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

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.

Key words： electric vehicle; nonsynchronizer automated mechanical transmission (NSAMT); planetary gear; coordinated shift control; dynamic tooth alignment

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
A_{\mathrm{c}\mathrm{a}\mathrm{r}}	Frontal area of vehicle, m2
\mathit{A}	Coefficient matrix of the state vector
{\mathit{A}}_{\mathrm{d}}	Discretization matrix of \mathit{A}
{\mathit{B}}_u	Coefficient matrix of the input vector
{\mathit{B}}_{u\mathrm{d}}	Discretization matrix of {\mathit{B}}_u
{\mathit{B}}_w	Coefficient matrix of the disturbance vector
{\mathit{B}}_{w\mathrm{d}}	Discretization matrix of {\mathit{B}}_w
c_{\mathrm{c}}	Viscous damping coefficient of the planet carrier, N∙m·(rad/s)−1
c_{\mathrm{p}}	Viscous damping coefficient of the planet gear, N∙m·(rad/s)−1
c_{\mathrm{r}}	Viscous damping coefficient of the ring gear, N∙m·(rad/s)−1
c_{\mathrm{s}}	Viscous damping coefficient of the sun gear, N∙m·(rad/s)−1
c_{\mathrm{s}\mathrm{l}\mathrm{v}}	Viscous damping coefficient during the axial movement of the sleeve, N·(m/s)−1
C_{\mathrm{D}}	Aerodynamic drag coefficient
\mathit{C}	Damping matrix
{\mathit{C}}_{\text{ς}i}	Feature matrix of the ith gear
{\mathit{C}}_{\text{ς1}}	Feature matrix of the first gear
{\mathit{C}}_{\text{ς2}}	Feature matrix of the second gear
f	Coefficient of rolling resistance
f_{\mathrm{f}\mathrm{l}\mathrm{o}\mathrm{o}\mathrm{r}}(\cdot )	Downward rounding function
f_{\mathrm{c}\mathrm{e}\mathrm{i}\mathrm{l}}(\cdot )	Upward rounding function
F_{\mathrm{s}\mathrm{f}\mathrm{t}\mathrm{m}\mathrm{a}\mathrm{x}}	Maximum shift force, N
F_{\mathrm{s}\mathrm{l}\mathrm{v}}	Axial combined force exerted on the sleeve
g	Gravity coefficient, m/s2
G_{\mathrm{c}\mathrm{u}\mathrm{r}}	Current gear
G_{\mathrm{P}}	Gear phase
G_{\mathrm{t}\mathrm{g}\mathrm{t}}	Target gear
h_{\mathrm{c}\mathrm{a}}	Distance between the tooth tip of the sleeve and the tooth tip of the dog gear in the neutral gear, m
h_{\mathrm{d}\mathrm{o}\mathrm{g}}	Tooth height of the dog gear, m
h_{\mathrm{f}\mathrm{d}}	Axial distance between the tooth tip of the dog gear and the maximum-width place of its tooth, m

H_{\mathrm{L}}	Distance between point B and the tooth tip of SL in the neutral gear, m
i_0	Final ratio
i_{\mathrm{t}\mathrm{g}\mathrm{t}}	Ratio of the target gear
j	Vehicle jerk, m/s3
J_{\mathrm{c}\mathrm{e}}	Inertia of the planet carrier, kg·m2
J_{\mathrm{p}}	Inertia of planet gear, kg·m2
J_{\mathrm{r}\mathrm{e}}	Inertia of the ring gear, kg·m2
J_{\mathrm{s}\mathrm{e}}	Inertia of the sun gear, kg·m2
\mathit{J}	Inertia matrix
k	Discrete time
k_{\mathrm{e}\mathrm{n}}	Time of starting engagement
l_0	Past trajectory of point A2
l_1	Original estimated trajectory of point A2
l_2	New estimated trajectory of point A2 after adjustment
m_{\mathrm{c}\mathrm{a}\mathrm{r}}	Vehicle mass, kg
m_{\mathrm{s}\mathrm{l}\mathrm{v}}	Mass of the sleeve, kg
N	Number of planetary gears
n	Rotation speed, r/min
n_{\mathrm{s}}	Rotation speed of the sun gear, r/min
n_{\mathrm{r}}	Rotation speed of the ring gear, r/min
n_{\mathrm{c}}	Rotation speed of the planet carrier, r/min
R_{\mathrm{w}}	Wheel rolling radius, m
t	Continuous time, s
t_{\mathrm{A}\mathrm{B}}	Time of the process from point A to point B, s
T_{\mathrm{c}}	External torques of the planet carrier, N∙m
T_{\mathrm{e}\mathrm{n}\mathrm{d}}	Torque output of the drive motor at the end of the gear shifting, N∙m
T_{\mathrm{L}\mathrm{M}}	Torque output of the load motor, N∙m
T_{\mathrm{m}}	Torque output of the drive motor, N∙m
T_{max}	Maximum torque of the drive motor in full speed range, N∙m
T_{\mathrm{m}\mathrm{m}\mathrm{a}\mathrm{x}}	Maximum torque of the drive motor with the current speed, N∙m
T_{\mathrm{m}\mathrm{p}}	Average torque of the drive motor, N∙m
T_{\mathrm{m}\mathrm{r}\mathrm{e}\mathrm{f}}	Reference torque of the drive motor, N∙m
T_{\mathrm{r}}	External torques of the ring gear, N∙m
T_{\mathrm{s}}	External torques of the sun gear, N∙m
u_{\mathrm{a}}	Vehicle velocity, km/h
\mathit{u}	Input vector of the system
v	Vehicle velocity, m/s
v_{\mathrm{s}\mathrm{l}\mathrm{v}}	Axial moving speed of the sleeve, m/s
\mathit{w}	Disturbance vector of the system
W_{\mathrm{d}\mathrm{o}\mathrm{g}}	Maximum tooth width of the dog gear, m
\mathit{x}	State vector of the system
x_{\mathrm{s}\mathrm{l}\mathrm{v}}	Axial moving displacement of the sleeve, m
x_{\mathrm{s}\mathrm{l}\mathrm{v}\mathrm{r}\mathrm{e}\mathrm{f}}	Reference displacement of the sleeve, m
x_{\mathrm{s}\mathrm{l}\mathrm{v},\mathrm{A}}	Axial moving displacement of the sleeve at point A, m

x_{\mathrm{s}\mathrm{l}\mathrm{v},\mathrm{B}}	Axial moving displacement of the sleeve at point B, m
{\mathit{y}}_{\text{ς}}	Output vector of the system
{\mathit{\text{z}}}_{\mathrm{d}\mathrm{o}\mathrm{g}}	Number of teeth of the dog gear
\alpha	Road slope, rad
{\beta }_{\mathrm{d}\mathrm{o}\mathrm{g}}	Tooth face chamfer angle of the dog gear, (° )
{\gamma }_{\mathrm{d}\mathrm{o}\mathrm{g}}	Tooth side chamfer angle of the dog gear, (° )
{\delta }_{\mathrm{c}\mathrm{a}\mathrm{r}}	Inertia coefficient of vehicle
\delta x_{\mathrm{s}\mathrm{l}\mathrm{v}}	Change of x_{\mathrm{s}\mathrm{l}\mathrm{v}} in a sampling period, m
\delta {\omega }_{\mathrm{\Delta }}	Change of \mathrm{\Delta }\omega in a sampling period, rad/s
\delta {\theta }_{\mathrm{\Delta }}	Change of \mathrm{\Delta }\theta in a sampling period, rad
{\theta }_{\mathrm{D}\mathrm{G}2}	Rotation angle of the dog gear of the second gear, rad
{\theta }_{\mathrm{d}\mathrm{o}\mathrm{g}}	Rotation angle corresponding to one tooth pitch of the target dog gear, rad
{\theta }_{\mathrm{r}}	Rotation angle of the ring gear, rad
{\theta }_{\mathrm{s}}	Rotation angle of the sun gear, rad
{\theta }_{\mathrm{s}\mathrm{l}\mathrm{v}}	Rotation angle of the sleeve, rad
{\theta }_{\mathrm{\Delta }\mathrm{d}}	Dynamic-predicted target angle difference between the sleeve and the target dog gear, rad
\tau	Correction factor of predicted torque
\lambda	Characteristic parameter of the planetary mechanism
\chi	Time scaling coefficient
\omega	Rotation speed, rad/s
{\omega }_{\mathrm{e}\mathrm{n}\mathrm{d}}	Speed of the drive motor at the end of the gear shifting, rad/s
{\omega }_{\mathrm{m}}	Speed of the drive motor, rad/s
{\omega }_{\mathrm{s}}	Rotation speed of the sun gear, rad/s
{\omega }_{\mathrm{r}}	Rotation speed of the ring gear, rad/s
{\omega }_{\mathrm{c}}	Rotation speed of the planet carrier, rad/s
\mathrm{\Delta }n	Rotation speed difference between the sleeve and the target dog gear, rpm
\mathrm{\Delta }\omega	Rotation speed difference between the sleeve and the target dog gear, rad/s
\mathrm{\Delta }{\omega }_{\mathrm{r}\mathrm{e}\mathrm{f}}	Reference rotation speed difference between the sleeve and the target dog gear, rad/s
\mathrm{\Delta }\theta	Rotation angle difference between the sleeve and the target dog gear, rad
\mathrm{\Delta }{\theta }_{\mathrm{r}\mathrm{e}\mathrm{f}}	Reference rotation angle difference between the sleeve and the target dog gear, rad
\mathrm{\Delta }{\theta }_{\mathrm{E}\mathrm{P}}	Angle threshold of the engagement point, rad
\mathrm{\Delta }{\theta }_{\mathrm{\Sigma }}	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).

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