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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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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

A car :

Frontal area of vehicle, m2

A :

Coefficient matrix of the state vector

A d :

Discretization matrix of A

B u :

Coefficient matrix of the input vector

B ud :

Discretization matrix of Bu

B w :

Coefficient matrix of the disturbance vector

B wd :

Discretization matrix of Bw

c c :

Viscous damping coefficient of the planet carrier, N·m·(rad/s)−1

c p :

Viscous damping coefficient of the planet gear, N·m·(rad/s)−1

c r :

Viscous damping coefficient of the ring gear, N·m·(rad/s)−1

c s :

Viscous damping coefficient of the sun gear, N·m·(rad/s)−1

c slv :

Viscous damping coefficient during the axial movement of the sleeve, N·(m/s)−1

C d :

Aerodynamic drag coefficient

C :

Damping matrix

C ςi :

Feature matrix of the ith gear

C ς1 :

Feature matrix of the first gear

C ς2 :

Feature matrix of the second gear

f :

Coefficient of rolling resistance

f floor (·):

Downward rounding function

f ceil(·):

Upward rounding function

F sftmax :

Maximum shift force, N

F slv :

Axial combined force exerted on the sleeve

g :

Gravity coefficient, m/s2

G cur :

Current gear

G P :

Gear phase

G tgt :

Target gear

h ca :

Distance between the tooth tip of the sleeve and the tooth tip of the dog gear in the neutral gear, m

h dog :

Tooth height of the dog gear, m

h fd :

Axial distance between the tooth tip of the dog gear and the maximum-width place of its tooth, m

H L :

Distance between point B and the tooth tip of SL in the neutral gear, m

i 0 :

Final ratio

i tgt :

Ratio of the target gear

j :

Vehicle jerk, m/s3

J ce :

Inertia of the planet carrier, kg·m2

J p :

Inertia of planet gear, kg·m2

J re :

Inertia of the ring gear, kg·m2

J se :

Inertia of the sun gear, kg·m2

J :

Inertia matrix

k :

Discrete time

k en :

Time of starting engagement

l o :

Past trajectory of point A2

l 1 :

Original estimated trajectory of point A2

l 2 :

New estimated trajectory of point A2 after adjustment

m car :

Vehicle mass, kg

m slv :

Mass of the sleeve, kg

N :

Number of planetary gears

n :

Rotation speed, r/min

n s :

Rotation speed of the sun gear, r/min

n r :

Rotation speed of the ring gear, r/min

n c :

Rotation speed of the planet carrier, r/min

R w :

Wheel rolling radius, m

t :

Continuous time, s

t AB :

Time of the process from point A to point B, s

T c :

External torques of the planet carrier, N·m

T end :

Torque output of the drive motor at the end of the gear shifting, N·m

T LM :

Torque output of the load motor, N·m

T m :

Torque output of the drive motor, N·m

T max :

Maximum torque of the drive motor in full speed range, N·m

T mmax :

Maximum torque of the drive motor with the current speed, N·m

T mp :

Average torque of the drive motor, N·m

T mref :

Reference torque of the drive motor, N·m

T r :

External torques of the ring gear, N·m

T s :

External torques of the sun gear, N·m

u a :

Vehicle velocity, km/h

u :

Input vector of the system

v :

Vehicle velocity, m/s

v slv :

Axial moving speed of the sleeve, m/s

w :

Disturbance vector of the system

W dog :

Maximum tooth width of the dog gear, m

x :

State vector of the system

x slv :

Axial moving displacement of the sleeve, m

x slvref :

Reference displacement of the sleeve, m

x slv,A :

Axial moving displacement of the sleeve at point A, m

x slv,B :

Axial moving displacement of the sleeve at point B, m

y ς :

Output vector of the system

Z dog :

Number of teeth of the dog gear

α :

Road slope, rad

β dog :

Tooth face chamfer angle of the dog gear, (°)

γ dog :

Tooth side chamfer angle of the dog gear, (°)

δ car :

Inertia coefficient of vehicle

δx slv :

Change of xslv in a sampling period, m

δω Δ :

Change of Δω in a sampling period, rad/s

δθ Δ :

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

θ r :

Rotation angle of the ring gear, rad

θ s :

Rotation angle of the sun gear, rad

θslv:

Rotation angle of the sleeve, rad

θ Δd :

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

ω end :

Speed of the drive motor at the end of the gear shifting, rad/s

ω m :

Speed of the drive motor, rad/s

ω s :

Rotation speed of the sun gear, rad/s

ω r :

Rotation speed of the ring gear, rad/s

ω c :

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

Δω ref :

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

Δθ ref :

Reference rotation angle difference between the sleeve and the target dog gear, rad

Δθ EP :

Angle threshold of the engagement point, rad

Δθ Σ :

Total change of the rotation angle difference, rad

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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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Authors and Affiliations

  1. School of Mechanical and Automotive Engineering, South China University of Technology, Guangzhou, 510641, China

    Xiaotong Xu, Yutao Luo & Xue Hao

  2. Guangdong Provincial Key Laboratory of Automotive Engineering, Guangzhou, 510641, China

    Xiaotong Xu, Yutao Luo & Xue Hao

Authors
  1. Xiaotong Xu
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  2. Yutao Luo
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Correspondence to Yutao Luo.

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Xu, X., Luo, Y. & Hao, X. Coordinated shift control of nonsynchronizer transmission for electric vehicles based on dynamic tooth alignment. Front. Mech. Eng. 16, 887–900 (2021). https://doi.org/10.1007/s11465-021-0653-3

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