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

Xiaotong XU, Yutao LUO, Xue HAO

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PDF(8342 KB)
Front. Mech. Eng. ›› 2021, Vol. 16 ›› Issue (4) : 887-900. DOI: 10.1007/s11465-021-0653-3
RESEARCH ARTICLE

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

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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.

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Keywords

electric vehicle / nonsynchronizer automated mechanical transmission (NSAMT) / planetary gear / coordinated shift control / dynamic tooth alignment

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Xiaotong XU, Yutao LUO, Xue HAO. Coordinated shift control of nonsynchronizer transmission for electric vehicles based on dynamic tooth alignment. Front. Mech. Eng., 2021, 16(4): 887‒900 https://doi.org/10.1007/s11465-021-0653-3

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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).

RIGHTS & PERMISSIONS

2021 Higher Education Press 2021.
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