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Real time estimation of brake disc temperature and brake torque using an extended Kalman filter
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DOI：10.1080/00423114.2026.2699816.png)
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Abstract
En 中文
The friction coefficient at the pad–disc interface plays a vital role in determining braking performance, yet it exhibits significant nonlinearity and variability under different thermal and dynamic conditions. Most production vehicles do not estimate this parameter in real time, leading to inconsistent braking behaviour and potential safety issues. This paper presents a physics based estimation framework for real time inference of disc temperature and brake friction coefficient using standard onboard sensor data. The proposed estimator incorporates vehicle and wheel dynamics to calculate virtual braking torque and employs an Extended Kalman Filter to estimate disc temperature and infer the friction coefficient as a function of temperature and clamping pressure. A hybrid update scheme is introduced, activating the estimator only during braking phases to ensure stability and convergence while preserving accuracy. Validation is conducted in both high fidelity simulation and a production vehicle instrumented with pad embedded thermocouples; after delay compensation, the estimator converges rapidly at brake onset and maintains consistent performance under single brake tests and repeated braking–coasting transitions. The estimated friction and temperature also enable accurate reconstruction of braking torque, demonstrating applicability to control refinement, diagnostics, and brake system monitoring.
Keywords:
Brake friction coefficient
disc temperature estimation
extended Kalman filter
real-time estimation
brake thermal modeling
vehicle dynamics
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V
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3.9
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3.1K
Citations:
8.9K
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