RESEARCH ARTICLE

Coordinated shift control of nonsynchronizer transmission for electric vehicles based on dynamic tooth alignment

  • Xiaotong XU ,
  • Yutao LUO ,
  • Xue HAO
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  • School of Mechanical and Automotive Engineering, South China University of Technology, Guangzhou 510641, China; Guangdong Provincial Key Laboratory of Automotive Engineering, Guangzhou 510641, China

Received date: 16 Apr 2021

Accepted date: 27 Jul 2021

Published date: 15 Dec 2021

Copyright

2021 Higher Education Press 2021.

Abstract

Multispeed transmissions can enhance the dynamics and economic performance of electric vehicles (EVs), but the coordinated control of the drive motor and gear shift mechanism during gear shifting is still a difficult challenge because gear shifting may cause discomfort to the occupants. To improve the swiftness of gear shifting, this paper proposes a coordinated shift control method based on the dynamic tooth alignment (DTA) algorithm for nonsynchronizer automated mechanical transmissions (NSAMTs) of EVs. After the speed difference between the sleeve (SL) and target dog gear is reduced to a certain value by speed synchronization, angle synchronization is adopted to synchronize the SL quickly to the target tooth slot’s angular position predicted by the DTA. A two-speed planetary NSAMT is taken as an example to carry out comparative simulations and bench experiments. Results show that gear shifting duration and maximum jerk are reduced under the shift control with the proposed method, which proves the effectiveness of the proposed coordinated shift control method with DTA.

Cite this article

Xiaotong XU , Yutao LUO , Xue HAO . Coordinated shift control of nonsynchronizer transmission for electric vehicles based on dynamic tooth alignment[J]. Frontiers of Mechanical Engineering, 2021 , 16(4) : 887 -900 . DOI: 10.1007/s11465-021-0653-3

Nomenclature

Abbreviations
AMT Automated mechanical transmission
CLAMT Clutchless automated mechanical transmission
DG Dog gear
DG1 Dog gear of the first gear
DG2 Dog gear of the second gear
DM Drive motor
DTA Dynamic tooth alignment
EV Electric vehicle
LM Load motor
NSAMT Nonsynchronizer automated mechanical transmission
PC Planet carrier
PID Proportion integration differentiation
PLCD Permanent linear contactless displacement
PMSM Permanent magnet synchronous motor
RG Ring gear
SG Sun gear
SL Sleeve
Variables
Acar Frontal area of vehicle, m2
A Coefficient matrix of the state vector
Ad Discretization matrix of A
Bu Coefficient matrix of the input vector
Bud Discretization matrix of Bu
Bw Coefficient matrix of the disturbance vector
Bwd Discretization matrix of Bw
cc Viscous damping coefficient of the planet carrier, N∙m·(rad/s)−1
cp Viscous damping coefficient of the planet gear, N∙m·(rad/s)−1
cr Viscous damping coefficient of the ring gear, N∙m·(rad/s)−1
cs Viscous damping coefficient of the sun gear, N∙m·(rad/s)−1
cslv Viscous damping coefficient during the axial movement of the sleeve, N·(m/s)−1
CD Aerodynamic drag coefficient
C Damping matrix
Cςi Feature matrix of the ith gear
Cς1 Feature matrix of the first gear
Cς2 Feature matrix of the second gear
f Coefficient of rolling resistance
ffloor() Downward rounding function
fceil() Upward rounding function
Fsftmax Maximum shift force, N
Fslv Axial combined force exerted on the sleeve
g Gravity coefficient, m/s2
Gcur Current gear
GP Gear phase
Gtgt Target gear
hca Distance between the tooth tip of the sleeve and the tooth tip of the dog gear in the neutral gear, m
hdog Tooth height of the dog gear, m
hfd Axial distance between the tooth tip of the dog gear and the maximum-width place of its tooth, m
HL Distance between point B and the tooth tip of SL in the neutral gear, m
i0 Final ratio
itgt Ratio of the target gear
j Vehicle jerk, m/s3
Jce Inertia of the planet carrier, kg·m2
Jp Inertia of planet gear, kg·m2
Jre Inertia of the ring gear, kg·m2
Jse Inertia of the sun gear, kg·m2
J Inertia matrix
k Discrete time
ken Time of starting engagement
l0 Past trajectory of point A2
l1 Original estimated trajectory of point A2
l2 New estimated trajectory of point A2 after adjustment
mcar Vehicle mass, kg
mslv Mass of the sleeve, kg
N Number of planetary gears
n Rotation speed, r/min
ns Rotation speed of the sun gear, r/min
nr Rotation speed of the ring gear, r/min
nc Rotation speed of the planet carrier, r/min
Rw Wheel rolling radius, m
t Continuous time, s
tAB Time of the process from point A to point B, s
Tc External torques of the planet carrier, N∙m
Tend Torque output of the drive motor at the end of the gear shifting, N∙m
TLM Torque output of the load motor, N∙m
Tm Torque output of the drive motor, N∙m
Tmax Maximum torque of the drive motor in full speed range, N∙m
Tmmax Maximum torque of the drive motor with the current speed, N∙m
Tmp Average torque of the drive motor, N∙m
Tmref Reference torque of the drive motor, N∙m
Tr External torques of the ring gear, N∙m
Ts External torques of the sun gear, N∙m
ua Vehicle velocity, km/h
u Input vector of the system
v Vehicle velocity, m/s
vslv Axial moving speed of the sleeve, m/s
w Disturbance vector of the system
Wdog Maximum tooth width of the dog gear, m
x State vector of the system
xslv Axial moving displacement of the sleeve, m
xslvref Reference displacement of the sleeve, m
xslv,A Axial moving displacement of the sleeve at point A, m
xslv,B Axial moving displacement of the sleeve at point B, m
yς Output vector of the system
zdog Number of teeth of the dog gear
α Road slope, rad
βdog Tooth face chamfer angle of the dog gear, (° )
γdog Tooth side chamfer angle of the dog gear, (° )
δcar Inertia coefficient of vehicle
δxslv Change of xslv in a sampling period, m
δωΔ Change of Δω in a sampling period, rad/s
δθΔ Change of Δθ in a sampling period, rad
θDG2 Rotation angle of the dog gear of the second gear, rad
θdog Rotation angle corresponding to one tooth pitch of the target dog gear, rad
θr Rotation angle of the ring gear, rad
θs Rotation angle of the sun gear, rad
θslv Rotation angle of the sleeve, rad
θΔd Dynamic-predicted target angle difference between the sleeve and the target dog gear, rad
τ Correction factor of predicted torque
λ Characteristic parameter of the planetary mechanism
χ Time scaling coefficient
ω Rotation speed, rad/s
ωend Speed of the drive motor at the end of the gear shifting, rad/s
ωm Speed of the drive motor, rad/s
ωs Rotation speed of the sun gear, rad/s
ωr Rotation speed of the ring gear, rad/s
ωc Rotation speed of the planet carrier, rad/s
Δn Rotation speed difference between the sleeve and the target dog gear, rpm
Δω Rotation speed difference between the sleeve and the target dog gear, rad/s
Δωref Reference rotation speed difference between the sleeve and the target dog gear, rad/s
Δθ Rotation angle difference between the sleeve and the target dog gear, rad
Δθref Reference rotation angle difference between the sleeve and the target dog gear, rad
ΔθEP Angle threshold of the engagement point, rad
ΔθΣ Total change of the rotation angle difference, rad

Acknowledgements

This work was supported by the Science and Technology Planning Project of Guangdong Province, China (Grant Nos. 2015B010119002 and 2016B010132001).
1
Ahssan M R, Ektesabi M M, Gorji S A. Electric vehicle with multi-speed transmission: a review on performances and complexities. SAE International Journal of Alternative Powertrains, 2018, 7( 2): 169– 181

DOI

2
Roozegar M, Angeles J. A two-phase control algorithm for gear-shifting in a novel multi-speed transmission for electric vehicles. Mechanical Systems and Signal Processing, 2018, 104 : 145– 154

DOI

3
Tian Y, Ruan J G, Zhang N. Modelling and control of a novel two-speed transmission for electric vehicles. Mechanism and Machine Theory, 2018, 127 : 13– 32

DOI

4
Fietkau P, Kistner B, Munier J. Virtual powertrain development. Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering, 2020, 234( 14): 3288– 3301

DOI

5
Wang W C, Li J Q, Sun F C. Pseudo-spectral optimisation of smooth shift control strategy for a two-speed transmission for electric vehicles. Vehicle System Dynamics, 2020, 58( 4): 604– 629

DOI

6
Kim S J, Song C, Kim K S. Analysis of the shifting behavior of a novel clutchless geared smart transmission. International Journal of Automotive Technology, 2014, 15( 1): 125– 134

DOI

7
Li L, He K, Wang X Y. Sensor fault-tolerant control for gear-shifting engaging process of automated manual transmission. Mechanical Systems and Signal Processing, 2018, 99 : 790– 804

DOI

8
Yang Y, Wang J S. Synchronous control strategy for electric vehicle based on no clutch shifting. In: Proceedings of the International Conference on Electric Information and Control Engineering. Wuhan: IEEE, 2011, 778– 781

DOI

9
Sun Z Q, Sanada K, Gao B Z. Improved decoupling control for a powershift automatic mechanical transmission employing a model-based PID parameter autotuning method. Actuators, 2020, 9( 3): 54–

DOI

10
Alizadeh H V, Helwa M K, Boulet B. Constrained control of the synchromesh operating state in an electric vehicle’s clutchless automated manual transmission. In: Proceedings of the IEEE Conference on Control Applications. Nice: IEEE, 2014, 623– 628

DOI

11
Tseng C Y, Yu C H. Advanced shifting control of synchronizer mechanisms for clutchless automatic manual transmission in an electric vehicle. Mechanism and Machine Theory, 2015, 84 : 37– 56

DOI

12
Dong X Y, Xi J Q, Chen H Y. The power system active-synchronizing control of the PHEV during the AMT shifting process. Applied Mechanics and Materials, 2011, 80–81: 2011–1159

13
Mo W W, Wu J L, Walker P D. Shift characteristics of a bilateral Harpoon-shift synchronizer for electric vehicles equipped with clutchless AMTs. Mechanical Systems and Signal Processing, 2021, 148 : 107166–

DOI

14
Mo W W, Walker P D, Zhang N. Dynamic analysis and control for an electric vehicle with harpoon-shift synchronizer. Mechanism and Machine Theory, 2019, 133 : 750– 766

DOI

15
Liu H B, Lei Y L, Li Z J. Gear-shift strategy for a clutchless automated manual transmission in battery electric vehicles. SAE International Journal of Commercial Vehicles, 2012, 5( 1): 57– 62

DOI

16
Alowayed A, Fernandes D, Jeunehomme E. Design of an electric motor transmission system without friction synchronization. In: Proceedings of the International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. Anaheim: ASME, 2019, 1– 10

DOI

17
Wang X Y, Li L, He K. Dual-loop self-learning fuzzy control for AMT gear engagement: design and experiment. IEEE Transactions on Fuzzy Systems, 2018, 26( 4): 1813– 1822

DOI

18
Zhang J W, Chai B B, Lu X Y. Active oscillation control of electric vehicles with two-speed transmission considering nonlinear backlash. Proceedings of the Institution of Mechanical Engineers, Part K: Journal of Multi-body Dynamics, 2020, 234( 1): 116– 133

DOI

19
Huang W, Zhang J L, Huang J F. Optimal speed regulation control of the hybrid dual clutch transmission shift process. World Electric Vehicle Journal, 2020, 11( 1): 11–

DOI

20
Zhu X Y, Zhang H, Xi J Q. Optimal speed synchronization control for clutchless AMT systems in electric vehicles with preview actions. In: Proceedings of the American Control Conference. Portland: IEEE; 2014, 4611– 4616

21
Zhu X Y, Zhang H, Fang Z D. Speed synchronization control for integrated automotive motor–transmission powertrain system with random delays. Mechanical Systems and Signal Processing, 2015, 64–65: 46– 57

22
Chen Z Q, Zhang B J, Zhang N. Optimal preview position control for shifting actuators of automated manual transmission. Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering, 2019, 233( 2): 440– 452

DOI

23
Chen H X, Tian G Y. Modeling and analysis of engaging process of automated mechanical transmissions. Multibody System Dynamics, 2016, 37(4): 345– 369

24
Tian F, Wang L J, Sui L Q. Active synchronizing control of transmission shifting without a synchronizer for electric vehicles. Journal of Tsinghua University (Science and Technology), 2020, 60( 2): 101– 108

DOI

25
Setiawan Y D, Roozegar M, Zou T. A mathematical model of multispeed transmissions in electric vehicles in the presence of gear shifting. IEEE Transactions on Vehicular Technology, 2018, 67( 1): 397– 408

DOI

26
Mousavi M S R, Pakniyat A, Helwa M K. Observer-based backstepping controller design for gear shift control of a seamless clutchless two-speed transmission for electric vehicles. In: Proceedings of the 12th IEEE Vehicle Power and Propulsion Conference (VPPC). Montreal: IEEE, 2015

27
Chaari F, Abbes M S, Rueda F V. Analysis of planetary gear transmission in non-stationary operations. Frontiers of Mechanical Engineering, 2013, 8( 1): 88– 94

DOI

28
Tian Y, Yang H T, Mo W W. Optimal coordinating gearshift control of a two-speed transmission for battery electric vehicles. Mechanical Systems and Signal Processing, 2020, 136( 1): 106521–

DOI

29
Tian Y, Zhang N, Zhou S L. Model and gear shifting control of a novel two-speed transmission for battery electric vehicles. Mechanism and Machine Theory, 2020, 152( 2): 103902–

DOI

30
Walker P, Zhu B, Zhang N. Powertrain dynamics and control of a two speed dual clutch transmission for electric vehicles. Mechanical Systems and Signal Processing, 2017, 85 : 1– 15

DOI

31
Roozegar M, Angeles J. Gear-shifting in a novel modular multi-speed transmission for electric vehicles using linear quadratic integral control. Mechanism and Machine Theory, 2018, 128 : 359– 367

DOI

32
Fang S N, Song J, Song H J. Design and control of a novel two-speed uninterrupted mechanical transmission for electric vehicles. Mechanical Systems and Signal Processing, 2016, 75 : 473– 493

DOI

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