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Vehicle Dynamic Control for In-Wheel Electric Vehicles Via Temperature Consideration of Braking Systems

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Abstract

−Vehicle dynamic control (VDC) systems play an important role with regard to vehicle stability and safety when turning. VDC systems prevent vehicles from spinning or slipping when cornering sharply by controlling vehicle yaw moment, which is generated by braking forces. Thus, it is important to control braking forces depending on the driving conditions of the vehicle. The required yaw moment to stabilize a vehicle is calculated through optimal control and a combination of braking forces used to generate the calculated yaw moment. However, braking forces can change due to frictional coefficients being affected by variations in temperature. This can cause vehicles to experience stability problems due an improper yaw moment being applied to the vehicle. In this paper, a brake temperature estimator based on the finite different method (FDM) was proposed with a friction coefficient estimator in order to solve this problem. The developed braking characteristic estimation model was used to develop a VDC cooperative control algorithm using hydraulic braking and the regenerative braking of an in-wheel motor. Performance simulations of the developed cooperative control algorithm were performed through cosimulation with MATLAB/Simulink and CarSim. From the simulation results, it was verified that vehicle stability was ensured despite any changes in the braking characteristics due to brake temperatures.

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Abbreviations

v :

vehicle velocities

v x :

vehicle longitudinal velocities

v y :

vehicle lateral velocities

γ :

vehicle yaw rate

β :

vehicle sideslip angle

ν f, ν r :

front and rear tire velocities, respectively

δ f, δ r :

front and rear steering angles, respectively

α f, α r :

front and rear tire slip angles, respectively

F yf, F yr :

front and rear lateral tire forces, respectively

a, b :

longitudinal distances from the C.G to the front and rear tire, respectively

d :

tire tread

I γ :

vehicle yaw moment of inertia

M :

control yaw moment

C f :

cornering stiffness values of the front tires

C r :

cornering stiffness values of the rear tires

K us :

understeer coefficient

q f :

friction heat

T fb :

braking torque

ω w :

wheel velocity

q d :

disk friction heat

q p :

pad friction heat

β heat :

heat distribution factor

ρ d, ρ p :

disk and pad density, respectively

c d, c p :

disk and pad specific heat, respectively

k d, k p :

disk and pad thermal conductivity, respectively

A d, A p :

pad and disk area, respectively

F o :

Fourier number

h :

convective heat transfer coefficient

B i :

Biot number

F b :

estimated braking force

μ :

estimated friction coefficient

T p :

estimated pad temperature

r d e :

disk effective radius

r w :

wheel radius

F N :

normal force applied to the disk

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Correspondence to Sung-Ho Hwang.

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Park, J., Kwon, M., Du, G. et al. Vehicle Dynamic Control for In-Wheel Electric Vehicles Via Temperature Consideration of Braking Systems. Int.J Automot. Technol. 19, 559–569 (2018). https://doi.org/10.1007/s12239-018-0053-9

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  • DOI: https://doi.org/10.1007/s12239-018-0053-9

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