5.3, the variation of the friction factors were determined. For the control sample the indentation rolling resistance factor was found to be 7% to 26% higher than that found for the 10 Hz input values. For the Sulfron sample these values are 8% to 39% higher. It can be concluded that if the method of Jonkers is evaluated with values of the storage modulus and tan-delta that are measured at 10Hz, the yielded results will be lower than the results of the method of Jonkers when master curve data is used. Besides this side note, the method of Jonkers is still capable of delivering a comparison between two different rubber compounds. It is however known that it overestimates the indentation rolling resistance. In the next chapter the indentation rolling phenomenon as modelled by Jonkers will be studied, to explore the possibilities to gain more accurate results with it.

48 Master of Science Thesis Chapter 6

Proposed method

In the previous section the methods of Jonkers was selected to be used in this study to determine the indentation rolling resistance. As stated earlier, Jonkers’ method overestimates the indentation rolling resistance, since it does not take the effect of the belt speed on the contact length into account. A possible solution to reduce this shortcomings could be found in the creation of a modified Jonkers method, in which the influence of the belt speed on the contact length is taken into account. It is preferable that this new method does not require more rubber property data, since that would require expensive and time-consuming experiments. The modification to the Jonkers method is based on the following analysis of a single roller, with a belt that is always loaded to the same degree.

6.1 Analysis

When the belt speed increases, it is observed that the contact length decreases (as is shown in Figure 6.2). Due to the assumption that the filling degree of the belt is constant, the distributed load qR, which is the sum of the gravitational forces of the belt and the load on the roller per meter of roller width, does not vary with the speed of the belt for a continuous material flow. This distributed load is defined by Jonkers as [18]:

Z C0 qR = σdx (6.1) A

Where A and C’ are the ﬁrst and last contact points and σ is the pressure that acts on the roll. Figure 6.1 shows this relation graphically. Jonkers deﬁnes the pressure as a sinusoidal function of the loading frequency:

σ(ω) = σ0sin(ωt) (6.2)

Due to the decreasing contact length, the maximum stress σ0 must increase, to be able to transmit an equal amount of pressure. According to Jonkers, the maximum stress and maximum strain (0) of a viscoelastic material are linked to the measured material properties by the following relation:

Master of Science Thesis 49 Figure 6.1 The distributed load of the belt and load mass on the roll.

Figure 6.2 Observed eﬀect of the belt speed on the contact length.

σ E0 = 0 cos(δ) (6.3) 0

An increasing stress can therefore lead to the following conclusions for an increasing σ0:

1. 0 increases proportional to σ0, so that σ0/0 remains equal

2. E0 increases

3. cos(δ) decreases

The ﬁrst conclusion is obviously incorrect, since it is observed that for an increasing belt speed, the indentation does not increase, but decreases. This leaves the variation of the two material parameters, E0 and cos(δ). This makes sense, since the belt speed is related to the loading

50 Master of Science Thesis frequency, an entity that is known to be of inﬂuence on the material properties. Three hypotheses can now be stated:

1. E0 varies proportional with the belt speed. cos(δ) remains equal 2. cos(δ) varies inversely proportional with the belt speed. E0 remains equal 3. Both E0 and cos(δ) vary with the belt speed

It is known from other studies, e.g. [25], that both E0 and cos(δ) vary with the harmonic loading frequency. Since the related factor δ also occurs in the Jonkers friction factor and E’ and tan- delta are not represented to the same proportions, a solution could be to simply multiply the total Jonkers friction factor with a correction factor that is dependent on the belt speed. This modiﬁed function can be expressed as follows:

4 " # 3 0 1 (π + 2δ)cos(δ) f = CV f(δ) = CV πtan(δ) (6.4) ij 2 4p1 + sin(δ)

This factor results in the normal Jonkers equation for CV = 1. The exact shape of CV and the values of its parameters a, b and x should be determined based on a number of measurements on existing conveyors and then veriﬁed by predicting the energy consumptions of other case studies of which the results are known from measurements. For this purpose, the results of conventional steel cord conveyor belts might be enough to reach an acceptable result. If equation 6.4 is reshaped to use it in the DIN 22 101 calculations, the result is:

" # 4 1 F 1 (π + 2δ)cos(δ) 3 F h 3 0 W C Z fij = = CV πtan(δ) p 0 2 (6.5) FZ 2 4 1 + sin(δ) E D

As was earlier found in Chapter 5, the method of Lodewijks is able to yield quite accurate results for the estimation of the indentation rolling resistance of belt conveyors[19]. To determine an approximation for the correction factor CV , results of the method of Lodewijks and the method of Jonkers will be calculated and compared for diﬀerent belt speeds. Since it is assumed that the belt load is an important factor, multiple correction factors will be determined for diﬀerent belt loads.

The correction factor CV can be determined by comparing the results of the method of Jonkers with those of the method of Lodewijks:

CV fij = fim (6.6)

CV follows directly from this equation:

fim CV = (6.7) fij

6.2 Set-up

The case parameters and the material parameters that were given by Lodewijks are used to determine the curve of CV for diﬀerent belt speeds and belt loads [15]. These case parameters

Master of Science Thesis 51 are shown in Table 6.1 along with the belt loads. The belt loads were determined for typical belt weights and load weights that occur in belt conveyor systems.

Table 6.1 Case and material parameters that are used for the determination of the correction factor CV .

V 0.1 - 10 m/s Fz(empty belt) 250 N R 0.0795 m Fz(Light load) 1,000 N h 0.008 m Fz(Normal load) 2,000 N E1 7 MPa Fz(Heavy load) 3,000 N E2 250 MPa Fz(Very heavy load) 4,000 N η 1875 Pa s

52 Master of Science Thesis For each belt load the curves of the methods of Jonkers and Lodewijks were determined, which are shown in Figures 6.3 to 6.7 on the left sides. From these curves the resulting curves of the correction factor CV were determined and the accompanying equations were found. The right-sides of Figures 6.3 to 6.7 show these curves.

Figure 6.3 Results of the methods of Jonkers and Lodewijks and the resulting correction factor CV for a belt load of 250 N.

Figure 6.4 Results of the methods of Jonkers and Lodewijks and the resulting correction factor CV for a belt load of 1,000 N.

Figure 6.5 Results of the methods of Jonkers and Lodewijks and the resulting correction factor CV for a belt load of 2,000 N.

Master of Science Thesis 53 Figure 6.6 Results of the methods of Jonkers and Lodewijks and the resulting correction factor CV for a belt load of 3,000 N.

Figure 6.7 Results of the methods of Jonkers and Lodewijks and the resulting correction factor CV for a belt load of 4,000 N.

54 Master of Science Thesis It is clear that the effect of the correction factor becomes greater for lower belt loads, since the method of Lodewijks reacts more heavily to the load variations. To check if the obtained results are plausible, the case study that was performed by Wheeler is examined [19]. The following specifications were used in the calculations: D 0.15 m Fz 2,000 N v 6 m/s E0 6,435,822 Pa Tan-delta 0.32281 H 5 mm In the calculations of Wheeler, the method of Jonkers resulted in an indentation rolling resistance factor of 0.0155, the method of Lodewijks resulted in a factor of 0.01 and experimental results were found to yield a factor of 0.095. This indicates that the value of the correction factor in this case should be 0.61, by dividing the results of these methods. From Figure 6.5 a value of the correction factor of 0.58 is found that is based on the belt speed of 6 m/s, which indicates that the modified Jonkers method would result in a power consumption that is slightly lower than that calculated by Wheeler and that the correction factor therefore causes an overshoot in the desired effect. It has to be noted that this does not give any indication about the validity of this method for other belt loads. The correction factor and the modified Jonkers method will be verified in the next chapter by comparing it to a theoretical study done by Lodewijks [6].

Master of Science Thesis 55 56 Master of Science Thesis Chapter 7

Veriﬁcation

To assess the performance of the proposed modification of the method of Jonkers a comparison has to be made with measurements on an actual conveyor that has been outfitted with an Aramid-based conveyor belt. Unfortunately, few of these belts are operational and the technical details of these conveyors are not released. Nevertheless it is possible to get some insight in the before mentioned performances, since a case study has been performed by Lodewijks in 2011 [6]. In his research he evaluated the energy consumptions of various belt types for four belt conveyor systems of the Optimum Collieries in South Africa. This case study will be used in this chapter to verify the results that are obtained with both the original Jonkers method and the proposed modified Jonkers method.

7.1 Optimum Collieries

The Optimum Collieries is a large coal mining facility in South Africa in which a system of overland conveyors connect the key parts. Four conveyors of this system were evaluated by Lodewijks according to their original design parameters to predict the potential energy savings that could be achieved by applying Aramid products [6]. The basic speciﬁcations of these conveyors are shown in Table 7.1. Figure 7.1 shows the head of one of the conveyors of the Optimum Collieries.

Table 7.1 The basic input parameters of the four belt conveyor systems of the Optimum Collieries [6].

Belt conveyor KW-01 KW-02 KW-03 KW-05 Material Coal Coal Coal Coal Capacity MTPH 2.200 2.200 1.800 1.800 Belt speed m/s 5.75 5.75 5.75 5.75 Belt width mm 1.200 1.200 1.050 1.050 Belt rating N/mm ST 1400 ST 1400 ST 900 ST 900 Belt mass (original) kg/m 31.7 31.7 22.6 22.6 Belt mass (Twaron carcass) kg/m 18.8 18.8 15.9 15.9 Length m 5.280 2.700 3.720 3.304 Height change m 26.5 3.3 -13.4 -5.05

Master of Science Thesis 57 Figure 7.1 Belt conveyor KW-05 of the Optimum Collieries overland system [6].

Although the majority of the input parameters were known, some assumptions had to be made to be able to perform the calculations:

• The drive eﬃciency is 100%

• The addition of Sulfron to the compounds causes no signiﬁcant increase in belt mass

• The values of the lengths and weights of the idler rolls are assumptions

• The conveyor track consists for one third of horizontal curves, in which a diﬀerent idler spacing is used (half of the idler spacing on straight parts)

The original conveyor belts of the Optimum Collieries were made of a mixture of 60% Natural Rubber (NR) and 40% Styrene-Butadiene-Rubber (SBR). In the research of Lodewijks, the four belt conveyor systems were evaluated for six rubber types and two carcass types. The rubber types varied in terms of the amount of Sulfron that was added and the use of SBR or Butadiene- Rubber (BR). The two carcass types are steel cords, which was the carcass type of the original conveyors belts, and a Twaron fabric carcass. Since the rubber compounds that were tested for this study consisted of NR/BR, the results that were calculated with this data are compared to the results of Lodewijks that were obtained for the NR/BR belts in his research (see Table 7.2).

58 Master of Science Thesis Table 7.2 Comparison of belt options from Lodewijks [6] with the four belt options in this study.

Rubber type Carcass Composition Compare with Rubber 4 Steel cord NR / BR Comparison belt Rubber 4 Twaron fabric NR / BR Twaron belt Rubber 6 Steel cord NR / BR, 2 phr Sulfron 3001 Sulfron belt Rubber 6 Twaron fabric NR / BR, 2 phr Sulfron 3001 Twaron+Sulfron belt

7.2 Results

For all four belt conveyor systems the power requirements of a fully loaded belt and an empty belt are calculated and compared with the results from Lodewijks, for both the original method of Jonkers and the proposed modiﬁcation. The results of the power requirements for fully loaded conveyors are shown in the next section, after which the resulting power requirements of the empty conveyors are shown in Section 7.2.2. Finally, a discussion about the obtained results can be found in Section 7.2.3.

7.2.1 Veriﬁcation power requirements for loaded conveyors

All four belt conveyors of the Optimum Collieries case were evaluated for the situation that they are fully loaded. The correction factor Cv that is used in the modified method of Jonkers is based on the average normal force on each of the idler rolls. The results of these calculations for the method of Jonkers, the modified method of Jonkers and the results that were presented by Lodewijks are shown in Figures 7.2 to 7.5. Table 7.3 summarises these results. It can be seen that the modified method of Jonkers always provides a better estimation when compared to the results of Lodewijks than the original method, even though it still shows significant deviations. The fourth conveyor, KW-05, shows that the modified method of Jonkers results in power consumptions that are lower than those presented by Lodewijks. Since the method of Lodewijks is known to be rather precise, this result could lead to underestimated drives for new belt conveyor systems.

Figure 7.2 Resulting power requirements of belt conveyor KW- 01 for loaded belts.

Master of Science Thesis 59 Figure 7.3 Resulting power requirements of belt conveyor KW- 02 for loaded belts.

Figure 7.4 Resulting power requirements of belt conveyor KW- 03 for loaded belts.

Figure 7.5 Resulting power requirements of belt conveyor KW- 05 for loaded belts.

60 Master of Science Thesis Table 7.3 Summary of the resulting power requirements for the loaded belt conveyors of the Optimum Collieries.

Belt conveyor Belt type Jonkers Jonkers Lodewijks original Modiﬁcation [kW] [kW] [kW] KW-01 Comparison belt 2,470 1,528 1,277 Twaron belt 2,014 1,258 1,084 Sulfron belt 1,950 1,221 1,095 Twaron+Sulfron belt 1,597 1,011 933 KW-02 Comparison belt 1,201 720 430 Twaron belt 968 582 358 Sulfron belt 936 563 364 Twaron+Sulfron belt 755 456 304 KW-03 Comparison belt 1,019 464 377 Twaron belt 869 390 320 Sulfron belt 776 345 304 Twaron+Sulfron belt 659 288 256 KW-05 Comparison belt 943 447 572 Twaron belt 809 382 497 Sulfron belt 726 341 474 Twaron+Sulfron belt 622 291 411

Table 7.4 Summary of the resulting power savings for the loaded belt conveyors of the Optimum Collieries.

Belt conveyor Belt type Jonkers Jonkers Lodewijks original Modiﬁcation [%] [%] [%] KW-01 Comparison belt 0 0 0 Twaron belt 18 18 15 Sulfron belt 21 20 14 Twaron+Sulfron belt 35 34 27 KW-02 Comparison belt 0 0 0 Twaron belt 19 19 17 Sulfron belt 22 22 15 Twaron+Sulfron belt 37 37 29 KW-03 Comparison belt 0 0 0 Twaron belt 15 16 15 Sulfron belt 24 26 19 Twaron+Sulfron belt 35 38 32 KW-05 Comparison belt 0 0 0 Twaron belt 14 15 13 Sulfron belt 23 24 17 Twaron+Sulfron belt 34 35 28

Master of Science Thesis 61 Not surprisingly the resulting power savings are higher for the method of Jonkers and the modiﬁed method of Jonkers, since they result in higher power consumptions for all belts. As stated earlier, belt conveyor KW-05 shows a diﬀerent pattern in its resulting power requirements. This will be discussed elaborately in Section 7.2.3. The next section shows the results that were calculated for the empty conveyors.

7.2.2 Veriﬁcation power requirements for empty conveyors

Similar as was done for the loaded conveyors, the power requirements and the resulting power savings of the four belt conveyors were determined for the situation in which they are running empty. Although less important for the determination of the annual energy consumption, the power requirements of the empty belts can give more insight in the performance and applicability of the proposed modified method of Jonkers. Figures 7.6 to 7.9 show the results of the three methods, where the correction factor that is used for the modified method of Jonkers is again selected based on the average normal force on each of the idler rolls. As can be seen, the use of the correction factor causes the modified method of Jonkers to result in power consumptions that are considerably lower than those presented by Lodewijks. From the magnitudes of the resulting power requirements of the original method of Jonkers it can be seen that the correction factor causes the correction to be too severe.

Figure 7.6 Resulting power requirements of belt conveyor KW- 01 for empty belts.

62 Master of Science Thesis Figure 7.7 Resulting power requirements of belt conveyor KW- 02 for empty belts.

Figure 7.8 Resulting power requirements of belt conveyor KW- 03 for empty belts.

Figure 7.9 Resulting power requirements of belt conveyor KW- 05 for empty belts.

Master of Science Thesis 63 Table 7.5 Summary of the resulting power requirements for the empty belt conveyors of the Optimum Collieries.

Belt conveyor Belt type Jonkers Jonkers Lodewijks original Modiﬁcation [kW] [kW] [kW] KW-01 Comparison belt 568 277 422 Twaron belt 329 87 246 Sulfron belt 440 215 352 Twaron+Sulfron belt 255 68 205 KW-02 Comparison belt 290 142 163 Twaron belt 168 45 95 Sulfron belt 225 110 137 Twaron+Sulfron belt 131 35 80 KW-03 Comparison belt 278 74 201 Twaron belt 197 52 137 Sulfron belt 216 57 168 Twaron+Sulfron belt 152 40 115 KW-05 Comparison belt 247 65 247 Twaron belt 175 46 168 Sulfron belt 192 51 206 Twaron+Sulfron belt 135 36 141

Table 7.6 Summary of the resulting power savings for the empty belt conveyors of the Optimum Collieries.

Belt conveyor Belt type Jonkers Jonkers Lodewijks original Modiﬁcation [%] [%] [%] KW-01 Comparison belt 0 0 0 Twaron belt 42 68 42 Sulfron belt 22 22 17 Twaron+Sulfron belt 55 76 51 KW-02 Comparison belt 0 0 0 Twaron belt 42 68 42 Sulfron belt 22 22 16 Twaron+Sulfron belt 55 76 51 KW-03 Comparison belt 0 0 0 Twaron belt 29 19 32 Sulfron belt 22 22 16 Twaron+Sulfron belt 45 45 43 KW-05 Comparison belt 0 0 0 Twaron belt 14 15 32 Sulfron belt 23 24 17 Twaron+Sulfron belt 34 35 43

64 Master of Science Thesis In contrast with the results that were obtained for the loaded conveyors, the power requirements that are determined with the method of Jonkers do not greatly exceed those of Lodewijks. In the next section the possible causes of these results are discussed, along with those that were found for the loaded conveyors.

7.2.3 Discussion results Optimum Collieries veriﬁcation

In the case of the loaded conveyors, the results of the modified method of Jonkers give better approximations of the results of Lodewijks than the original method of Jonkers. However, the final conveyor, KW-05, shows that the modified Jonkers method results in power requirements that are too low. When all of the results that are calculated for that conveyor of both methods are viewed together, it seems that there is something else that disturbs the resulting power requirements. For the empty conveyors, the other three conveyor systems show that the method of Jonkers always yields a higher power requirement. For KW-05 this is not the case, as it even shows a power requirement that is lower than that presented by Lodewijks. A possible explanation is that this conveyor might have a different route in which more horizontal curves are present. This would result in varying average idler spacings and could therefore result in a different power requirement. The two most probable causes that can explain the large deviations of the power requirements of the modified method of Jonkers for the empty belts are malfunction of the correction factor Cv and the calculation input of the method of Jonkers. A malfunction in the correction factor might be found in the fact that it is based on a set of material parameters that date from 1995 [15]. It is possible that a different dataset, based on newer samples may show a different pattern. If this is the case, that new set should result in a correction factor of around 0.8 for this case. Figure 7.10 shows the resulting power requirements for a Cv of 0.8 for conveyor KW-01 as an example. It is clear that it would give a better approximation to the results presented by Lodewijks. Further research is required to confirm this possibility.

Figure 7.10 Resulting power requirements of belt conveyor KW-01, when Cv = 0.8 is used for the empty belt.

The second cause for the deviating empty power requirements is that the material parameters that were used as input are not correct. This seems to be supported by the fact that the results of KW-05 are even lower than those presented by Lodewijks. For the empty conveyors the same storage modulus and tan-delta are used as were used for the loaded conveyors. Since the smaller normal forces on the idler rolls that occur for the empty conveyors cause the indentation to be

Master of Science Thesis 65 less deep, the contact length will also be smaller. This results in a loading frequency that is higher and will therefore lead to different material properties and probably higher results. Based on the obtained results it is advised that the modified method of Jonkers is only used to determine the power consumptions of the loaded conveyor belts. For the empty belts the original method of Jonkers should be used. In the next section a case study of a fictive belt conveyor will be shown that uses this conclusion.

66 Master of Science Thesis Chapter 8

Case study

To illustrate the possible savings that can be achieved by using Aramid products a ﬁctive belt conveyor system is evaluated. The ﬁrst section of this chapter will show all of the input parameters, after which the calculation of the power consumption is performed for the case that master curve data is available in Section 8.2. The third section will show the results that were generated for the same case study, but for the situation in which only single values for the material properties are known.

8.1 Case study: stockpile conveyor

The fictive belt conveyor that will be evaluated in this case study transports coal from a stockpile to a ship loading installation (see Figure 8.1). The main specifications are shown in Table 8.1. It is assumed that the feeding point of the belt conveyor is at a fixed location and that the transported coal is discharged into a silo at the ship loader.

Figure 8.1 Fictive belt conveyor that will be evaluated as a case study.

The conveyor is operational for 250 days per year. On these days, the conveyor runs fully loaded for 16 hours and empty for 2 hours. It is assumed that the top cover layer and the bottom cover layer are made from the same material. Figure 8.2 shows the speciﬁcations of the idler sets for both strands of the belt conveyor. The cross sections of the steel cord belt and the Twaron belt are shown in Figure 8.3 and the conveyor proﬁle is shown in Figure 8.4.

Master of Science Thesis 67 Table 8.1 Main speciﬁcations of a ﬁctive belt conveyor installation.

Capacity 2,200 MTPH Drive eﬃciency 0.95 - Belt speed 5 m/s Mass Steel cord belts 28 kg/m Belt width 1,000 mm Mass Twaron belts 21 kg/m Bulk density 800 kg/m3 Idler spacing carry strand 1.2 m Angle of surcharge 25 o Idler spacing return strand 2.4 m Turnover No -

Figure 8.2 Idler conﬁgurations of a ﬁctive belt conveyor system

Figure 8.3 Cross sections of the two belt types of a ﬁctive belt conveyor system

Figure 8.4 Belt conveyor proﬁle for a ﬁctive belt conveyor system.

Similar as in the veriﬁcation chapter, four belt types will be evaluated: a normal steel cord belt (comparison belt), a Twaron carcass belt (Twaron belt), a steel cord belt with Sulfron added to the rubber compounds (Sulfron belt) and a Twaron carcass belt with Sulfron added to the rubber compounds (Twaron+Sulfron belt). It is assumed that the addition of Sulfron only inﬂuences the rubber material properties. The master curve data that was presented in Chapter 5 will be used to determine storage moduli and the tan-delta’s of the rubber compounds.

68 Master of Science Thesis 8.2 Calculation of the energy consumptions with master curve data

The determination of the energy consumptions of all belt types begins with the calculation of the forces that act on the diﬀerent rolls. These forces consist of the force that the mass of the belt and the mass of the load exert. Since the load forces are equal for all belt types, they only need to be calculated once. A simple procedure as proposed by Jonkers is used in this study [18]. This procedure begins with the calculation of the total cross section area of the load A, which can be calculated in m2 by:

Q A = (8.1) 3.6ρv

In which the capacity Q is entered in Metric Tonnes Per Hour (MTPH), the bulk density ρ in kg/m3 and the belt speed v in m/s. With the values from Section 8.1, the cross section area becomes 0.153 m2. Jonkers proposed that the forces on each of the rolls can be calculated by evaluating the forces that are shown in Figure 8.5. The equations for these forces are the following:

0 0 00 2 Fzc = Gm + GB + 2GBsin λ (8.2)

G00 F = m + G00 cosλ (8.3) zs cosλ B

0 Where Fzc and Fzs are the forces on the centre roll and each of the side rolls, respectively. Gm 0 00 00 and GB are the forces that the load and the belt exert on the centre roll and Gm and GB are the forces of the load and the belt on each of the side rolls. λ is the trough angle.

Figure 8.5 Forces exerting on the idler rolls according to Jonkers [18].

The forces of the load on each of the rolls can be calculated by using the ratio of the cross section area above each roll (A’ for the centre roll and A” for each of the side rolls) and the total cross section area of the total load:

Master of Science Thesis 69 A0 G0 = ρd (8.4) m A ic

A00 G00 = ρd (8.5) m A ic

With ρ being the bulk density of the load and dic the idler spacing of the carry strand. For the forces that the belt exert, the ratio of the belt width above each of the rolls can be used, together with the mass of the belt per meter of conveyor length, GB:

l G0 = m G (8.6) B B B

B − l G00 = 0.5 m G (8.7) B B B

Where lm is the length of the centre roll and B is the width of the belt, both in meters. With this method the following results were found:

0 Gm 1,090 N G”m 174 N 0 GB(Steel cord) 132 N G”B(Steel cord) 99 N 0 GB(T waron) 99 N G”B(T waron) 74 N By using equations 8.2 and 8.3, the total forces on each of the rolls can now be calculated. The results were found to be: Steel cord Twaron Fzc 1,321 N 1263 N Fzs 316 N 299 N Fzce 231 N 173 N Fzse 70 N 52 N Fzr 330 N 247 N

Fzce and Fzse denote the forces on the centre rolls and each of the side rolls for the carry strand when the conveyor runs empty and Fzr is the force on each of the rolls of the return strand. By using the iterative procedure described in Section 5.5.1, the appropriate storage moduli and tan-delta’s can be determined for each roll. For the force on the centre roll of the carry strand in the case of the comparison belt, the storage modulus was found to be 8.68 MPa and the tan-delta is equal to 0.249. The indentation rolling resistance factors can now be determined for this roll by using the method of Jonkers (equation 4.18). The indentation rolling resistance factor now becomes:

4 1 " # 3 1 (π + 2δ)cos(δ) FZ h 3 fij = πtan(δ) (8.8) 2 4p1 + sin(δ) E0D2

" # 4 1 1 (π + 2 · 0.244)cos(0.244) 3 1, 321N · 0.008m 3 fij = π · 0.249 = 0.009 (8.9) 2 4p1 + sin(0.244) 8.68 MP a · 0.2m2

70 Master of Science Thesis The same procedure can be repeated for the side rolls and the rolls of the return idlers, after which the total indentation rolling resistance can be calculated. For the comparison belt, this indentation rolling resistance factor was found to be 0.032 for a loaded conveyor. For an empty conveyor the indentation rolling resistance factor is calculated to be 0.024. These obtained values of the indentation rolling resistance factors can now be used in the DIN 22 101 calculations to calculate the main resistances that are caused by the indentation rolling resistances. From equation 3.3 the following equations can be derived for the loaded and empty situation for each ﬂight of the conveyor i:

0 0 0 FHi = Li · fi · g · [mR + (2mG + mL) · cos(θ)] (8.10)

0 0 FHi,empty = Li · fi,empty · g · [mR + (2mG · cos(θ))] (8.11)

By summing up the calculated main resistances for each flight of the conveyor track, the total main resistance for a loaded conveyor was found to be 53,135 N. For an empty conveyor this total main resistance was found to be 13,969 N. By using the ratio by which the indentation rolling resistance contributes to the main resistances that was determined in Section 3.3, the calculated main resistances need to be divided by 68% to compensate for neglecting the bulk and belt flexure resistance and the idler bearing resistance in the calculations above. For an empty conveyor this percentage is found to be 85%, due to the disappearance of the bulk flexure resistance. The corrected values of the main resistances for a loaded and an empty conveyor now become 78,140 N and 16,434 N, respectively. The secondary resistance factor that is used to account for the secondary resistances is found to be 1.10, based on the total conveyor length of 900 meters. The mass of the load per meter of conveyor length was calculated from the capacity and the speed and is 122 kg/m. With this the gradient resistance can be determined:

0 2 FSt = mLgH = 122kg/m · 9.81m/s · 12m = 14, 388N (8.12)

The total motional resistances can now be calculated for the loaded and the empty conveyor by:

Floaded = C · FH + FSt = 1.10 · 78, 140N + 14, 388N = 100, 342N (8.13)

Fempty = C · FH = 1.10 · 16, 434N = 18, 078N (8.14)

With these total motional resistances, the belt speed and the drive eﬃciency, the power requirements can now be determined:

F v 100, 342N · 5m/s P = loaded = = 501.7kW (8.15) loaded η 0.95

F v 18, 078N · 5m/s P = empty = = 90.4kW (8.16) empty η 0.95

Master of Science Thesis 71 By multiplying these power requirements with the number of operating hours per day and the number of operating days per year the annual energy consumption can be determined. It was calculated to be 2,052 MWh per year. To obtain the results of the comparison belt for the modified method of Jonkers, the indentation rolling resistance factors that were calculated with equation 8.9 need to be multiplied with the appropriate correction factor. The values of this correction factor was found to be 0.54 for the loaded conveyor. The empty conveyor will not be corrected, as was found to be the best method in Chapter 7. By repeating the procedure with the corrected indentation rolling resistance factors from equation 8.10 to equation 8.16, the results of the modified method of Jonkers can be calculated for the comparison belt. The required power of the loaded conveyor is now calculated to be 303.3 kW. The resulting annual energy consumption now becomes 1,258 MWh. This entire calculation was done for the other three belt types as well and the results of all belts are shown in Figures 8.6 and 8.7 and are summarised in Table 8.2. For the empty conveyors only the original power requirements are shown, since they are also used in the calculation of the modified method of Jonkers.

Figure 8.6 Results of the case study of a ﬁctive belt conveyor.

Figure 8.7 Calculated annual energy consumption of a ﬁctive belt conveyor system.

72 Master of Science Thesis Table 8.2 Results of the ﬁctive belt conveyor

Power requirements Power savings Method Carcass Rubber Loaded Empty Loaded Empty type type [kW] [kW] [%] [%] Jonkers Steel cord Control 502 90 0 0 (original) Twaron Control 478 76 5 16 Steel cord Sulfron 443 79 12 13 Twaron Sulfron 425 67 15 26 Jonkers Steel cord Control 303 90 0 0 (modiﬁcation) Twaron Control 291 76 4 16 Steel cord Sulfron 272 79 10 13 Twaron Sulfron 262 67 14 26

For this belt conveyor system, this method predicts that energy savings up to 15% are possible. The next section will show the results of the same case, if it is calculated without master curve data.

Master of Science Thesis 73 8.3 Calculation of the energy consumptions without master curve data

If there is no master curve data available, the method of Jonkers can be used with single values of the storage modulus and tan-delta for each of the rubber types. For the calculations that were shown in the previous section the master curve data from Chapter 5 was used, which was created for a reference temperature of 35oC. For the calculations in this section the it is assumed that the values of the storage modulus and tan-delta are known for the same temperature and a loading frequency of 10 Hz. These values were determined from the temperature sweeps that were performed for both samples (see Appendix 11) and are shown in Table 8.3.

Table 8.3 Material properties for both rubber types at 10 Hz and 35oC.

Rubber type E0 [kW] tan(δ) [-] Control sample 6,93 0,20 Sulfron sample 6,13 0,16

With these values the same procedure is followed as was used in the previous section. These diﬀerent values of the storage modulus and tan-delta come into play from equation 8.8. The ﬁnal results can be seen in Figures 8.8 and 8.9.

Figure 8.8 Results of the case study of a ﬁctive belt conveyor.

74 Master of Science Thesis Figure 8.9 Calculated annual energy consumption of a ﬁctive belt conveyor system.

Table 8.4 Results of the ﬁctive belt conveyor.

Power requirements Power savings Method Carcass Rubber Loaded Empty Loaded Empty type type [kW] [kW] [%] [%] Jonkers Steel cord Control 446 77 0 0 (original) Twaron Control 416 63 7 19 Steel cord Sulfron 384 65 14 17 Twaron Sulfron 359 52 20 32 Jonkers Steel cord Control 273 77 0 0 (modiﬁcation) Twaron Control 257 63 6 19 Steel cord Sulfron 240 65 12 17 Twaron Sulfron 226 52 17 32

It is clear that both with and without master curve data the method shows that Aramid products can decrease the power requirements and thus the energy consumption of this belt conveyor system. By comparing the two methods, it is clear that the use of master curve data results in higher power requirements than the single values approach. As was stated in the introduction, this method should be made usable for Teijin employees, who often lack the proper technical background to work through the procedure on their own. A software application was developed to allow these employees to use this method, which will be shown in the next chapter.

Master of Science Thesis 75 76 Master of Science Thesis Chapter 9

Software application

To make the solution from the previous chapters usable for Teijin employees, an application was developed, in which both the original and the modiﬁed Jonkers method can be used to predict the energy savings of an existing or a new belt conveyor system. A system of requirements was created for the application, which will be shown in the following section. Section 9.2 explains the system architecture that was used and the various components. Section 9.3 shows the results of the case study from Chapter 8, which are recalculated with this software application.

9.1 System of requirements

The following requirements will have to be fulﬁlled to create a functional software application:

• The user can enter the specifications of the client’s belt conveyor system. • The user can choose which aramid-based belt type is to be evaluated. • The user can enter the specifications of the alternative conveyor belt. • The application will evaluate the energy consumption of the client’s belt conveyor for one or more aramid-based conveyor belt types. • The application will evaluate the energy consumption of a standard conveyor belt for the client’s belt conveyor. • The application compares the energy consumptions of the different belt types and determines the potential energy savings of the selected aramid-based conveyor belts. • The application presents the obtained information to the user.

Besides these requirements, a number of speciﬁcations were made:

• The calculations that are performed to determine the energy consumptions are based on DIN 22 101. • The program only considers troughed belt conveyors. • The program only considers belt conveyors lengths of 80 meters or higher. It can however cope with sections that are shorter than 80 meter.

Master of Science Thesis 77 • The program will be written in Microsoft Excel, which has a Visual Basic back-end. • The tool should be usable and understandable by people without a technical background.

9.2 System architecture

The actions that are required to perform the calculation of the energy savings require a logical order in which the processes within the application should occur. Figure 9.1 shows the main structure of the application in which this order is visible.

Figure 9.1 Main architecture of the developed application.

The large blocks in the centre column represent the basic functions of the application for the energy calculations and the calculations of the other beneﬁcial aspects. The surrounding blocks represent secondary functions that make the application a more complete solution. The next section will show the general solving structure that the software uses to evaluate a belt conveyor system.

9.2.1 Calculation

The main solving procedure for the evaluation of the energy savings is shown in Figure 9.2. The sequence is worked through from the top to the bottom. The ﬁrst two blocks, the calculation of

78 Master of Science Thesis the forces of the load on the rolls and the calculation of the energy consumption of the comparison belt are always evaluated. In the application, the user can select for each of the Aramid-based conveyor if they need to be evaluated. After the calculation of their energy consumptions, the results are compared to the energy consumptions of the comparison belt in order to determine the possible energy savings.

Figure 9.2 Sequence for the calculation of the energy savings of the different conveyor belt types.

9.2.2 Calculation of a conveyor belt

The software follows the calculation procedure that was used in the case study in Chapter 8. For every case, this begins with the calculation of the load forces. After that, the calculation of the energy savings of each conveyor belt type can be determined by the same procedure (see Figure 9.3). Finally, the results of each of the evaluated Aramid-based conveyor belts are compared to those of the comparison belt to obtain the possible annual energy savings.

Master of Science Thesis 79 Figure 9.3 Calculation sequence for the determination of the energy consumption of any conveyor belt type.

80 Master of Science Thesis 9.3 Recalculation of the case study

The case study that was presented in Chapter 8 is recalculated with the software application to show the work flow. In this section, all of the steps that are involved with this calculation are shown. Since it does not add value to the presentation of the work flow, the splash screen is not shown. The first step of the process is to enter the case information: the personal information of the client, his company and the user. This is shown in Figure 9.4.

Figure 9.4 Step 1 of the calculation by using the software application: entering the personal information.

Master of Science Thesis 81 In the second step the proﬁle of the belt conveyor is fed to the software by entering all of the intersection points (see Figure 9.5).

Figure 9.5 Step 2 of the calculation by using the software application: entering the belt conveyor proﬁle.

The main speciﬁcations of the belt conveyor that do not change with the change of the belt type are entered in the third step. Figure 9.6 shows this step.

Figure 9.6 Step 3 of the calculation by using the software application: main speciﬁcations of the belt conveyor system.

82 Master of Science Thesis In step 4 the conﬁguration and speciﬁcations of the idler sets of both the carry strand and the return strand are entered (Figure 9.7).

Figure 9.7 Step 4 of the calculation by using the software application: the idler speciﬁcations.

Master of Science Thesis 83 For each of the four conveyor belt types the speciﬁcations of the geometry of the belt and the rubber compound material is provided. For the comparison belt (and therefore also for the Sulfron belt) the user can specify what type of carcass is used, to allow for the comparison of the Aramid-based conveyor belts with steel cord belts and other fabric carcass belts. Figure 9.8 shows this data entry screen for the comparison belt. With the button ’Use master curve data’ the user can choose whether master curve data is used or single values of the material properties E’ and tan-delta. The master curve data is stored on a separate worksheet in the Excel workbook, from which the software can iteratively obtain the values for the storage modulus and tan-delta. This master curve needs to be created for the appropriate temperature in advance of running the software application.

Figure 9.8 Step 5, 6, 7 and 8 of the calculation by using the software application: entering speciﬁcations of the diﬀerent conveyor belt types. Here, the entry screen of the comparison belt is shown.

84 Master of Science Thesis The final step of the calculation procedure is the results screen (see Figure 9.9). On it, the user can specify which calculation method he wants to use (original Jonkers method or modified Jonkers method). The ’calculate’ button starts the entire calculation procedure, which is not shown to the user. The results are presented both in numbers and as a chart on the screen. The user is offered an option to export the obtained results to an external Excel file, to be able to give the results to the client.

Figure 9.9 Step 9 of the calculation by using the software application: starting the calculation and showing the results.

The results that are calculated with the application are similar to those calculated in Chapter 8, which indicates that the software works as expected. From this point these results can be entered into the CBM for the calculation of the ﬁnancial and ecological savings that can be achieved with aramid-based belt conveyors.

9.4 Extra options

If an existing steel cord conveyor belt is to be replaced with a Twaron carcass belt, it might occur that some parts of the structure of the belt conveyor system need to be adjusted. To provide the client with a complete overview of what has to be done to implement an Aramid-based conveyor belt, the software application can determine a number of design aspects that might need attention. The most important of these design aspects is lift-oﬀ of the belt, which can occur in concave curves for empty conveyors if the local belt tension is high enough. A second important aspect is the length of the transitions, where the conveyor belt is formed in or out of its trough shape. The determination of the limitations of both of these design aspects are calculated by using procedures that are provided by DIN 22 101. Since they do not add value to the subject of this study, the exact methods will not be shown. In the next section conclusions will be drawn based on the results that are presented in this report, after which recommendations are stated in Chapter 11.

Master of Science Thesis 85 86 Master of Science Thesis Chapter 10

Conclusions

The following conclusions can be drawn from the results of this report: The indentation rolling resistance was found to be the most important cause of the energy consumptions of belt conveyor systems. It has therefore been chosen to be the primary target for the determination of the total energy consumption of belt conveyor systems. In literature it is found that the method of Lodewijks yields accurate results for the calculation of the indentation rolling resistance. However, the transformation of the measured material properties into the required Maxwell model parameters is not always successful. The three parameter model that was given by Lodewijks showed results that showed the opposite effect of what can be expected. A verification with a five parameter expansion of this model did show the expected trend in the indentation rolling resistance of a normal rubber compound and a compound that has been made low rolling resistant by the addition of Sulfron. From this it can be concluded that the three parameter model cannot describe the material behaviour properly by using the total master curves that were created for the two rubber types. It has been shown that by cutting these master curves above a certain frequency, the three parameter model can yield quite accurate results for loaded conveyor belts, but significantly underestimates the power requirements for the empty conveyor belts. Due to the complexity of the total process of determining the energy consumption of a belt conveyor system with the method of Lodewijks, this method is considered not practical for this study. The proposed modification to the method of Jonkers can significantly improve the estimation of the indentation rolling resistance for loaded belt conveyors. For empty conveyor belts, the modified method shows a correction of the original Jonkers method that is too severe and therefore yields power requirements that are too low. From these results it can be concluded that for the purpose of generating a first estimation of the energy consumption of a belt conveyor system, the modified method of Jonkers should be used for the loaded conveyor belts and the original method of Jonkers for the empty conveyor belts. The accuracy of this approach needs to be verified by comparing it with experimental results. Regardless of the method that is used, the performance of the different Aramid-based conveyor belts follow the trend that was observed by Lodewijks [6]. The application of these Aramid products can significantly reduce the energy consumption of a belt conveyor system. On an annual basis, the energy consumption of a belt conveyor system can be reduced by 40%. The software application that has been developed to create a usable version of the modified method of Jonkers and the original method of Jonkers has showed that it is capable to deliver

Master of Science Thesis 87 the right results as were calculated for the case study in this report.

88 Master of Science Thesis Chapter 11

Recommendations

Based on the conclusions of this report and the findings that were done during the study, some recommendations can be stated: Since this developed method and software application are based on theoretical models, validation of both is required. This is also true for the real performance of Aramid-based conveyor belts. For this purpose, measurements on an actual conveyor of which the belt type will be changed are required. With the outcome of those measurements, the modified method of Jonkers can be adjusted, if required, to obtain a better method for the estimation of the energy consumption of generic belt conveyor systems. It was found that the Prony series approximation of the measured material properties did not yield plausible Maxwell model parameters. In previous studies it has been reported to do this properly, so a future study is required to determine for what circumstances this approach works and for which it does not. Sequently, if this is determined, the method of Lodewijks could be applied instead of the modified Jonkers method to estimate the energy consumption of generic belt conveyor systems. The variation of the energy consumptions that can be obtained with the iterative process of the method of Jonkers in comparison with the use of single values for the storage modulus and tan-delta has been estimated roughly in this report, with variations of 7% to 40%. A more accurate study of these variations could be valuable for the interpretation of the results that can be obtained by single values. The developed software application is based on Visual Basic and Microsoft Excel, which implies that it is a computer-based application. If the frequency of use of this software application becomes significant, a conversion step to a web-based application is advised, so it can be accessed more easily.

Master of Science Thesis 89 90 Master of Science Thesis Appendix A: research paper

Master of Science Thesis 91 1

Modiﬁcation to the method of Jonkers to reduce its overestimation of the indentation rolling resistance

Sjoerd Drenkelford

Abstract

A method has been developed to calculate the first estimation of the energy consumptions of conveyor belts, in order to show the potential of Aramid-based conveyor belts. The methodology of DIN 22 101 is used as the primary method of the calculations. To determine the indentation rolling resistance, which is the largest consumer of energy in a belt conveyor system, the method of Jonkers is used. A modification to this method of Jonkers is presented, which is meant to reduce its overestimation of the power requirements of belt conveyors. This modification is found to give better approximations of the power consumptions for loaded conveyors, but causes an underestimation of the power requirements of empty conveyors.

Nomenclature Benefit Model was created by Teijin Aramid, which C Secondary resistance factor - based its results on the calculated energy consump- E0 Storage modulus Pa tions of the various Aramid-based conveyor belts. D Idler roll diameter m This study shows the development of a method to f friction factor DIN 22 101 - calculate the first estimations of these energy con- fij Indentation rolling resistance - sumptions, which is intended for use in an industrial factor (Jonkers) application. fim Indentation rolling resistance - factor (Lodewijks) Aramid-based conveyor belts F Total motional resistance N Two Aramid products can be used in conveyor belts FH Main resistance N to make them less energy-consuming: Twaron and FN Secondary resistance N Sulfron. Twaron is a high-strength artificial fibre FS Special resistance N material that can be woven into a fabric carcass. FSt Gradient resistance N Such a carcass is much lighter than a conventional FW Indentation rolling resistance N steel cord carcass and can therefore reduce the en- force ergy consumption of a conveyor belt. Figure 1 shows FZ Normal force N a graphic representation of a belt with a Twaron g Gravitational acceleration m/s2 carcass. A Twaron fabric carcass also results in a h Thickness cover layer m conveyor belt that requires less rubber to encase the L Length conveyor m tensile members, since it is an almost flat surface,

mB0 Mass belt kg/m which also reduces the total weight of the belt. m Mass load kg/m G0 The second Aramid product, Sulfron, is a rubber m Mass rolls kg/m R0 compund ingredient, that can be added to the rub- P Required power W ber covers of the conveyor belt. It reduces the inden- v Belt speed m/s tation rolling resistance and increases the ﬂexibility δ Loss angle o and resistance to abrasion of the belt (see Figure 2). 0 Maximum strain - η Drive eﬃciency - θ Inclination angle conveyor o σ0 Applied stress Pa ω Loading frequency Hz

Introduction Aramid-based conveyor belts can signiﬁcantly reduce the energy consumption of belt conveyor systems. Since they have not proven themselves in ﬁeld tests, the industry has been retained in the adaptation of these conveyor belts. To quantify the potential cost Figure 1: Twaron fabric carcass. savings and environmental savings, the Customer 2

Three Aramid-based conveyor belts will be consid- The gradient resistance FSt is the resistance that the ered in this study, besides a normal steel cord belt: belt conveyor experiences to lift the bulk material if a steel cord belt with Sulfron in its rubber covers, the head and the tail of the conveyor are located a Twaron fabric carcass belt and a Twaron fabric on diﬀerent heights. It follows the law of potential carcass belt with Sulfron in its rubber covers. energy:

F = H g m0 (5) St · · L

Special resistances FS occur when belt conveyor systems are badly aligned or when special installations are applied. This will not be taken into account in this study. With this assumption the total motional resistance of a belt conveyor system according to DIN 22 101 becomes: Figure 2: Pellets of Sulfron that can be added to the rubber compounds of a conveyor belt. F = C L f g [mR0 +(2mG0 +mL0 )cos(θ)]+H g mL0 DIN 22 101 · · · · · · (6) As a primary basis for the calculation of the energy consumption of a belt conveyor system, the method- Which can be used in equation 1 to calculate the ology of DIN 22 101 is used [DIN 22 101, 1982]. This total power requirement of a belt conveyor system. method determines the energy consumption based on the resistances that a conveyor belt experiences Causes of energy consumption along its track. The power requirement P of a belt A study performed by Hager and Hintz has shown conveyor according to DIN is equal to: that the main resistance can be divided into four partial resistances that each occur along the entire track of the conveyor and therefore each contribute F v P = · (1) to the friction factor f [Hager and Hintz, 1993]: η

The total motional resistance F , consists of four 1. Indentation rolling resistance components: 2. Idler bearings resistance 3. Bulk flexure resistance F = FH + FN + FSt + FS (2) 4. Belt flexure resistance The main resistance FH is the resistance that builds up along the entire track of the conveyor and forms Combined with the secondary resistance, the gradi- the most important part of the total motional resis- ent resistance and the special resistances, this gives tance for long overland belt conveyors. According to 7 causes that consume energy in belt conveyor sys- DIN 22 101 this resistance can be determined by: tems. The indentation rolling resistance is identified as the largest component and is responsible for 61% of the total resistance [Hager and Hintz, 1993]. Due F = L f g [m0 + (2m0 + m0 ) cos(θ)] (3) H · · · R G L · to its large contribution, it is the most important component to determine for the calculation of the The friction factor f is used to relate the masses of friction factor f. It was found that the indentation all the components to a motional resistance. It is the rolling resistance accounts for 68% of the main re- only place where material properties are of influence sistances, for flat and inclined conveyors. This per- and will be user later on in this paper. centage will be used to estimate the main resistance, based on the indentation rolling resistance. The secondary resistances FN are local resistances, as caused by for instance belt scrapers. They do not Indentation rolling resistance increase with the length of the conveyor track and There are several theoretical methods available in lit- are generally taken into account by multiplying the erature to calculate the indentation rolling resistance main resistance with a factor C. This factor is proof a belt conveyor system, like Hunter [Hunter, 1961], vided by DIN 22 101 and for a belt conveyor of 1,000 May [May, 1959], Spaans [Spaans, 1991], Jonkers m it will be 1.09. The following equation describes [Jonkers, 1980] and Lodewijks [Lodewijks, 1995]. this factor C: Due to their dependence on Maxwell model parameters, the methods of Hunter, May and Lodewijks

FN have been considered too complex for the industrial C = 1 + (4) application that this study is intended for. The FH 3 method of Spaans requires a sample of the total results and it should be determined for belt speeds belt to be able to function correctly, so it is also in the range of 0.1 to 1 m/s. considered not practical. This leaves the method of Jonkers, which is Since no experimental data is available for Aramid- based conveyor belts at the time of this study, it was Jonkers considers the indentation to follow a sinu- chosen to determine this correction factor by com- soidal pattern and because of this assumption, he paring the results of the method of Jonkers with the is able to express the indentation rolling resistance results of the method of Lodewijks, which is known force in a very concise equation. For the use in the to give accurate results. The correction factors were method of DIN 22 101, this force needs to be divided determined by using Maxwell model parameters and by the normal force, after which the friction factor case parameters that were provided by Lodewijks according to Jonkers is described by: [Lodewijks, 1995]:

E1 7 MPa

4 E2 250 MPa 3 1 3 FW 1 (π + 2δ)cos(δ) FZ h η 1,875 Pa.s fij0 = = πtan(δ) 2 D 159 mm FZ 2 " 4 1 + sin(δ) # E0D h 8 mm (7) p The correction factor was based on the ratio between Since the method of Jonkers is known to overesti- the results of the two methods. mate the indentation rolling resistance [Lodewijks, 1995], it will yield energy consumptions that are too high and will therefore give a less realistic prediction of the potential savings that can be achieved with the application of Aramids in conveyor belts. To re- CV fij = fim (11) duce this overestimation, an empiric modiﬁcation is proposed, based on the following analysis.

Proposed modification Figure 3 shows the curves of the correction factor, Jonkers describes the distributed load as an integral based on the varying belt speed and five different of the pressure distribution over the contact length belt loads. [Jonkers, 1980]:

C0 qR = σdx (8) ZA In which:

σ(ω) = σ0sin(ωt) (9)

For an increasing belt speed it is observed that the Figure 3: Correction factor curves. contact length decreases. This implies that the maximum stress σ0 has to increase, in order to transfer Veriﬁcation and results the same amount of pressure. The maximum stress The performance of this modiﬁed method of Jonkers and the maximum strain (0) within a viscoelastic is assessed by comparing the results with a case material are related according to Jonkers by: study of four belt conveyors of the Optimum Col- lieries, that was performed by Lodewijks [Lodewi-

σ0 jks, 2011]. This case considers four conveyors that E0 = cos(δ) (10) transport coal and all have the same belt speed of 0 5.75 m/s. The speciﬁcations of the four conveyors Since the maximum strain, which is related to the are shown below: indentation depth, is observed to decrease, it can Belt conveyor KW-01: be concluded that the storage modulus E0 and the Capacity 2,200 MTPH loss angle δ vary with the changing belt speed. This Belt width 1,2 m agrees with the fact that E0 and δ change with the Belt mass (Steel cord) 31.7 kg/m loading frequency, which is related to the contact Belt mass (Twaron fabric) 18.8 kg/m length. This variation can be accounted for by mul- Lenght 5,280 m tiplying equation 7 with a correction factor Cv. This Height change 26.5 m empiric factor needs to be determined by relating the outcome of the method of Jonkers to experimental Belt conveyor KW-02: 4

Capacity 2,200 MTPH Belt width 1.2 m Belt mass (Steel cord) 31.7 kg/m Belt mass (Twaron fabric) 18.8 kg/m Lenght 2,700 m Height change 26.5 m Belt conveyor KW-03: Capacity 1,800 MTPH Belt width 1.05 m Belt mass (Steel cord) 22.6 kg/m Belt mass (Twaron fabric) 15.9 kg/m Figure 5: Results of belt conveyor KW-02 (loaded) Lenght 3,720 m Height change 26.5 m Belt conveyor KW-05: Capacity 1,800 MTPH Belt width 1,05 m Belt mass (Steel cord) 22.6 kg/m Belt mass (Twaron fabric) 15.9 kg/m Lenght 3,304 m Height change -5.05 m

The following assumptions had to be done to per- Figure 6: Results of belt conveyor KW-03 (loaded) form the calculations for these belt conveyors: - The drive efficiency is 100% - The addition of Sulfron to the compounds causes no significant increase in belt mass - The values of the lengths and weights of the idler rolls are assumptions - The conveyor track consists for one third of horizontal curves, in which a different idler spacing is used (half of the idler spacing on straight parts) The three Aramid-based belt types and a compari- Figure 7: Results of belt conveyor KW-05 (loaded) son belt (plain rubber and a steel cord carcass) were evaluated with the original method of Jonkers and the modified method of Jonkers. The results were compared with those that were presented by Lodewi- jks [Lodewijks, 2011] and are shown in Figures 4 to 11.

Figure 8: Results of belt conveyor KW-01 (empty)

Figure 4: Results of belt conveyor KW-01 (loaded)

Figure 9: Results of belt conveyor KW-02 (empty) 5

better estimation of the power requirements than the original method of Jonkers for the loaded belt conveyors. For the empty conveyors, the modified method causes an underestimation, so it is therefore recommended to use the modified method to determine the power requirements for loaded conveyors and the original method of Jonkers for the empty conveyors. It is clear that the proposed correction factor should Figure 10: Results of belt conveyor KW-03 (empty) be verified with experimental results to improve it, since it shows quite deviating results. Nevertheless, it can give a better indication of the energy consumptions of belt conveyor systems than the original method of Jonkers, due to the fact that the power requirements of the loaded belt conveyors is much more important in the determination of the energy consumption than the power requirements of the empty belts. This is caused by the fact that belt conveyors , since belt conveyors run more hours when they are loaded, than when they are empty.

References Figure 11: Results of belt conveyor KW-05 (empty) DIN 22 101; DIN 22 101: Belt conveyors for bulk The results show that the modified method of materials - Fundamentals for calculation and design, Jonkers is better able to give an approximation of Deutsches Institut fürNormung, 1982 the power requirements for the loaded belt conveyors. For the empty conveyors, the correction is too Hager, M., Hintz, A.; The energy-saving design of severe and causes an underestimation of the power belts for long conveyor systems, Bulk Solids Han- requirements. The last belt conveyor, KW-05 dis- dling, 1993 plays a trend that is not identified at the other three belt conveyors. The method of Jonkers shows values Hunter, S.C.; The rolling contact of a rigid cylin- for the empty conveyor that are lower than those der with a viscoelastic half space, Journal of Applied presented by Lodewijks. The fact that the modified Mechanics, 1961 method of Jonkers shows values for the loaded con- Jonkers, C.O.; The indentation rolling resistance of veyor that are lower than those of Lodewijks, sug- belt conveyor - A theoretical approach, Fördern und gest that there is another reason that this conveyor Heben, 1980 shows these deviating values. A possible cause is the unknown ratio of curves-to-straight sections. May et al; Rolling friction of a hard cylinder over a viscoelastic material, Journal of Applied Physics, The most probable cause of the deviation of the 1959 results of the empty conveyor belts is that the same material properties are used, although they are Lodewijks, G.;The rolling resistance of conveyor known to vary with the loading frequency, which in belts, Bulk Solids Handling, 1995 its turn depends on the load on the belt. It is recommended that this effect is studied in future research. Lodewijks, G.;The next generation of low loss conveyor belts, Bulk Solids Handling, 2011 Conclusions The modified method of Jonkers is able to yield a Spaans, C; The calculation of the main resistance of belt conveyors, Bulk Solids Handling, 1991 Appendix B: draft of research paper for BeltCon 2015

Master of Science Thesis 97 Aramid in conveyor belts -

Extended lifetime, energy savings and environmental effects

Henk van de Ven, Heidi Beers (Teijin Aramid), Gabriel Lodewijks, Sjoerd Drenkelford (Delft University of Technology)

Abstract

In the recent years, aramid fabric as reinforcement in conveyor belts gradually finds its position among the traditional textile and steel cord reinforcement materials. The main arguments for this trend are enhanced lifetime and energy savings. Aramid is already in use for more than three decades in some niche applications such as phosphate mines and steel production plants because of its corrosion- and heat resistance properties. The background of aramid as reinforcement material is briefly described here. Practical examples are reported, demonstrating increased life time, and consequently reducing maintanance and maximizing output. In mining operations, the transportation of minerals and overburdens accounts for a significant share of energy consumption and CO2 emissions. Aramid in conveyor belts reduce the weight of the belt and lower the rolling resistance. This leads to energy savings and less CO2 emissions. With the Customer Benefit Model, an Eco Efficiency based tool, quatitative proof is provided that saving the environment and financially sound buisness cases go hand-in-hand. The potential energy saving by using aramid in the carcass and as additive in cover compounds is an input parameter for the Customer Benefit Model. An energy saving calculation tool, based on DIN 22101, has been developed and will be explained in this paper. The model is using a combination of Jonker’s and Lodewijks’ theories [1,2].

Background

The properties of aramid will only be briefly described here since it has been covered at Beltcon by Arts and Lodewijks previously [3,4]. For the sake of completeness, the relevant details are summarized. Poly-paraphenylene terephthalamide, typically abbreviated as aramid from aromatic amide, is a very strong and light weight synthetic fiber. It has a high modulus, is thermally stable, and highly impact and chemically resistant. It can be used in conveyor belts in two different ways, as Twaron® reinforcement fabric in the carcass and as a chemically treated aramid-based additive Sulfron® to the bottom cover compound in order to lower the Rolling Resistance. For the carcass, mainly the so-called straight warp fabric constructions is applied. A schematic view of the fabric embedded in rubber is shown in Figure 1. It consist of aramid cords in the warp direction, polyamid 6.6. in the weft direction, hold together with a polyamid binder yarn in the warp. Similar to the commonly used textile fabrics (EP), the aramid fabric is treated with a Resorcinol-Formaldehyde-Latex (RFL) dip formulation to obtain sufficient adhesion between the fabric and skim compound.

Figure 1: schematic representation of straight warp aramid DPP fabric construction

The key advantage of using aramid based fabrics over a steel cord carcass is its lightness as shown in Figure 2. Aramid fibers have a density of just 1.44 g/cm3 and thereby five times stronger than steel on a weight-to-weight basis.

Figure 2: Tenacity and elongation characteristics of reinforcement materials

Compared to the textile materials, Polyamid 6.6 and Polyester, the high tenacity and heat resistance of aramid are the most important parameters to consider. It allows the use of a single fabric layer reaching high strength classes up to at least 3150 N/mm.

The second aramid use in conveyor belts is the addition of the aramid-based additive Sulfron® to the bottom cover compound. During mixing at elevated temperature it reduces the carbon black filler-filler interaction (Payne effect) resulting in a compound with improved hysteresis properties [5]. The result, a lower ratio of the loss and storage modulus of the compound, expressed as tan δ, can be measured using ASTM D5992 Dynamic Mechanical Analysis [6]. To this end, a standard NR/BR compound formulation was mixed with 3 phr of Sulfron®. The tan δ of the control and the Sulfron® compound were measured in a Gabo Eplexor DMA equipment at 2% dynamic strain at a frequency of 10Hz. The effect of adding Sulfron® to a compound on the indentation rolling resistance has also been tested at the University of Hannover, Institute of Transport and Automation Technology, according to DIN 22123 [7]. The compound compositions as mentioned above was extruded over a steel plate with cover thicknesses of 6-8 mm. The results obtained from both analyses are shown in Figure 3. The tan δ of the Sulfron®–doped compound was in the range of 6 to 15% lower depending on the temperature. Both outcomes, DMA and IRR, are expressed as a relative improvement against the control compound. As can be seen, the improvement in Indentation Rolling Resistance measured at a conveyor belt follows the trend as found with DMA analysis on lab scale.

Figure 3: relative improvement of tan δ and IRR of Sulfron® doped compound Extended life time and additional advantages of using aramid

One of the traditional applications of aramid fabrics in conveyor belts has been in corrosive environments. Good examples are in Tunesia at the CPG (Gafsa) phosphate mine where a 4,6- km aramid belt was in operation for 9 years before being replaced again with aramid. Another aramid belt in a phosphate mine in Tampa (Florida, US) has been replaced last year after 13 years in operation. The aramid fabric retained about 85% of its original strength [8]. Rubber cover wear and tear were the reason for replacement in both cases.

With its unique set of properties, aramid can be a solution for belts applied under extreme conditions having short life time. It should be studied case-by case. Some design parameters like transition length should be taken into account before replacing textile belts for example. The flexibility of the aramid fabric compared to steel cord has proven its functionality in a 110- m reclaimer belt in the Chinese Zhanjiang Port. This class St1600 belt had an average life time of six months because of the high turning frequency around the pulleys. The aramid belts have reached an average life time of fifteen months. Because of its dense and strong weft (the weaving threads in transversal direction), the aramid fabric also acts as an integrated breaking layer. This means that in the conveying of sharp and heavy rocks, like in copper mining, there is intrinsic protection against belt slitting, and no costly additional breaking layer or slitting detection is needed. An example in a copper mine, where a short steel belts typically had a very limited service life – typically as little as one month – an aramid belt recently ran for a full six months, which is well beyond the expected life expectancy of the previous non-aramid belts in this installation. After six months, the belt, which was still working fine, was taken out for residual testing by a Polish Mining University [9].

In Table 1, a St2500 and aramid DPP 2500 belt having typical dimensions are listed. The roll diameters have been calculated for both. It can be seen that at equal diameter of 2.71 m, the roll length of the aramid belt exceeds the length of the steel cord belt by far. Consequently, the number of splices in a long haul conveying system can be reduced considerably. For a 5-km belt to be installed, the number of splices is reduced from 17 to 12 in the example shown. It certainly contributes to limit downtime of the system and saves installation costs.

Steel cord belt St2500 Aramid belt DPP2500 Cord/fabric thickness [mm] 6,7 3 Min Cover [mm] 6 x 6 6 x 4 Width [mm] 1200 1200 Belt weight [kg/m] 38,3 20,5 300m roll 425 m roll 300m roll 425 m roll Diameter [m] 2,71 3,23 2,28 2,71 Total belt weight [kg] 11488 16274 6153 8718 Table 1: belt weights and roll diameters of typical St2500 and DPP2500 belts

Estimating the potential energy savings by using aramids

In order to get an indication on the potential energy savings in case a steel cord carcass will be replaced with an aramid fabric carcass, a software model to calculate the energy consumption under given conditions has been developed. The use of a Low Rolling Resistance compound is optional to be included. The yearly energy savings are input for Teijin Aramid’s Customer Benefit Model (CBM) to quantify the financial and environmental effects and will be explained in the next section.

Theory and explanation ‘modified Jonkers’ Input Gabriel Lodewijks , add references if needed

Environmental impact and financial aspects

The TUV-certified software program Customer Benefit Model (CBM) as developed by Teijin Aramid gives its customers and chain partners insight in the environmental and financial benefits of comparative belt solutions [10]. The Eco Efficiency based model provides a balanced calculation, always from the perspective of the end user, making use of life cycle analysis and life cycle costing. It shows that saving the environment and the making of sound business cases can go hand-in-hand, from the Total Cost of Ownership (TCO) and Life Cycle Analysis (LCA) perspectives.

With the Customer Benefit Model, a steel reinforced belt is compared with an aramid based belt. This leads to a significant weight reduction of the belt. Optional is the use of the LRR additive Sulfron®. The total energy savings for the use of both aramid based products compared to steel reinforced belts are estimated using the ‘energy calculation tool’ described in the previous section. Based on these savings, the resulting environmental impact is quantified.

The total life cycle comparison is represented in the schedule below:

In the CBM program only the effects of raw materials and use phase are taken into account. This is a conservative approach as there are benefits to be expected, financially and environmentally, in other parts of the life cycle as well. It is assumed that the life time of a long haul steel cord belt is equal to that of an aramid reinforced belt. There is not sufficient evidence that this can be altered in favor of the aramid reinforced belts, apart from those belts used in highly corrosive environments and in cases where slitting frequently rips the steel cord belt.

The outcome of the CBM software program will be demonstrated on the basis of the Optimum Collories case as presented on the Beltcon 16 in 2011 [4]. An existing 5,3 km long steel reinforced conveyor belt in South Africa that has been re-designed with aramid as reinforcing carcass. Sulfron® was added to lower rolling resistance. The weight of the aramid reinforced belt was 40% less than the steel belt. Energy savings of approximately 7000 MWh during a 5 year lifetime can be achieved. It reduced the energy necessary for belt operation with approximately 15%, combined with the LRR additive Sulfron® even up to 25% . Along with this energy saving, CO2 and particulate matter (PM10) emissions will be approximately 15% lower in the use phase of the aramid belt. This is shown in de diagrams below:

Calculations are based on eco- profiles from the GABI database of PE International [11].

The financial benefits for the raw materials and use phase were quantified and expressed in a payback time of the investment, and the Net Present Value (NPV) . For the situation as described above, the payback time is about a year assuming a purchase price of the aramid belt 10% higher than the steel cord belt. This varies from case to case obviously. The program also predicts the influence on the pay back time in case energy prices are expected to change on the mid-term after installation, either going down or upward.

Other aspects to shorten the pay back time have not been taken into account in the example shown above. One is being mentioned in the previous section describing the increase in maximum roll diameter resulting in less transportation costs, less splices, and shorter downtime. These variables can be reviewed individually and included in the decision making process.

Higher costs for CO2 emissions are expected as the result of upcoming regulation and/or legislation like emission trading systems and carbon tax. In the schedule below, the countries where carbon pricing is in place (situation 2014, in the meantime Australia stopped with the carbon pricing, recently South Korea started with emission trading).

The Customer Benefit Model is a next step on Eco Efficiency Analysis (EAA) as TUV certified tool. Variables and scenarios are implemented in the program making it possible to adapt to changing situations: belt prices, energy prices, raw material prices, eco-profiles etc. In sum, a business case for every specific situation.

Conclusions

Gabriel : conclusie nodig om te eindigen??

References

1. Jonkers C.O. (1980), “The indentation rolling resistance of belt conveyor - a theoretical approach”, Fordern und Heben. 2. Lodewijks G. (1995), “The rolling resistance of conveyor belts”, Bulk Solids Handling 15, pp.15-22. 3. Arts K. (2009), “Case study: aramid reinforced conveyor belt in Maritsa Istok power plant”, Proceedings of the Beltcon 15 conference, Johannesburg, Republic of South Africa, September 2-3, 2009 4. Lodewijks G. (2011), “The Next Generation Low Loss Conveyor Belts”, Proceedings of the Beltcon 16 conference, Johannesburg, Republic of South Africa, August 3-4, 2011. 5. Huntink N. (2011), “Using Sulfron to Improve Rolling Resistance and Durability of Tires”, Fall 180th Technical Meeting of the Rubber Division of the American Chemical Society, Cleveland, Ohio. 6. ASTM D5992 -96 (re-approved 2006), “Standard Guide for Dynamic Testing of Vulcanized Rubber and Rubber-Like Materials Using Vibratory Methods.” 7. ITA University Hannover, “Test Rig for Determination of Indentation Rolling Resistance of Conveyor Belts according to DIN 22123.” 8. Info from bilateral discussions with Fenner Dunlop USA, October 2014. 9. Moore P. (Jan. 2015) , “Conveying cost down”, International Mining magazine. 10. Xxxxxxxxx references for Lodewijks 11. TUV EEA certificate nr. CO 600948550001, TUV Rheinland Nurnberg 2014 12. GaBi LCA Database v.6.3, 2013 PE International Stuttgart

Appendix C: results DMA tests

11.1 Control sample, 3Hz

Results Dynamic Mechanical Analysis: NR/BR, 3Hz Strain dyn f T E’ E” |E*| tan δ % Hz oC MPa MPa MPa 0,3 3,0 -49,7 114,624 91,125 146,432 0,794992 0,4 3,0 -48,7 105,767 88,5534 137,943 0,837251 0,4 3,0 -46,0 86,0469 70,945 111,522 0,824492 0,5 3,0 -43,2 63,902 50,5057 81,4511 0,790362 0,7 3,0 -40,5 47,2642 35,2299 58,9496 0,745382 0,8 3,0 -37,7 35,3941 24,5383 43,0682 0,693288 1,0 3,0 -35,4 27,7814 17,7895 32,9889 0,640338 1,2 3,0 -33,0 22,6528 13,2857 26,2613 0,586492 1,4 3,0 -30,7 19,1653 10,27 21,7435 0,535866 1,5 3,0 -28,5 16,5805 8,04858 18,4308 0,485423 1,7 3,0 -26,0 14,6702 6,44824 16,0248 0,439547 1,8 3,0 -23,7 13,2273 5,30265 14,2506 0,400888 1,9 3,0 -21,3 12,1757 4,46276 12,9678 0,366531 2,0 3,0 -19,0 11,3905 3,84776 12,0229 0,337803 2,0 3,0 -16,8 10,8279 3,40982 11,3521 0,314911 2,0 3,0 -13,8 10,1713 2,93191 10,5855 0,288253 2,0 3,0 -10,7 9,66664 2,60289 10,0109 0,269265 2,0 3,0 -7,6 9,24221 2,35748 9,53814 0,255078 2,0 3,0 -4,4 8,86469 2,16326 9,12482 0,244031 2,0 3,0 -1,3 8,52923 2,00287 8,76124 0,234824 2,0 3,0 4,8 8,2228 1,86887 8,4325 0,227279 2,0 3,0 5,0 7,91318 1,77928 8,11075 0,22485 2,0 3,0 7,3 7,73281 1,71034 7,91969 0,221179 2,0 3,0 10,6 7,53695 1,64124 7,71358 0,217759 2,0 3,0 13,9 7,35061 1,5758 7,51762 0,214377 2,0 3,0 17,2 7,18297 1,51463 7,34092 0,210865

Master of Science Thesis 107 Resumed: Results Dynamic Mechanical Analysis: NR/BR, 3Hz Strain dyn f T E’ E” |E*| tan δ % Hz oC MPa MPa MPa 2,0 3,0 20,1 7,04581 1,46724 7,19696 0,208243 2,0 3,0 23,3 6,91616 1,42291 7,06101 0,205737 2,0 3,0 26,3 6,78397 1,38005 6,92292 0,203429 2,0 3,0 29,3 6,66376 1,3418 6,79751 0,201357 2,0 3,0 32,5 6,55069 1,30762 6,67993 0,199615 2,0 3,0 35,5 6,44125 1,27119 6,56549 0,197352 2,0 3,0 38,6 6,32661 1,23307 6,44565 0,194902 2,0 3,0 41,7 6,20534 1,19132 6,31866 0,191984 2,0 3,0 44,7 6,06566 1,13575 6,17108 0,187243 2,0 3,0 47,6 5,93544 1,08908 6,03453 0,183487 2,0 3,0 50,8 5,82183 1,04566 5,91499 0,179611 2,0 3,0 53,1 5,75355 1,01746 5,84282 0,176841 2,0 3,0 55,3 5,68807 0,985201 5,77276 0,173205 2,0 3,0 57,4 5,62521 0,953857 5,70551 0,169568 2,0 3,0 59,5 5,5634 0,925908 5,63992 0,166429 2,0 3,0 61,6 5,49878 0,899789 5,57192 0,163634 2,0 3,0 63,8 5,42877 0,876179 5,49902 0,161396 2,0 3,0 65,9 5,36609 0,852927 5,43345 0,158947 2,0 3,0 67,8 5,29253 0,832948 5,35768 0,157382 2,0 3,0 70,3 5,22486 0,809708 5,28723 0,154972 2,0 3,0 72,3 5,15138 0,788757 5,21141 0,153116 2,0 3,0 74,5 5,08609 0,76717 5,14362 0,150837 2,0 3,0 76,5 5,02369 0,747093 5,07894 0,148714 2,0 3,0 78,5 4,96321 0,728474 5,01638 0,146775 2,0 3,0 80,5 4,8953 0,709028 4,94638 0,144839

108 Master of Science Thesis 11.2 Sulfron sample, 3Hz

Results Dynamic Mechanical Analysis: NR/BR/2 phr Sulfron D3515, 3Hz Strain dyn f T E’ E” |E*| tan δ % Hz oC MPa MPa MPa 0,3 3,0 -50,1 90,285 76,6025 118,403 0,848451 0,4 3,0 -48,7 85,904 75,2858 114,225 0,876394 0,4 3,0 -46,2 71,1205 62,046 94,3813 0,872407 0,5 3,0 -43,5 53,7698 45,0671 70,1586 0,838149 0,6 3,0 -41,0 40,1457 31,6335 51,1112 0,787968 0,8 3,0 -38,3 30,72 22,4491 38,0484 0,730765 1,0 3,0 -36,0 24,0385 15,9407 28,8437 0,66313 1,1 3,0 -33,8 19,8213 11,9185 23,1287 0,601295 1,3 3,0 -31,5 16,7789 9,02394 19,0515 0,537817 1,5 3,0 -29,2 14,6135 6,99208 16,2001 0,478467 1,6 3,0 -26,9 13,0409 5,53826 14,1682 0,424683 1,7 3,0 -24,6 11,8624 4,48096 12,6805 0,377746 1,8 3,0 -22,4 10,9698 3,71228 11,5809 0,338409 1,9 3,0 -20,1 10,2753 3,13674 10,7434 0,305269 2,0 3,0 -17,9 9,74911 2,7265 10,1232 0,279667 2,0 3,0 -15,7 9,29927 2,40144 9,60434 0,25824 2,0 3,0 -12,7 8,81147 2,06859 9,05102 0,234761 2,0 3,0 -10,4 8,53661 1,90259 8,74606 0,222874 2,0 3,0 -8,2 8,27199 1,7595 8,45704 0,212705 2,0 3,0 -6,1 8,04752 1,64429 8,21379 0,204322 2,0 3,0 -3,9 7,81887 1,54247 7,96956 0,197275 2,0 3,0 -1,7 7,61527 1,45577 7,75317 0,191165 2,0 3,0 -0,4 7,41966 1,37822 7,54658 0,185752 2,0 3,0 4,4 7,24336 1,31486 7,36173 0,181526 2,0 3,0 4,9 7,08093 1,2638 7,19282 0,17848 2,0 3,0 6,6 6,95673 1,22472 7,06371 0,176049 2,0 3,0 8,7 6,82999 1,19062 6,93299 0,174322 2,0 3,0 11,1 6,70013 1,15753 6,79938 0,172762 2,0 3,0 13,3 6,59333 1,12402 6,68846 0,170478 2,0 3,0 15,7 6,49009 1,09344 6,58155 0,168478 2,0 3,0 17,9 6,39212 1,06555 6,48032 0,166698 2,0 3,0 19,9 6,31424 1,04071 6,39943 0,164819 2,0 3,0 22,2 6,22737 1,01853 6,31011 0,163557 2,0 3,0 24,3 6,1495 0,995488 6,22956 0,161881 2,0 3,0 26,5 6,07267 0,973859 6,15026 0,160368 2,0 3,0 28,7 5,99818 0,954931 6,07372 0,159203

Master of Science Thesis 109 Resumed: Results Dynamic Mechanical Analysis: NR/BR/2 phr Sulfron D3515, 3Hz Strain dyn f T E’ E” |E*| tan δ % Hz oC MPa MPa MPa 2,0 3,0 30,9 5,9256 0,937173 5,99925 0,158157 2,0 3,0 32,9 5,86741 0,916205 5,93852 0,156151 2,0 3,0 35,0 5,79004 0,899584 5,85951 0,155367 2,0 3,0 37,2 5,72461 0,877364 5,79146 0,153262 2,0 3,0 39,4 5,63777 0,857177 5,70256 0,152042 2,0 3,0 41,4 5,55649 0,835572 5,61896 0,150378 2,0 3,0 43,5 5,46354 0,813397 5,52375 0,148877 2,0 3,0 45,8 5,37298 0,79521 5,4315 0,148002 2,0 3,0 47,9 5,30667 0,773187 5,3627 0,145701 2,0 3,0 50,1 5,24498 0,747722 5,298 0,14256 2,0 3,0 52,0 5,18035 0,723194 5,23058 0,139603 2,0 3,0 54,3 5,13648 0,697653 5,18364 0,135823 2,0 3,0 56,3 5,10336 0,667285 5,1468 0,130754 2,0 3,0 58,5 5,05626 0,639424 5,09653 0,126462 2,0 3,0 60,5 4,99533 0,614517 5,03298 0,123018 2,0 3,0 62,7 4,92771 0,592788 4,96324 0,120297 2,0 3,0 64,9 4,865 0,574459 4,8988 0,11808 2,0 3,0 66,9 4,79676 0,558043 4,82911 0,116337 2,0 3,0 68,9 4,73802 0,54258 4,76899 0,114516 2,0 3,0 71,1 4,67554 0,528216 4,70529 0,112974 2,0 3,0 73,3 4,61897 0,51367 4,64745 0,111209 2,0 3,0 75,5 4,56477 0,499888 4,59206 0,10951 2,0 3,0 77,7 4,51393 0,487066 4,54013 0,107903 2,0 3,0 79,6 4,46561 0,474498 4,49075 0,106256 2,0 3,0 80,7 4,42909 0,463475 4,45327 0,104643

110 Master of Science Thesis 11.3 Control sample, 6Hz

Results Dynamic Mechanical Analysis: NR/BR, 6Hz Strain dynamic f T E’ E” |E*| tan δ % Hz oC MPa MPa MPa 0,2 6,0 -50,2 164,834 121,592 204,829 0,73766 0,3 6,0 -48,9 155,83 121,308 197,481 0,778465 0,3 6,0 -47,0 132,982 104,492 169,123 0,785758 0,4 6,0 -44,6 104,878 82,0648 133,169 0,78248 0,4 6,0 -42,3 79,9551 61,1205 100,641 0,764435 0,5 6,0 -40,2 62,23 46,2367 77,5269 0,742997 0,6 6,0 -37,9 48,3579 34,3475 59,3147 0,710276 0,7 6,0 -35,9 38,7482 26,2697 46,8136 0,677959 0,9 6,0 -34,0 31,9804 20,5573 38,0178 0,642809 1,0 6,0 -32,1 26,9709 16,4245 31,5784 0,608972 1,1 6,0 -30,2 23,1487 13,2172 26,6563 0,570968 1,3 6,0 -28,3 20,2264 10,8406 22,9483 0,535963 1,4 6,0 -26,4 17,945 8,96807 20,0611 0,499754 1,5 6,0 -24,5 16,0925 7,51835 17,7621 0,467196 1,6 6,0 -22,6 14,6885 6,39308 16,0194 0,435245 1,7 6,0 -20,8 13,5954 5,50509 14,6677 0,404924 1,8 6,0 -18,9 12,7449 4,8123 13,6232 0,377585 1,8 6,0 -17,0 12,0334 4,2495 12,7617 0,353143 1,9 6,0 -15,2 11,4431 3,80828 12,0602 0,332801 1,9 6,0 -13,3 10,9656 3,45613 11,4973 0,315181 2,0 6,0 -11,4 10,5197 3,1581 10,9835 0,300208 2,0 6,0 -9,6 10,1525 2,91913 10,5638 0,287529 2,0 6,0 -7,7 9,85212 2,72316 10,2215 0,276403 2,0 6,0 -5,8 9,59443 2,56154 9,93049 0,266982 2,0 6,0 -4,0 9,35393 2,42058 9,66205 0,258777 2,0 6,0 -2,2 9,13757 2,29922 9,4224 0,251622 2,0 6,0 -0,5 8,91276 2,18825 9,17746 0,245518 2,0 6,0 3,1 8,72497 2,09159 8,97217 0,239725 2,0 6,0 3,6 8,57147 2,0277 8,80805 0,236564 2,0 6,0 5,0 8,42092 1,96009 8,64603 0,232764 2,0 6,0 7,0 8,27702 1,89928 8,49214 0,229464 2,0 6,0 8,8 8,13338 1,84602 8,34025 0,226969 2,0 6,0 10,8 7,98304 1,79484 8,18232 0,224831 2,0 6,0 12,6 7,8716 1,74811 8,06337 0,222078 2,0 6,0 14,7 7,75267 1,70836 7,93866 0,220358 2,0 6,0 16,2 7,67219 1,67302 7,85248 0,218062

Master of Science Thesis 111 Resumed: Results Dynamic Mechanical Analysis: NR/BR, 6Hz Strain dynamic f T E’ E” |E*| tan δ % Hz oC MPa MPa MPa 2,0 6,0 17,9 7,58428 1,64388 7,76039 0,216748 2,0 6,0 19,7 7,51522 1,61385 7,68655 0,214744 2,0 6,0 21,6 7,42454 1,58509 7,59185 0,213493 2,0 6,0 23,5 7,35263 1,55249 7,51474 0,211147 2,0 6,0 25,4 7,26613 1,52497 7,42443 0,209874 2,0 6,0 27,1 7,1808 1,49695 7,33517 0,208465 2,0 6,0 29,0 7,10136 1,46876 7,25166 0,206827 2,0 6,0 30,7 7,03272 1,44034 7,1787 0,204805 2,0 6,0 32,6 6,94446 1,41533 7,08722 0,203807 2,0 6,0 34,4 6,87957 1,38526 7,01765 0,201358 2,0 6,0 36,2 6,80026 1,35949 6,93482 0,199917 2,0 6,0 38,0 6,72116 1,3293 6,85135 0,197779 2,0 6,0 39,7 6,6435 1,29773 6,76906 0,195338 2,0 6,0 41,7 6,56418 1,27241 6,68636 0,193842 2,0 6,0 43,5 6,50398 1,24269 6,62164 0,191067 2,0 6,0 45,1 6,43141 1,21958 6,54602 0,189629 2,0 6,0 46,9 6,36552 1,1959 6,47688 0,187872 2,0 6,0 48,7 6,31695 1,16547 6,42356 0,184499 2,0 6,0 50,6 6,24978 1,13969 6,35285 0,182356 2,0 6,0 52,2 6,20635 1,11141 6,30507 0,179077 2,0 6,0 54,2 6,14784 1,08356 6,2426 0,176251 2,0 6,0 56,0 6,09123 1,05772 6,18238 0,173646 2,0 6,0 57,6 6,02711 1,03391 6,11515 0,171543 2,0 6,0 59,4 5,95008 1,0125 6,03561 0,170165 2,0 6,0 61,0 5,88819 0,990566 5,97093 0,168229 2,0 6,0 62,7 5,81873 0,97172 5,89931 0,166999 2,0 6,0 64,7 5,74884 0,954474 5,82753 0,166029 2,0 6,0 66,4 5,69182 0,937049 5,76844 0,164631 2,0 6,0 68,4 5,62311 0,92101 5,69803 0,16379 2,0 6,0 69,9 5,56878 0,905174 5,64187 0,162544

112 Master of Science Thesis Resumed: Results Dynamic Mechanical Analysis: NR/BR, 6Hz Strain dynamic f T E’ E” |E*| tan δ % Hz oC MPa MPa MPa 2,0 6,0 71,8 5,50877 0,888789 5,58001 0,161341 2,0 6,0 73,7 5,44175 0,875143 5,51167 0,16082 2,0 6,0 75,2 5,38453 0,857611 5,4524 0,159273 2,0 6,0 77,0 5,32074 0,841893 5,38693 0,158229 2,0 6,0 79,0 5,25789 0,824935 5,32221 0,156895 2,0 6,0 80,5 5,19622 0,809722 5,25893 0,155829 2,0 6,0 79,6 4,70384 0,522628 4,73278 0,111107 2,0 6,0 80,9 4,65208 0,511333 4,6801 0,109915

Master of Science Thesis 113 11.4 Sulfron sample, 6Hz

Results Dynamic Mechanical Analysis: NR/BR/2 phr Sulfron D3515, 6Hz Strain dyn f T E’ E” |E*| tan δ % Hz oC MPa MPa MPa 0,2 6,0 -50,0 127,901 102,401 163,843 0,800625 0,3 6,0 -49,4 124,263 104,657 162,463 0,842216 0,3 6,0 -47,3 108,75 92,0946 142,506 0,846844 0,3 6,0 -44,9 86,3234 73,0986 113,116 0,846799 0,4 6,0 -42,7 66,0002 54,9724 85,8952 0,832913 0,5 6,0 -40,8 51,1684 41,1782 65,6799 0,804759 0,6 6,0 -38,6 40,1182 30,765 50,5565 0,766859 0,7 6,0 -36,5 32,052 23,1519 39,5391 0,722322 0,9 6,0 -34,7 26,5422 18,0202 32,0814 0,678926 1,0 6,0 -32,9 22,4497 14,1787 26,5523 0,631576 1,1 6,0 -31,1 19,4069 11,3502 22,4823 0,584854 1,2 6,0 -29,2 17,144 9,25473 19,4825 0,539824 1,4 6,0 -27,3 15,3439 7,58223 17,115 0,494153 1,5 6,0 -25,5 13,9334 6,31188 15,2964 0,453005 1,6 6,0 -23,6 12,8025 5,29447 13,8541 0,413549 1,7 6,0 -21,8 11,9177 4,51465 12,7441 0,37882 1,8 6,0 -19,9 11,2094 3,88884 11,8648 0,346928 1,8 6,0 -18,1 10,6352 3,39379 11,1636 0,319108 1,9 6,0 -16,3 10,1496 3,00339 10,5847 0,295912 1,9 6,0 -14,3 9,74215 2,68299 10,1048 0,2754 2,0 6,0 -12,5 9,38616 2,42717 9,69491 0,25859 2,0 6,0 -10,7 9,07457 2,21759 9,3416 0,244374 2,0 6,0 -8,9 8,82005 2,04791 9,05468 0,232188 2,0 6,0 -7,1 8,59308 1,90712 8,80216 0,221937 2,0 6,0 -5,3 8,39218 1,78885 8,58072 0,213157 2,0 6,0 -3,5 8,19246 1,6826 8,36346 0,205384 2,0 6,0 -1,7 8,02377 1,59435 8,18063 0,198703 2,0 6,0 -0,4 7,85624 1,51561 8,0011 0,192918 2,0 6,0 4,0 7,69583 1,44481 7,83028 0,187739 2,0 6,0 4,0 7,56886 1,39072 7,69556 0,183742 2,0 6,0 5,3 7,45719 1,34294 7,57715 0,180087 2,0 6,0 7,1 7,34316 1,30041 7,45742 0,177091 2,0 6,0 8,9 7,23312 1,26113 7,34224 0,174355 2,0 6,0 10,7 7,1325 1,22415 7,23678 0,17163 2,0 6,0 12,7 7,02141 1,18935 7,12143 0,169389 2,0 6,0 14,4 6,93397 1,15793 7,02999 0,166994

114 Master of Science Thesis Resumed: Results Dynamic Mechanical Analysis: NR/BR/2 phr Sulfron D3515, 6Hz Strain dyn f T E’ E” |E*| tan δ % Hz oC MPa MPa MPa 2,0 6,0 16,3 6,83959 1,13101 6,93247 0,165362 2,0 6,0 18,0 6,77004 1,10843 6,86018 0,163725 2,0 6,0 19,8 6,70029 1,08785 6,78802 0,162359 2,0 6,0 21,6 6,62609 1,06852 6,71169 0,161259 2,0 6,0 23,3 6,5609 1,04793 6,64406 0,159724 2,0 6,0 25,1 6,49189 1,02974 6,57305 0,158619 2,0 6,0 26,9 6,42578 1,01052 6,50475 0,15726 2,0 6,0 28,6 6,36478 0,992099 6,44163 0,155873 2,0 6,0 30,5 6,29649 0,975163 6,37156 0,154874 2,0 6,0 32,3 6,24051 0,955793 6,31328 0,153159 2,0 6,0 34,1 6,16889 0,937018 6,23965 0,151894 2,0 6,0 35,8 6,09796 0,917515 6,1666 0,150463 2,0 6,0 37,4 6,03702 0,896179 6,10317 0,148447 2,0 6,0 39,3 5,96526 0,876774 6,02935 0,14698 2,0 6,0 41,1 5,89749 0,852726 5,95882 0,144591 2,0 6,0 42,8 5,83274 0,829505 5,89143 0,142215 2,0 6,0 44,6 5,78016 0,807688 5,83632 0,139734 2,0 6,0 46,4 5,72344 0,785148 5,77704 0,137181 2,0 6,0 48,1 5,67732 0,760497 5,72803 0,133954 2,0 6,0 49,9 5,62806 0,739072 5,67638 0,131319 2,0 6,0 51,6 5,58199 0,718985 5,6281 0,128804 2,0 6,0 53,5 5,5144 0,700523 5,55872 0,127035 2,0 6,0 55,2 5,47929 0,686002 5,52207 0,125199 2,0 6,0 57,1 5,42289 0,671794 5,46434 0,123881 2,0 6,0 58,7 5,36419 0,656435 5,4042 0,122374 2,0 6,0 60,4 5,30536 0,642676 5,34414 0,121137 2,0 6,0 62,2 5,2363 0,629648 5,27402 0,120247 2,0 6,0 64,0 5,18173 0,617895 5,21844 0,119245 2,0 6,0 65,8 5,12474 0,606737 5,16053 0,118394 2,0 6,0 67,4 5,06046 0,596244 5,09546 0,117824 2,0 6,0 69,0 5,0111 0,584798 5,0451 0,116701 2,0 6,0 70,8 4,96006 0,575163 4,9933 0,115959 2,0 6,0 72,7 4,90563 0,564706 4,93803 0,115114 2,0 6,0 74,4 4,85868 0,554376 4,89021 0,1141 2,0 6,0 76,3 4,80334 0,544373 4,83409 0,113332 2,0 6,0 78,0 4,75646 0,532824 4,78621 0,112021

Master of Science Thesis 115 11.5 Control sample, 10Hz

Results Dynamic Mechanical Analysis: NR/BR, 10Hz Strain dyn f T E’ E” |E*| tan δ % Hz oC MPa MPa MPa 2,0 6,0 79,6 4,70384 0,522628 4,73278 0,111107 2,0 6,0 80,9 4,65208 0,511333 4,6801 0,109915 0,2 10,0 -49,8 202,756 162,363 259,753 0,800782 0,2 10,0 -49,3 197,071 166,843 258,212 0,846615 0,2 10,0 -47,3 170,985 145,373 224,431 0,850208 0,3 10,0 -45,0 136,654 115,116 178,679 0,842392 0,3 10,0 -42,7 104,671 85,6743 135,263 0,818508 0,4 10,0 -40,7 80,9676 64,0457 103,236 0,791004 0,5 10,0 -38,4 62,6401 47,4742 78,5976 0,757889 0,6 10,0 -36,5 49,4711 35,7962 61,0635 0,723577 0,7 10,0 -34,7 40,3546 27,9613 49,0951 0,69289 0,8 10,0 -33,0 33,6682 22,222 40,3406 0,660029 0,9 10,0 -31,1 28,6238 17,9593 33,7914 0,627423 1,0 10,0 -29,3 24,6489 14,5984 28,6475 0,592254 1,1 10,0 -27,6 21,6191 12,1195 24,7845 0,560592 1,3 10,0 -25,8 19,1952 10,1232 21,701 0,52738 1,4 10,0 -24,0 17,2683 8,5514 19,2697 0,495207 1,5 10,0 -22,2 15,695 7,27811 17,3004 0,463721 1,6 10,0 -20,4 14,5161 6,27704 15,8152 0,432418 1,6 10,0 -18,7 13,5604 5,48999 14,6296 0,404853 1,7 10,0 -16,9 12,7853 4,85311 13,6754 0,379585 1,8 10,0 -15,2 12,1341 4,33152 12,884 0,356971 1,8 10,0 -13,5 11,583 3,91158 12,2256 0,337701 1,9 10,0 -11,8 11,1176 3,56494 11,6751 0,320658 1,9 10,0 -10,0 10,6985 3,27339 11,188 0,305968 2,0 10,0 -8,4 10,3242 3,02611 10,7586 0,293109 2,0 10,0 -6,6 10,0048 2,82057 10,3948 0,281921 2,0 10,0 -4,9 9,73978 2,64689 10,093 0,271761 2,0 10,0 -3,2 9,49673 2,4993 9,8201 0,263175 2,0 10,0 -1,6 9,28558 2,37214 9,58379 0,255465 2,0 10,0 -0,4 9,07617 2,25841 9,35293 0,248829 2,0 10,0 4,4 8,88859 2,16279 9,14794 0,243322 2,0 10,0 4,6 8,68979 2,06652 8,93213 0,237811 2,0 10,0 5,9 8,47759 1,98827 8,70763 0,234533 2,0 10,0 7,5 8,37221 1,92977 8,59173 0,230497 2,0 10,0 9,3 8,25762 1,87935 8,46878 0,22759

116 Master of Science Thesis Resumed: Results Dynamic Mechanical Analysis: NR/BR, 10Hz Strain dyn f T E’ E” |E*| tan δ % Hz oC MPa MPa MPa 2,0 10,0 11,0 8,13886 1,83151 8,34239 0,225032 2,0 10,0 12,7 8,0351 1,78578 8,23115 0,222248 2,0 10,0 14,5 7,91937 1,74389 8,1091 0,220205 2,0 10,0 16,1 7,8257 1,70497 8,00928 0,217867 2,0 10,0 17,8 7,72683 1,67175 7,90561 0,216356 2,0 10,0 19,4 7,64455 1,63794 7,81806 0,214262 2,0 10,0 21,1 7,55187 1,60662 7,72088 0,212745 2,0 10,0 22,8 7,46231 1,57552 7,62682 0,211131 2,0 10,0 24,5 7,38362 1,5454 7,54361 0,209302 2,0 10,0 26,3 7,29355 1,51907 7,45006 0,208276 2,0 10,0 27,9 7,22624 1,49078 7,37841 0,206301 2,0 10,0 29,4 7,15412 1,46472 7,30253 0,204738 2,0 10,0 31,3 7,06876 1,44088 7,21412 0,203838 2,0 10,0 32,9 7,00384 1,41308 7,14497 0,201758 2,0 10,0 34,6 6,93375 1,38753 7,07122 0,200112 2,0 10,0 36,3 6,8502 1,36315 6,98451 0,198994 2,0 10,0 37,9 6,78613 1,33517 6,91623 0,19675 2,0 10,0 39,6 6,71714 1,30724 6,84316 0,194613 2,0 10,0 41,3 6,62527 1,27729 6,74727 0,192791 2,0 10,0 42,9 6,56176 1,2448 6,67879 0,189705 2,0 10,0 44,3 6,50216 1,21505 6,61472 0,186869 2,0 10,0 46,1 6,44026 1,18205 6,54784 0,18354 2,0 10,0 47,8 6,39483 1,14475 6,49649 0,179011 2,0 10,0 49,4 6,34355 1,11283 6,44042 0,175428 2,0 10,0 51,1 6,28105 1,08575 6,3742 0,172861 2,0 10,0 52,8 6,22763 1,06068 6,31731 0,170318 2,0 10,0 54,3 6,16857 1,03988 6,25561 0,168578 2,0 10,0 56,1 6,1051 1,02041 6,18979 0,16714 2,0 10,0 57,7 6,05029 1,00176 6,13266 0,165571 2,0 10,0 59,2 5,9933 0,985436 6,07377 0,164423 2,0 10,0 61,0 5,93348 0,970421 6,01231 0,16355 2,0 10,0 62,5 5,88174 0,954517 5,95869 0,162285 2,0 10,0 64,3 5,82206 0,941596 5,89771 0,161729 2,0 10,0 65,7 5,77354 0,926617 5,84743 0,160494 2,0 10,0 67,2 5,71817 0,913753 5,79072 0,159798 2,0 10,0 69,0 5,65866 0,901601 5,73003 0,159331

Master of Science Thesis 117 Resumed: Results Dynamic Mechanical Analysis: NR/BR, 10Hz Strain dyn f T E’ E” |E*| tan δ % Hz oC MPa MPa MPa 2,0 10,0 70,6 5,60705 0,887241 5,67681 0,158237 2,0 10,0 72,2 5,55292 0,873293 5,62118 0,157267 2,0 10,0 73,6 5,49617 0,861498 5,56327 0,156745 2,0 10,0 75,5 5,44107 0,846624 5,50654 0,155599 2,0 10,0 77,0 5,37853 0,835047 5,44297 0,155256 2,0 10,0 78,6 5,32546 0,817926 5,38791 0,153588 2,0 10,0 80,4 5,26569 0,804787 5,32683 0,152836 2,0 10,0 80,3 5,22143 0,792725 5,28126 0,151821

118 Master of Science Thesis 11.6 Sulfron sample, 10Hz

Results Dynamic Mechanical Analysis: NR/BR/2 phr Sulfron D3515, 10Hz Strain dyn f T E’ E” |E*| tan δ % Hz oC MPa MPa MPa 0,2 10,0 -49,7 170,459 145,852 224,341 0,855643 0,2 10,0 -49,4 165,725 148,599 222,59 0,896655 0,2 10,0 -47,7 146,747 132,37 197,628 0,902025 0,2 10,0 -45,5 118,868 107,059 159,972 0,900656 0,3 10,0 -43,3 91,5769 80,6957 122,058 0,881179 0,4 10,0 -41,4 71,2019 61,1399 93,8499 0,858684 0,4 10,0 -39,2 55,2036 45,392 71,4694 0,822264 0,5 10,0 -37,4 43,7842 34,4457 55,7096 0,786716 0,6 10,0 -35,6 35,5429 26,4926 44,3301 0,745368 0,7 10,0 -33,9 29,702 20,9795 36,3641 0,706334 0,8 10,0 -32,3 25,2782 16,8062 30,3551 0,664848 1,0 10,0 -30,6 21,9688 13,7332 25,9081 0,625125 1,1 10,0 -28,8 19,3297 11,2849 22,3827 0,583814 1,2 10,0 -27,1 17,2466 9,36696 19,6261 0,543121 1,3 10,0 -25,4 15,6077 7,89377 17,4904 0,50576 1,4 10,0 -23,8 14,2767 6,68912 15,766 0,468535 1,5 10,0 -22,1 13,1979 5,71959 14,3839 0,433372 1,6 10,0 -20,4 12,3501 4,95734 13,3079 0,4014 1,6 10,0 -18,7 11,6262 4,30933 12,3992 0,370656 1,7 10,0 -17,1 11,0529 3,80929 11,6909 0,344643 1,8 10,0 -15,4 10,5605 3,39502 11,0928 0,321484 1,8 10,0 -13,7 10,131 3,04262 10,578 0,300329 1,9 10,0 -12,1 9,76109 2,75905 10,1435 0,282658 1,9 10,0 -10,5 9,43175 2,52134 9,76295 0,267325 1,9 10,0 -8,8 9,14073 2,31855 9,4302 0,253651 2,0 10,0 -7,1 8,87145 2,14421 9,1269 0,241698 2,0 10,0 -5,5 8,63701 2,00265 8,86615 0,231869 2,0 10,0 -3,9 8,42841 1,87816 8,63514 0,222837 2,0 10,0 -2,2 8,24614 1,77389 8,43478 0,215117 2,0 10,0 -0,7 8,07426 1,68185 8,24756 0,208298 2,0 10,0 2,0 7,91162 1,60003 8,07179 0,202238 2,0 10,0 4,4 7,74706 1,52634 7,89599 0,197021 2,0 10,0 4,6 7,63191 1,47094 7,77237 0,192735 2,0 10,0 6,0 7,50317 1,42286 7,63689 0,189634 2,0 10,0 7,7 7,40987 1,38428 7,53806 0,186815 2,0 10,0 9,3 7,31438 1,34709 7,43739 0,18417

Master of Science Thesis 119 Resumed: Results Dynamic Mechanical Analysis: NR/BR/2 phr Sulfron D3515, 10Hz Strain dyn f T E’ E” |E*| tan δ % Hz oC MPa MPa MPa 2,0 10,0 11,0 7,21081 1,31401 7,32956 0,182228 2,0 10,0 12,7 7,11594 1,28242 7,23058 0,180218 2,0 10,0 14,5 7,01204 1,25284 7,12308 0,178669 2,0 10,0 15,9 6,93178 1,22905 7,03989 0,177306 2,0 10,0 17,5 6,85423 1,2065 6,9596 0,176022 2,0 10,0 19,3 6,76934 1,18285 6,87191 0,174736 2,0 10,0 21,0 6,709 1,16045 6,80862 0,172969 2,0 10,0 22,6 6,64006 1,13899 6,73704 0,171533 2,0 10,0 24,3 6,5608 1,11862 6,65548 0,170501 2,0 10,0 25,9 6,50121 1,09721 6,59315 0,168771 2,0 10,0 27,5 6,43703 1,07801 6,52667 0,16747 2,0 10,0 29,2 6,36446 1,05991 6,45211 0,166535 2,0 10,0 30,8 6,31231 1,04043 6,39748 0,164826 2,0 10,0 32,3 6,25134 1,02259 6,33443 0,163579 2,0 10,0 34,0 6,18573 1,0051 6,26686 0,162486 2,0 10,0 35,5 6,13014 0,98585 6,20891 0,16082 2,0 10,0 37,3 6,06088 0,967621 6,13764 0,15965 2,0 10,0 38,7 6,01409 0,945687 6,08799 0,157245 2,0 10,0 40,4 5,95971 0,924039 6,03092 0,155048 2,0 10,0 42,2 5,89025 0,899757 5,95858 0,152754 2,0 10,0 43,8 5,84041 0,875851 5,90572 0,149964 2,0 10,0 45,4 5,78826 0,856003 5,85121 0,147886 2,0 10,0 47,1 5,73538 0,83561 5,79594 0,145694 2,0 10,0 48,7 5,69063 0,814342 5,7486 0,143102 2,0 10,0 50,2 5,65141 0,792007 5,70664 0,140143 2,0 10,0 51,6 5,60552 0,772247 5,65846 0,137766 2,0 10,0 53,4 5,56386 0,750365 5,61423 0,134864 2,0 10,0 55,1 5,50712 0,731581 5,5555 0,132843 2,0 10,0 56,6 5,45727 0,712418 5,50358 0,130545 2,0 10,0 58,2 5,39132 0,695881 5,43605 0,129074 2,0 10,0 59,9 5,34119 0,682245 5,38459 0,127733 2,0 10,0 61,4 5,2873 0,668125 5,32935 0,126364 2,0 10,0 63,2 5,22333 0,655469 5,2643 0,125489 2,0 10,0 64,5 5,17363 0,644094 5,21357 0,124495 2,0 10,0 66,2 5,11805 0,63328 5,15708 0,123734 2,0 10,0 68,0 5,06615 0,621822 5,10416 0,122741

120 Master of Science Thesis Resumed: Results Dynamic Mechanical Analysis: NR/BR/2 phr Sulfron D3515, 10Hz Strain dyn f T E’ E” |E*| tan δ % Hz oC MPa MPa MPa 2,0 10,0 69,6 5,01764 0,612115 5,05484 0,121993 2,0 10,0 71,0 4,96916 0,601964 5,00549 0,12114 2,0 10,0 72,6 4,92372 0,591811 4,95915 0,120196 2,0 10,0 74,2 4,87236 0,581573 4,90695 0,119362 2,0 10,0 75,9 4,82868 0,572053 4,86245 0,11847 2,0 10,0 77,5 4,78235 0,561974 4,81526 0,11751 2,0 10,0 79,0 4,73377 0,551401 4,76578 0,116482 2,0 10,0 80,5 4,68887 0,540792 4,71995 0,115335 2,0 10,0 80,9 4,64963 0,532194 4,67999 0,114459

Master of Science Thesis 121 11.7 Control sample, 20Hz

Results Dynamic Mechanical Analysis: NR/BR, 20Hz Strain dyn f T E’ E” |E*| tan δ % Hz oC MPa MPa MPa 0,1 20,0 -49,8 278,9 194,122 339,807 0,696029 0,2 20,0 -49,5 275,512 202,546 341,953 0,735161 0,2 20,0 -47,5 244,756 184,072 306,248 0,752062 0,2 20,0 -45,6 204,425 158,355 258,585 0,774639 0,2 20,0 -43,8 164,517 128,978 209,048 0,78398 0,3 20,0 -42,0 131,259 102,715 166,671 0,782535 0,3 20,0 -40,4 105,801 81,8959 133,794 0,774054 0,4 20,0 -38,5 84,9892 64,303 106,574 0,756602 0,4 20,0 -36,9 69,8386 51,6933 86,8886 0,740182 0,5 20,0 -35,3 57,9505 41,7362 71,4155 0,720204 0,6 20,0 -33,8 48,9432 34,299 59,765 0,700791 0,6 20,0 -32,2 41,7095 28,2995 50,4038 0,67849 0,7 20,0 -30,7 36,0282 23,6924 43,1203 0,657607 0,8 20,0 -29,2 31,4174 19,923 37,2019 0,634137 0,9 20,0 -27,7 27,7097 16,9581 32,487 0,611993 1,0 20,0 -26,3 24,656 14,5043 28,6058 0,588265 1,1 20,0 -24,8 22,1508 12,5316 25,4499 0,565741 1,2 20,0 -23,3 20,0853 10,8806 22,8431 0,541719 1,2 20,0 -21,8 18,4168 9,53341 20,738 0,517647 1,3 20,0 -20,3 17,0572 8,3988 19,0128 0,492392 1,4 20,0 -18,9 15,9024 7,45856 17,5646 0,469021 1,5 20,0 -17,4 14,9378 6,65448 16,353 0,44548 1,6 20,0 -16,1 14,115 5,98595 15,3318 0,424086 1,6 20,0 -14,6 13,4298 5,42869 14,4855 0,404226 1,7 20,0 -13,2 12,8476 4,94962 13,768 0,385257 1,7 20,0 -11,8 12,3293 4,54073 13,1388 0,368289 1,8 20,0 -10,4 11,8755 4,18162 12,5902 0,352121 1,8 20,0 -8,9 11,4667 3,8747 12,1037 0,337908 1,8 20,0 -7,5 11,1112 3,61066 11,6832 0,324955 1,9 20,0 -6,2 10,7763 3,37856 11,2935 0,313519 1,9 20,0 -4,8 10,4963 3,18259 10,9682 0,303211 1,9 20,0 -3,3 10,2371 3,01051 10,6706 0,294078 2,0 20,0 -1,9 9,97861 2,85133 10,378 0,285744 2,0 20,0 -0,6 9,76924 2,71829 10,1404 0,27825 2,0 20,0 -0,2 9,54378 2,58303 9,88715 0,270651 2,0 20,0 4,9 9,34777 2,478 9,67064 0,26509

122 Master of Science Thesis Resumed: Results Dynamic Mechanical Analysis: NR/BR, 20Hz Strain dyn f T E’ E” |E*| tan δ % Hz oC MPa MPa MPa 2,0 20,0 4,8 9,14494 2,3771 9,44884 0,259936 2,0 20,0 5,5 8,95706 2,29476 9,24634 0,256195 2,0 20,0 6,6 8,84725 2,23705 9,12569 0,252852 2,0 20,0 7,8 8,71392 2,19427 8,98594 0,251812 2,0 20,0 9,4 8,58502 2,1404 8,84782 0,249318 2,0 20,0 10,9 8,47687 2,08709 8,73003 0,24621 2,0 20,0 12,5 8,36378 2,03394 8,60754 0,243185 2,0 20,0 14,0 8,24514 1,98264 8,48017 0,240461 2,0 20,0 15,5 8,15012 1,93569 8,37684 0,237504 2,0 20,0 17,1 8,04636 1,89414 8,2663 0,235404 2,0 20,0 18,5 7,97575 1,85653 8,18898 0,232771 2,0 20,0 19,9 7,90273 1,82243 8,11014 0,230607 2,0 20,0 21,2 7,83052 1,79241 8,03304 0,2289 2,0 20,0 22,6 7,76333 1,7634 7,96109 0,227145 2,0 20,0 24,2 7,70259 1,73644 7,89589 0,225436 2,0 20,0 25,4 7,6479 1,71407 7,83763 0,224123 2,0 20,0 26,8 7,59779 1,68775 7,78299 0,222137 2,0 20,0 28,2 7,53805 1,66373 7,71946 0,220711 2,0 20,0 29,6 7,47457 1,64029 7,65243 0,219449 2,0 20,0 31,0 7,42141 1,61427 7,59495 0,217516 2,0 20,0 32,4 7,36424 1,58947 7,53382 0,215837 2,0 20,0 33,9 7,29456 1,56592 7,46075 0,214669 2,0 20,0 35,2 7,24612 1,53617 7,40716 0,211999 2,0 20,0 36,7 7,18503 1,51151 7,3423 0,210369 2,0 20,0 38,1 7,12726 1,48287 7,27989 0,208057 2,0 20,0 39,4 7,05412 1,45439 7,20249 0,206175 2,0 20,0 40,9 6,99144 1,42397 7,13498 0,203674 2,0 20,0 42,2 6,92658 1,40093 7,06683 0,202254 2,0 20,0 43,7 6,85601 1,37957 6,99343 0,20122 2,0 20,0 45,0 6,79946 1,35664 6,93348 0,199521 2,0 20,0 46,4 6,73886 1,33713 6,87024 0,19842 2,0 20,0 47,9 6,67192 1,3198 6,80121 0,197814 2,0 20,0 49,3 6,62309 1,29918 6,74931 0,19616 2,0 20,0 50,7 6,56611 1,28198 6,69009 0,195243 2,0 20,0 52,1 6,51583 1,25853 6,63626 0,193149 2,0 20,0 53,5 6,46423 1,24327 6,5827 0,192331

Master of Science Thesis 123 Resumed: Results Dynamic Mechanical Analysis: NR/BR, 20Hz Strain dyn f T E’ E” |E*| tan δ % Hz oC MPa MPa MPa 2,0 20,0 54,7 6,4412 1,21774 6,5553 0,189054 2,0 20,0 56,2 6,40113 1,18995 6,5108 0,185897 2,0 20,0 57,5 6,35899 1,16435 6,46471 0,183103 2,0 20,0 59,0 6,31959 1,13562 6,42081 0,179699 2,0 20,0 60,5 6,27606 1,11046 6,37354 0,176936 2,0 20,0 61,8 6,22403 1,08715 6,31826 0,17467 2,0 20,0 63,3 6,17584 1,06388 6,2668 0,172265 2,0 20,0 64,7 6,12645 1,04527 6,21498 0,170616 2,0 20,0 65,8 6,07796 1,02778 6,16425 0,169099 2,0 20,0 67,2 6,0263 1,01221 6,11072 0,167966 2,0 20,0 68,5 5,97411 0,997538 6,05682 0,166977 2,0 20,0 69,9 5,92477 0,982446 6,00568 0,16582 2,0 20,0 71,4 5,87685 0,968968 5,9562 0,164879 2,0 20,0 72,7 5,82446 0,955956 5,90238 0,164128 2,0 20,0 74,0 5,77587 0,94248 5,85226 0,163176 2,0 20,0 75,4 5,72564 0,928961 5,80051 0,162246 2,0 20,0 76,8 5,67074 0,916279 5,74429 0,16158 2,0 20,0 78,3 5,62181 0,902055 5,69372 0,160456 2,0 20,0 79,6 5,56886 0,888602 5,63931 0,159566 2,0 20,0 80,6 5,52255 0,875164 5,59146 0,158471

124 Master of Science Thesis 11.8 Sulfron sample, 20Hz

Results Dynamic Mechanical Analysis: NR/BR/2 phr Sulfron D3515, 20Hz Strain dyn f T E’ E” |E*| tan δ % Hz oC MPa MPa MPa 0,1 20,0 -50,0 245,309 204,336 319,264 0,832973 0,1 20,0 -49,8 247,276 214,674 327,461 0,868157 0,1 20,0 -48,2 223,951 197,667 298,708 0,882636 0,2 20,0 -46,4 188,456 170,125 253,886 0,902729 0,2 20,0 -44,6 151,645 138,098 205,103 0,910669 0,2 20,0 -42,8 119,417 108,001 161,012 0,904405 0,3 20,0 -41,2 95,6531 85,2509 128,13 0,891251 0,3 20,0 -39,3 76,4979 66,431 101,316 0,868402 0,4 20,0 -37,7 61,507 51,5601 80,2593 0,83828 0,4 20,0 -36,2 50,7919 41,1929 65,3962 0,811013 0,5 20,0 -34,8 42,6688 33,3308 54,144 0,781151 0,6 20,0 -33,3 36,3208 27,2452 45,4038 0,750128 0,7 20,0 -31,8 31,3673 22,5835 38,6512 0,71997 0,8 20,0 -30,4 27,3777 18,8236 33,2245 0,687552 0,9 20,0 -28,9 24,1945 15,8744 28,9374 0,656114 0,9 20,0 -27,5 21,5263 13,4079 25,3605 0,62286 1,0 20,0 -26,0 19,4014 11,473 22,5398 0,591352 1,1 20,0 -24,6 17,6536 9,88847 20,2344 0,560141 1,2 20,0 -23,1 16,1855 8,55234 18,3061 0,528395 1,3 20,0 -21,8 14,9999 7,47645 16,7599 0,498433 1,4 20,0 -20,3 14,002 6,55657 15,461 0,468261 1,4 20,0 -18,9 13,1757 5,8037 14,3973 0,440484 1,5 20,0 -17,5 12,4814 5,16907 13,5095 0,41414 1,6 20,0 -16,1 11,8911 4,64074 12,7646 0,390271 1,6 20,0 -14,7 11,3967 4,19691 12,1449 0,368256 1,7 20,0 -13,3 10,9553 3,8111 11,5992 0,347878 1,7 20,0 -11,9 10,5603 3,47698 11,1179 0,329251 1,8 20,0 -10,5 10,2186 3,18975 10,7049 0,312151 1,8 20,0 -9,2 9,91851 2,9516 10,3484 0,297585 1,9 20,0 -7,8 9,64701 2,74169 10,029 0,284201 1,9 20,0 -6,3 9,39553 2,55588 9,73696 0,272031 1,9 20,0 -5,0 9,16403 2,39323 9,47137 0,261155 1,9 20,0 -3,6 8,95183 2,25078 9,23046 0,251433 2,0 20,0 -2,2 8,7555 2,12626 9,00998 0,242849 2,0 20,0 -0,8 8,56759 2,01286 8,80086 0,234939 2,0 20,0 -0,3 8,39288 1,9129 8,60811 0,227919

Master of Science Thesis 125 Resumed: Results Dynamic Mechanical Analysis: NR/BR/2 phr Sulfron D3515, 20Hz Strain dyn f T E’ E” |E*| tan δ % Hz oC MPa MPa MPa 2,0 20,0 4,4 8,24098 1,8298 8,44168 0,222037 2,0 20,0 4,1 8,07572 1,75183 8,26355 0,216925 2,0 20,0 5,7 7,89278 1,66727 8,06695 0,21124 2,0 20,0 7,2 7,76589 1,61148 7,93133 0,207508 2,0 20,0 8,6 7,6497 1,56733 7,80861 0,204888 2,0 20,0 10,1 7,52835 1,5298 7,68221 0,203205 2,0 20,0 11,5 7,42474 1,49467 7,57369 0,20131 2,0 20,0 12,9 7,34123 1,46145 7,48528 0,199074 2,0 20,0 14,3 7,25668 1,42998 7,39623 0,197057 2,0 20,0 15,7 7,17861 1,39989 7,31383 0,195008 2,0 20,0 17,0 7,11439 1,37308 7,24568 0,193 2,0 20,0 18,4 7,05105 1,34846 7,17883 0,191242 2,0 20,0 19,9 6,97913 1,32564 7,10391 0,189943 2,0 20,0 21,2 6,93123 1,3023 7,05252 0,187889 2,0 20,0 22,6 6,87351 1,28009 6,99169 0,186236 2,0 20,0 24,0 6,81921 1,25815 6,9343 0,1845 2,0 20,0 25,4 6,76354 1,23559 6,87547 0,182683 2,0 20,0 26,9 6,69665 1,21508 6,806 0,181446 2,0 20,0 28,3 6,65035 1,19283 6,75648 0,179364 2,0 20,0 29,7 6,59911 1,17262 6,70248 0,177694 2,0 20,0 31,1 6,54724 1,15373 6,64811 0,176216 2,0 20,0 32,5 6,49375 1,13443 6,5921 0,174696 2,0 20,0 33,8 6,44457 1,11289 6,53995 0,172686 2,0 20,0 35,3 6,39357 1,09435 6,48655 0,171164 2,0 20,0 36,7 6,33435 1,07421 6,42479 0,169585 2,0 20,0 38,0 6,2823 1,05346 6,37001 0,167687 2,0 20,0 39,4 6,22763 1,032 6,31256 0,165714 2,0 20,0 40,9 6,15374 1,01261 6,2365 0,164553 2,0 20,0 42,3 6,10543 0,989126 6,18503 0,162008 2,0 20,0 43,7 6,04731 0,971542 6,12485 0,160657 2,0 20,0 45,1 5,99609 0,953819 6,07148 0,159074 2,0 20,0 46,5 5,94142 0,938239 6,01504 0,157915 2,0 20,0 47,7 5,90203 0,920481 5,97338 0,15596 2,0 20,0 49,1 5,85237 0,905677 5,92203 0,154754 2,0 20,0 50,5 5,80529 0,891102 5,87328 0,153498 2,0 20,0 51,9 5,76486 0,875494 5,83097 0,151867

126 Master of Science Thesis Resumed: Results Dynamic Mechanical Analysis: NR/BR/2 phr Sulfron D3515, 20Hz Strain dyn f T E’ E” |E*| tan δ % Hz oC MPa MPa MPa 2,0 20,0 53,3 5,72268 0,862562 5,78732 0,150727 2,0 20,0 54,6 5,67823 0,850888 5,74163 0,149851 2,0 20,0 56,0 5,67688 0,818657 5,73561 0,144209 2,0 20,0 57,4 5,63639 0,805514 5,69366 0,142913 2,0 20,0 58,8 5,59912 0,785734 5,65398 0,140332 2,0 20,0 60,1 5,57119 0,761144 5,62294 0,136622 2,0 20,0 61,6 5,53074 0,744042 5,58056 0,134529 2,0 20,0 62,9 5,48412 0,728684 5,53232 0,132872 2,0 20,0 64,1 5,43354 0,715197 5,4804 0,131627 2,0 20,0 65,5 5,38191 0,702879 5,42762 0,1306 2,0 20,0 67,0 5,33123 0,690793 5,3758 0,129575 2,0 20,0 68,3 5,28408 0,680668 5,32774 0,128815 2,0 20,0 69,5 5,23114 0,67029 5,27391 0,128134 2,0 20,0 70,9 5,18558 0,659679 5,22737 0,127214 2,0 20,0 72,2 5,14076 0,65015 5,1817 0,12647 2,0 20,0 73,5 5,09313 0,640333 5,13323 0,125725 2,0 20,0 74,9 5,04988 0,631049 5,08915 0,124963 2,0 20,0 76,2 5,0076 0,6222 5,04611 0,124251 2,0 20,0 77,7 4,96157 0,613025 4,9993 0,123555 2,0 20,0 79,1 4,91952 0,603514 4,9564 0,122677 2,0 20,0 80,3 4,87593 0,594385 4,91202 0,121902

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130 Master of Science Thesis