Design of a high-speed transmission for an electric vehicle Carlos Daniel Pires Rodrigues Dissertation submitted to Faculdade de Engenharia da Universidade Porto for the degree of: Mestre em Engenharia Mecânica Advisor: Prof Jorge Humberto Oliveira Seabra Co-Advisor: Prof José Antúnio dos Santos Almacinha Unidade de Tribologia, Vibraỗừes e Manutenỗóo Industrial Departamento de Engenharia Mecânica Faculdade de Engenharia da Universidade Porto Porto, Julho de 2018 The work presented in this dissertation was performed at the Tribology, Vibrations and Industrial Management Unit Department of Mechanical Engineering Faculty of Engineering University of Porto Porto, Portugal Carlos Daniel Pires Rodrigues E-mail: up201305002@fe.up.pt, cdpr@outlook.com Faculdade de Engenharia da Universidade Porto Departamento de Engenharia Mecõnica Unidade de Tribologia, Vibraỗừes e Manutenỗóo Industrial Rua Dr Roberto Frias s/n, Sala M206 4200-465 Porto Portugal Abstract For decades, the hegemony of internal combustion vehicles has led to an improvement, by the automotive industry, of transmissions, in order to increase the torque and reduce the rotational speed from the engine These transmissions are quite complex, having up to speeds, with the aim of retrieving the highest possible efficiency from the considerably inefficient internal combustion engines Nowadays, environmental concerns and strong governmental regulations, as well as, buying incentives, have presented electric vehicles as a viable solution to consumers while being in line with the new global paradigm of sustainability Electric vehicles turn to electric motors to transform electric energy in mechanical energy Since these motors are widely used in other industrial applications, they are already a mature technology They have an ideal torque and power curves regarding vehicle operation Due to these favourable characteristics, the transmission of an electric vehicle is simpler, presenting itself as a conventional reducer with respect to the overall geometry, having usually only one speed ratio between the input and the output However, the high rotational speed associated with compact electric motors, makes it necessary to take some factors into account when designing a transmission: gear design, lubrication method selection, as well as rolling bearing selection are just some of the concerns that will be further elaborated in this thesis, in order to reduce power losses, ensuring a good efficiency and, at the same time, control the noise generated The mechanical differential, which is present in all internal combustion vehicles, is a system that provides the vehicle with the capacity to change direction steadily, however it cannot be continually controlled Thus, the idea of using an electronic differential seems interesting, since it would reduce the number of mechanical components and, through the ever-increasing network of sensors and data acquired by the vehicles themselves, it is possible to independently control the rotational speed of each front wheel continuously, leading to greater safety and comfort when the vehicle is changing direction Keywords: lubrication electric vehicles, transmission, gears, electronic differential, splash i Resumo Durante largas décadas, a hegemonia dos veículos de combustão interna levou a um aperfeiỗoamento por parte da indỳstria automúvel das transmissừes para aumentar o binário e reduzir a velocidade provenientes motor Estas transmissões são bastante complexas, podendo ter até velocidades, de forma a extrair o mais rendimento possível dos pouco eficientes motores de combustóo interna Atualmente, preocupaỗừes ambienteais e fortes regulaỗừes governementais, bem como, elevados incentivos de compra, tornaram os veículos elộtricos como uma soluỗóo viỏvel para os consumidores e que vai de encontro ao novo paradigma mundial de sustentabilidade Os veículos elétricos recorrem a motores elétricos para transformar a energia elétrica em energia mecânica Uma vez que estes motores são amplamente utilizados em outras aplicaỗừes industriais, jỏ se apresentam como uma tecnologia madura Eles possuem uma curva de binário e de potència ideal para os automóveis Devido a estas características favoráveis, a transmissão de um veículo elétrico é mais simples, apresentando-se como um redutor convencional em termos geométricos, tendo apenas uma razão de velocidades entre a entrada e a saída Porộm, a elevada velocidade de rotaỗóo associada aos motores elộtricos compactos, leva a que sejam necessỏrios cuidados na concepỗóo da transmissóo: desenvolvimento das engrenagens, escolha mộtodo de lubrificaỗóo ideal e escolha dos rolamentos são apenas algumas das questões que seróo aprofundadas nesta dissertaỗóo, de forma a que as perdas de potência sejam reduzidas, garantindo uma boa efficiência e, ao mesmo tempo, controlar o ruído gerado O diferencial mecânico, presente em todos os veículos de combustão interna, é um sistema que proporciona a capacidade para um veículo curvar de forma correta, mas que não é possível regular enquanto veículo está em movimento Assim, surgiu a ideia de usar um diferencial eletrónico, reduzindo o número de componentes mecânicos e, através da cada vez mais elevada rede de sensores e informaỗóo adquirida pelos próprios vculos, seja possível realizar um controlo independente e continuado das velocidades de rotaỗóo das duas rodas da frente, levando a uma maior seguranỗa e conforto quando o veớculo estỏ a mudar de direỗóo iii Nús somos o que fazemos O que não se faz não existe.’ Padre António Vieira v Acknowledgements I would like to thank my thesis advisor Prof Jorge Seabra and co-advisor Prof José Almacinha of the Faculty of Engineering at University of Porto They consistently allowed this thesis to be my own work and steered me in the right direction providing guidance and support, as well as recommendations and several revisions throughout the semester I would also like to thank all my friends which provide a very pleasant environment to evade, for short periods of time, the work atmosphere Finally, I give my warmest thanks to my family, in particular to my parents, for the continuous encouragement and everything that they have provided me along the years, and whose support after all is the most essential vii Safety against incipient crack Required safety Result (%) Cross section 'C-C Smooth shaft' Comment Position (Y-Coordinate) (mm) External diameter (mm) Inner diameter (mm) Notch effect Mean roughness (µm) [S] [Smin] [S/Smin] 12.777 1.200 1064.8 Smooth shaft [y] [da] [di] 34.000 30.000 0.000 Smooth shaft 8.000 [Rz] Tension/Compression Bending Torsion Shearing Load: (N) (Nm) Mean value [Fzdm, Mbm, Tm, Fqm] 0.0 0.0 99.4 0.0 Amplitude [Fzda, Mba, Ta, Fqa] 0.0 0.0 99.4 2.3 Maximum value [Fzdmax, Mbmax, Tmax, Fqmax] 0.0 0.1 337.8 Cross section, moment of resistance: (mm²) [A, Wb, Wt, A] 706.9 2650.7 5301.4 706.9 Stresses: (N/mm²) [σzdm, σbm, τm, τqm] (N/mm²) [σzda, σba, τa, τqa] (N/mm²) [σzdmax,σbmax,τmax,τqmax] (N/mm²) Technological size influence 0.000 0.000 0.000 [K1(σB)] [K1(σS)] 0.000 0.015 0.026 18.743 18.743 63.726 0.842 0.842 Tension/Compression Bending Torsion Notch effect coefficient Geometrical size influence Influence coefficient surface roughness Surface stabilization factor Total influence coefficient [ß] [K2(d)] [KF] [KV] [K] Present safety for endurance limit: Equivalent mean stress (N/mm²) Equivalent mean stress (N/mm²) [σmV] [τmV] Fatigue limit of part (N/mm²) [σWK] Influence coefficient of mean stress sensitivity [ψσK] Permissible amplitude (N/mm²) [σADK] Permissible amplitude (N/mm²) [σANK] Effective Miner sum [DM] Load spectrum factor [fKoll] Safety against fatigue [S] Required safety against fatigue [Smin] Result (%) [S/Smin] Present safety for proof against exceed of yield point: Static notch sensitivity factor Increase coefficient Yield stress of part (N/mm²) Safety yield stress Required safety Result (%) [K2F] [γF] [σFK] [S] [Smin] [S/Smin] 1.000 1.000 0.860 1.000 1.162 1.000 0.907 0.920 1.000 1.189 32.464 18.743 347.567 399.414 254.774 0.208 0.022 0.022 0.300 1.000 0.246 0.334 0.334 0.300 1.000 9.855 1.200 821.3 0.144 206.535 206.535 0.300 1.000 1.000 1.000 715.457 1.000 1.000 715.457 6.482 1.200 540.2 1.000 1.000 413.069 Present safety for proof of avoiding incipient crack on hard surface layers: Safety against incipient crack [S] Required safety [Smin] Result (%) [S/Smin] Cross section 'D-D Shoulder' 1.000 0.907 0.860 1.000 1.264 Shoulder 17/19 295 36.085 1.200 3007.1 0.000 0.004 0.007 3.9 D Shaft calculation KISSsoft report Comment Position (Y-Coordinate) (mm) External diameter (mm) Inner diameter (mm) Notch effect [D, r, t] (mm) Mean roughness (µm) Y= 58.00mm [y] [da] [di] 45.000 58.000 35.000 0.000 0.100 [Rz] Shoulder 5.000 8.000 Tension/Compression Bending Torsion Shearing Load: (N) (Nm) Mean value [Fzdm, Mbm, Tm, Fqm] 0.0 0.0 99.4 0.0 Amplitude [Fzda, Mba, Ta, Fqa] 0.0 0.1 99.4 4.0 Maximum value [Fzdmax, Mbmax, Tmax, Fqmax] 0.0 0.2 337.8 Cross section, moment of resistance: (mm²) [A, Wb, Wt, A] 962.1 4209.2 8418.5 962.1 Stresses: (N/mm²) [σzdm, σbm, τm, τqm] (N/mm²) [σzda, σba, τa, τqa] (N/mm²) [σzdmax,σbmax,τmax,τqmax] (N/mm²) Technological size influence 0.000 0.000 0.000 [K1(σB)] [K1(σS)] 0.000 0.027 0.047 11.803 11.803 40.131 0.842 0.842 Tension/Compression Bending Torsion Stress concentration factor References stress slope Notch sensitivity factor Notch effect coefficient Geometrical size influence Influence coefficient surface roughness Surface stabilization factor Total influence coefficient [a] [G'] [n] [ß] [K2(d)] [KF] [KV] [K] Present safety for endurance limit: Equivalent mean stress (N/mm²) Equivalent mean stress (N/mm²) [σmV] [τmV] Fatigue limit of part (N/mm²) [σWK] Influence coefficient of mean stress sensitivity [ψσK] Permissible amplitude (N/mm²) [σADK] Permissible amplitude (N/mm²) [σANK] Effective Miner sum [DM] Load spectrum factor [fKoll] Safety against fatigue [S] Required safety against fatigue [Smin] Result (%) [S/Smin] Present safety for proof against exceed of yield point: Static notch sensitivity factor Increase coefficient Yield stress of part (N/mm²) Safety yield stress Required safety Result (%) [K2F] [γF] [σFK] [S] [Smin] [S/Smin] 6.536 23.759 1.973 3.313 1.000 0.860 1.000 3.476 5.666 23.759 1.973 2.873 0.897 0.860 1.000 3.364 3.369 11.500 1.677 2.010 0.897 0.920 1.000 2.327 20.444 11.803 116.236 150.113 130.198 0.061 0.035 0.035 0.300 1.000 0.080 0.956 0.956 0.300 1.000 9.897 1.200 824.8 0.069 121.807 121.807 0.300 1.000 1.000 1.000 715.457 1.000 1.000 715.457 10.293 1.200 857.8 1.000 1.000 413.069 Present safety for proof of avoiding incipient crack on hard surface layers: Safety against incipient crack [S] Required safety [Smin] Result (%) [S/Smin] 16.993 1.200 1416.1 Remarks: - The shearing force is not considered in the analysis specified in DIN 743 - Cross section with interference fit: The notching factor for the light fit case is no longer defined in DIN 743 The values are imported from the FKM-Guideline 18/19 296 0.000 0.006 0.009 6.8 End of Report lines: 19/19 297 788 D Shaft calculation KISSsoft report KISSsoft Release 03/2017 F KISSsoft University license - Universidade Porto File Name : Changed by: shaftCSpeed Carlos Rodrigues on: 02.07.2018 at: 14:51:47 THERMALLY SAFE OPERATING SPEED CALCULATION (according to DIN ISO 15312 and DIN 732) Lubricant Lubrication type: Castrol ATF Dex II Multivehicle Immersion lubrication - Oil level up to the middle of the lower bearing Mean bearing temperature [Tm] 85.000 °C Temperature of bearing environment 75.000 °C 75.000 70.000 °C °C [Tu] [TB] [Tref] Lubricant - service temperature Lubricant temperature - Reference conditions Shaft 'Shaft 1', Rolling bearing 'Rolling bearing': Thermal nominal speed according to DIN ISO 15312: Type of support Bearing number Design series Speed Coefficient Deep groove ball bearing (single row) SKF 6209 62 [n] 1201.300 1/min [f0r] 2.000 (Depends upon type of design and lubrication at reference conditions) Coefficient [f1r] (Depends upon type of design and load at reference conditions) Heat sink reference surface [As] Reference load [P1r] 0.000200 7759.734 1.080 Bearing mean diameter Bearing-specific reference heat flow density kinematic viscosity (for reference conditions) [dm] [qr] [νr] 65.000 16.000 12.000 Thermal nominal speed [nθr] 9306.785 Thermally safe operating speed according to mm kW/m² mm²/s 1/min DIN 732: Coefficient [f0] 4.000 (Depends upon type of design and lubrication) Coefficient [f1] 0.000161 (Depends upon type of design and load) Heat flow (dissipated by the bearing support surface) Total heat flow [ΦS] [Φ] 0.024 0.024 Dynamic equivalent load kinematic viscosity at service temperature [P1] [ν] 695.422 13.108 Lubricant film parameter [KL] 10.948 Charge parameter Speed ratio [KP] [fn] 0.296 0.227 Thermally safe operating speed [nθ] 2113.113 Shaft 'Shaft 1', Rolling bearing 'Rolling bearing': Thermal nominal speed according to mm² kN DIN ISO 15312: 1/2 298 kW kW N mm²/s 1/min Type of support Bearing number Deep groove ball bearing (single row) SKF 6309 Design series Speed 63 [n] 1201.300 Coefficient [f0r] (Depends upon type of design and lubrication at reference conditions) Coefficient [f1r] (Depends upon type of design and load at reference conditions) Heat sink reference surface [As] Reference load [P1r] 1/min 2.300 0.000200 11388.273 1.575 Bearing mean diameter Bearing-specific reference heat flow density kinematic viscosity (for reference conditions) [dm] [qr] [νr] 72.500 16.000 12.000 Thermal nominal speed [nθr] 8850.783 Thermally safe operating speed according to mm² kN mm kW/m² mm²/s 1/min DIN 732: Coefficient (Depends upon type of design and lubrication) Coefficient [f0] 4.600 [f1] 0.000202 (Depends upon type of design and load) Heat flow (dissipated by the bearing support surface) Total heat flow Dynamic equivalent load kinematic viscosity at service temperature Lubricant film parameter [ΦS] [Φ] [P1] [ν] [KL] 0.035 0.035 1589.647 13.108 10.948 Charge parameter Speed ratio Thermally safe operating speed [KP] [fn] [nθ] 0.612 0.218 1928.546 kW kW N mm²/s 1/min The reference conditions for calculating the thermal nominal speed are taken from the DIN ISO 15312 standard End of Report lines: 2/2 299 90 Appendix E Deep groove rolling bearings The following appendix consists of the rolling bearings product sheets from the SKF catalogue A total of six bearings are present in the transmission, two in each shaft, where: • Shaft A - 6205 ETN9 and 6305 ETN9; • Shaft B - x 6308; • Shaft C - 6209 and 6309 301 E Deep groove rolling bearings 6205 ETN9 Dimensions d   25 mm D   52 mm B   15 mm d1 ≈ 33.1 mm D2 ≈ 46.21 mm r 1,2 mm da 30.6 mm Da max 46.4 mm max mm Abutment dimensions Calculation data Basic dynamic load rating C   17.8 kN Basic static load rating C0   9.3 kN Fatigue load limit Pu   0.4 kN Reference speed     28000 r/min Limiting speed     18000 r/min Calculation factor kr   0.025   Calculation factor f0   13   Mass Mass bearing     302 0.12 kg 6305 ETN9 Dimensions d   25 mm D   62 mm B   17 mm d1 ≈ 36.35 mm D1 ≈ 51.62 mm r 1,2 1.1 mm da 32 mm Da max 55 mm max mm Abutment dimensions Calculation data Basic dynamic load rating C   26 kN Basic static load rating C0   13.4 kN Fatigue load limit Pu   0.57 kN Reference speed     24000 r/min Limiting speed     16000 r/min Calculation factor kr   0.03   Calculation factor f0   12   Mass Mass bearing   303   0.22 kg E Deep groove rolling bearings ► 6308 SKF Explorer Dimensions d   40 mm D   90 mm B   23 mm d1 ≈ 56.11 mm D2 ≈ 77.7 mm r 1,2 1.5 mm da 49 mm Da max 81 mm max 1.5 mm Abutment dimensions Calculation data Basic dynamic load rating C   42.3 kN Basic static load rating C0   24 kN Fatigue load limit Pu   1.02 kN Reference speed     17000 r/min Limiting speed     11000 r/min Calculation factor kr   0.03   Calculation factor f0   13.2   Mass Mass bearing     304 0.63 kg ► 6209 SKF Explorer Dimensions d   45 mm D   85 mm B   19 mm d1 ≈ 57.6 mm D2 ≈ 75.19 mm r 1,2 1.1 mm da 52 mm Da max 78 mm max mm Abutment dimensions Calculation data Basic dynamic load rating C   35.1 kN Basic static load rating C0   21.6 kN Fatigue load limit Pu   0.915 kN Reference speed     17000 r/min Limiting speed     11000 r/min Calculation factor kr   0.025   Calculation factor f0   14.2   Mass Mass bearing   305   0.42 kg E Deep groove rolling bearings ► 6309 SKF Explorer Dimensions d   45 mm D   100 mm B   25 mm d1 ≈ 62.18 mm D2 ≈ 86.7 mm r 1,2 1.5 mm da 54 mm Da max 91 mm max 1.5 mm Abutment dimensions Calculation data Basic dynamic load rating C   55.3 kN Basic static load rating C0   31.5 kN Fatigue load limit Pu   1.34 kN Reference speed     15000 r/min Limiting speed     9500 r/min Calculation factor kr   0.03   Calculation factor f0   13   Mass Mass bearing     306 0.83 kg Appendix F Radial shaft seals In this appendix, the product sheets of the radial shaft seals, selected from the SKF catalogue, with the respective specifications are listed The final transmission has two radial shaft seals, one in the input shaft (A) and the other in the output shaft (C), with the following designation: • Input shaft seal - 20x30x7 CRW1 R; • Output shaft seal - 35x47x7 CRW1 R 307 F Radial shaft seals 20x30x7 CRW1 R US stock number     7905 Design     CRW1 Lip material     R Dimensions d1   20 mm D   30 mm b   mm Application and operating conditions Pressure differential   max 0.07 MPa Operating temperature   -40 °C Operating temperature   max 100 °C Operating temperature, short period   max 120 °C Rotational speed   max 17189 r/min Shaft surface speed   max 18 m/s 308 35x47x7 CRW1 R US stock number     13938 Design     CRW1 Lip material     R Dimensions d1   35 mm D   47 mm b   mm Application and operating conditions Pressure differential   max 0.07 MPa Operating temperature   -40 °C Operating temperature   max 100 °C Operating temperature, short period   max 120 °C Rotational speed   max 9822 r/min Shaft surface speed   max 18 m/s 309 ... center of mass Overall transmission height Flange height Gear tooth height First stage transmission ratio Second stage transmission ratio Overall transmission ratio Axial distance between flange and... Manufacturing allowance (gear lead variation) Horizontal static friction Aerodynamic drag, Axial force Grading force Radial force Rolling resistance Tractive force Shearing force X Shearing force... limited available configurations and the aftermarket maintenance is sparse and far economic, for consumers, compared to ICEs Native electric vehicle models have an indisputable advantage compared