# Survey on Modelling and Techniques for Friction Estimation in Automotive Brakes
## 2 Techniques for the Estimation of BLCF in Automotive Disc Brakes
### Assessment of [PERSON]'s Model
The identification procedure led to the following model parametrization:_ \(a\ =\ 5.8452\ \times\ 10^{-1}\left[\frac{1}{K^{\circ}s}\right];\text{b}\ =\ 5.5604\ \times 10^{-4}\left[\frac{1}{N \cdot m}\right]\)_;_ \(\text{c}\ =\ 3.2979\ \times\ 10^{-2}\left[\frac{1}{s}\right]\)_;_ \(\varepsilon\ =\ 1.6454\ \times\ 10^{\xi}\left[\frac{N\cdot m}{s}\right]\)_;_ \(\gamma\ =\ 9.5996\ \times\ 10^{-4}\left[\frac{K}{N\cdot m}\right]\)_. As shown in Figure 5a, it is noticeable that in the presence of increasing temperature the simulated profile remains aligned to the experimental reference. This result was anticipated since the model under discussion takes into account the friction dependence against the temperature._  
In Figure 5b, the validation test against the second dataset is instead reported. Although a lack of accuracy is evident corresponding to the low temperature values (the first five seconds), the model exhibits good overall capability in predicting the braking toque, even for varied brake actuation frequency. Thanks to the inclusion of a temperature-dependent term in the analytical formulation, the model remains close to the experimental profile. In Figure 6, the resulting braking torque has been plotted against the actuated pressure in order to examine the model's ability to reproduce the hysteresis effect. It appears clear that the model under analysis does not capture the hysteresis behaviour of the BLCF against the pressure oscillations. Figure 5: (**a**) Results of the identification process (first dataset); (**b**) results of the validation process (second dataset). Comparison between the experimental and the model-predicted braking torque. Figure 6: The measurements of the first dataset show a memory effect (hysteresis) of BLCF against the braking pressure and a clear dependence of the resulting braking torque on rising temperature. The model is capable of capturing the temperature dependence but not the frictional lag against the pressure. This issue has been addressed in [7], wherein the [PERSON]'s model is used in conjunction with the Bouc-Wen model in order to capture the hysteresis dynamics against varying pressure. This solution overcomes the evident limitation of Equation (2) so that the negative influence of the brake hysteresis on the vehicle dynamics can be accounted for. The work in [7] eventually concludes that the model is not capable of capturing the fast dynamics of BLCF and the relative error between the real and the estimated BLCF can reach values up to 15-20%. In conclusion, the dynamic model [17] assessed here is not suitable for online prediction of BLCF. It does not reproduce the frictional hysteresis against the pressure despite its ability to render other dynamic behaviours such as the influence of the temperature on the BLCF. Nevertheless, a strong drawback of this model is the requirement of an ad hoc parametrization depending on the specific plant. The following subsection puts forth cellular automata as an effective tool to describe the friction and wear on the nanometre scale. It is worth remarking that direct observation of the friction layer during a brake application is not possible. Hereunto, the cellular automata provide a detailed insight into the dynamics of the contact interface and represent a supporting tool for model-based approaches.