Simulation Driven Product Development of a Thick Laminated Composite Connecting Rod

Department of Construction Sciences Solid Mechanics

ISRN LUTFD2/TFHF-19/5231-SE(1-35)

Simulation driven product development of a thick laminated composite connecting rod

Master’s Dissertation by Adrian Tosteberg

Supervisors: P¨ar-Ola Jansell, Deputy Managing Director - Altair Engineering Nordics Daniel K¨ampe, Technical Manager - Koenigsegg Automotive Jonas Engqvist, Research Engineer - Solid Mechanics, Faculty of Engineering LTH

Examiner: H˚akan Hallberg, Associate Professor - Solid Mechanics, Faculty of Engineering LTH

Copyright c 2019 by the Division of Solid Mechanics, and Adrian Tosteberg Printed by Media-Tryck AB, Lund, Sweden For information, address: Division of Solid Mechanics, Lund University, Box 118, SE-221 00 Lund, Sweden Webpage: www.solid.lth.se Contents

1 Abstract 1

2 Acronyms 1

3 Acknowledgements 1

4 Introduction 2 4.1 Background ...... 2 4.2 Objectives ...... 2 4.3 Company background ...... 2 4.4 Project description ...... 2 4.5 Boundaries ...... 2

5 Methodology 3 5.1 General approach ...... 3 5.2 Pre-study ...... 3 5.2.1 Product understanding ...... 3 5.2.2 Scope ...... 4 5.2.3 Boundary Conditions ...... 5 5.2.4 Failure and Material Theory ...... 5 5.2.5 Optimisation Goals ...... 7 5.2.6 Creation of Design Workspace ...... 7 5.2.7 Thermal requirements ...... 8 5.2.8 Chemical Requirements ...... 8 5.2.9 Manufacturing Options ...... 9 5.2.10 Know-How and Involvement ...... 9 5.3 Load step extraction and validation ...... 9 5.4 Topology Optimization ...... 10 5.5 Load path analysis ...... 10 5.6 Design for manufacturing ...... 10 5.7 Composite Optimisation ...... 12 5.7.1 Thick laminated composites optimisation ...... 12 5.7.2 Phase 1 - Free size optimisation ...... 14 5.7.3 Phase 2 - Ply based Sizing optimisation ...... 15 5.7.4 Phase 3 - Stacking optimisation ...... 16

6 Results & Discussion 16 6.1 Pre-study ...... 16 6.1.1 Boundary Conditions ...... 16 6.1.2 Mechanical Optimisation goals ...... 17 6.2 Multi-Body Simulation ...... 18 6.3 Flex body MBS ...... 21 6.4 Topology Optimisation ...... 21 6.5 Load Path Analysis ...... 22 6.6 Thick Laminate Modelling ...... 24 6.7 Composite Optimisation ...... 26 6.8 Manufacturing ...... 28 6.8.1 Core and Inserts ...... 28 6.8.2 Molds ...... 29 6.9 Benchmarking ...... 30

7 Conclusion 32

8 Appendix 33 Adrian Tosteberg March 13, 2019

1 Abstract

This master thesis explores options for efficient simulation in the product development process of a composite part. It’s method is a result of observation of the development process within two leading companies, both renowned specialists in their respective domains. Koenigsegg Automotive, is probably the most famous and carbon fiber intensive supercar producing company in the world. Altair Engineering is a leading simulation based software and consultant company, leading the way in implementation of machine learning and optimisation in the composite product development process. To learn and illustrate the process, a case study is performed: Concept development and optimisation of a thick laminated carbon fiber connecting rod for small volume production series Koenigsegg engine.

2 Acronyms

PCP Peak Cylinder Pressure [bar] UD Unidirectional ﬁber weave Small-end Part of connecting rod that interfaces with piston pin

Big-end Part of connecting rod that interfaces with crankshaft Shank Middle section (often proﬁled) of connecting rod transferring forces between its two ends

Gudgeon pin Connects piston to connecting rod through its small end MBS Multi Body Simulation DOF Degree Of Freedom Figure 1: Nomenclature [2]

3 Acknowledgements

To the following persons, I am deeply grateful for your trust, specialist guidance and interest throughout this project: Pär-Ola Jansell, Daniel Kämpe, Jonas Engqvist, Thomas Johansson, Johannes Nelson, Philip Jepson, Urban Carlsson, Lasse Holst, Markus Härder, Christian von Koenigsegg, Anton Llano, Fredrik Hanson, Joakim Truedsson, Erik Magnemark, Fredrik Nord- gren, Vitor Finotto, Fredrik Wettermark, Magnus Lundgren.

Keywords connecting rod, carbon ﬁber, composite optimisation, thick laminate modelling

1 Adrian Tosteberg March 13, 2019

4 Introduction 4.1 Background In the performance car industry, it is argued that lightweight is the main design objective (Chapman[1]). When it comes to quickly rotating parts in the drivetrain, the effect is emphasized, as the dynamic inertia of reciprocating and spinning mass directly affects acceleration and response, efficiency, NVH (noise, vibrations, harshness), fatigue life, wear and vehicle dynamics. In the case of lightened connecting rods, the weight saving benefits is multiplied, because the balancing system and crankshaft can be further lightened behind it, submitting engine bearings and cylinder liner to less stress and heating.

The shift towards the use of carbon reinforced composites for chassis parts has revolutionized the automotive world since the late 90s, but has for various reasons almost completely stayed out of engines and especially engine internals.

4.2 Objectives This study aims to map a robust design process, eﬀective enough to tackle extreme composite applications. It is intended to guide a simulation engineer working with structural composite projects. Furthermore, it will attempt to provide a starting point for further research and developments of composite engine internals. It will address challenges with the working environment and the design procedure, as well as attempt to ﬁnd a particular solution.

4.3 Company background Koenigsegg Automotive is a world renowned swedish supercar manufacturing company, known for continuously beating their own and others speed and performance world records since the early 2000nds. It is the product of its creator’s Christian von Koenigsegg vision, who together with his team of specialists and craftsmen, keep driving technical innovation in the propulsion and composite sector.

Altair Engineering is a leading product development software based company, driven by the core- value of innovation through simulation. The company is dedicated to bringing tools with specialized superhuman abilities, such as machine learning and optimisation, into the various stages of the product lifecycle.

4.4 Project description This study will explore the technical part of the product development process related with design and simulation of a structural composite part. To illustrate the process, a particular solution to a central but widely considered unexplored area of composite applications, engine internals, will be attempted. To illustrate the procedure, a case study of a relatively complexly loaded composite engine connecting rod concept for Koenigsegg is performed.

4.5 Boundaries While it is obvious that the composite product development cycle encompasses more than solely structural and technical solutions, this paper is written with the simple perspective that these features are the core of value generation, and are prioritized thereafter. The insight that the physical complexity of almost any product will near on infinite, while the development resources are in themselves finitely bound, makes efficiency a critical factor for success.

The thermodynamic deﬁnition of “eﬃciency”, is the ratio of the useful work performed by a process to the total energy input. Similarly, in the product development process, this implies the capacity of producing desired results with little or no waste, in the most direct or productive manner available.

Setting boundaries for the simulation process equates to a strategic reduction in optimisation resolution over lower priority physical phenomenon. These potential issues are instead left to present themselves and their respective priority during validation and testing. Experience, and the way of the engineering approach, will set the priority list for a particular project.

2 Adrian Tosteberg March 13, 2019

5 Methodology 5.1 General approach The following method is a result from personal product development experience, Koenigsegg’s quality norms, and Altair engineering’s design cycle perspective. It is believed to be general enough for most composite product development processes.

1. Prestudy: Determination of product requirements and input data for simulation (a) Product understanding: explore primary and secondary functioning principles, physical phenomena at play and failure mechanisms (b) Decide simulation scope (c) Collect/calculate necessary mechanical boundary conditions (d) Creation of design workspace (e) Thermal requirements (f) Chemical requirements (g) Explore available manufacturing options and determine requirements (h) Involve and gather experience from key manufacturing players 2. Optimisation of Shape (a) Topology optimisation (b) Load path analysis (c) Design simpliﬁcation for manufacturing 3. Composite Optimisation (a) Free size optimisation (b) Size optimisation (c) Stacking optimisation 4. Manufacturing and testing (outside the scope of this thesis)

5.2 Pre-study 5.2.1 Product understanding To achieve a perspective of the size and challenges of the project to come, it is sensible to quickly map out the product’s functioning principles. In this case, the primary mechanism, the reason for which a crankshaft exists, is to translate the reciprocating linear motion of the piston to a rotational torque on the crankshaft, which in turn will propel the vehicle.

For an in depth understanding of the secondary phenomenon at play in the product, a good starting point can lie in its failure mechanisms. Scanning for relevant studies is a good starting point, otherwise specialists can be consulted while keeping an eye out for solutions already on the market. It is necessary to explore the diﬀerences and complications arising from converting a homogeneous isotropic part into a composite material. Each failure mode is fundamentally linked with one or many physical phenomena, which should be accounted for from the beginning of the composite product development.

In the case of the connecting rods, the most common causes of failure found are listed below:

• Yield strength exceeded • Low cycle thermal fatigue • High cycle stress induced fatigue

• Over-temperature (material properties change, expansion clearance issue) • High RPM big end distortion (inertial forces)

3 Adrian Tosteberg March 13, 2019

• Compressive buckling (at PCP or hydrolock) • Elastic stretch into valves • Tapped bolt hole failure

• Bolt stretching and fatigue • Oil starvation bearing and journal failure and fretting (tribology) • Big-end or small-end bushing rotation • Stress concentration at sharp corners

• Surface crack propagation

In this context, the advantages/disadvantages of a composite design can then be explored: + Composite anisotropy allows for further stiﬀness and strength design freedom + Composite strength to weight ratio surpasses metallic competitors + Composite manufacturing methods allow greater geometrical freedom

- Delamination phenomenon - Energy dissipation through viscous damping - Poor composite heat conduction and ineﬀective bushing cooling

- Matrix systems commonly sensitive to temperature and environment chemistry - Unfavorable composite compressive behavior (kink bands [14]) - Composites tribological characteristics The distinguishing features that make product success likely compared to competitors and previous attempts: • Low series high budget production with tolerable high manufacturing complexity • Connecting rod disassembly not necessarily required • Route of hybrid material, with core or exoskeleton pretensioning the ﬁbers has not been attempted • Simulation intensive approach is diﬀerent from most previous hands-on attempts • Extensive inhouse tradition of composite know how and motivation

5.2.2 Scope Out of the challenges listed above, which are critical to tackle in a simulation approach? Efficient simulation suggests reaching a specific goal to investment ratio. It should be remembered that most products are never ideal, but just good enough for its set requirements. Furthermore, simulation and the use of simplification models for complex physical phenomena will invariably distinguish itself from reality. A validation feedback loop with physical testing is required, with 5 iteration attempts not being uncommon. The feedback is critical also to delimit the scope of the optimisation study. In physical testing, secondary physical phenomenons may not present themselves as critical, and are thus not worth optimising towards.

In this case study, a time/resource constraint will exclude the following activities: • Mechanical material characterisation of special ﬁber/matrix combinations

• Thermal simulation (curing, working temperature) • Mechanical prototype validation and optimisation feedback • Tribological investigation

4 Adrian Tosteberg March 13, 2019

• High cycle dynamic fatigue simulation Scoping is useful for determining that already proven technology is to be used for dealing with challenges of tribological nature as well for as setting optimisation goals for the macro-mechanical behavior. It can now be determined that the optimisation study will focus on mechanical strength and stiﬀness of a thick laminated composite. The load steps will be deduced from a transient multibody simulation including a crankshaft section, connecting rod (including bushings), gudgeon pin and piston. All challenges falling outside of the direct scope of the simulation are only to be balanced in an engineering mindset during the decision taking process; to simplify processes down the road and reduce required iteration cycles.

5.2.3 Boundary Conditions Collecting the input parameters for the topology optimisation is the next step of the product development sequence, speciﬁcally, mechanical/load boundary conditions and geometrical workspace constraints.

The typical loading scenario of interest is the worst case running conditions, with material fatigue and an overall safety factor included. Peak compression stresses in the connecting rod member will be achieved during the combustion phase, as the combustion chamber reaches peak cylinder pressure. Peak tensile loading is expected to occur at maximum rpm during the exhaust phase exactly as the piston reaches TDC, while the piston experiences peak motion prescribed acceleration (see equation 11) without counteracting high cylinder pressure.

5.2.4 Failure and Material Theory Before a failure criterion is chosen for optimisation objective, a measure of the stress state in the composite is required. A simple method of achieving this is by the method of calculating a homogenised stress state per composite ply. Because of orthotropic nature of the fiber reinforcements, each ply will have a specific orientation dependent stiffness matrix Cijkl to which both constituents fiber and matrix contribute.

The material stiffness matrix can be found either by mechanical testing and characterization, or from its constituent properties. In the latter case, simpler unidirectional fibers bound by a uniform matrix in a weave can be calculated with simple rule of mixtures for longitudinal and transverse modulus. The upper bound for the direction parallel to the fibers:

L Ec = fEf + (1 − f)Em (1)

Lower bound for direction transverse to ﬁbers:

T Ef Em Ec = (2) fEm + (1 − f)Ef where

• f is the volume fraction of ﬁbers

• Ec is the material property of the composite

• Ef is the material property of the ﬁbers

• Em is the material property of the matrix It can also be modelled along with more complex weaves and twills by the method of micro-scale finite element setup. The software Multi-Scale Designer quickly builds meshed models of the micro-structure from a set of weave specifications such as in figure 2 below:

5 Adrian Tosteberg March 13, 2019

(a) UD (b) Weave

Figure 2: Weave model used to calculate macro ply properties from micro constituents

Multi-Scale Designer computes homogenised cubic cell characteristics from the individual components, that can be substituted in a macro scale model. In practice, getting access to specific macro characteristics of certain fiber/matrix combos is com- plicated because of the multitude of combinations, and expenses of mechanical characterisation required for every single one. Instead, reverse characterisation can be performed to extract miss- ing micro properties. Oftentimes, a specific fiber/matrix combo material model is wanted, but macro properties exist only for the same matrix with another fiber combination. Usually dry fiber characteristics are given in datasheets by manufacturers, and so the matrix properties can be in- verse characterised by a trust region algorithm or ant colony probabilistic algorithm. Now the composite macro properties can be computed with any known fiber combination.

After the stiffness matrix has been established in local ply coordinates, it is rotated to the desired orientation in the laminate’s reference frame. Once the stiffness matrix is computed, it is substituted in the classical finite elements formulation, where for assumed small strains and linear elastic behavior, each ply mesh cell obeys Hooke’s law:

σij = Cijklεkl (3) The assumption of linear elastic theory are made because of the low deformation tolerance accepted in the solution. A direct relationship between the stress and strain simplifies the optimisation task, and can safely be assumed because of the safety factors used towards yielding conditions. For shell elements (such as the composite PCOMPG) that will be used to model composites in this thesis, the stress state is resolved in the two dimensions of the shell element only, ie. the normal stress through the thickness is not considered. Shells can be subjected to in plane actions, plane strain, bending and transverse shear. Single layered shell elements assume bending stiffness dictated by the first order shear deformation Mindlin-Reissner theory of plates, see equation 4 below:       σ11 C11 C12 0 0 0 ε11       σ22 C12 C22 0 0 0  ε22       σ23 =  0 0 C44 0 0  ε23 (4)       σ   0 0 0 C 0  ε   31  55   31 σ12 0 0 0 0 C66 ε12 and thus:       N11 Z h C11 C12 0 ε11       N22 = C12 C22 0  ε22 (5) −h N12 0 0 C66 ε12 where C is the [6x6] stiffness matrix

6 Adrian Tosteberg March 13, 2019

The extensional and bending stiﬀness can then be integrated according to Mindlin theory[4].

Multi-layered ply elements also have inherent stiffness due to the separation and placement of mid-ply integration points further from the mid-plane axis of deformation of the stacked element, in effect making normal stresses contribute to bending stiffness through their area moment of inertia.

The reduced stiﬀness matrix can then be multiplied with the strain rotated into the coordinate system of the ply, to compute local stresses. These are then rotated back into the global coordinate system, where elemental states can be saved in global matrices.

Because of the modelling method that will be explored in this thesis, and the small deformations at play, the importance of minimizing error in bending is deemed low and ﬁrst order (CQUAD4) shell elements were used for computational eﬃciency reasons.

Isotropic components that are not being optimised are modeled using second order tetrahedral elements with 10 integration points to capture bending and resolve complex stresses in all components that were not approximated with the stacked thick laminated composite method.

5.2.5 Optimisation Goals The current steel connecting rods are currently suﬃcient in terms of strength, and proven in terms of reliability. The purpose of switching to composite technology is purely to reduce the engine’s inertia, translating to minimizing connecting rod oscillating and rotational mass and inertia. Be- cause of the untested nature of the problem, at the time this thesis was started no successful commercialized composite connecting rods had been released to market, the objective of the prototype was shifted. It was agreed that priority should lie in fabricating a proof of concept to be physically tested, where minimizing mechanical failure chance was top priority.

During the optimisation attempts with objectives of direct stress minimization, for the sake of testing solver suitability for this task, simple Von Mises peak stresses will be kept down. If this hard method of optimisation proves to be a success, optimisation of ply strength ratios (ie. lin- earized failure indices) towards more complex tension/compression separated failure criterions can be explored, such as Tsai-Wu stress envelope for transversely isotropic materials:

2 2 2 F22F33 − F23 ≥ 0; F11 − F12 ≥ 0 (6)

This method thus translates to optimising against ﬁrst-ply failure. Results analysis from stress constrained optimisation strategies will reveal why a failure criteria objective was eventually not used

Alternatively, a suitable optimisation strategy to safeguard against delamination, is looking to minimize interlaminar and through thickness shear and compressive stresses (Wisnom[6]). In this context, the composite model presented in this thesis has options for minimizing Von Mises stresses in interlaminate elements (CBUSH 1D stresses) as well as looking directly at the intra-laminar shear stress (SB ﬁeld in the PCOMPG card).

A proposal for future in depth analysis, is to explore crack theory with the energy balance approach. Once a prototype rod is built, the size of the largest crack can be analysed through destructive microscopy or non destructive X-ray or ultrasonic techniques. The strain energy per unit crack area can then be calculated and the critical stress that would grow the crack found by comparing with the potential energy of the stressed cell (Mahishi [12]). This method can be explored if it found that crack growth induced delamination occurs before ﬁrst-py failure during the mechanical testing stage.

5.2.6 Creation of Design Workspace The topology optimisation will provide an indication of favourable regions of load bearing. It needs to be restricted to a volume that does not interfere with its surroundings during its operation. Clearances need to be determined towards these parts. Final parts tolerances, thermal expansion and parts deformation under load is taken into consideration.

7 Adrian Tosteberg March 13, 2019

In practice, multiple methods of determining the workspace exists and a solution will often be tailor made for each problem. Because of the complexity of geometry and relative movements in this case, a large dummy connecting rod was modelled and placed in the assembly at different crankshaft angles. For every position, the interfering regions (plus clearances) are cut out from the dummy. The resulting geometry is then “smoothened” to capture positions between the steps, as well as simplified for handling and meshing purposes, see figure 3a below.

(a) Designeable workspace (b) Interface assembly

Figure 3: design workspace and its interaction with neighbouring components in the engine crankcase

5.2.7 Thermal requirements Material evaluation requires comparison at cold and hot operating temperatures. The lower temperature is given by the coldest expected outside temperature. The upper limit is given by neighbouring piston pin temperature, engine oil temperature sprayed to cool and lubricate the connecting rod ends, as well as heat generated within the rod and bushings during high load/rpm operation.

Discussion with engine specialists indicated a conservative operating temperature estimate of “as low as” 90◦C at the connecting rod small end. The reasoning is that the piston is cerakoted minimizing some heat conduction from the combustion chamber. Furthermore, heat blockage occurs at the interface between the piston and piston pin . The piston pin is also cooled through its length by the pumped lubricating oil, injected at 80◦C, which is only in contact with the connecting rod at its center. Finally, the oil layer responsible for glide in the small end bearing further insulates the connecting rod in this fully ﬂoating design.

On the other hand, extrapolation from research data on more conventional engine design under full load, give a relevant higher temperature bound of between 154 − 173◦C to keep in mind(Furuhama[7]).

5.2.8 Chemical Requirements Contrary to metals, some polymer matrices are aﬀected by chemicals within the oil or combustion gases that seep into the crankcase through piston ring blow-by. The particular reactive substances gathered are:

• Hydrocarbon (some paraﬃnic) petroleum distillates • Oleﬁns

8 Adrian Tosteberg March 13, 2019

• Benzeneamine reaction products • Ethanol (trace quantities)

5.2.9 Manufacturing Options Koenigsegg in house expertise lay in the development and production of structural parts made with hand-laid pre-impregnated matrix/ﬁber uncured weave on mold. As the layup is completed, the part is vacuum bagged and cured in the autoclave. Possibilities for layup around a core, or making hollow parts with this method exists. Because of the nature of the layup and weave, the precision in the stacking and orientation of the layers is in the order of millimeters and degrees.

Filament winding is another fabrication method with high ﬁber orientation complexity possibility. It will then have to be vacuum molded in a split mold or with vacuum bagging for a structural matrix to set.

At any rate, bushing regions with high tolerance requirements need CNC post trimming. A design incorporating sacriﬁcial ﬁber layers or a thicker epoxy outside will be required for this.

A sandwich or core material can be hydrocut out from foam, metal, honeycomb, or 3D printed. The last option enables more complex shapes, a wide material variety, as well as inclusion of continuous ﬁbers in a load bearing core concept.

Matrix compatibility with above substances is a criterion for choice, although coatings or lin- ers as in use by the aviation industry are also an option to protect the connecting rod.

5.2.10 Know-How and Involvement An eﬀective way of “leap frogging” within the development of a new concept is to involve experi- enced specialists in a well framed brainstorm session, early in the project. The purpose should be to open as many doors as possible early on, encouraging and building upon all presented sugges- tions. Their combined experience will often provide proven solutions to faced challenges.

Diﬀerent meetings should be setup to include only relevant players for each challenge tackled. early involvement of technical specialists and the manufacturing division will incite interest and maximise chances of adoption, while detecting critical project steps early.

5.3 Load step extraction and validation As the problem has been defined, boundary conditions set, and workspace drawn, the next step is to fix the overall geometry of the part to be developed. In the case of complex loading or rapidly moving mechanisms, it can be hard to capture all the critical loads. A multibody simulation can be setup to reveal part joints loading history for the different connections to the part. Fatigue can thus be accurately accounted for, as well as peak loads introduced in a structural part.

In the case of the Koenigsegg connecting rod, a rigid body dynamic assembly consisting of a crankshaft section, connected to the engine block (ground) driving a high strength steel connecting rod and piston pair was setup, with and without piston combustion pressure force curves, to encompass the four strokes of the engine. A pseudo titanium connecting rod model (Manley steel geometry with density adapted to reach titanium rod weight), believed to be closer to the ﬁnal weight of the composite connecting rod was chosen, because its ﬁnal weight was thought closer to the optimised composite connecting rod. The analysis was setup in MotionView using MotionSolve to compute the interface stresses required for an equivalent static loadcase, a suitable load format for the optimisation tasks.

The most thorough approach at this stage is to replace the part of interest with a flexible body, capturing dynamic geometrical effects such as deformation due to loading and eigenmode excitation. For this, a solver will require a discretized geometry with associated stiffness and inertia. In practice, this requires meshing and a modal analysis. Altair’s solver OptiStruct can perform result simplification by creating a “superelement” (19 resulting DOFs in this case, with associated

9 Adrian Tosteberg March 13, 2019 condensed sparse stiﬀness matrix). The problem was solved with a direct method Block Lanczos eigenvalue extraction algorithm. Modes that should be taken into account are generally taken as below twice the highest excitation frequency, in this case maximum engine RPM. Higher modes are considered unlikely to be excited. It should be noted that eigenfrequencies are dependent on inertia, so the piston mass was included in the modal analysis in the way of a point mass located in the small-end centre. The eigenmodes are found through base or ground motion. Base motion can be seen as a mechanically locked in some constrained degrees of freedom, after which the part is “shaken” in the DOFs of the global coordinate system, and the response calculated.

The eigenmodes are interesting to study because they reveal the dynamic deformation modes. The superelement stiﬀness matrix can then be substituted instead of the rigid characteristics in the MBS. Capturing ﬂex is interesting because of the ability to model contact, load dissipation and for analysis of the internal stress distribution.

A reality check on the working steel connecting rod submitted to the extracted load steps can then be performed, verifying that safety factors are inline with design speciﬁcations.

5.4 Topology Optimization The topology optimisation aim is to get an understanding of preferential or critical areas to place material for a specified strength or stiffness target. The Solid Isotropic Material with Penalization (SIMP) technique is the most widely spread, and works by decomposition of the workspace into elements with an associated weight function between 0 and 1, for zero density and full density elements respectively. A penalization factor depending on the degree of element starvation is applied to the stiffness matrix of these intermediate density elements. The element strain energy is included in the filtering criteria, bringing the elements to a state of either filled or void. Furthermore a proximity filter is used to avoid element level “porosity” in the optimised structure (Lu[13]) The following optimisation setup was used:

Objective: Minimize volume fraction of material

Optimisation Constraints: Volume fraction upper bound: 0.3 Compliance per load step: • Lower Bound: same as full workspace • Upper Bound :175% of workspace compliance

The optimised structure will serve as basis for the composite part design and load path analysis. To avoid issues with balancing and for simplicity, symmetry conditions along x and y plane were used.

5.5 Load path analysis Once the ideal load bearing topology has been established, post processing of the final design iteration subjected to load step forces reveal the internal stress state. Cross section cuts, iso profile views with element density filters and tensor field analysis are tools that are used to understand the physics of the deformation and critical load paths and directions.

Understanding of the load paths and deformation phenomenons, allows design objectives to be set in an informed manner, that the ﬁnal design determined by manufacturing constraints should aim to fulﬁll.

5.6 Design for manufacturing A number of questions should first be investigated to guide reasoning around design choices: 1. Part specifications (a) Form: Does the part present complex outer features or an intricate inner structure? Can it be simplified?

10 Adrian Tosteberg March 13, 2019

• The optimised solution presents relatively complex geometry features for a composite part, variable composite thickness, potentially separate load bearing structures and junctions • The part can be simplified as long as it stays within the outer boundaries of the workspace. Furthermore, great freedom in lamination schedule can reduce the required complexity of the outer shape • The composite will be using continuous fibres with very high length/diameter ratio (b) Size: What is the approximate final size of the part to be produced? • 200x100x30mm (c) Mechanical properties: What loading and fatigue scenarios will the part be subjected to? What is the target weight? • Primarily mechanical stress during peak compression and tensile state • Ultimate target weight is below 600g of a steel rod, and preferably below 540g of a titanium rod, its closest competitor. (d) Environment: What humidity levels, temperatures, UV or chemicals will be present in the expected part’s working environment? • Primarily engine oil contact • Some gasoline/water vapours • 80 − 120◦C working temperature • Cold start clearances from −20◦C 2. Material and design choices • Access to extensive carbon fiber epoxy prepreg know how and availability • Design should be suitable for manual and automated layup if scaling 3. Production requirements (a) Batch volume and acceptable production cycle time • 8 per V8 car x 20 per year = 160/year (b) Budget for acquiring new equipment • Appropriate for low series production (c) Capacity to utilize pre-existing equipment • Potential for reuse of tools for manual layup and autoclave curing according to Koenigsegg inhouse traditions 4. Quality assurance (a) Reinforcements positioning tolerances: fibre orientation and placement, particulate spread, reinforcement volume fraction map • Positioning tolerances are low, since critical bearing interfaces and connecting rod split will be precision machined. (b) Reinforcement/matrix interface adhesion level • Material supplier manufacturing recommendations will be followed. Sacrificial testing will reveal internal adhesion issues. (c) Acceptable porosity or air volume fraction • Low, they can serve as crack nucleation zones causing fatigue. Split mold with vacuum lines will extract trapped air and excess resin. (d) Completion of design objectives • Mechanical testing in a test engine will determine if objectives are met 5. Verification of production optimisation (a) Cost optimisation • Minimization of man hours required during layup/assembly (b) Production volume optimisation

11 Adrian Tosteberg March 13, 2019

• Adaptation from manual layup to automated tape layering if necessary (c) Choice of consumables • Molds, tubing, release agents, ﬁlms and fabrics, personal protective equipment from current Koenigsegg suppliers

The choice of manufacturing technique is the next large decision to make. Three manufacturing proposals were selected for evaluation with the manufacturing specialists.

Manual prepreg layup is the natural option for low series/prototype production, allowing high fiber aspect ratios, high geometry and fiber orientation complexity designs. Automated Tape Lay- ing could improve production cycle time and increase reproducibility at the expense of reducing part complexity and tooling costs. Even higher production capacities could be achieved through Resin Transfer Moulding or Structural Reaction Injection Molding. However, the added complexity of making preforms, tooling costs and lack of experience with such methods are significant downsides.

5.7 Composite Optimisation 5.7.1 Thick laminated composites optimisation In contrast to the vast majority of composite product development projects, the imagined geometry of the composite connecting rod is not a thin walled structure. In ﬁnite elements, thin walled structures, where the thickness is by far smaller than the two remaining dimensions of the part, are usually modelled with shell elements. In fact, the typical 3-phase composite optimisation technique used by optistruct use shell elements with multiple integration points and material orientations throughout its thickness. However, unlike solid 3D elements shell element formulation only take into account the 2D stress state parallel to its surfaces. Thus the Von Mises or other composite stress resultant will not capture the through laminate loads(Johansen[3]), which is deemed acceptable in thin walled geometry where the cross thickness variation is low.

With these shell elements however, powerful and automated optimisation techniques exist and are the most eﬃcient to use because they do not require manual design of experiments (DoE) technique and building of a response surface to ﬁnd optimums.

To minimize the impact of cross thickness stresses, the idea of stacking node coupled shell elements parallel to the load paths was imagined. This method results in a semi-continuous volume mesh, where neighbouring stack elements will influence each other by the way of spring linked mid- plane nodes. The effect on the laminate shells used (PCOMPP property), would be that for two stacked elements with four plies each, the top ply of the bottom element will not uniquely influence the bottom ply of the top element as in traditional FEM, but it is rather the average deformation of the bottom element that will affect all plies of the top one, and vice versa. As long as a thick volume is discretized with a fine enough stack of shells, cross thickness variations in deformation and stress states is still resolved by this averaged method. On figure 4, it can be seen how shell elements are directly node linked to neighbouring elements on surfaces, while cross-linked through 3d spring elements with tunable directional stiffnesses and no rotational stiffness. It should be noted that each shell, is composed of four superposed UD plies in different directions with total laminate thickness such that no voids exist between modelled surfaces.

12 Adrian Tosteberg March 13, 2019

Figure 4: Nodal connections in thick laminated composite model

As a simple allegory, the shell surfaces can be seen as stacked pieces of toast transferring loads through a sticky jam middle section, while allowing some inter-movement of layers for continuous deformation fields. The coupling of nodes in between stacked shell elements should be done so as to transfer stresses and deformations across the part thickness. Infinitely stiff elements in all DOF’s imply that all successive layers will deform uniformly whereas on the other hand, infinitely flexible elements will not transmit any deformation information to its neighbour. To avoid discontinuities in material deformation and stress fields, one should seek spring constants that both achieve the purpose of distributing loads from one layer to the next, while allowing for a relaxing effect with some intra laminar material deformation depending on matrix stiffness.

An over-stiffening effect restricting the global deformation of the part will occur in instances where shell elements movements is restricted by the node connected springs. Effort was made to reduce this effect by making sure no slave node was connected to more than one master node per adjacent shell, because the springs would unload the cell with the two master nodes on it. A method of taking into account spring loading could counter this effect, and would further provide a 3D stress state to element nodes, but was not explored in this study because of time constraints.

Instead, the method should focus on providing a lightweight calculation with deformation behavior close to a solid model’s in order to yield valuable optimisation responses. The model can also be used for extracting stress states in the composite, but higher degree of uncertainty in results will be present due to the uncaptured 3D stress and the fact that some in plane stresses can distribute out to springs.

To verify the method, simple test coupons will ﬁrst be analysed and have their spring rates tuned, to bring insights and conﬁdence to approach the full scale connecting rod problem at a second stage.

First two simple models are setup to test in plane and out of plane bending behavior. The reference model is a one component global ply PCOMPG laminate composed of 40 shell elements, containing 10 UD plies in the sequence [90/ − 45/0/45/0]SE, see ﬁgure 5b. The second is built out of ten PCOMPG components with 40 shell elements each, featuring interconnected nodes. In both models the total laminate is 1 unit thick with each ply measuring 0.1 units in thickness.

13 Adrian Tosteberg March 13, 2019

(b) ply ordering (a) stacked laminate

Figure 5: layup of the 10 stacked surface components

Both models end nodes are then rigidly ﬁxed in one end while a traction or normal force is applied to the nodes of the opposite end. The deformation behavior and stress states can then be contrasted in the case for in plane and out of plane loading.

The next step is to setup a shell layered connecting rod model for composite optimisation. Once the manufacturing method and design has been ﬁxed, the model is built. To account for variations in composite thickness, the number of stacked shells will vary along the length of the connecting rod, as can be seen from ﬁgure 6 below:

Figure 6: layered buildup around core of connecting rod

The method of construction consisted of creating oﬀset shell meshed outer surface inwards with 1mm separation. Parts of layers that interfere with the core were then removed.

Nodes could then be connected with 3D spring elements of CBUSH type, with user definable stiffnesses in all 6 DOFs. A search tolerance could be specified such that all nodes would only cou- ple to one respective node on neighbouring surface meshes. Some manual cleanup was required, mostly towards the core, where the meshes would no longer perfectly match up even though element size was similar.

5.7.2 Phase 1 - Free size optimisation Generally, the first stage of the composite optimisation process is the free size optimisation. It works by varying both structure and material simultaneously, in continuous thickness variations with reinforcements in critical areas. Super-plies are created, serving as the total designeable workspace of a particular fiber orientation. Because the outer geometry is fixed by the vacuum mold, and the inner by the core, this step is only used in our case to generate a basis for the next step being sizing optimisation. Because thickness will be prescribed, and variations are controlled

14 Adrian Tosteberg March 13, 2019 by the number of layers of whole plies, local reinforcements cannot be placed. However, Optistruct can automatically generate a sizing model by creating sizing design variables with pre-optimised starting thicknesses and user deﬁnable bounds and design variable property relationships, saving the time of setting these up manually.

Four stacking directions [0,+45,-45,90] are initiated for the unidirectional plies, with the 0 orientation being parallel to the length axis of the connecting rod (y-direction). The decision not to use manufacturing or balance constraints was taken after test runs indicated that these aﬀected convergence, at times producing less ideal results. Instead lamination schedule decisions such as replacing +/- 45 plies with twill weave to keep balance, or deciding on weave manufacturing thickness can be taken after the ideal layup has been reached.

In order for any orientation to be able to alone occupy the whole design space between two shell elements, super-ply thickness is set to 1mm, creating 4mm thick layers, initially violating the 1mm total laminate thickness condition. This can be done by editing in the solver ﬁle directly and appending the line “OUTPUT,FSTOSZ,YES,1,ADVFREE”.

The optimisation objective was set to minimize weighted compliance, in other words, minimizing the combined strain energy in the four extracted extreme load steps. In the case for composites aligning the fibers with the load paths not only increases stiffness, but also distributes the normal load to the fibers instead of the matrix, allowing for greater strength.

1 X C = W FTU (7) W 2 i i i i where CW is the weighted compliance or strain energy W is weight factor FT is the transposed force vector U is displacements th i denotes the i load step, load case

Even weight factoring is used, because extreme strain energies achieved in a particular load step will achieve correspondingly higher priority in the optimisation strategy.

This indirect approach was used instead of a hard optimisation constraint on minimizing peak stresses, because it proves more reliable in practice with the solver algorithms.

As the ﬁrst phase of the optimisation is run, most material will be removed from the unloaded ﬁber orientations, setting up phase 2 for quick convergence.

Design variables: [0, +45, −45, 90] oriented plies in the 22 stacked laminates. They are to be used to initiate sizing variable in phase 2.

Optimisation response: Weighted compliance in all four load cases.

Optimisation constraints: Laminate thickness restricted to 1mm to avoid interference and superposition of plies between adjacent laminates

Objective function: Minimize weighted compliance

5.7.3 Phase 2 - Ply based Sizing optimisation In this stage, the design variables are the whole ply thicknesses. The optimisation is setup such that the four orientations compete for the available 1mm design space assigned to each shell layer.

Design Variables:

15 Adrian Tosteberg March 13, 2019

Thickness of plies generated in free-size phase.

Optimisation Responses

1. Weighted compliance over all four loadcases 2. Weighted compliance over all four loadcases 3. Minimize peak stresses Optimisation Constraints:

1. None 2. Maximum allowable stress should be 10% lower than result in optimisation 1 3. None

In all three optimisations the total laminate thickness per shell was also restricted to 1mm to avoid interference and superposition of plies between adjacent laminates

5.7.4 Phase 3 - Stacking optimisation The stacking optimisation finds the ideal way of shuffling the plies within a laminate. Because the optimisation yielded low variation in ply orientation with heavy bias towards 0 plies, this step brings little further benefit and will be skipped in favour of a manufacturing driven stacking sequence: A +/- 45 twill must separate three successive UD plies. To avoid delamination and crack propagation, a certain variation in fiber orientation is thus enforced, causing obstructions for development of crack planes, while provide minimum stiffness in other than in main direction in case of unforeseen stresses.

Furthermore, it was decided that an outer layer of drapeable twill surrounding the whole connecting rod is to be laid. Its purpose is to cover the stacked ply edges, such that width and positioning imprecisions resulting in uneven sides and favourable sites for crack nucleation are minimized. A fine covering twill conforming to the underneath layers while filling voids with epoxy will counteract this effect.

6 Results & Discussion 6.1 Pre-study 6.1.1 Boundary Conditions Gas loads arise from the diﬀerential pressure on both sides of the piston. While the crank facing side has only small pressure variation, due to the large crankcase volume and crankcase ventilation, the combustion chamber end naturally has large pressure variations(Atkins[8]). This is due to two phenomena: First, during the compression stroke of the Otto cycle, the piston moves from BDC (bottom dead centre at maximum volume) to TDC (top dead centre at minimum volume) ideally resulting in an isentropic compression of the turbo compressed intake air. In practice, some entropy is generated as friction, and heat conduction from gas to chamber will reduce the peak pressure achieved. Secondly, during the ignition phase, the rapid heat generation due to combustion of the air/fuel mixture results in a rapid pressure increase while the piston remains close to TDC.

The combustion chamber pressure acts on the piston cross-area to induce a compression load into the connecting rod small end. From monitored cylinder pressure vs crank angle data. A compressive peak force of 83kN is calculated. It should be noted that this ﬁgure assumes normal full load operating conditions, and that pre-detonation or knocking, could cause even higher PCP in abnormal faulty operating conditions.

16 Adrian Tosteberg March 13, 2019

Inertial loads are deduced from maximum engine speed, piston assembly mass and piston motion equations:

Figure 7: Geometric layout of piston pin, crank pin and crank center

The cosine rule gives: l2 = r2 + x2 − 2rxcos(A) (8) Rearranging this equation and using trigonometric identities, the following equation can be ob- tained: x = rcos(A) + pl2 − r2sin2(A) (9) which can be simpliﬁed by taking the ﬁrst two harmonics of the Taylor series expansion: r2cos2(A) x = rcos(A) + l(1 − ) (10) 2l2 Taking the second derivative with respect to time, gives: rcos(2A) a = −rw2(cos(A) + ) (11) l where w is the angular velocity.

Independently of other constants, peak piston acceleration is thus found at A=0, when both cosines are in phase.

The acceleration is then multiplied by the reciprocating mass, usually considered 1/3 of the connecting rod mass (german approximation factor) plus the mass of the piston assembly, resulting in -26kN (@ 8500rpm) of oscillation induced forces being applied to the big end.

Additionally, centrifugal forces will subject the bearing to an additional 2/3 of the connecting rod mass to the acceleration of the big end. The centripetal acceleration is thus estimated to 8kN, being transmitted through the big end bearing.

Force balance results in a transmitted force to the small-end bearing being the negative of the sum of gas force with the force required to accelerate the piston, 83 - 20 = 63kN.

To validate these numbers, and capture the dynamic secondary out of axis forces, a multi-body simulation is setup during the preparatory phase to the topology optimisation process in order to determine load cases.

6.1.2 Mechanical Optimisation goals In the pre-study understanding section, tribological mechanisms have been related to small-end ovalization, while impact toughness is achieved through load distribution through ﬂex and material toughness. In the name of eﬃciency and the study’s primary goal of strength and endurance

17 Adrian Tosteberg March 13, 2019 safety margins, tribology and ideal deformation behavior challenges can be eﬀectively be avoided by copying the current designs behavior. Thus, conservation of the overall and local small-end stiﬀness of the metallic connecting rod could be set as optimisation constraints, if revealed to be a failure point during prototype testing.

Ovalization is defined as the difference in deformation of the small end bushing top and lower nodes, and was measured to 0.02mm, see figure 8. Connecting rod flex was measured as the sum of the deformation between the center nodes of load introduction in both the compressive and tensile load case (0.25mm).

In turn, these are determined by a rough ﬁnite element analysis of the current setup, validated against a multi-body CAE simulation performed by the engine specialist.

(a) compressive loading (b) tensile loading

Figure 8: Deformation analysis of Manley steel connecting rod (visually exaggerated deformed state)

Stress distribution simulation determined that local Von Mises stress maximums achieved of 1000 MPa in bushings and 900 MPa in steel connecting rod body, equivalent to a safety factor of 1.6 towards 300M steel yield strength (1600 MPa) in the load bearing body. Because of the unproven design of the composite rods, the critical nature of a failure, a lower safety factor must be avoided in the new design. In fact, objectives reevaluation with engine and composite specialists placed peak stress reduction as the primary objective of the optimisation. The reasoning is that stress distribution and the subsequent weight gains, will generally act in favor of maximum loading conditions, fatigue life, and layup irregularities. Because of the strong weight savings in switching to CF from titanium, doubling the speciﬁc strength, or more than quadrupling steel’s, see table 1, weight reductions are expected even in a strength safety factor optimisation (maximisation) scenario.

6.2 Multi-Body Simulation Two local compression state maximas were noted occurring during detonation (1) in ﬁgure 9 and as the centripetal force aligns with axis of the connecting rod at 360◦ crank angle degrees (CAD), while peak tensile state is occurs at the piston travels through TDC.

18 Adrian Tosteberg March 13, 2019

Material Density Stiﬀness E Yield stress Speciﬁc −3 ρ[kg.m ] [GPa] σy[MP a] strength [MP a.m3/tn] Steel 300M 8000 205 1586 198 Aluminium T6 2800 75 413 148 Titanium alloy 4500 115 1000 222 CF weave 1600 70 600 375 CF UD 1600 135 1300 813

Table 1: Material comparison

Figure 9: MBS results of titanium weight connecting rod

From the polar force plot in ﬁgure above, four extreme load cases are extracted. The three ﬁrst are extracted during the combustion cycle, and the inertial case during the exhaust cycle.

19 Adrian Tosteberg March 13, 2019

Loadstep F N smallend F T smallend F N bigend F T bigend

N 1. combustion FC,max [kN] -62 0 -50 -3 T 2. combustion Fmaxtp [kN] -9 8 -10 11 T 3. combustion Fmin [kN] -25 2 -26 -10 N 4. inertial FT,max [kN] 20 0 33 0

Table 2: Extracted load-steps, normalN and transverseT to the connecting rod axis

Loads are introduced in the structure in normal and transverse components through Multi Point Constraints (MPC), see ﬁgure 10. This is one of the common ways approximating radial posi- tive pressure bearing loads in components. The load components parallel and orthogonal to the connecting rod axis will be acting on a master node which transmits the load through a series of (RBE3) links to a section surface of the bearing quartile transferring the majority of loads. To avoid over stiﬀening the section of coupled nodes, and creating drastic non-physical transition zones in between quadrants, relative motion between (slave) dependent nodes is allowed.

(a) Load introduction small-end (b) Load introduction big-end

Figure 10: Load introduction in components format through MPC

The loads are balanced by an inertia relief function in eﬀect to achieve a static simulation. Trans- lational and rotational accelerations are being applied over the connecting rod so as to counter any rigid body motions otherwise resulting from unbalanced external loads. This is called an equivalent static loading method (ESL) which eases the task and computational costs of simulating dynamic problems. Automatic support (constraint) generation is performed by OptiStruct for the linear static analysis, making the task very time eﬃcient.

From table 2, the peak compressive force appearing in load-case 1 in the small end, stands out as a critical stress because of its highest stress amplitude overall. It is therefore validated against the results achieved in the pre-study section. The small end bearing force during the combustion phase at TDC is the resultant of the compressive gas force and the tensile piston inertia force: -83.1 kN + 20.3 kN = 62.8 kN, which is exactly what the MBS predicted. The peak tensile force can be extracted from the fourth load-case, ie. at the big-end bushing during TDC while on the exhaust stroke. This force is the sum of the calculated reciprocating force with the centripetal force: 25.6kN + 8.0kN = 33.6 kN, perfectly validating the second most extreme case of the MBS simulation.

For modal analysis, connecting rod supports simulating the eﬀect of the bearings was set up. They were deﬁned as completely unrestrictive for degrees of freedom in the x, y, and rotation about the z axis for both ends. Furthermore, the small end was allowed to rotate about y, as the

20 Adrian Tosteberg March 13, 2019 piston is not self restricting rotation along the axis of the cylinder wall.

6.3 Flex body MBS An attempt at performing a ﬂex body MBS was done for the pseudo titanium connecting rod. The geometry was discretized with a tetrahedral mesh. To achieve better element collapse (0.2), some boundary mesh nodes were replaced, creating in eﬀect an approximate geometry that in theory was well suited for analysis.

In practice, it was concluded that the design was safe from resonance. However, user error trans- lated approximate geometry to approximate contact modelling due to inaccuracies in positioning of the bearing center-points and poorly defined movement, causing unrealistic forced deformation behavior and oscillation. A strategy to remedy this was made, consisting of simulating with both the ideal geometry and approximate discretized model. However, the time constraint would be exceeded, and result uncertainty high. Upon verification of the rigid body setup results, the decision to skip flex body modelling was made. Design of the optimisation process is to be prioritized. Input parameters can always be further researched in case of extra time or failure during prototype testing.

6.4 Topology Optimisation Now that the load cases have been generated, and the maximum outer dimensions of the part have been found by the method of subtracting all interfering bodies with a clearance of 1mm at various crank angles see ﬁgure 3a below, the topology optimisation could be setup:

Figure 11: Result of the topology optimisation with cross-sectional cut in shank top beam (densities between 0.1-1 shown)

As can be seen from ﬁgure 11, the industry standard beam shaped shank stands out with two principal load bearing members connecting the small-end to the big-end. Shear forces transmitted between them and support for the big end bearing is provided by the web in the region close to the big-end.

21 Adrian Tosteberg March 13, 2019

Reinforcements around the outer extremities of the bearings counter the deformation of the bearing races, unloading them by providing rigid backing.

It should be noted that the three clover leaf like shape around the big end is combined result of the discretized and few number of load step samples, with the approximated component separated transverse and longitudinal load introduction method. They are therefore non physical, and should feature even round shape around the whole big-end section until they merge with the shank on both sides.

6.5 Load Path Analysis Within the optimised structure, the element major and minor stresses are plotted in tensor format, to reveal the load paths.

Some telling features stand out from the load path analysis, for example how ﬁbers should be oriented to best cope with stresses in the various sections of the connecting rod.

Figure 12: Major and minor loads in big end during load-case 1: compression

In the regions of load introduction close to the big end bearing, where normal forces are introduced in the structure, the tensors are generally observed to be oriented normal to the bearing surface. In the rest of the bearing, the loads are oriented along the surface because of deformation driven ovalization of the bushing, see ﬁgure 12. This region is therefore well suited to a metallic insert because of the variation in load directions.

Further away from the bearings, in the clover “leafs”, the load paths are clearly aligned with the bearing surface, making the ideal case for strongly anisotropic composite material.

22 Adrian Tosteberg March 13, 2019

Figure 13: Major and minor loads in shank section during load-case 3

The load paths are very telling throughout the load-cases in the shank section. The two main beams are oriented with the major and minor loads, see figure 13. The final design should therefore strive to orient fiber layers along the pathways. Between the beams, loads are smaller and oriented normal to the beams.

In the small end, the loading state can be observed from ﬁgure 14 below:

Figure 14: Major and minor loads in small-end during load-case 4: inertial

In the small end, the loads continue from the shank beams to surround the small end. These conditions are favourable for continuous plies with ﬁber oriented along the load-paths.

Similarly to the big-end, the region closest to the bearing surface will experience rotating internal stressing normal to the surface where external loads are introduced. This region is well suited for isotropic material.

23 Adrian Tosteberg March 13, 2019

6.6 Thick Laminate Modelling For optimisation of thick composite geometries, two laminate modelling strategies were evaluated. The ﬁrst was based on the idea of creating tie contacts between layers. In eﬀect, the nodes of the slave surface are normal projected to a neighbouring master surface, and then linked to the nodes closest to its projection.

A model consisting of ten one millimeter thick composite elements (PCOMPG) were compared to a 10 mm thick PCOMPG element with 10 tied internal 1mm plies, both with identical layup of [90, −45, 0, 45, 0]S.

While the shell tie method yielded acceptable in plane deformation with 2% over-stiffening, and 7% increase in peak stress for the stacked test coupons compared to a single PCOMPG element with 10 plies, the out of plane over-stiffening effect was dramatic. The out of plane deformation over stiffening of 47% (or reduction in peak displacement) while the peak stress are reduced by 13%. The lack of tunability of this model made it largely unsuitable for further geometry scaling or complex loading scenarios.

Instead, the same model was used with spring linked nodes, coupling the nodes of each layer to the the equivalent node of the layer on top and below. This yielded much closer fitting results even with “rigidly” defined springs. It should be noted that the solver approximates “rigid” with spring rates in the order of 100 MN/mm in DOFs x, y and z. Zero stiffness was defined in the three rotational spring DOFs to allow for intra-laminar shear. A comparative displacement analysis showed 0.6% and 3% difference in displacement for in plane loading and out of plane loading respectively (figure 24). Concerning the stress distribution, ply-by-ply analysis revealed almost identical stress states, see figure 15 for out of plane, or appendix figure 25 for in plane stress state.

(a) Single stacked PCOMPG element (b) 10 node linked stacked PCOMPG elements

Figure 15: Stress distribution comparison in the top ply of the multi ply element model against the stacked single ply model during out of plane loading

This indicates that the spring linked model has potential to be scaled to complex geometries and loading conditions, with eventual tuning of the spring constants towards a homogeneous model to improve accuracy.

Thus, a solid modelled connecting rod with isotropic material property was built, and spring rates tuned accordingly, before material anisotropy could be introduced and optimisation begun.

First of, it was noticed that rotational spring rate aﬀected displacement continuity and convergence,

24 Adrian Tosteberg March 13, 2019 see ﬁgure 16 below:

(b) shell modeled with rigid rota- (a) solid modelled (c) shell modeled with zero rotational DOFs tional stiﬀness

Figure 16: Displacement distribution comparison of solid model, shell modeled with rigid rotational DOFs, shell modeled with zero rotational stiﬀness

It should be noted that computationally, the rotationally rigid springs analysis as seen in figure 16b took thirty times less CPU-hours to compute. Furthermore, there is less displacement dis- continuity on both sides of core as well as closer fitting displacement amplitudes. Rigid rotational spring stiffnesses are thus preferred in this case.

Spring rate tuning in x, y and z directions established that 1e8 N/mm produced a reasonable trade-off in displacement and stresses across the various load-cases. It should be noted that variation in results was higher for the complex geometry and loading conditions. The difference in displacement was close to 15% for all load cases while the peak stress difference between 9% up to 48% for the tensile case.

25 Adrian Tosteberg March 13, 2019

(a) Solid model (b) Shell model

Figure 17: Stress distribution comparison in the solid isotropic connecting rod against the isotropic stacked laminate model during the most crucial phase: combustion

While stress incongruity in ﬁgure 17 is signiﬁcant, the models show similar stress distributions and deformation behavior and are therefore still useful for optimisation purposes. A large safety margin should however be used when extracting peak stress values from the stacked laminate approach, because of the uncertainty in local absolute values.

6.7 Composite Optimisation Because of the way the optimisation algorithms are written, and the laws that govern how their design variables are varied, one should be careful when selecting the optimisation objective. The physical purpose of the optimisation was decided to minimize failure risks during testing. In this context, ultimate strength and fatigue induced delamination are the two main concerns. In both cases, the stress amplitudes are the main driving variable and should be minimized. Three different composite optimisation schemes for keeping down stresses were evaluated. The first method is an indirect method of keeping down stresses. In composite optimisation problems, strength and stiffness are orthotropic and and strongly dependent one upon the other. The classical and robust optimisation objective is compliance minimization, where the strain energy throughout the structure is minimized. The energy being proportional to the deformation in equation (7) seen previously, is minimized by stiffening the whole structure. In practice, this will result in aligning most amounts of fibers with the main loading directions, fibers being much stiffer and stronger than their surrounding matrix. Thus, when a stiffness optimised part is loaded, most loads are directed through the fibers yielding high ultimate strength. The second attempted method is one of introducing soft constraints. On the contrary to hard optimisation constraints, which must definitely be true for convergence to a feasible design, soft optimisation constraints influence the design by providing an optimisation path without shadow- ing the main objective. For the soft optimisation path, weighted compliance was still taken as the objective but stress constraints were set lower than in the “free” optimisation, to attempt to shave the peaks of the local stress maximas. In the third case a hard optimisation was attempted with the objective of directly minimizing peak tensile and compressive stresses.

The results of the optimisations can be compared in terms of biasing of zero layers. In ﬁgure 18 below, the proportion of layers in the 0 direction from the three optimisation methods can be observed.

26 Adrian Tosteberg March 13, 2019

(a) before sizing optimisation (b) scheme 1

Figure 18: Thickness (or proportion) of 0 oriented layers from diﬀerent optimisations setups

(a) before sizing optimisation (b) scheme 1

Figure 19: Stress distribution in optimised designs free size (pre- sizing optimisation), 1, 2, 3

Figure 19 shows that all three optimisation methods converged to diﬀerent solutions, all better than the initial setup, pre-optimised from the free size optimisation. In all instances, the region of peak stresses has been vastly reduced in size and amplitude. However, it is interesting to note some variance in the results: It appears that the method of hard constrained optimisation for stress reduction in composites is the worst out of the three, providing only 25% reduction in peak stress with a large remaining zone

27 Adrian Tosteberg March 13, 2019 above the arbitrarily set 150 MPa homogenized composite stress (ply based Von Mises) threshold for compressive loading. The method of soft constraints worked much better, reducing peak stress with 49% which is the most of all methods, and vastly reducing the zone of peak stresses. The indirect classical method of weighted compliance yielded only a non signiﬁcantly higher peak stress, while achieving the smallest high stress zone out of all methods. In this case, even stress distribution takes the priority, making this the best suited option.

The source of the difference in results lie in the way the optimisation is performed. During compliance optimisation, the state of deformation directly determines the compliance and thus the behavior of the next iteration can be efficiently predicted. In the case of varying design variables affecting stiffness to achieve a variation in stress, the deformation must first be calculated and the stress state can then eventually be estimated from node interpolation rendering the task more complex. Furthermore, a core difference is that the stress minimization analysis only drives the design according to the few elements with highest stress state at that particular iteration. It is possible, that after a certain number of iterations these elements are no longer the most stressed, and so the algorithm leaves them to optimise the structure locally at the new highest stress peak. Not only does this produce slower progress, but it can also hinder convergence. If stress relaxation in one region leads to the growth of another local stress maxima, focus may jump back and forth making the optimisation unstable and stagnate before ideal global state has been reached. Compliance on the other hand is a global tool taking into account all elements deformation and stiffness while modifying its design variable, proving to be more robust in this instance. Regarding the soft constrained stiffness optimisation, it can be noted that a lower peak stress was indeed achieved, but at the cost of stressing a significant neighbouring region increasing in this way the failure area. Because of the discrete way the load-steps were extracted from a continuous load variation, it is possible that a stress state intermediary to the extracted load steps would concentrate further in this region, making it less safe because of its narrowly driven design.

6.8 Manufacturing The main prototype focus being generating a safe design, with low cyclic peak stresses capable of inducing delamination, kink-bands or ﬁber failure, occupation of the full workspace volume was deemed preferable. It should be noted that various designs of carbon ﬁber connecting rods have been attempted for the odd last 30 years, almost like the impossible quest for the holy grail of composites specialists and engine builders. Most of the time, failure to adapt the design for any kind of production scales or skyrocketing manufacturing costs have been their demise. The manufacturing method explored in this paper is still expensive compared to traditional forged or single piece milled connecting rods, however it is reasonably adapted for small scale production.

6.8.1 Core and Inserts Three design alternatives stand out from the manufacturing method selection process and core material analysis. It is unlikely that a scrap optimised milling layout can be achieved with a core milled in one piece. However, for a ﬁrst prototype, whole core elements could be milled directly out of a block of titanium for simplicity. Alternative manufacturing methods would be a split design, with either a thin or thick shank section split from the lathed bushing ends, depending on how crucial ﬁber bend radii appear during testing.

28 Adrian Tosteberg March 13, 2019

(a) Core and inserts (b) Hybrid rod assembled

Figure 20: Sectioned core and custom inserts (not updated with latest render)

The thin core option seen in ﬁgure 20 with hourglass design can be milled out of a prefabricated 22x100x(Nx6)mm pre-cured sheet of carbon ﬁbre or milled out of titanium or steel. If the strong radius bends reveal problematic during testing, a thicker core option can be explored. An oval rod of (22xN)x30x100 is rolled with cf prepreg, then length is cut up in sections and along major axis to make hour glass halves. Small and big-end bushing interfaces need to be milled out as well as a smooth interface towards the outer reinforcement layers. Alternatively this can also be milled or 3D printed from a titanium alloy.

The small-end bushing is lathed or bought already extruded, either from a titanium or a steel rod. The big-end halves can be milled in a stacked fashion to minimize material loss, starting with the high tolerance inside, and then milling the outer surface where tolerances are less crucial if the part were to move slightly during milling. The next piece’s inside will be milled close to the last milled outside. All metal surfaces facing composites can be prepared for bonding to epoxy, by surface roughening. Making bushings out of titanium will require the additional manufacturing step of TiN or CrN surface deposition to avoid bearing surfaces from galling.

It should be noted that the split design introduces an interface between direct load transfer between the composite on both sides. A low stiffness metal could help distribute compressive loads at this interface, but tensile loads will be carried through the screws, like in a traditional metal rod. The special connecting rod screws are usually tightened to very specific elongation, inducing a static compressive stress in the region of proximity. This can reveal to be an issue during testing, in which case inserts and design will need to be re-imagined to lower the compressive stresses induced in the composite. On the other hand, the compressive state may also have beneficial consequences considering crack closure and limiting crack propagation.

6.8.2 Molds The layup is performed with prepreg stacked around the milled core. Two split mold halves milled out of aluminium or molding steel with low thermal expansion coeﬃcient are pushed together compacting the prepreg. Vacuum lines and dry weaves can be placed to minimize excess resin. The mold is then placed in an oven for curing according to the appropriate temperature curve speciﬁed by the prepreg manufacturer.

Because of the simple geometry of the connecting rod, molds can be directly milled from a piece of solid aluminium without needing to do mold masters beforehand.

29 Adrian Tosteberg March 13, 2019

6.9 Benchmarking The final weight of the concept is the most important benchmark factor. As can be seen from figure 21, the prototype titanium alloy connecting rod is already 10% lighter than the currently in use steel connecting rod, and in both cases the proportion of weight in the load bearing body is high. This means that the potential for improving the split design is low, and that almost all the mass makes up useful load bearing structure. In the three rightmost composite configurations however, the distribution of mass away from the load bearing body, to the inserts and screws required to hold the composite halves together, reveal that significant optimisation and weight saving potential in this part of the connecting-rod remains. Still, considering that the over-dimensioned proof of concept composite rod achieves simulated safety factors higher than the metal counterparts, and that they are already achieving 10% and 15% weight saving compared to the titanium rod, proves the potential for composites in this application.

Figure 21: Chart comparing connecting-rod weights depending on conﬁgurations

Stress wise, the optimised hybrid composite design results in a 25% unloading of bearing races with highest peak stresses in small end during combustion that are down from 270 to 200 MPa. During inertial tensile loading, the internal stresses are higher in the big end bearing, and down 60% from 800 Mpa to 300 MPa.

Figure 22: Displacement of the composite connecting rod against the steel rod

30 Adrian Tosteberg March 13, 2019

Figure 22 above reveal that if testing proves successful, extensive further lightening of the composite connecting rod shank can be performed before longitudinal ﬂex becomes an issue, making an even stronger case for its usefulness. It should be noted that in its lighter titanium core spec, it is multiple times stronger than the current steel counterpart, see ﬁgure 23:

(b) split metal core with steel (c) steel connecting rod (a) optimised composite UD stack bushings/titanium shank

Figure 23: Failure-Ratio benchmark

The composite failure of figure 23a is calculated with the asymmetric and weaker compression limit failure envelope of the Tsai-Wu criterion. Metal failure ratios of figure 23b and 23c calculated as the ratio of Von Mises stress to yield stress. In both cases, lower values represent higher safety factors, with the composite or metal part yielding at the value of 1. Combined with the much higher tensile strength of UD Torax T1000 UD in a DeltaTech DT195N resin, the estimated safety factor is five-fold.

31 Adrian Tosteberg March 13, 2019

7 Conclusion

All in all, this thesis has mapped a smart path through the CAE product development phase of a composite structural part. By using advanced optimisation schemes and analysis, it results in products that have high chances of meeting speciﬁcations and aims to minimize the amount mechanical testing iteration cylces required before converging to a marketable solution. The methods explored in this paper should still be validated and tuned during mechanical testing, and provide detailed insight for redesign when failure occurs. Furthermore, it has pioneered a novel way for practical micro-structure optimisation of thick laminated composites. The “toast stacked laminate” method can lead the way for further applied thick walled or solid geometry optimisation, by providing material orientation and macro-geometry con- trol which is diﬃcult with solid modelling and inaccurate or impossible with shells only. It can be a viable and practical solution to the rapidly growing composites optimisation market with applications such as in aeronautics, automotive, sporting goods and prosthetics.

Specifically, the connecting rod study has explored the assumption that a micro-structure fo- cused optimisation would prevail over pure topology based metal connecting rods. Indeed, the composites optimisation approach has met design criteria, producing a safe prototype ready for manufacturing and first stage testing. It is considerably lighter than its steel counterpart, and depending on core/insert configuration, the beefed up composite part achieves weight figures under both metal rod’s. Considering that it is achieving much higher failure safety factors, and that weight optimisation of the inserts and core has only been touched upon, the potential for a composite connecting rod is confirmed. The manufacturing cost are expected to be higher than for forged steel, with more production steps and more costly base materials. Likely, manufacturing costs are in the ballpark of a milled titanium rod for a smart low series production. However, automatisation and smart manufacturing has the potential to result in much cheaper mass produced parts. Considering the efficiency savings that will accumulate during hours of operation, a composite connecting rod could pay off even purely from an economical perspective. Thus, a solution to a major bottleneck for combustion engine system improvements may be solved. With the potential of reduced inertia, friction and heat generation in the powertrain, a new generation of higher performance and more efficient combustion engines could lie around the corner. A thorough prototype testing programme, with efficient simulation based design iterations, is believed to be the way forward from here.

32 Adrian Tosteberg March 13, 2019

8 Appendix

Figure 24: Comparison of the out of plane deformation of a 10 ply pcompg coupon with surface tied stack of 10 pcompg elements

Figure 25: Comparing the max ply stress of a 10 ply pcompg coupon with surface tied stack of 10 pcompg elements (in plane deformation)

33 Adrian Tosteberg March 13, 2019

References

[1] Chapman, Colin. “Lotus Philosophy.” Lotus Philosophy | Lotus Cars, www.lotuscars.com/about-us/lotus-philosophy [2] Taware, Ravira Y, and Abhay A Utpat. “Analysis of Connecting Rod Used in Two Wheeler under Static Loading by FEA.” International Journal of Engineering Trends and Technology (IJETT), 20 , no. 1, Feb. 2015, doi:http://www.ijettjournal.org/2015/volume-20/number-1/IJETT-V20P207.pdf [3] Johansen, L., and E. Lund. “Optimisation of Laminated Composite Structures Using Delami- nation Criteria and Hierarchical Models.” Struct Multidisc Optim, vol. 38, no. 4, May 2009, pp. 357–375., doi:https://doi.org/10.1007/s00158-008-0280-1. [4] “Mindlin–Reissner Plate Theory.” Wikipedia, Wikimedia Foundation, 20 Sept. 2017, en.wikipedia.org/wiki/Mindlin%E2%80%93Reissner_plate_theory. [5] Sjølund, J.h., and E. Lund. “Structural Gradient Based Sizing optimisation of Wind Turbine Blades with Fixed Outer Geometry.” Composite Structures, vol. 203, 1 Nov. 2018, pp. 725–739., doi:10.1016/j.compstruct.2018.07.031. [6] Wisnom, M. R. “The Role of Delamination in Failure of Fibre-Reinforced Composites.” Philo- sophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol. 370, no. 1965, 2012, pp. 1850–1870., doi:10.1098/rsta.2011.0441. [7] Furuhama, Shoshi, et al. Temperature Measurement of the Connecting Rod, Piston Pin and Crankpin Bearing If an Automobile Gasoline engine. 33rd ed., vol. 9, 1996, pp. 181–189, Tem- perature Measurement of the Connecting Rod, Piston Pin and Crankpin Bearing of an Auto- mobile Gasoline engine. https://www.jstage.jst.go.jp/article/jsme1958/9/33/9_33_181/_pdf/-char/en [8] Atkins, K.e., et al. A Discussion of the Various Loads Used to Rate Reciprocating Compressors. http://www.engdyn.com/images/uploads/95-rod_load_paper_(kea).pdf [9] Kane, Jack, and EPI Inc. “Piston Motion Basics.” Power and Torque: Understanding the Relationship Between the Two, by EPI Inc., www.epi-eng.com/piston_engine_technology/ piston_motion_basics.htm. [10] “Piston Motion Equations.” Wikipedia, Wikimedia Foundation, 10 Aug. 2018, en.wikipedia. org/wiki/Piston_motion_equations [11] Chen, Wei, et al. “An Aﬀordable Approach for Robust Design of Thick Laminated Composite Structure.” optimisation and Engineering, vol. 1, no. 3, 2000, pp. 305–322., doi:10.1023/a:1010078107194. [12] Mahishi, Jayant M. “An Integrated Micromechanical and Macromechanical Approach to Frac- ture Behavior of Fiber-Reinforced Composites.” Engineering Fracture Mechanics, vol. 25, no. 2, 1986, pp. 197–228., doi:10.1016/0013-7944(86)90218-3. [13] Lu, Jianan, and Yonghua Chen. “Performance Evaluation of Particle Swarm Optimization and Solid Isotropic Material with Penalization in Topology Optimization.” 2012 IEEE International Conference on Computational Intelligence for Measurement Systems and Applications (CIMSA) Proceedings, IEEE, 2 July 2012, doi:10.1109/CIMSA.2012.6269594 [14] Goutianos, Stergios. “Compressive behaviour of carbon-ﬁbre polymer composite materials.” University of London, 2003. https://www.sems.qmul.ac.uk/research/honours/doc.php?id=199 [15] HyperWorks documentation https://altairhyperworks.com/hwhelp/Altair/2017/help/hm/hwsolvers.htm?results_ output_by_optistruct.htm

34 Adrian Tosteberg March 13, 2019

[16] Oliva, Marc. “Rear Cross Frame Re-Design and Optimization in Carbon Fiber.” LTH, 2014. https://upcommons.upc.edu/bitstream/handle/2099.1/24276/Oliva_Marc_Master_ Thesis.pdf