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Study on impact characteristics of electric powertrain in regenerative braking process

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Abstract

Electromagnetic torque reversal may lead to gear impact during regenerative braking of electric vehicles. To simulate the dynamic response of gear transmission during impact, an electromechanical non-smooth model is established by combining the permanent magnet synchronous motor model with the gear transmission model. In this model, the coast-side mesh stiffness and impact damping are further coupled based on considering the drive-side mesh stiffness, meshing damping, and electromagnetic characteristics. The theoretical model is validated against an experimental platform. The mechanism of gear impact is revealed through the analysis of the gear contact force. Furthermore, the effects of driving status and internal excitations on the impact characteristics are studied. The results show that the initial braking speed and regenerative braking torque greatly influence the impact times and impact force. The impact times for various backlashes change little. Changing rotor inertia and torsional damping can effectively improve impact characteristics. The research provides theoretical support for dynamic load study and life prediction of the electric powertrain.

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Data availability

All data generated or analyzed during this study are included in this published article.

Abbreviations

a e :

Relative acceleration under the supporting forces

b :

Half of backlash

c m :

Meshing damping

c i m :

Impact damping

c tin, c t mid, c tout :

Torsional damping of input, intermediate, and output shaft

c in, c mid, c out :

Bending damping of input, intermediate, and output shaft

e m(θ):

Static transmission error

F m :

Normal dynamic contact force

I g, I p :

Inertia of driving and driven gear

I r :

Inertia of rotor

i :

The ith meshing tooth pair

i d, i q :

Stator current for d–q axis

k max :

Maximum single tooth meshing stiffness

k tin, k t mid, k tout :

Torsional stiffness of input, intermediate, and output shaft

k in, k mid, k out :

Bending stiffness of input, intermediate, and output shaft

k b U 1, c b U 1 :

Support stiffness and damping of bearing 1

L d, L q :

Stator induction for d–q axis

m e :

Equivalent mass of gear pair

m t :

Total vehicle mass

m g1 ~ m g4 :

Mass of gear 1 to gear 4

m b 1 ~ m b6 :

Mass of bearing 1 to bearing 6

N b :

Number of gear teeth meshing at the same time

O p :

Geometric center of driving gear

p n :

Number of pole pairs

p bt :

Transverse base pitch

R pb, R pp :

Base circle radius and pitch circle radius of driving gear

R g p, R ga :

Pitch circle radius and root circle radius of driven gear

R gb :

Base circle radius of driven gear

R g1 ~ R g4 :

Base circle radius of gear 1 to gear 4

R t :

Rolling radius of tire

r s :

Armature resistance

T e :

Electromagnetic torque

u :

Distance between the meshing point on front face and start point

u d, u q :

Stator voltage for d–q axis

U :

Direction of displacement

W r :

Work done by contact force during restitution

W c :

Work done by contact force during compression

α 0 :

Pressure angle of indexing circle

α m :

Angle between the plane of action and the positive y-axis

α p :

Pressure angle of pitch circle

α r :

Pressure angle of tooth root circle

α k :

Minimum stiffness ratio

β b :

Helix angle of base circle

β d :

Helix angle of indexing circle

δ 0 :

Deformation at the end of the impact

δ m ax :

Maximum deformation during the impact

δ m :

Relative displacement in the meshing line direction

ε :

Coefficient of restitution

ε α, ε β, ε γ :

Transverse contact ratio, overlap contact ratio, and total contact ratio

ε pre, ε post :

Pre-restitution coefficient and post-restitution coefficient

θ a :

Rotational angle of tire

θ b :

Rotation angle of coast-side contact

θ d :

Rotation angle of drive-side contact

θ p :

Driving gear rotation angle

θ r :

Rotation angle of rotor

θ m :

Mesh period of gear

θ g1 ~ θ g4 :

Rotation angle of gear 1 to gear 4

λ :

Correction coefficient of rotating mass

μ :

Hysteresis damping factor

ξ c :

Influence factor of supporting force on impact force

ζ m :

Meshing damping coefficient

Ψ f :

Permanent magnet flux

TVMS:

Time-varying meshing stiffness

PMSM:

Permanent magnet synchronous motor

FEM:

Finite element method

CLM:

Contact line method

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Acknowledgements

This work is supported by the National Natural Science Foundation of China (Grant numbers U1764257 and U1864210).

Funding

This study was funded by the National Natural Science Foundation of China (U1764257 and U1864210).

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Authors and Affiliations

  1. National Key Laboratory of Vehicular Transmission, Beijing Institute of Technology, Room 412, Building 9, Beijing, 100081, People’s Republic of China

    Kun Liu, Wei Wu & Shihua Yuan

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  1. Kun Liu
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  2. Wei Wu
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  3. Shihua Yuan
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Correspondence to Wei Wu.

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Liu, K., Wu, W. & Yuan, S. Study on impact characteristics of electric powertrain in regenerative braking process. Nonlinear Dyn 109, 2459–2477 (2022). https://doi.org/10.1007/s11071-022-07524-1

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  • DOI: https://doi.org/10.1007/s11071-022-07524-1

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