Secondary Controlled Swing Drive

Karl Pettersson

Fluid and Mechanical Engineering Systems

Master Thesis Department of Management and Engineering LIU-IEI-TEK-A--09/00549--SE

Datum 2009-02-10 Avdelning, institution Date 02/10/2009 Division, Department Institutionen för ekonomisk och industriell utveckling Fluid och mekanisk systemteknik Department of Management and Engineering Fluid and Mechanical Engineering Systems

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Svenska/Swedish Licentiatavhandling ISRN X Engelska/English X Examensarbete LiU-IEI-TEK-A--09/00549--SE C-uppsats Serietitel och serienummer ISSN D-uppsats Title of series, numbering ______Övrig rapport

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URL för elektronisk version

http://www.ep.liu.se

Titel Title Secondary Controlled Swing Drive

Författare Author Karl Pettersson

Sammanfattning Abstract

The purpose of the thesis has been to design and simulate different concepts of a secondary controlled swing drive for a wheel excavator. Secondary control is a known technology in the field of hydraulics that offers precise positioning as well as the possibility of energy recuperation. Secondary control is today used in certain industrial applications and is rather unemployed in mobile machinery. An excavator moves high loads in cyclic motions which are ideal conditions for energy recuperating systems. A study of the potential of a secondary controlled swing drive is therefore interesting. The focus has been on testing different circuit architectures and emergency brake concepts.

The results of the design process have been three types of circuit architectures and two types of hydraulic safety concepts. The results of the simulation have shown that the open and closed circuit architecture have similar energy efficiency. The closed circuit with low pressure accumulator however offers the best controllability. At least 20% energy savings can be achieved by storing the kinetic energy when braking.

A hydraulic emergency brake must function, independent on the direction of rotation of the excavator during a failure. The first principle recognises the rotation direction and changes the swivel angle of the secondary unit so that a braking torque is created. In the second principle a pressure difference is built up over the secondary unit that always results in a braking torque. Simulations have shown that the principle with recognition of the speed direction is the most effective safety concept.

Nyckelord: Sekundärreglering, Hjulgrävare, Energiåtervinning, Hydrostatisk Transmission

Keywords: Secondary Control, Excavator, Energy Recuperation, Hydrostatic Transmission

Abstract

The purpose of the thesis has been to design and simulate different concepts of a sec- ondary controlled swing drive for a wheel excavator. Secondary control is a known technology in the field of hydraulics that offers precise positioning as well as the pos- sibility of energy recuperation. Secondary control is today used in certain industrial applications and is rather unemployed in mobile machinery. An excavator moves high loads in cyclic motions which are ideal conditions for energy recuperating systems. A study of the potential of a secondary controlled swing drive is therefore interesting. The focus has been on testing different circuit architectures and emergency brake con- cepts.

The results of the design process have been three types of circuit architectures and two types of hydraulic safety concepts. The results of the simulation have shown that the open and closed circuit architecture have similar energy efficiency. The closed circuit with low pressure accumulator however offers the best controllability. At least 20% energy savings can be achieved by storing the kinetic energy when braking.

A hydraulic emergency brake must function, independent of the direction of rotation of the excavator during a failure. The first principle recognises the rotation direction and changes the swivel angle of the secondary unit so that a braking torque is created. In the second principle a pressure difference is built up over the secondary unit that always results in a braking torque. Simulations have shown that the principle with recognition of the speed direction is the most effective safety concept. Preface

This master thesis is written in Bosch Rexroth AG in the mobile hydraulics department in Elchingen. My examinator in Linköping University is Professor Karl-Erik Rydberg. My official supervisor has been Dr. Seppo Tikkanen who helped me with schematic design and dimensioning. My other supervisor has been Sebastian Oschmann who has helped me much in almost all possible ways. Finally I would like to thank the other students in the ESY department for helping me with ideas and several software prob- lems.

Karl Pettersson Contents

Contents

1 Introduction 12 1.1 Excavator Swing Drive ...... 12 1.2 State-of-the-Art ...... 13 1.3 History of Secondary Control ...... 14

2 Secondary Controlled Swing Drive 17 2.1 Basic Principle ...... 17 2.2 Circuit Architecture ...... 19 2.2.1 Open Circuit ...... 19 2.2.2 Closed Circuit ...... 21 2.2.3 Secondary Unit in Bent-axis Design ...... 23 2.3 Emergency Brake Concepts ...... 23 2.3.1 Mechanical Brake ...... 24 2.3.2 Two Directions Hydraulic Brake ...... 25 2.3.3 One Direction Hydraulic Brake ...... 25 2.4 Control Units ...... 26 2.4.1 EP Control ...... 27 2.4.2 ED Control ...... 29 2.4.3 HD Control ...... 29 2.4.4 DG Control ...... 31 2.4.5 Modified Control Unit ...... 31 2.5 Safety Concept Design ...... 32 2.5.1 EP 1-Way ...... 32 2.5.2 EP 2-Way ...... 33 2.5.3 HD 1-Way ...... 34 2.5.4 HD 2-Way ...... 35 2.6 Pilot Circuit ...... 35 2.6.1 Closed Circuit With Low Pressure Accumulator ...... 35 2.6.2 Closed Circuit With Volume Equaliser ...... 37 2.6.3 Open Circuit ...... 37

Karl Pettersson 4 Contents

3 Dimensioning 39 3.1 Current System ...... 39 3.2 Inertia Model ...... 40 3.3 Secondary Controlled System ...... 41 3.3.1 Working Point ...... 41 3.3.2 Pressure Level ...... 42

4 Simulation 51 4.1 AMESim ...... 51 4.2 Description of Models ...... 51 4.2.1 Diesel Engine ...... 51 4.2.2 Inertia ...... 51 4.2.3 Hydraulic Machines ...... 52 4.2.4 Valves ...... 52 4.2.5 Control Units ...... 52 4.2.6 Failure Mode ...... 53 4.2.7 Reference Signal ...... 53 4.3 Control Algorithms ...... 54 4.3.1 Control of the Primary Unit ...... 54 4.3.2 Control of The Secondary Unit ...... 54

5 Results 56 5.1 Circuit Architecture ...... 56 5.1.1 Functionality ...... 56 5.1.2 Energy ...... 59 5.2 Safety Concept ...... 61 5.2.1 Functionality ...... 62

6 Conclusions 71 6.1 Circuit Architecture ...... 71 6.2 Safety Concepts ...... 71 6.3 Future ...... 72

A DIN EN 474-5 74

B Simulation Models 76 B.1 Closed Circuit with LP Accumulator, 1-Way emergency brake and HD control unit ...... 77

Karl Pettersson 5 Contents

B.2 Closed Circuit with Volume Equaliser, 1-Way emergency brake and HD control unit ...... 78 B.3 Closed Circuit with LP Accumulator, 2-Way emergency brake and HD control unit ...... 79 B.4 Closed Circuit with LP Accumulator, 1-Way emergency brake and EP control unit ...... 80 B.5 Closed Circuit with LP Accumulator, 2-Way emergency brake and EP control unit ...... 81 B.6 Open Circuit with 2-Way emergency brake and HD control unit . . . . 82

C Matlab m-files 83 C.1 workingpoint.m ...... 84 C.2 Limits.m ...... 85 C.3 wpsolver.m ...... 87

Karl Pettersson 6 List of Figures

List of Figures

1 Excavator swing/slew drive ...... 12 2 Crawler excavator ...... 13 3 The AGV transports carrying containers in a harbour ...... 15

4 Principle of a traditional hydrostatic drive ...... 17 5 Secondary controlled system with a hydraulic motor as secondary unit . 18 6 Secondary controlled system in open circuit ...... 20 7 The Bosch Rexroth A4VSO pump ...... 20 8 The Bosch Rexroth A11VO pump ...... 21 9 Secondary controlled system in closed circuit ...... 21 10 Secondary controlled system with volume equaliser ...... 22 11 The Bosch Rexroth A4VG pump ...... 22 12 Principle with mechanical emergency brake ...... 25 13 Principle of swivel angle control for swashplate hydraulic machines . . . 26 14 Principle with electric pressure reducers in the pressure lines ...... 27 15 Standard version of the EP control unit for A4VG (extract from [1]) . . 27 16 Characteristics of the EP control unit (extract from [1]) ...... 28 17 The EP control unit when affected by an external pressure ...... 28 18 Standard version of the HD control unit for A4VG (extract from [1]) . 29 19 Characteristics of the HD control unit (extract from [1]) ...... 30 20 The HD control unit when affected by an external pressure ...... 30 21 Standard version of the DG control unit for A4VG (extract from [1]) . 31 22 Designed safety concept with EP control unit and 1-Way emergency brake 32 23 Designed safety concept with EP control unit and 2-Way emergency brake 33 24 Designed safety concept with HD control unit and 1-Way emergency brake 34 25 Designed safety concept with HD control unit and 2-Way emergency brake 35 26 Principle of supplying pilot pressure to the secondary unit in a closed circuit with LP accumulator ...... 36 27 Principle of supplying pilot pressure to the secondary unit in a closed circuit with volume equaliser ...... 37

Karl Pettersson 7 List of Figures

28 Principle of supplying pilot pressure to the secondary unit in an open circuit ...... 38

29 Configuration of the swing drive for the excavator ...... 39 30 Angle and speed when slewing to 90 ◦ with maximum torque used . . . 42 31 Set pressure for option 1 ...... 44 32 Swivel angle of the primary and the secondary unit at maximum torque 45 33 Characteristics for the secondary unit with option 1 ...... 46 34 Set pressure for option 2 ...... 47 35 Characteristics for the secondary unit with option 2 ...... 48 36 The chosen set pressure and the ideal set pressure for the closed circuit 49 37 Characteristics for the secondary unit with chosen machine sizes in closed circuit ...... 50 38 Characteristics for the secondary unit with chosen machine sizes in open circuit ...... 50

39 The control principle of the primary unit ...... 54 40 The control principle of the secondary unit ...... 55

41 Functionality of the open circuit ...... 56 42 Functionality of the closed circuit with low pressure accumulator . . . . 57 43 Functionality of the closed circuit with volume equaliser ...... 58 44 The energy consumptions of the open circuit ...... 59 45 The energy consumptions of the closed circuit with low pressure accu- mulator ...... 60 46 The energy consumptions of the closed circuit with volume equaliser . . 60 47 The total energy consumptions of all circuit architectures ...... 61 48 EP1W braking positive speed during loss of electrical control ...... 62 49 EP1W braking negative speed during loss of electrical control . . . . . 63 50 EP1W braking positive speed during stop of diesel engine ...... 64 51 EP2W braking during loss of electrical control ...... 65 52 HD1W braking positive speed during loss of electrical control ...... 66 53 HD1W braking negative speed during loss of electrical control . . . . . 67 54 HD1W braking positive speed during stop of diesel engine ...... 68 55 HD2W braking during loss of electrical control ...... 69 56 HD2W braking during stop of diesel engine ...... 70

Karl Pettersson 8 List of Tables

List of Tables

1 Matrix of options for emergency brake and control unit ...... 32

2 Table of dimensions for the current swing drive ...... 40 3 Values for the inertia model ...... 40 4 Calculated Component Sizes ...... 48 5 Real Component Sizes ...... 49

6 Rankings of the circuit architectures ...... 71

Karl Pettersson 9 Nomenclature

Nomenclature

Quantities

a rad/s2 Angular Acceleration Ekin J Kinetic energy Eloss J Energy lost due to friction i − Gear ratio J kgm2 Moment of inertia Nm kvf /rpm Coefficient of viscous friction n rpm Angular speed npmax rpm The highest speed where the set pressure still is at maximum p bar Pressure PW Power p0 bar Precharge accumulator pressure p1 bar Minimum accumulator pressure p2 bar Maximum accumulator pressure pset bar Set pressure q L/min Flow t s Time T Nm Torque Tcf Nm Coulomb friction torque Ts Nm Static friction torque cm3 Vg /rev Displacement Vgas L Accumulator gas volume V0 L Accumulator volume at p0 V1 L Accumulator volume at p1 V2 L Accumulator volume at p2 α − Swivel angle γ − Polytropic exponent ∆p bar Pressure difference ∆VL Volume difference ηvol − Volumetric efficiency ηhm − Hydromechanical efficiency θ ◦ Angle ω rad/s Angular speed rad ωpmax /s The highest speed where the set pressure still is at maximum

Karl Pettersson 10 Nomenclature

Index

acc Accumulator avg Average calc Calculated DE Diesel Engine m Motor max Maximum min Minimum p Pump ref Reference tot Total wp Working point

Abbreviations

EP 1W Safety concept with EP Control unit and 1-Way emergency brake EP 2W Safety concept with EP Control unit and 2-Way emergency brake HD1W Safety concept with HD Control unit and 1-Way emergency brake HD2W Safety concept with HD Control unit and 2-Way emergency brake HST Hydrostatic Transmission HP High Pressure LP Low Pressure SCHT Secondary Controlled Hydrostatic Transmission

Karl Pettersson 11 1 Introduction

1 Introduction

1.1 Excavator Swing Drive

An excavator is an engineering vehicle used for earth moving, demolition, heavy lifting or material handling. It consists of an undercarriage with wheels or tracks and a pivoting upper platform with an articulated arm to perform the work. The arm can be attached with various attachements depending on the purpose. The rotating movement is called swing or slew and is driven hydraulically. The power source of the excavator is normally a diesel engine that drives one or many hydraulic pumps. The pumps supply oil flow to the hydraulic system that actuates the different work functions together with the drive transmission. The swing drive is hence driven by a hydraulic motor creating a rotating motion. The excavator can rotate 360◦ an infinitely number of times but normally operates within a specific working cycle. When used for earth moving, a typical duty cycle is to dig at one position, rotate a certain angle, dump the load in a dumper and slew back.

Figure 1: Excavator swing/slew drive

Karl Pettersson 12 1 Introduction

1.2 State-of-the-Art

The hydraulic systems of wheel excavators and smaller crawler excavators today are normally Closed-centre Load-Sensing systems. The swing drive is connected parallel to the other working hydraulics. One or multiple pumps supply oil flow to every actuator in an open loop circuit. Each function, including the slew drive, is valve controlled often with hydraulic compensators making the speed proportional to the throttled area. The swing drive often uses a fixed hydraulic motor which is controlled from a proportional valve. When moving the control valve to one side, oil flow through the created orifice and gives the fixed motor a certain speed. The pump is pressure controlled to meet the highest load.

Figure 2: Crawler excavator

In heavier excavators, Open-centre systems have traditionally been more common partly because of its simplicity. This applies to some extent also today, specifically in crawler excavators with an operational weight over 20 tons. Open-centre refers to the middle position of the control spool valve which is active during zero joystick sig- nal, causing the flow to be directed to the reservoir. The pump is controlled to match the spool positions, swivelling out following a joystick movement. To the operator this

Karl Pettersson 13 1 Introduction

system will feel different depending on the load. A heavier load will be noticed by the operator since pressure needs to be built up for a longer time hence the joysticks out- put will feel different. This is also a reason why open-centre systems still is frequently employed in larger excavators.

Another feature is the separate circuit for the slew drive consisting of a closed loop hydrostatic transmission (HST). The swing can now be controlled without valves and consequently with less throttling losses. The primary unit is speed controlled produc- ing a certain flow by swivelling out according to the joystick signal. The motor can either be fixed or variable and achieves an output speed depending on its displacement. Separation of the slew gear from the working hydraulics also prevents mutual influences in the case of parallel movements. This type of system is also common in heavier ex- cavators where the loads are so high that additional pumps are needed nonetheless [8].

1.3 History of Secondary Control

The principle of Secondary Control was first patented in England in 1962 by the en- gineers Pearson and Burret. The basic idea was a speed controlled hydraulic motor working in a constant pressure system. This was achieved by adjustment of the dis- placement volume of the motor with a hydraulic tachometer attached to the axle of the motor. At this time was though the technology not sufficiently advanced to control the high dynamics of the system why it would not be further developed. 1977 the idea was also born in the Army University of Hamburg independent of the earlier patent. A co- operation with Mannesmann Rexroth made it possible to initiate tests and eventually simulate different concepts of secondary controlled systems. Experiments were made with different types of controllers, motors and also with both a hydraulic and an elec- tric tachometer for the velocity feedback. The cooperation ended in 1986, but at that time several orders had already been booked from the industry. In 1992 a patent ap- plication was accepted from Mannesmann Rexroth for the combination of an electrical tachometer and an electrical swivel angle feedback. As designed, the secondary control principle was consequently protected for the company until the year 2000 [3]. During this time, secondary control in the industry became more common, but only used in certain extreme applications. The advantages compared to a normal hydrostatic drive with primary control were mainly [3]:

Karl Pettersson 14 1 Introduction

• Higher efficiency

• Higher dynamic response

• Energy recuperation

• Better accuracy in speed, torque and positioning

The disadvantages involve:

• Higher costs

• More electronics and increased complexity

• Control problems

In the early stages of secondary control described above, the problems with a stable control were the main factors for holding the interest back. Solving those problems, as the electronics developed, the advantages were still not sufficient to convince the industry. The energy issue was not as big as it is today and the lower fuel consumption could not yet make up for the higher costs. Electronically controlled devices were not trusted and one put a value of having a completely hydraulic drive. This is why the last advantage often was the decisive one when choosing in favour of a secondary con- trolled system. In applications demanding high precision positioning with high loads, secondary control is superior to a standard hydrostatic transmission. One example is an automated transport vehicle used when transporting containers in a harbour. The vehicles are without drivers and uses a secondary controlled drive transmission that can position the transport within 20 mm [3]. The application can be seen in Figure 3.

Figure 3: The AGV transports carrying containers in a harbour

Today secondary control is well known within the industry but is still not commonly used. The above mentioned explanations still apply today, however with increasing

Karl Pettersson 15 1 Introduction

fuel prices and decreased costs for advanced electronic components the system gets interesting in more and more applications. In mobile machinery high loads are moved in cyclic motions which are ideal conditions for energy recuperation systems.

Karl Pettersson 16 2 Secondary Controlled Swing Drive

2 Secondary Controlled Swing Drive

2.1 Basic Principle

A conventional closed circuit hydrostatic transmission consists of a hydraulic pump with variable displacement and a hydraulic motor with fixed displacement. By varying the displacement of the pump a flow is created in the circuit. The flow causes the motor to turn and a certain speed is acquired depending on its displacement. The flow is hence always proportional to the speed of the motor:

1000ηvolm · qm nm = (2.1) Vgm

If the driven load increases the system will respond with raising the pressure in the circuit so that the new torque demand is met:

V ∆pη T = gm hmm (2.2) m 20π

Figure 4: Principle of a traditional hydrostatic drive

In a secondary controlled system, one or more speed controlled actuators are connected in parallel. A hydraulic primary unit keeps a constant pressure level in the energy line of the circuit.

Karl Pettersson 17 2 Secondary Controlled Swing Drive

Figure 5: Secondary controlled system with a hydraulic motor as secondary unit

The secondary unit is variable and can work as both pump and motor. It must be able to be controlled over centre allowing positive and negative torque in any speed directions. This is commonly refered to as four quadrant operation. The output torque is directly proportional to the displacement of the secondary unit since the pressure is kept constant:

V · α · ∆p · η T = gmmax m hmm (2.3) m 20π When increasing the swivel angle the flow requirement raises according to:

Vgmmax · αm · nm qm = (2.4) 1000ηvolm Putting (2.3) and (2.4) together:

20πTm · nm qm = (2.5) 1000∆p · ηhmm · ηvolm With a constant pressure difference comes that:

qm ∝ Tm · nm (2.6)

We now have the unusual relationship that a change in torque produces a certain change in flow. A constant speed without any load torque would hence produce zero flow. Such a relationship makes the secondary controlled hydrostatic transmission (SCHT) particularly energy efficient since the load can move at high speeds without necessarily having big flow losses. The secondary unit is speed controlled, meaning that a reference speed affects the displacement so that the speed is always kept. An

Karl Pettersson 18 2 Secondary Controlled Swing Drive

increased load will hence make the secondary unit respond in a higher swivel angle to create an equal torque and keep the reference speed.

When using a conventional HST, a change in torque will cause the oil column in the circuit to compress or expand. This triggers a hydraulic spring effect which may have a great impact on the system stability. Increased control time of the pump have a damping effect which keeps the system under control, but makes it dynamically slower [3]. A corresponding change of torque makes the SCHT react with a change in swivel angle. The new torque demand is directly met and no hydraulic spring effect will occur since the secondary unit is acting in a constant pressure.

When lowering a load or braking an inertia, the secondary unit starts acting as a pump effectively generating flow from the negative load torque. The swivel angle is controlled over centre and the flow is directed back into the energy line. The corresponding recovered energy can be used to other parallel functions, stored in the accumulator or directed back to the energy source.

2.2 Circuit Architecture

Similar to traditional hydrostatic transmissions, a secondary controlled system can be used in either open or closed circuits. The difference is mainly whether the pump suction comes from the reservoir or directly from the motor. Four quadrant operation without control valves is possible in both cases. When braking, the secondary unit starts acting as a pump and delivers flow from the low pressure side back to the accumulator on the high pressure side.

2.2.1 Open Circuit

An open circuit system needs the reservoir to be either pressurised or mounted higher than the pump to avoid cavitation. The low pressure side can also be pressurised with an auxiliary pump in a so called pre-fill operation. The filling pump must then be big enough to produce the maximum flow of the secondary unit.

Karl Pettersson 19 2 Secondary Controlled Swing Drive

Figure 6: Secondary controlled system in open circuit

The secondary unit must be constructed with a large suction port to work in an open circuit. Since the high pressure (HP) side never changes in the open circuit four quadrant operation is demanded from the secondary unit. An axial piston machine that swivels over centre is able to to this. Bent-axis machines swivelling over centre are normally large and expensive why a swashplate design would be the best option. The Rexroth A4VSO pump (Figure 7) is a suitable secondary unit which meets the above requirements.

Figure 7: The Bosch Rexroth A4VSO pump

The primary unit has almost the same requirements, even though negative swivel angles only would be used to unload the diesel engine. When braking, the reversed flow is loading the accumulator, making the kinetic energy available for reuse. Since the primary unit is working as a pump in a constant pressure system, no negative swivel angles are required. The Rexroth A11VO (Figure 8)is a swashplate pump suitable for this concept. The A4VSO is also possible to use as primary unit if unloading the diesel engine is necessary. Further discussions regarding this is made in Chapter3.3.2.

Karl Pettersson 20 2 Secondary Controlled Swing Drive

Figure 8: The Bosch Rexroth A11VO pump

2.2.2 Closed Circuit

The closed circuit transmission has a direct connection between the low pressure side of the primary and the secondary unit. According to this, the same amount of oil will always circulate between the high and the low pressure side. With energy recu- peration in forms of a hydraulic accumulator this cannot be the case. Depending on the movements performed, the accumulator will contain different volumes of oil and a problem arises of how to keep the balance of oil volume in the circuit. For an increasing volume in the accumulator the same amount needs to be inserted to the low pressure side and vice versa. The use of an additional accumulator on the low pressure side is the standard way for covering the lack of oil volume. This accumulator will of course have lower pressure levels but should be able to store the same amount of oil. Figure 9 shows the SCHT in closed circuit:

Figure 9: Secondary controlled system in closed circuit

Karl Pettersson 21 2 Secondary Controlled Swing Drive

Another way to resupply oil flow into the circuit is to use the information of how much is going in to the HP accumulator and distribute the same amount to the LP side. This can be done hydraulically according to Figure 10.

Figure 10: Secondary controlled system with volume equaliser

The motor (1) under the accumulator rotates proportionally to the flow. Depending on whether the accumulator is loading or unloading, the flow from the pump (2) goes out of or into the low pressure side, keeping the oil volume in the circuit constant. The pump displacement should be of somewhat similar size as the motor to create the same flow in both directions. This is to handle both quick acceleration and quick braking.

The A4VG is the closed circuit version of the A4VSO and is suitable to use as the secondary unit. The option of unloading the diesel engine or not still remains, but the A4VG is in both cases the most cost effective alternative to use as the primary unit.

Figure 11: The Bosch Rexroth A4VG pump

Karl Pettersson 22 2 Secondary Controlled Swing Drive

2.2.3 Secondary Unit in Bent-axis Design

A bent-axis motor is normally a better option to use as a motor because of its good starting efficiency. Bent-axis motors with the possibility of swivelling over centre are however not as common anymore. The heavy housing and difficulties to control makes it unfavourable and also expensive to use. Although there is a possibility of using a motor in bent-axis design combined with switching valves. This eliminates the need of negative swivel angles. The high and low pressure sides are here switched depending on which direction the motor is turning so that four quadrant operation is possible. The circuit architecture can be both open and closed. However does this system imply additional components, throttling losses and demands a precise control of the switching valves to avoid pressure peaks. For these reasons this concept is not further investigated in this thesis, but could however be interesting in future investigations.

2.3 Emergency Brake Concepts

Switching from a traditional HST to a secondary controlled system will most probably mean switching the hydraulic motor. An electrically controlled motor with variable displacement over centre is now required which would not be the case in a conventional transmission. This is however not done without complications regarding safety issues during system breakdown. Three different failures of the system are considered:

• Electrical breakdown

• Loss of hydraulic pressure

• Diesel engine stop

Requirements regarding emergency stops for earth moving machinery are regulated by European Union norms handling earth moving machinery. The corresponding german norm is called DIN EN 474. Part 5 of this norm handles hydraulic excavators and states safety regulations regarding the swing drive. During a breakdown should the top frame of the excavator be able to stop the rotational motion within a certain angle depending on the angular speed. An extract is displayed in Appendix A and shows this relationship in the figure called Bild C.1.

The emergency brake in conventional drives do not face the same difficulties as in the SCHT. In a conventional closed circuit HST, the motor is fixed or variable with

αmmin > 0. A breakdown would automatically block the flow from the pump side. A positive swivel angle causes the motor to still produce flow. Pressure is built up

Karl Pettersson 23 2 Secondary Controlled Swing Drive

and a braking torque will eventually be created according to (2.3). Depending on the direction of the speed one of the sides will have high pressure and a braking torque is always created due to this. A valve controlled drive would have control valves separat- ing the pump and motor sides. When a breakdown occurs the motor is isolated from the energy line and flow is blocked in the same way.

In the secondary controlled system the motor is controlled over-centre, enabling nega- tive swivel angles. A loss of electrical control would set the swivel angle of the motor to zero since the stroke cylinder of the control unit seeks its equilibrium position. With zero swivel angle and hence zero torque, the load can rotate freely even though flow is blocked from the pump according to (2.6). A breakdown in the secondary controlled system must consequently be handled differently from the traditional hydraulic sys- tems. A separate emergency brake has to be installed that is not electrically activated since the brake also has to work during an electrical breakdown.

An emergency braking procedure can either be done by a hydraulically controlled me- chanical brake or by letting the hydraulic motor create a braking torque. When a failure occurs, the circuit goes into a failure mode which ensures braking independently of the type of emergency. Recognising that a failure has occurred is of course done in differ- ent ways depending on what has happened. Loss of electric control can easily be done by using an electrically controlled spool valve which switches position when current is lost. A hydraulic pressure is then activated and failure mode is reached. Recognising a loss of pressure and a stop of the diesel engine can hence be done electrically and thus activate the same failure mode.

2.3.1 Mechanical Brake

The principle with a mechanical brake is the simplest one. The valve for recognising failure mode is connected to a mechanical disk brake at the axle of the secondary unit. At a failure the valve would automatically block the flow and the mechanical brake would be activated. This concept needs no throttling and very few components, however could the mechanical brake have problems braking a big inertia as the top frame of an excavator. This would cause the dimensions of the brake and consequently the price to go up. Another problem is that a mechanical brake would wear each time it is used and would have to be replaced after a certain number of times. Such a system is hard for a manufacturer to sell and for these reasons this solution is not further examined in this thesis.

Karl Pettersson 24 2 Secondary Controlled Swing Drive

Figure 12: Principle with mechanical emergency brake

2.3.2 Two Directions Hydraulic Brake

The hydraulic emergency brake is achieved by control of the swivel angle, since the torque is proportional to the displacement of the secondary unit. One option is to determine the direction of the angular speed and choose according to this how the swivel angle should be controlled. No sensors and electronics can be used to achieve this since the brake has to be operational when electric control is lost. A certain swivel angle is however not enough to be sure to brake the motion, a pressure difference over the motor is also necessary. A hose break would cause a loss of pressure in the circuit and the secondary unit would not be able to create a torque to brake. Since the emergency brake is able to be controlled in both directions it is enough to block the high pressure (HP) side of the transmission to be sure that a braking torque can be accomplished. This means that only one side of the secondary unit must be able to be pressure resistant.

2.3.3 One Direction Hydraulic Brake

Another option is to always control the swivel angle to the same direction when a failure occurs. Now both sides have to be blocked and dependent of the angular speed one of the sides will have the high pressure. The emergency brake will now act as described for the HST. It is now necessary for the secondary unit to be pressure resistant on both sides. This fact excludes the use of the one direction emergency brake in an open circuit architecture.

Karl Pettersson 25 2 Secondary Controlled Swing Drive

2.4 Control Units

The control unit refers to the configuration of how the swivel angle of the hydraulic machine is controlled. This is important to consider in the SCHT due to the need of influence from the emergency brake circuit. The swivel angle of a hydraulic machine in swashplate design is normally controlled by a control valve and a stroke cylinder as shown in Figure 13.

Figure 13: Principle of swivel angle control for swashplate hydraulic machines

The control valve (1) affects the position of the stroke cylinder (2) and is normally supplied by the pilot pressure in the circuit. The link between the valve and the piston is a mechanical feedback (3) which moves the positions of the pressure ports to the valve. The swashplate is always affected when pressure rises in the machine and the mechanical feedback counteracts this movement. This is not a standard in all control units but it helps controlling the swashplate to its reference position. The control valve can either be controlled by electrical solenoids or by hydraulic pressures. The complex control algorithms in secondary control are however done electrically and an electrical controller is therefore a necessity. The option of having hydraulic pressures affect the control valve must therefore be modified. An electrical signal has to be transformed to pressures in the control lines. This can be achieved by using electrically controlled pressure reducers in the control lines as shown in Figure 14. Each pressure reducing valve sets a certain pressure in the line corresponding to the electrical signal.

Karl Pettersson 26 2 Secondary Controlled Swing Drive

Figure 14: Principle with electric pressure reducers in the pressure lines

Overviewing the Rexroth control units the following options are available in their stan- dard versions.

2.4.1 EP Control

The EP controller is the most straightforward option where the control signal directly can be taken in as electric currents. It uses proportional solenoids to move the control valve and each solenoid is assigned to one direction of flow to the cylinder. Figure 15 shows the standard version of the EP controller for A4VG and Figure 16 its character- istics.

Figure 15: Standard version of the EP control unit for A4VG (extract from [1])

Karl Pettersson 27 2 Secondary Controlled Swing Drive

Figure 16: Characteristics of the EP control unit (extract from [1])

The ports X1 and X2 are suitable to connect to the emergency brake circuit. At a loss of electric control the control valve would seek its middle position and the swivel angle go towards zero. A pressure rise in one of the ports would push the stroke cylinder to the other direction according to earlier discussions. The mechanical feedback is however still active, moving the pressure ports so that pilot pressure is connected to the other side and the pressurised side is connected with the reservoir. The described process is displayed in Figure 17.

Figure 17: The EP control unit when affected by an external pressure

The feedback counteracts the emergency brake and a certain oil flow is now needed to keep the swivel angle at maximum. Since the pilot pressure is external, it is always possible to cut it off at a failure mode. This would stop the pilot pressure to push the stroke cylinder back when affected. The connection to the reservoir is however not possible to affect without modifying the control unit. Consequently would the emergency pressure be more connected to the tank line as the stroke cylinder moves. Springs acting to keep the cylinder centred create forces that have to be overcome by

Karl Pettersson 28 2 Secondary Controlled Swing Drive

the emergency pressure. An emergency brake circuit will accordingly have to produce a certain flow and pressure to keep the swivel angle at maximum. The flow will be dependent of the orifice area of the tank port and the actual produced flow of the emergency brake circuit will affect how high value the swivel angle can reach statically. These are of course dimensioning issues with regards to how fast the emergency brake needs to be. The fact remains however that using an EP controller, the mechanical feedback will work against the installed emergency brake.

2.4.2 ED Control

The above mentioned problems are avoided when a mechanical feedback not is used. The ED control is another version of the EP, but without the mechanical feedback. This will cause a nonlinear relationship between the swivel angle and the control signal depending on the pressure in the machine. Driving the load forward will now feel "heavier" the higher the load is. This is however not a preferable behaviour even though an emergency brake circuit will be easier to implement. The emergency pressure can now push the stroke cylinder without being connected to the reservoir as the cylinder moves. The demanded flow now only needs to cover the lost oil volume through the orifice in the middle position. A secondary unit would however preferably have a mechanical feedback in the control unit if possible and the designed concept will focus on principles using this feature.

2.4.3 HD Control

Hydraulic control uses hydraulic pressures to control the control valve instead of electric currents.

Figure 18: Standard version of the HD control unit for A4VG (extract from [1])

Karl Pettersson 29 2 Secondary Controlled Swing Drive

Figure 19: Characteristics of the HD control unit (extract from [1])

The pressure in the two control lines Y1 and Y2 are linear to the position of the stroke cylinder, each pressure line handles one direction. The electric pressure reducers shown in Figure 14 have to be adapted according to this relationship. The mechanical feedback is also in use, but with the emergency brake is now no longer counteracted. The emergency brake circuit can now be connected directly to the control lines (Y1 and Y2) instead of acting on the stroke cylinder (X1 and X2). An emergency brake acting on the HD controller will affect the stroke cylinder according to Figure 20.

Figure 20: The HD control unit when affected by an external pressure

Emergency brake pressure will push the control valve so that the supplied pilot pressure is connected with one side of the stroke cylinder. The mechanical feedback will move the ports according to the movement of the cylinder making the middle position active statically. The stroke cylinder moves consequently according to the principle in the

Karl Pettersson 30 2 Secondary Controlled Swing Drive

normal mode, using the pilot pressure. One difference is that a failure mode now also has to ensure that pilot pressure is not lost.

2.4.4 DG Control

Direct operated hydraulic control has the control pressures directly acting on the stroke cylinder.

Figure 21: Standard version of the DG control unit for A4VG (extract from [1])

In this case electrically controlled pressure reducers would have to be used as done with the HD control. Emergency brake is applied via valves in X1 and X2 and without mechanical feedback the only flow required will be the leakage flow in the cylinder. This is the least demanding control principle to the emergency brake circuit. No position feedback exists however to control the swivel angle which creates similar problems as with the ED controller.

2.4.5 Modified Control Unit

A modified control unit can also be an option when adapting the controller to the emer- gency brake circuit. For example could different pressure ports be installed, directly to the stroke cylinder. This would be suitable for the EP controller to lower the flow de- mand at a failure mode. However will modified control units imply additional costs and the concepts designed in this thesis have been focused on using existing components.

Karl Pettersson 31 2 Secondary Controlled Swing Drive

2.5 Safety Concept Design

Focusing primarily on the use of a mechanical feedback in the control unit, two control units are available: EP and HD. With the two types of emergency brakes, four different emergency brake circuits are possible.

Table 1: Matrix of options for emergency brake and control unit

Emergency Brake Control EP1W EP2W Unit HD1W HD2W

The designed schematics for each concept is described below.

2.5.1 EP 1-Way

Figure 22: Designed safety concept with EP control unit and 1-Way emergency brake

In normal mode, the spool valves (1) and (2) are held down by the electrical solenoids counteracting the spring force. During a loss of electric control the spring side will automatically be activated and failure mode will be entered. A pressure loss or a stop of diesel engine are recognised in other ways. When such a failure occurs the valves

Karl Pettersson 32 2 Secondary Controlled Swing Drive

should also be switched so that all types of breakdowns activates the same failure mode. Entering into failure mode, the first valve (1) cuts off pilot pressure to the EP controller and in the same time opens the way to the stroke cylinder. The stroke cylinder always moves in the same direction independently of the direction of the speed according to Chapter 2.3.3. The secondary unit will hence swivel out and pump flow to one of the sides depending on the direction of the speed. The other spool valve (2) allows high pressure to push down the cartridge valves (3) blocking both the high and low pressure sides. The highest of the two pressures are used for this matter once again making sure that the direction of speed will be indifferent. Pressure will hence be built up at one side creating a braking torque. Pressure relief valves (4) open at the maximum allowed pressure in the circuit, making sure that components are not damaged. The anti-cavitation valves (5) make sure that the created low pressure side not cavitates. As seen in Figure 15 the pressure relief valves and anti-cavitation valves are already included in the pump schematics.

2.5.2 EP 2-Way

Figure 23: Designed safety concept with EP control unit and 2-Way emergency brake

The 2-Way emergency brake can move the stroke cylinder to both sides depending on the rotation direction. To determine the direction hydraulically, a separate pump (1) is attached to the axle of the secondary unit. The pump can work in both directions cre- ating pressure on either side of the emergency brake circuit depending on the direction. The created pressure is used to push the stroke cylinder when a failure is recognised

Karl Pettersson 33 2 Secondary Controlled Swing Drive

(2). The direction that the cylinder should be pushed is determined by a 2-position spool valve (3) that switches sides depending on the pressure created and hence the rotational speed. Check valves are used to ensure that the configuration does not affect the performance in normal mode. A throttled connection to tank (4) is used to damp the braking motion. Only the high pressure side of the circuit now needs to be blocked. The additional pump must be big enough to create sufficient flow to move the stroke cylinder. This could cause a problem cosidering the effect of the mechanical feedback described in Chapter 2.4.1. In normal mode is the additional pump still turning and consumes thus wasted energy. It is therefore important to keep a very low pressure in the emergency brake circuit in normal mode.

2.5.3 HD 1-Way

Figure 24: Designed safety concept with HD control unit and 1-Way emergency brake

The emergency brake is in the HD control possible to perform by pushing the control valve instead of the stroke cylinder itself. Pilot pressure must not be cut off since it is the active pressure that eventually affects the stroke cylinder. This makes this concept dependent on that pilot pressure persists even at a breakdown.

Karl Pettersson 34 2 Secondary Controlled Swing Drive

2.5.4 HD 2-Way

Figure 25: Designed safety concept with HD control unit and 2-Way emergency brake

The HD2W is also dependent on that the pilot pressure is kept during failure mode. The combination of two direction emergency brake and HD control unit will however not demand the same flow from the additional pump as with EP control unit (see Chapter 2.4.3).

2.6 Pilot Circuit

2.6.1 Closed Circuit With Low Pressure Accumulator

Closed circuit pumps normally have a boost pump handling the supply of the low pressure side and the pilot pressure to the control unit. However will the secondary unit be rotating in both directions in this case. Accordingly will the attached boost pump not be able to keep a pilot pressure as shown for example in Figure 15. It is then necessary to find another supply of pilot pressure to the secondary unit.

Karl Pettersson 35 2 Secondary Controlled Swing Drive

Figure 26: Principle of supplying pilot pressure to the secondary unit in a closed circuit with LP accumulator

Figure 26 shows the designed solution for supplying pilot pressure to the secondary unit when using a low pressure accumulator. Since A4VG also is used as primary unit the attached boost pump (1) can be used to supply both control units. The LP accumulator is, in this type of circuit architecture, the supplier of oil to the low pressure side when braking. Dynamically can the boost pump itself not supply enough flow to cover swift braking because of a much lower displacement. The LP accumulator is hence emptied and the pressure will accordingly fall. Since this is the same pressure as supplied to the control units it is important to keep controllability by ensuring a high pilot pressure. The designed solution uses another accumulator (2) together with a check valve (3). During a pressure drop the check valve closes and the accumulator (2) becomes the only supplyer of pilot pressure. Since only lesser flows normally are needed for controlling, a small accumulator (1 − 2 L) is enough.

Karl Pettersson 36 2 Secondary Controlled Swing Drive

2.6.2 Closed Circuit With Volume Equaliser

Figure 27: Principle of supplying pilot pressure to the secondary unit in a closed circuit with volume equaliser

The boost pump of the primary unit is also used for supplying pilot pressure here. However will the the low pressure side no longer face a pressure drop when braking the inertia. As explained in Chapter 2.2.2 will now the volume equaliser supply the necessary oil flow to the low pressure side when braking. The supplied flow is the same that is inserted in the HP accumulator and consequently also the needed flow at the LP side of the secondary unit. Since the LP side no longer faces pressure drops is hence the additional accumulator not useful in normal mode.

2.6.3 Open Circuit

Open circuit pumps do not normally have an attached boost pump and pilot pressure must hence be taken from the circuit.

Karl Pettersson 37 2 Secondary Controlled Swing Drive

Figure 28: Principle of supplying pilot pressure to the secondary unit in an open circuit

Pressure from the HP side is reduced by a pressure reducing valve (1) into pilot pres- sure. Since no supply of the LP side is needed in the open circuit no pressure drops will occur during braking.

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3 Dimensioning

3.1 Current System

This chapter handles an example of a realisation of a typical wheel excavator with operational weight of 15 − 20 tons. The hydraulic system is valve controlled and supplied from an open circuit pump which supplies all the working hydraulics. It is a load-sensing system with closed-centre valves as described in Chapter 1.2. The swing drive is driven by a gearbox with an attached fixed hydraulic motor. The gearbox pinion drives the slewing ring and consequently the whole upper frame of the excavator. Two gears are hence active between the motor and the upper frame of the excavator. The configuration can be seen in Figure 29.

Figure 29: Configuration of the swing drive for the excavator

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Dimensions of the components used are given in Table 2.

Table 2: Table of dimensions for the current swing drive

Component Quantity Value Unit Gearbox Ratio 33.40 - 3 Motor Displacement 45 cm /rev Motor Maximum Flow 150 L/min Motor Maximum Pressure 220 bar Motor Maximum Torque 149.7 Nm Motor Maximum Speed 3200 rpm Gearbox Maximum Output Torque 4704 Nm Gear Ratio Slewing Ring 8.31 - Slewing Ring Torque 37126 Nm Slewing Ring Maximum Speed 11.5 rpm 3 Pump Displacement 95 cm /rev Diesel Engine Speed 3200 rpm

3.2 Inertia Model

The top frame of the excavator is in this thesis considered to have a constant moment of inertia. In reality would the position of the articulated arm change the centre of mass and therefore the inertia. The load in the bucket can also vary, increasing or decreasing the total mass of the load. The friction model used includes static, viscous and Coulomb friction. Any other torques, such as loads acting against the slew or gravitational forces acting when standing in a slope, are considered zero.

Table 3: Values for the inertia model

Quantity Nomenclature Value Unit Moment of Inertia J 102000 kgm2 Static Friction Ts 3700 Nm Coulomb Friction Tcf 3600 Nm Nm Viscous Friction kvf 600 /rpm

The equation of motion:

Jω˙ = Tm · itot − Tcf − kvf · n (3.1)

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The values used derive from earlier measurements made on a wheel excavator with an operational weight of 22 tons. The moment of inertia is scaled down according to the weight of the test excavator. Any difference in dimensions such as arm lengths has not been taken into account. The Coulomb and static friction values are also scaled down with the weight fraction since these values should be proportional to the normal force and hence the weight of the top frame. Same thing is valid for the coefficient of the viscous friction. These values are taken with the arms in middle position and should not be considered as exact values.

3.3 Secondary Controlled System

When dimensioning the secondary controlled system the aim have been to reach the same performance as the previous system so that a good comparison of additional costs and energy savings can be made. The new system, as designed in this application, is considered to be in a separate circuit only handling the slew function. Since secondary control works in a constant pressure level, this is a necessity.

3.3.1 Working Point

The pump of the SCHT is mounted on the same shaft as the diesel engine and the existing pump. The total power of the additional circuit is hence limited by the size of the pump and not the capacity from the power source. The diesel engine is assumed to have enough power to supply the secondary controlled system. The size of the chosen pump therefore sets the working point of the maximum power in the circuit. This point represents at what speed, the maximum torque of the secondary unit can be reached:

Pmax = Tmmax · nwp (3.2)

At the current system the pump is supplying all work hydraulics and is therefore larger than necessary when only the swing drive is active. The working point for that system is hence nwp = nmax. In normal excavator operations the maximum torque would not be used in the maximum speed. As described in Chapter 1.1 a standard duty cycle of an excavator involves slewing back and forth between the dumper and the digging position. The rotation angle various of course depending on the situation but is here considered to be 90◦. Using the maximum given torque for starting and stopping, the

Karl Pettersson 41 3 Dimensioning

maximum acceleration and deceleration can be calculated: 1 a = (T · i − T − k · n) (3.3) max J mmax tot cf vf 1 a = (−T · i − T − k · n) (3.4) min J mmax tot cf vf Using these accelerations in the typical work cycle of 90◦, the maximum speed where the excavator needs to start decelerating can be calculated. This is done numerically in Matlab in Appendix C.1 and the results shown in Figure 30.

Figure 30: Angle and speed when slewing to 90 ◦ with maximum torque used

This is consequently the maximum speed where the excavator need its maximum torque. The working point is hence set to nwp = 7.2 as seen in Figure 30.

3.3.2 Pressure Level

To reach the maximum torque at the slewing ring a certain motor size is needed also depending on the gear ratio and the chosen pressure level in the circuit. In secondary control the secondary unit works in constant pressure, but if the primary unit is con- trolled to keep the same pressure level at all time the accumulator pressure will also

Karl Pettersson 42 3 Dimensioning

stay constant. This means that no energy storage can be made in the accumulator when braking the inertia. The oil flow will instead be directed back to the primary unit. A torque can be created which acts to unload the diesel engine. This type of energy recuperation is however not ideal since fuel consumption only will be lowered when other functions demand power from the engine. An energy storage in the ac- cumulator can be used when accelerating the inertia and is hence not dependent on the other functions. To achieve as much energy recuperation as possible the pressure level should vary between the minimum and maximum values of the accumulator. The optimal would therefore be a pressure of 150 bar at maximum speed and 330 bar at zero speed. The accumulator pressure can then be raised by the redirected flow from braking the inertia. All kinetic energy can be stored in the accumulator since the ac- cumulator reaches its maximum pressure while zero speed is reached.

Having the pressure level vary depending on the speed is not a common solution for the secondary control system which normally always works at the same pressure level. Using secondary control in this application is however mostly because of its energy recuperation capabilities and its efficiency. A lower pressure difference at higher speeds also means that the secondary unit works with higher swivel angles to create the same torque. This increases the overall efficiency of the motor, especially when constructed in swashplate design. As mentioned above the pressure level also affects the necessary size of the secondary unit. A lower pressure demands a bigger displacement to create the same torque according to (2.2). A choice must thus be made of how the primary unit should control the pressure level in the circuit. This Set pressure is hence the reference pressure for the controller of the primary unit. This is a cost versus efficiency issue since a larger secondary unit is more expensive but gives the system a possibility to keep a lower pressure at the working point. This gives the system increased possibilities to store energy as discussed above. A larger accumulator will however be both expensive and require more space. Removing the grey zone in between, two options can be stated:

1. Small units - Less energy storage - Small accumulator

2. Large units - More energy storage - Large accumulator

Option 1

Initially the maximum pressure will be used at the working point so that the size of the secondary unit can be as small as possible, corresponding to option 1. A linear relationship for the set pressure is used according to Figure 31.

Karl Pettersson 43 3 Dimensioning

Figure 31: Set pressure for option 1

This type of pressure graph gives energy storage when braking from maximum speed to the point where the pressure reaches its maximum: npmax = nwp. Further braking is done with a full accumulator and the flow is then directed back to the primary unit. The needed size of the secondary unit can now be calculated when maximum swivel angle is used at the working point:

20π · Tmmax Vgm ≥ (3.5) (pset(nwp) − pLP ) · αmmax · ηhmm

The corresponding flow produced when reaching maximum torque at the working point is:

Vgm · αmmax · itot · nwp qmax = (3.6) 1000ηvolm Note that this flow is the flow produced at the working point when maximum torque is used. The flow is, according to discussions above, always proportional to the torque.

Rotating constantly at nwp will for example only need the flow corresponding to the torque created from friction. The size of the primary unit will be dimensioned after the maximum flow qmax needed by the secondary unit.

1000qmax Vgp ≥ (3.7) nDE · ηvolp · αpmax

When rotating at n > nwp the maximum torque can no longer be reached and hence must the swivel angle be limited according to this. If a too high swivel angle is used the motor will demand more flow than the pump can deliver which would make the pressure

Karl Pettersson 44 3 Dimensioning

drop and eventually the circuit to cavitate. The swivel angle must consequently be limited so that the maximum flow is not exceeded:

qmax · 1000ηvolm αm ≤ (3.8) Vgm · n · itot

The swivel angles of the primary and secondary unit, when maximum torque is used at all speeds, are shown in Figure 32.

Figure 32: Swivel angle of the primary and the secondary unit at maximum torque

To overview the characteristics better, the calculated speed-torque-graph and the limits for the secondary unit is displayed in Figure 33. The calculations are made for a closed circuit transmission.

Karl Pettersson 45 3 Dimensioning

Figure 33: Characteristics for the secondary unit with option 1

As seen will the produced motor torque eventually fall to the point where it meets the friction torque. This means that the drive is just powerful enough to accelerate up to the maximum speed. The size of the accumulator can now be calculated using the amount of kinetic energy that is going to be stored:

1   E = J ω2 − ω2 (3.9) kin 2 max npmax Elost ≈ (Tcf + kvf · navg) · ωavg (3.10)

Eacc = Ekin − Eloss (3.11)

The size of the accumulator is calculated according to:

Eacc(1 − γ) V1 = 1−γ ! (3.12)  p1  γ p1 · 100 1 − p2

The polytropic exponent is considered constant: γ = 1.6 at the corresponding pressure range and a temperature of 60 ◦C [3].

Option 2

When trying to maximize the stored energy during a braking motion the set pressure should not be higher than the created pressure from the secondary unit. It would hence be interesting to investigate how the pressure-speed curve would look like with an inactive primary unit. A set pressure following this curve would keep the primary unit at zero swivel angle and all of the kinetic energy can be loaded in the accumulator.

Karl Pettersson 46 3 Dimensioning

If the maximum torque is kept for braking the inertia from the maximum speed, the deceleration can be calculated:

Tmax(t) = Tmmax · itot + Tcf + kvf · n(t) (3.13) T (t) a (t) = m (3.14) max J n(t) = nmax − amax(t) · t (3.15)

The created flow from this movement is calculated according to (2.5) and is the same oil flow loading the accumulator:

20πTm(t) · n(t) qm(t) = (3.16) 1000(pacc(t) − pLP ) · ηhmm · ηvolm ˙ Vacc(t) = qm(t) (3.17)

The pressure in the accumulator is described by (3.18) and (3.19):

Vgas = V0 − Vacc (3.18) γ pacc · Vgas = const (3.19)

This is assuming a completely adiabatic process with a constant polytropic exponent γ. These relationships form a differential equation which is solved numerically in Appendix C.3. The obtained pressure-speed curve is shown in Figure 34

Figure 34: Set pressure for option 2

The characteristics according to this set pressure is shown in Figure 35

Karl Pettersson 47 3 Dimensioning

Figure 35: Characteristics for the secondary unit with option 2

An even higher torque is now available when n ≤ nwp because of the higher displace- ment of the pump. The accumulator should now dimensioned to store all kinetic energy: 1 E = Jω2 (3.20) kin 2 max Elost ≈ (Tcf + kvf · navg) · ωavg (3.21)

Eacc = Ekin − Eloss (3.22)

We now have the tools to calculate all component sizes for both options. Table 4 shows the calculated sizes for the primary and secondary unit and the high pressure accumulator for each option:

Table 4: Calculated Component Sizes

Closed Open cm3 cm3 Vgm = 33.0 /rev Vgm = 30.0 /rev cm3 cm3 Option 1 Vgp = 29.9 /rev Vgp = 27.1 /rev Vacc = 6.23 l Vacc = 6.23 l cm3 cm3 Vgm = 45.0 /rev Vgm = 39.6 /rev cm3 cm3 Option 2 Vgp = 40.7 /rev Vgp = 35.8 /rev Vacc = 12.45 l Vacc = 12.45 l

Diving into the grey zone between option one and two, it is important to be clear of how much one is willing to pay for increased efficiency. The price of the components,

Karl Pettersson 48 3 Dimensioning

the space available in the excavator and the fuel price must be taken into account. Dimensioning these components for a real implementation one must also consider the available sizes that actually are produced. Table 5 shows the closest available sizes for each pump:

Table 5: Real Component Sizes

Pump Displacement A4VSO - 40 71 A11VO - 40 60 A4VG 28 40 56

For the simulation performed in this thesis both the primary and secondary units are cm3 chosen to Vgp = Vgm = 40 /rev. This fits between the two options and priorities more energy recuperation than component costs. It makes it easy to compare the circuit architectures when the sizes are equal and it is also closer to reality since these sizes exist in the Bosch Rexroth program. The set pressure is now adapted as low as possible so that the maximum torque still is reachable at nwp:

20π · Tmmax pset(nwp) = (3.23) Vgm · ηhmm

A linear relationship is then used to simplify the control algorithms. The set pressure curve can be seen in Figure 36 together with the ideal set pressure for energy storage.

Figure 36: The chosen set pressure and the ideal set pressure for the closed circuit

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The corresponding characteristics can be seen in Figure 37:

Figure 37: Characteristics for the secondary unit with chosen machine sizes in closed circuit

With similar calculations for the open circuit the characteristics in Figure 38 are ob- tained.

Figure 38: Characteristics for the secondary unit with chosen machine sizes in open circuit

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4 Simulation

4.1 AMESim

AMESim is the main simulation software used for simulating hydraulic systems in Bosch Rexroth. The program is developed by LMS Imagine and is a powerful tool providing stable and complete system simulation for several tasks and industries. The software is based on component models representing real physical models. Because of its proximity to real components the program is simple to use and the models easy to overview. The components are connected with physical variables and work in both directions, in contrast to MatLab Simulink. The program comes with standard libraries containing hydraulic, pneumatic, mechanical, thermal and electric components.

4.2 Description of Models

Basic principle of the different parts of the constructed models are described below. The complete models can be seen in Appendix B. The simulation is focused on the comparison of the different concepts and no validation of the models have been made comparing them to real test values.

4.2.1 Diesel Engine

As power source in the excavator a diesel engine is used with a certain torque and speed capacity. In the model the diesel motor is assumed to have enough power to always keep the given speed 2300 rpm. The diesel motor is hence modelled as a constant speed source connected to the pump giving it unlimited power in the simulation.

4.2.2 Inertia

The rotary load which represents the top frame of the excavator is simulated according to the inertia model presented in Chapter 3.2. This means that no other torque will affect the inertia but friction and the torque needed to accelerate it. It is therefore important to differ from the discussions in Chapter 3 regarding torque deamands and

Karl Pettersson 51 4 Simulation

the simulated torques. For example is the case when the excavator is standing in a slope not simulated.

4.2.3 Hydraulic Machines

Models for the A4- and A11-units exist in the Rexroth simulation library. These models only represent the rotary units transforming torque and speed to pressure and flow. Both the mechanical and volumetric efficiencies in all four quadrants are taken from test values in look-up tables. Models for boost pumps and other hydraulic machines have been taken from the standard AMESim hydraulic library to keep the model simple. Parameter values such as inertia and displacement is however taken from [1].

4.2.4 Valves

To represent the seat valve used in the emergency stop, a simple 2/2 spool valve is used in a supercomponent also to keep the model as simple as possible. The purpose of the seat valve is to completely block the flow at a failure mode and to keep little throttling in normal mode. No dynamic behaviour or geometric dimensions are interesting in this study. More complex modelled seat valves exist in the standard library, but are not used for this reason. The electric pressure reducing valves are also modelled by the use of a 3/3 spool valve with a proportional controller. Other valves such as check valves, pressure relief valves and shuttle valves are taken from the standard AMESim hydraulic library.

4.2.5 Control Units

The model for the EP control unit is also from the Rexroth simulation library and takes in currents for the electric solenoids, pilot pressure and the connection to the reservoir. The given model is built with hydraulic components and gives a good model of its dynamic behaviour. It is important to use a rather advanced model of the EP con- troller since its behaviour have influence on the performance of the system. In normal mode it affects the flow requirements of the pilot pressure circuit. In failure mode it is crucial to know how much flow is needed to affect the stroke cylinder sufficiently. This is one of the most vital points when investigating if an EP controller is advisable to use.

A corresponding model for the HD controller is not available. A simple model of the principle of the HD control unit has instead been built using a spool valve and a linear hydraulic cylinder. The built model takes in two hydraulic pressures which are compared and transformed into a desired position of the stroke cylinder according to

Karl Pettersson 52 4 Simulation

Figure 19. The spool valve is PID controlled to move the cylinder to this position. This is done with signal feedback of the cylinder position to simulate the mechanical feedback. The orifice areas of the control valve is important to consider since the flow needed affects the performance of the emergency brake. To get the characteristics right the model for the EP control unit was tested separately. The calculated orifice areas was then inserted in the constructed HD model so that the same flows were achieved. Other parameters such as spring stiffness, cylinder stroke, frictions and masses were used from the EP model. The stroke cylinders position directly affects the output swivel angle which is given as a signal between -1 and 1.

4.2.6 Failure Mode

To simulate the loss of electric control a signal source with values switching instan- taneously between 0 and 1 is used. The signal is multiplied with all control signals representing electric currents. 1 being the normal mode, not affecting the electric sig- nals and 0 the failure mode, effectively resetting all electric signals. Some signals in the model, however is only used to simulate something that would not be an electrical signal in reality, these are of course not affected by the failure mode.

A hose break is simulated by making a spool valve connect the high pressure line to the reservoir. A similar signal source opens the spool valve when switching from 1 to 0. The signal is also used to recognise when a loss of pressure occurs and activates the same failure mode described above. This is of course not the case in reality where recognition of pressure loss has to be used. This function is however not interesting when comparing the concepts or testing the system.

A diesel engine stop resets the constant speed signal to the primary unit simulating that the engine has stopped turning. This also makes the system go into failure mode and react in the same way as with a hose break or loss of electric control signal.

4.2.7 Reference Signal

The reference signal, which in reality comes from the joystick, is taken from the block Trajectory Designer. The supercomponent exists in the Rexroth simulation library and is used to get a continuous reference trajectory. It takes in values for the minimum and maximum speed and acceleration and transforms the position reference input to smooth signals for position, velocity and acceleration. This keeps derivatives and integrations possible in all time steps and makes the signal stay within the limits. The mininum

Karl Pettersson 53 4 Simulation

and maximum values are calculated from values given in Chapter 3.1.

4.3 Control Algorithms

4.3.1 Control of the Primary Unit

The primary unit is controlled both with a feed forward signal and a feedback controller.

The feed forward signal first calculates the flow demand qcalc from the secondary unit and then the swivel angle αpref needed from the primary unit to create the same flow. To handle the disturbances and the inaccuracies in the servo signal a feedback is used. The difference between the current set pressure and the actual pressure in the circuit are compared and controlled with a traditional PID-controller. The feedback and the feed forward are then added and saturated to keep the control signal within limits.

Figure 39: The control principle of the primary unit

Note that this type of controller can be used for both energy recuperation principles - Accumulator storage and unloading of the diesel engine. A too high actual pressure would lead the controller to negative swivel angles and the flow in the machine would be reversed. The torque corresponding to this would act to unload the diesel engine until the actual pressure once again is restored to meet the set pressure. Not shown in Figure 39 is a reset signal acting when the inertia not is moving. This is to avoid keeping a constant high pressure when not needed.

4.3.2 Control of The Secondary Unit

The secondary unit is speed controlled in such a manner that the motor supplies sufficient torque to maintain the required speed. A feed forward signal is used to

Karl Pettersson 54 4 Simulation

make the motor speed follow the reference velocity signal. The reference speed is differentiated and a necessary motor torque Tmcalc is calculated at a given pressure difference over the motor. From the torque a necessary swivel angle can be calculated

αmref . Acceleration, speed and displacement feedback are used and controlled with gains. The output is added to the swivel angle reference signal.

Figure 40: The control principle of the secondary unit

The predefined maximum flow qmax limits the swivel angle so that the motor flow never exceeds this value. The saturation is only active in accelerating movements since the flow generated from the secondary unit, at braking motion, is not limited.

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5 Results

5.1 Circuit Architecture

The circuit architectures are here compared from two point of views - Functionality and Energy Consumption. A typical work cycle by the swing drive is tested on the different systems and compared.

5.1.1 Functionality

Open Circuit

Figure 41: Functionality of the open circuit

Karl Pettersson 56 5 Results

In Figure 41 the first graph shows the reference signal for the work cycle and the actual position of the inertia. The second graph shows how the accumulator pressure and the pressure on the HP side of the circuit follow the set pressure. During no motion the reference pressure is reduced to 30 bar in order to avoid keeping a high pressure when not used. Since the pilot pressure is also taken from the HP side (see Chapter 28) it is necessary to stay at this level to keep the controllability. When zero motion is recognised the security valve connected to the accumulator closes. This isolates the accumulator and allows it to stay over the minimum allowed pressure.

Closed Circuit with Low Pressure Accumulator

Figure 42: Functionality of the closed circuit with low pressure accumulator

The principle of using a low pressure accumulator gives the primary unit one large compressible oil volume on each side. This fact makes the pressure easier to control which is clearly seen when comparing Figure 42 with Figure 41.

Karl Pettersson 57 5 Results

Closed Circuit with Volume Equaliser

Figure 43: Functionality of the closed circuit with volume equaliser

Using the volume equaliser causes a pressure drop over the attached hydraulic motor to the accumulator. This is due to the level of pressure kept at the LP side. The addi- tional inertia that the volume equaliser implies needs to be accelerated and decelerated as flow is pumped in and out of the accumulator. This slows down the reaction of the pressure controller and makes it hard to follow the reference as seen in Figure 43.

According to the relationship q ∝ n · Vg will larger machines in the volume equaliser need less rotation speed. This will decrease the effect on the pressure control, but also imply larger and more expensive components. Both machines have a displacement of 3 25cm /rev in these simulations.

Karl Pettersson 58 5 Results

5.1.2 Energy

Open Circuit

Figure 44: The energy consumptions of the open circuit

Figure 44 shows the different parts of the energy consumption for a working cycle per- formed by the open circuit. Note that although the energy from the pilot pressure is kept almost constant during zero motion, the total energy is still increasing. This is due to the fact that the high pressure side is kept at 30 bar to ensure controllability (see Figure 28). If any external pressure is used for the control units it would be possible to lower the energy consumption during stand still even more. If implemented in the excavator pilot pressure could be taken from the existing boost pumps.

The energy inserted in the accumulator is negative during acceleration which corre- sponds to the accumulator being emptied. When decelarating the energy rises to zero showing that it is being loaded by the flow from the brake.

Karl Pettersson 59 5 Results

Closed Circuit with Low Pressure Accumulator

Figure 45: The energy consumptions of the closed circuit with low pressure accumulator

The closed circuit has a boost pump that is always demanding a certain power from the energy source. The pilot pressure energy is accordingly increasing even during during zero motion. The energy inserted in the accumulator corresponds to the pressure in the circuit shown in Figure 42. This type of circuit is hence optimal when storing as much energy as possible.

Closed Circuit with Volume Equaliser

Figure 46: The energy consumptions of the closed circuit with volume equaliser

Karl Pettersson 60 5 Results

Summary

Figure 47: The total energy consumptions of all circuit architectures

Figure 47 shows that there are only small differences between the three principles when it comes to energy consumption.

The amount of energy stored in the accumulator is according to the simulation results around 16 kJ every deceleration. The total energy used by the power source after one duty cycle is according to Figure 47 at t = 20 s around 130 kJ. A rough value of the 16·2 energy savings due to the energy storage is hence 130+16·2 ≈ 20 %. The total kinetic energy at the maximum speed reached is according to (3.10) around 28 kj which leads to an energy storage of around 60% of the kinetic energy. The losses comes mostly from the friction and also from the efficiency of the secondary unit and the accumulator.

5.2 Safety Concept

The safety concepts are compared regarding functionality of the emergency brake. The tests are taken from the closed loop circuit so that both one and two direction emer- gency brakes can be compared in the same environment. The two direction emergency brake in open circuit shows however similar results as for the closed circuit.

Karl Pettersson 61 5 Results

5.2.1 Functionality

The functionality of the safety concept is tested by activating the emergency brake at maximum speed, which would be the worst case. The graphs displayed are all results from entering the failure mode at t = 20 s. For the one direction brake there is a different behaviour depending on the speed direction while the two direction brake acts the same way. Simulating loss of electric control and loss of pressure shows similar results why graphs of both failures not are displayed.

EP1W

Figure 48: EP1W braking positive speed during loss of electrical control

The first graph in Figure 48 shows the speed of the inertia and the swivel angle of the secondary unit. When the failure occurs is the swivel angle directly affected by the emergency brake. The maximum swivel angle is never reached and the behaviour corresponds well to Figure 17. The pressures displayed in the second graph shows the effect of blocking both the HP and LP side. The peak is due to the fact that the cartridge valves close faster than the swivel angle is affected. The secondary unit will hence continue pumping flow to the LP side during this time difference and cause this

Karl Pettersson 62 5 Results

behaviour. Throttling the flow to the cartridge valves causes them to close slower and the peaks to dissapear. However will this make the emergency brake less effective when a pressure loss occurs.

Figure 49: EP1W braking negative speed during loss of electrical control

Figure 49 shows the same safety concept brake a negative speed. The swivel angle is still controlled to the positive direction and it is now the LP side that will have a pressure build up.

Karl Pettersson 63 5 Results

Figure 50: EP1W braking positive speed during stop of diesel engine

A stop of diesel engine causes the boost pump to stop turning and the supply pressure to decrease. When the supply flow dissapears and both ways are blocked the lowest pressure risks dropping below zero and cavitate. This occurs during an emergency brake with EP1W as seen in Figure 50. No total braking angle is displayed since the simulation should not be trusted once the pressure goes below zero. To avoid the cavitation it is necessary for further schematic changes activating pressure relief valves with lower cracking pressure. It is also possible to use additional small accumulators to supply flow during failure mode.

Karl Pettersson 64 5 Results

EP2W

Figure 51: EP2W braking during loss of electrical control

Figure 51 shows that the swivel angle behaves initially the same way as for the one direction brake, but goes towards zero as the speed decreases. The pressure that pushes the control valve is dependent on the speed which explains this behaviour. The two direction brake avoids pressure drops under zero since the anti-cavitation valves now open as soon as the pressure on the LP side is higher. The same behaviour occurs at all types of failures.

Karl Pettersson 65 5 Results

HD1W

Figure 52: HD1W braking positive speed during loss of electrical control

Emergency braking using the HD control unit behaves according to Figure 20. The effect can be seen in Figure 52 where the emergency brake is able to hold the swivel angle at maximum unlike the case with EP control unit. The oscillations caused when the inertia has stopped is a consequence of the oil compressing and decompressing on both sides.

Karl Pettersson 66 5 Results

Figure 53: HD1W braking negative speed during loss of electrical control

Braking negative speed shows equally good performance of the HD1W in Figure 53.

Karl Pettersson 67 5 Results

Figure 54: HD1W braking positive speed during stop of diesel engine

A stop of the diesel engine makes the system face the same cavitation problems as EP1W.

Karl Pettersson 68 5 Results

HD2W

Figure 55: HD2W braking during loss of electrical control

The HD2W in Figure 55 shows a similar behaviour as the EP2W but with a higher swivel angle movement. This gives a higher performance of the emergency brake.

Karl Pettersson 69 5 Results

Figure 56: HD2W braking during stop of diesel engine

The HD2W handles a stop of the diesel engine well and cavitation is avoided as for EP2W.

Karl Pettersson 70 6 Conclusions

6 Conclusions

6.1 Circuit Architecture

Table 6 ranks the different circuits regarding functionality, energy efficiency, ,control- lability and number of components needed.

Table 6: Rankings of the circuit architectures

Property Open LP Volume Equaliser Accumulator Functionality 1 1 1 Energy Efficiency 1 1 1 Controllability 2 1 3 Space Saving 1 3 2 Few Components 1 2 3

To summarise will an open circuit often be the best option if the suction issue can be solved. More control efforts are then needed to get optimal energy storage. If a closed circuit is used, the solution with low pressure accumulator is the best choice if the space can be found for the additional accumulator. Is this not the case can a volume equaliser be an option. Secondary control used as a swing drive shows good potential with energy savings of at least 20% due to the energy storage. The efficiency gained from the throttle free controlling and the lower flow losses will also affect the energy sav- ings. More advanced simulation models are though needed to get better values for this.

6.2 Safety Concepts

Results from the safety concepts clearly show that the concepts using the EP control unit do not manage to stay under the maximum allowed braking angle. This is of course due to the effect of the mechanical feedback when applying pressure in the external ports. If the existing configuration shall be used a higher flow must be available to

Karl Pettersson 71 6 Conclusions

keep the stroke cylinder positioned. An electric control unit could also be used if the external pressure ports were placed differently. The following points can be made as a summary:

• A hydraulic control unit together with electric pressure reducers is preferable to use as oppose to an electric control unit.

• Both types of principles for an emergency brake procedure brake the inertia shorter than the maximum allowed angle at all speeds.

• A one direction emergency brake uses less components and demands less energy. It is however impossible to use in an open circuit and comes with risks of cavita- tion when used in a closed circuit. This is especially the case at a diesel engine stop.

• A two direction emergency brake is to prefer even though it requires more com- ponents and have some energy consumption during normal operation.

6.3 Future

Following possible future investigations could be of interest:

• More advanced simulation of the systems with validated models.

• Simulation of the current system to use as reference for energy efficiency calcu- lations.

• Using a more advanced inertia model with varying torque and inertia over a standard duty cycle from test measurements.

• Simulation of a conventional closed circuit transmission as a separate circuit for the swing drive. This is also as reference for energy efficiency calculations since this is a common feature in excavators.

Karl Pettersson 72 Bibliography

Bibliography

[1] Bosch Rexroth AG, Elchingen. Product Catalog Mobile Hydraulics RE 90005- 01/07.06, 2007.

[2] Instutitionen för konstruktions- och produktionsteknik. Formelsamling i Hydraulik och Pneumatik, 1995.

[3] R. Kordak. Hydrostatic drives with control of the secondary unit, volume 6 of Hydraulic Trainer. Mannesmann Rexroth, Lohr am Main, 1996.

[4] G. Palmgren. On secondary controlled hydraulic systems. Technical report, Insti- tute of Mechanical Engineering, Linköping, 1988.

[5] K-E. Rydberg. Hydrauliska accumulatorer för energilagring. Technical report, Institute of Mechanical Engineering, Linköping, 1984.

[6] H. Murrenhoff T. Kohmäscher. Efficient recuperation of kinetic energy - hybrid versus hydrostatic approach. Technical report, Institute for Fluid Power Drives and Controls, Aachen, 2007.

[7] G. Chetail W. Herfs. Drive and control systems for excavators. In International Mobile Hydraulics Congress. Bosch Rexroth AG, 2003.

[8] G. Chetail W. Herfs. Excavators > 10tons. In International Mobile Hydraulics Congress. Bosch Rexroth AG, 2006.

[9] P. Wusthof. Secondary control technology and applications. Technical report, The Fluid Power Systems and Technology Division, Lohr am Main, 1998.

Karl Pettersson 73 A DIN EN 474-5

A DIN EN 474-5

Karl Pettersson 74 A DIN EN 474-5

EN 474-5:2006 (D)

C.3 Mindestanforderung

C.3.1 Schwenkbewegung

C.3.1.1 Test-Schwenkgeschwindigkeit

Die Test-Schwenkgeschwindigkeit ist die in C.2.2 definierte Arbeits-Schwenkgeschwindigkeit.

C.3.1.2 Verzögerungs-Schwenkwinkel βB

Der Verzögerungs-Schwenkwinkel βB muss kleiner sein als der größte der folgenden Werte:

βB = 90°

n2 × 360 β B = + β B0 2× n′B

Dabei ist

β B der Verzögerungs-Schwenkwinkel in Grad (°);

n = n die Test-Schwenkgeschwindigkeit in Umdrehungen pro Minuten (min-1);

-2 nB′ der konstante Wert 250 (min );

β B0 der konstante Wert 40 in Grad (°).

Legende X Oberwagen-Drehzahl [min-1] Y Verzögerungs-Schwenkwinkel [°]

Bild C.1 — Schwenk-Betriebsbremse

22 A&I-Normenabonnement - Robert Bosch GmbH Kd.-Nr.140250 Abo-Nr.00852392/002/001 2007-08-22 08:33:57

BA178AF3EC677050DBAC9B8DA5349567ADC990EEFF93F3B464D26DACD6B6339E7BF04648A5F049B7D0E120954C0D80B2F26EDCAB41A02D05F364669338C021F6267AE9EA1D7B4AE3432D1F0E0DBF3D6AF0B8692AA4AEBF96E0686FD140965131EE01B784AD84D2A999

Karl Pettersson 75 B Simulation Models

B Simulation Models

Karl Pettersson 76 B Simulation Models

B.1 Closed Circuit with LP Accumulator, 1-Way emergency brake and HD control unit

Karl Pettersson 77 B Simulation Models

B.2 Closed Circuit with Volume Equaliser, 1-Way emergency brake and HD control unit

Karl Pettersson 78 B Simulation Models

B.3 Closed Circuit with LP Accumulator, 2-Way emergency brake and HD control unit

Karl Pettersson 79 B Simulation Models

B.4 Closed Circuit with LP Accumulator, 1-Way emergency brake and EP control unit

Karl Pettersson 80 B Simulation Models

B.5 Closed Circuit with LP Accumulator, 2-Way emergency brake and EP control unit

Karl Pettersson 81 B Simulation Models

B.6 Open Circuit with 2-Way emergency brake and HD control unit

Karl Pettersson 82 C Matlab m-files

C Matlab m-files

Karl Pettersson 83 C Matlab m-files

C.1 workingpoint.m

%workingpoint.m %Tool for finding the necessary working point using inputs from the %example system clear %%%%%%%%%Inputs%%%%%%%% T_Ptorque=37126; %Nm n_max=11.5; %rpm T_cf=3636; %Nm k_vf=582; %Nm/rpm J=1.02e5; %kgm^2

%%%%%%%%%%%%%Speed and time vector%%%%%%%%%%%%% n_acc=linspace(0,11.5,100); t=linspace(0,10,100); delta_t=max(t)/length(t);

%%%%%%%%%%%%Accelerating movement%%%%%%%%%%%%%% T_acc=T_Ptorque-T_cf-k_vf*0.25*n_acc; %Nm a_acc=T_acc/J; %rad/s^2

n_acc(1)=0; for i=1:99 n_acc(i+1)=n_acc(i)+a_acc(i)*delta_t; %rad/s end

%%%%%%%%%%%%Test of working point%%%%%%%%%%%%% n_wp=7.2; %rpm n_wp=n_wp*pi/30; %rad/s

for i=1:100 if n_acc(i)

pos_final(1)=0; for i=1:99 pos_final(i+1)=pos_final(i)+n_final(i)*delta_t*180/pi; %degrees end

subplot(2,1,1) plot(t,pos_final) %degrees subplot(2,1,2) plot(t,n_final*30/pi) %rpm

Karl Pettersson 84 C Matlab m-files

C.2 Limits.m

%limits.m %Calculating the machine sizes and the characteristics curves

%%%%%%%%%%%Inputs%%%%%%%%%%% %clear %Excavator T_Ptorque=37126; %Nm n_max=11.5; %rpm i_tot=8.31*33.4; n_de=2300; %rpm T_mmax=149.7; %Nm

%Inertia T_cf=3636; %Nm k_vf=582; %Nm/rpm J=1.02e5; %kgm^2

%Efficiencies etha_hm=0.95; etha_vol=0.98; etha_acc=0.94; etha_P=0.95;

%Speed vector n=linspace(0,11.5,279); %rpm

%Choice of working point n_wp=7.2; %rpm

%%%%%%%%%%%%Machine Sizes%%%%%%%%%%%%%%

%Linear Set Pressure p2=330; %bar p1=150; %bar p_LP=0; %bar 30=Closed circuit, 0=Open circuit

p_wp=247; %bar

for i=1:279 if n(i)

% for i=1:279 % p_set(i)=p(280-i); % end

%Necessary Motor Displacement % V_gm=20*pi*T_mmax*i_tot/i_tot/(etha_hm*(p_wp-p_LP)); %cm^3/rev V_gm=40; %cm^3/rev

%Corresponding Flow At n=n_wp when T_m=T_mmax q_mmax=V_gm*n_wp*i_tot/(1000*etha_vol); %L/min

%Necessary Pump Displacement

Karl Pettersson 85 C Matlab m-files

%V_gp=q_mmax*1000/(etha_vol*n_de); %cm^3/rev V_gp=40; %cm^3/rev

%New q_mmax if V_gp is changed q_mmax=V_gp*n_de*etha_vol/1000; %L/min

%%%%%%%%%%%%%Power Limit%%%%%%%%%%%%%%%

P_max=q_mmax*(1e-3/60)*(p_wp-p_LP)*1e5*etha_vol^2; %W T_max=P_max./(n*pi/30+0.0000001);

%%%%%%%%%%%%%Swivel angles%%%%%%%%%%%%%

%Maximum alpha at each speed alpha_max=q_mmax*1000*etha_vol./(n*i_tot*V_gm+0.0001); for i=1:279 if alpha_max(i)>1 alpha_max(i)=1; end end

%Motor Flow when alpha=alpha_max q_m=V_gm*alpha_max.*n*i_tot/(1000*etha_vol);

%Pump Swivel Angle alpha_p=q_m*1000/(etha_vol*n_de*V_gp);

%%%%%%%%%%%%%%Torques%%%%%%%%%%%%%%%

% Maximum Motor Torque Available at the Load T_m=alpha_max*V_gm.*(p_set-p_LP)*etha_hm*i_tot/(20*pi);

% Friction Torque T_f=T_cf+n*k_vf;

%%%%%%%%%%%%Accumulators%%%%%%%%%%%

%Pressures p_0=90; %bar p_1=120; %bar p_2=300; %bar gamma=1.6;

%HP % E_kin=0.5*J*(n_max*pi/30)^2; %J % E_loss=(T_cf+0.5*n_max*k_vf)*0.5*n_max*pi/30; %J E_kin=0.5*J*((n_max*pi/30)^2-(n_wp*pi/30)^2); %J E_loss=(T_cf+0.75*n_max*k_vf)*0.75*n_max*pi/30; %J E_acc=etha_acc*(E_kin-E_loss); %J V_tot=E_acc/((p_2-p_1)*1e5); %m^3 V_0=1e3*V_tot*(p_1/p_0)/(1-(p_1/p_2)^(1/gamma)); %L

%LP p_0=16; p_1=20; p_2=30; V_0lp=1e3*V_tot*(p_1/p_0)/(1-(p_1/p_2)^(1/gamma)); %L

Karl Pettersson 86 C Matlab m-files

C.3 wpsolver.m

%wpsolver.m %Euler forward method for calculating the pressure built up when braking %with an inactive primary unit.

%%%%%%%%%%%Inputs%%%%%%%%%%% %clear n_max=11.5; %rpm T_Ptorque=37126; %Nm T_cf=3636; %Nm k_vf=582; %Nm/rpm J=1.02e5; %kgm^2 gamma=1.6; etha_hm=0.95; etha_vol=0.98; p_LP=30; %bar p_0=120; %bar p_1=150; %bar p_2=330; %bar

%%%%%%%%%%%%Calculated Values%%%%%%%%%% E_kintot=0.5*J*(n_max*pi/30)^2-(T_cf+0.5*n_max*k_vf)*0.5*n_max*pi/30; %J V_tot=E_kintot/((p_2-p_1)*1e5); %m^3 V_0=1e3*V_tot*(p_1/p_0)/(1-(p_1/p_2)^(1/gamma)); %L k=p_0*V_0^gamma; V_1=(k/p_1)^(1/gamma); %L %T_m=T_Ptorque+T_cf+0.5*n_max*k_vf; %Nm %a_max=T_m/J; %rad/s^2

%%%%%%%%%%%Time-dependent%%%%%%%%%%% delta_t=0.01; %s t(1)=0; n(1)=n_max; %rpm V_oil(1)=V_0-V_1; %L

for i=1:279 %Corresponding to the braking time 2.79 s if i>1 V_oil(i)=V_oil(i-1)+V_dot(i-1)*delta_t/60; %L t(i)=t(i-1)+delta_t; n(i)=n(i-1)-a_max(i-1)*delta_t*(30/pi); %rpm end V_gas(i)=V_0-V_oil(i); %L p(i)=(k/V_gas(i)^gamma); %bar T_m(i)=T_Ptorque+T_cf+n(i)*k_vf; %Nm a_max(i)=T_m(i)/J; %rad/s^2 q_m(i)=20*pi*T_m(i)*n(i)/(1000*(p(i)-p_LP)*etha_hm*etha_vol); %L/min V_dot(i)=q_m(i); %L/min end plot(n,p)

Karl Pettersson 87