Dynamics of Multi-speed Transmissions for Electric Vehicles: Modelling, Analysis and Validation Yuhanes Dedy Setiawan Liauw Department of Mechanical Engineering McGill University Montreal, Canada May 2018 A thesis submitted to McGill University in partial fulfillment of the requirements for the degree of Doctor of Philosophy © 2018 Yuhanes Dedy Setiawan Liauw 2018/05/15 i Abstract Electric vehicles (EVs) are growing in importance One promising technique to improve the performance and efficiency of EVs is the introduction of multi-speed transmissions (MSTs) Multiple speed ratios can maintain the traction motor at the most efficient operation region, especially for medium- and heavy-duty EVs In order to support the optimum design and control of MSTs for EVs, a thorough dynamics analysis is needed However, a complete mathematical model of MSTs for EVs has not yet been developed This model is needed to analyze and optimize the gear-shifting events such that a swift, seamless shifting can be achieved This task is currently conducted by means of simplified dynamics models The work reported here includes the formulation of a detailed model of a novel modular MST for EVs that takes into account discontinuities brought about by backlash and dry friction in the gear pairs The dynamic response of gear-shifting was simulated for validation, the results were verified experimentally on an in-house developed testbed of the novel MST In addition, multi-speed transmissions undergo topology changes during gear-shifting Nevertheless, this important phenomenon has been overlooked in transmission-model formulation, which results in an inaccurate prediction of the dynamic response To fill this gap, a topology-change model was formulated to address the topology change in vehicle transmissions during gear-shifting The velocity jump brought about by topology changes is given due attention A case study is included, whereby the model is implemented in a novel modular MST for EVs Both simulation and experimental tests were conducted for validation A good agreement between simulation and experimental results was achieved, which verifies the pertinence of the model It was concluded that the topology-change model improves the capability of transmission mathematical models in predicting the transmission dynamic response during gear-shifting Furthermore, the transmission model was used in a range-prediction model of EVs with MSTs Most range models are solely available for EVs with fixed gearing Moreover, transmissions are assessed solely with a constant efficiency in EV range-prediction procedures available in the literature A simple and accurate range model for EVs with MSTs is proposed in this dissertation In order to predict the range of EVs with MSTs reliably, the actual transmission efficiency was computed by means of a transmission model A case study aimed at predicting the range of the GM EV1 with a two-speed novel modular transmission is included Moreover, a simulation test with constant transmission efficiency, ii intended to underline the advantages brought about by the actual transmission efficiency in range-prediction, is provided The results indicate that the range of the two-speed GM EV1 simulated with constant transmission efficiency is 7.73% longer than the range of the standard GM EV1 Nevertheless, this number could actually reach up to 13.09% when the range is predicted with the actual efficiency This result was verified by means of the detailed model created in this dissertation that estimated a 12.76% of range improvement In summary, this thesis highlights the advantages of realistic models that lead to a reliable prediction of the transmission efficiency and the range of EVs with MSTs iii R´ esum´ e ´ sont de plus en plus r´epandus Une avenue prometteuse pour Les v´ehicules ´electriques (VE) ´ est l’utilisation des transmissions multi am´eliorer les performances et l’efficacit´e des VE vitesses (TMV) Des rapports de vitesse multiples permettent de maintenir le moteur de traction dans sa zone de fonctionnement le plus efficace, en particulier pour les v´ehicules ´electriques de moyenne et de grande puissance Pour arriver `a une conception et une ´ une analyse dynamique approfondie est commande optimales des TMV destin´ees `a des VE, ´ n’a pas `a ce n´ecessaire Cependant, un mod`ele math´ematique complet des TMV pour VE jour encore ´et´e ´elabor´e Ce mod`ele est n´ecessaire pour analyser et optimiser les changements de vitesse de sorte qu’un changement rapide et continu puisse s’effectuer Cette tˆache est actuellement men´ee `a l’aide de mod`eles dynamiques simplifi´es Le travail pr´esent´e ici aborde la formulation d’un nouveau mod`ele pour les TMV qui prend en compte les discontinuit´es provoqu´ees par des jeux et le frottement sec au niveau des pairs d’engrenages La r´eponse dynamique du changement de vitesse a ´et´e simul´ee pour ˆetre valid´ee, les r´esultats ont ´et´e v´erifi´es exp´erimentalement sur un banc d’essai maison de la nouvelle TMV De plus, les transmissions multi vitesses subissent un changement de topologie lors des changements de vitesse Toutefois, cet important ph´enom`ene a ´et´e n´eglig´e dans les formulations des mod`eles de transmission, se soldant en une pr´ediction inexacte de la r´eponse dynamique Pour r´epondre `a cette probl´ematique, un mod`ele des changements de topologie a ´et´e con¸cu pour pr´evoir ces derniers `a l’int´erieur de la transmission des v´ehicules lors des changements de vitesse Le saut de vitesse caus´e par ces changements a donc re¸cu ainsi l’attention n´ecessaire Une ´etude de cas est incluse, o` u le mod`ele est impl´ement´e sur ´ Des simulations ainsi que des tests exp´erimentaux une nouvelle TMV modulaire pour VE ont ´et´e men´es pour validation Une bonne concordance entre les r´esultats exp´erimentaux et de simulations a ´et´e observ´ee, ce qui confirme la pertinence du mod`ele Il a ´et´e conclu que le mod`ele de changements de topologie am´eliore la capacit´e des mod`eles math´ematiques de transmission de pr´evoir la r´eponse dynamique de cette derni`ere durant les changements de vitesse Finalement, le mod`ele de transmission est utilis´e pour pr´edire les distances pouvant ˆetre ´ munis de TMV Les mod`eles actuels n’existent que pour les v´ehicules parcourues par les VE `a engrenages fixes De plus, au travers de la litt´erature disponible, ces transmissions sont ´evalu´ees en consid´erant seulement un rendement constant en ce qui concerne la pr´ediction iv ´ munis de distances Un mod`ele simple et pr´ecis pouvant servir `a cette fin pour les VE d’une TMV est propos´e dans cette dissertation Pour pouvoir pr´edire avec fiabilit´e la distance pouvant ˆetre parcourue, c’est-`a-dire l’autonomie, le rendement r´eel est calcul´e `a l’aide d’un mod`ele de la transmission Une ´etude de cas portant sur l’autonomie de la GM EV1 avec une nouvelle transmission modulaire `a deux vitesses est incluse De plus, une simulation avec un rendement de transmission constant, effectu´ee pour souligner les avantages de prendre en compte le rendement r´eel dans la pr´ediction d’autonomie, est ´egalement fournie Les tests permettent de conclure que l’autonomie de la GM EV1 `a deux vitesses pr´edite avec un rendement constant est 7,73 % plus ´elev´ee que celle de la GM EV1 standard Cependant, ce nombre pourrait dans les faits atteindre 13,09 % lorsque la distance atteignable est pr´edite avec le rendement r´eel Ce r´esultat a ´et´e v´erifi´e `a l’aide d’un mod`ele d´etaill´e cr´e´e pour cette th`ese qui estime que l’am´elioration de l’autonomie est de l’ordre de 12,76 % Bref, cette th`ese met en lumi`ere les avantages de mod`eles plus ´ munis de r´ealistes qui permettent de mieux pr´edire le rendement et l’autonomie des VE TMV v Acknowledgments I would like to express my most sincere gratitude to all those who helped me during my study and meaningful life in Canada First of all, I would like to give my highest praise to God for all the help and guidance that I have received, to allow me to finish all my research and thesis in the PhD program Second, I would like to express my deepest gratitude to my supervisor, Professor Jorge Angeles, who has helped me significantly in completing my PhD program I really appreciate the kindness and support that he provided to me during my study in his excellent laboratory I would also like to express my sincere gratitude to the members of my thesis committee, Professors Jozsef Kăovecses and Arun Misra, for their helpful comments and suggestions throughout my work Furthermore, I would like to express my profound gratitude to Mehdi Roozegar, Dr Ting Zou and Dr Alexei Morozov for their great help and advice that allowed me to finish my research project and my PhD thesis Last but not least, I would like to express my deepest gratitude to my father, Joeng Ji Liauw, my mother, Erlani Go, my sister, Ciska Yuni Setiawan Liauw and all my relatives for their love, endless prayers, encouragement and support for me not only in completing the PhD program but also in the whole of my life vi vii Contents Introduction 1.1 Background 1.2 Multi-speed Transmissions for Electric Vehicles 1.3 Mathematical Models for Multi-speed Transmissions 1.4 Topology Changes in Multi-speed Transmissions 1.5 Range Model of Electric Vehicles with Multi-speed Transmissions 1.6 Research Plan: Description and Objectives 1.7 Claims of Originality 1.8 Thesis Organization 1 13 14 16 17 18 18 A Novel Modular Multi-speed Transmission 21 2.1 Design Principles 21 2.1.1 The Underdrive Gear Train 28 2.2 Testbed Set-up 32 Formulation of the Mathematical Model 3.1 A Multi-speed Transmission 3.2 Linear Complementarity Problem Formulation 3.3 Backlash Modelling 3.4 Friction Modelling 3.5 Model Parameterization 3.6 Modal Analysis 3.7 Simplified Model 37 38 47 50 51 52 54 54 viii Contents Gear-shifting Analysis 57 4.1 Simulation 57 4.1.1 Gear-shifting Mechanism 57 4.2 Experimental Validation 62 A Topology-change Model 5.1 Model Formulation 5.2 Case Study 5.3 Experimental Work and Simulation 5.3.1 Velocity-jump Calculation 5.4 Model Implementation Range Model of Electric Vehicles with Multi-speed Transmissions 6.1 Range Model Formulation 6.2 Case Study: An Electric Vehicle with a Two-speed Transmission 6.3 Gear-shifting Schedule 6.3.1 Range Simulation 6.4 Transmission Efficiency 6.5 Range Simulation with the Actual Transmission Efficiency 65 65 68 69 70 74 79 79 83 84 85 86 88 Conclusions and Recommendations for Further Research 91 7.1 Conclusions 91 7.2 Recommendations for Future Research 92 A Simulation Parameters 95 96 Simulation Parameters Table A.2: Simulation parameter values Parameter crp1 crp2 csp1 csp2 rc1 rc2 rp1 rp2 rr1 rr2 rs1 rs2 Value 52.931 28.381 30.558 18.971 0.0508 0.0508 0.0239 0.0119 0.0716 0.0597 0.0239 0.0358 Units Ns/m Ns/m Ns/m Ns/m m m m m m m m m Parameter Ip1 Ip2 Ipc1 Ipc2 Ir1 Ir2 Is1 Is2 ksp1 ksp2 krp1 krp2 Value 9.614 × 10−5 5.864 × 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Multi-speed Transmissions for Electric Vehicles 1.3 Mathematical Models for Multi-speed Transmissions 1.4 Topology Changes in Multi-speed Transmissions 1.5 Range Model of Electric. .. concerned with the dynamics of multi-speed transmissions in medium- and heavy-duty electric vehicles, such as trucks and buses Three primary tasks were carried out, namely, the formulation of a comprehensive