Clamping force estimation based on hysteresis modeling for electro-mechanical brakes


The Electro-Mechanical Brake (EMB) is anticipated by research communities and car manufacturers to be the future adopted brake system due to its advantages. However, to be competitively priced, the high cost load cell of EMB, which measures the clamping force to a disk, should be replaced by a clamping force estimation algorithm. For this purpose, a new clamping force estimator, compatible with readily available sensors, is proposed in this paper. This estimator determines the kissing point where the brake pads start to come into contact with the disk, and generates the characteristic curve of the polynomial function between the clamping force and the motor angle. Periodically updating the characteristic curve can enhance robustness to the pad’s changing thickness. Also, the model includes a description of the hysteresis of the clamping force in the overall algorithm, which prevents the estimation performance from decreasing in the transient state. The performance of the propose algorithm was validated by comparison with measured values on a developed EMB test bench.

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θ s :

electrical rotor angle, rad

w m,w s :

motor/synchronous angular velocity, rad/s

i d,i q :

motor current of d-axis/q-axis, A

v d,v q :

motor voltage of d-axis/q-axis, V

L d,L q :

self inductance of d-axis/q-axis, H

R :

stator resistance, Ω

ψ af :

flux linkage, Wb

n p :

number of pole pairs, -

T m :

motor torque, Nm

K m :

motor-torque constant, Nm/A

θ m :

motor angle, rad

p :

pitch of ball screw, m

GR :

total gear ratio, -

x screw :

displacement of ball screw, m

k screw :

translating gain of ball screw, m

k el :

gearing gain, m

F :

clamping force, N

η :

efficiency of ball screw, -

J tot :

total inertia, kg·m2

T L :

load torque, Nm

T f :

friction torque, Nm

θ 0 :

kissing point, rad

f cl(θ m):

characteristic curve, -

for, back :

forward/backward movement


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Correspondence to Seibum Choi.

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Park, G., Choi, S. & Hyun, D. Clamping force estimation based on hysteresis modeling for electro-mechanical brakes. Int.J Automot. Technol. 18, 883–890 (2017).

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  • Electro-Mechanical Brake (EMB)
  • Clamping force
  • Kissing point
  • Hysteresis
  • Estimation