# Survey on Modelling and Techniques for Friction Estimation in Automotive Brakes
## 3 Conclusions  
The goal of the present work is to identify a model capable of predicting the real BLCF in automotive disc brakes, by detailing the phenomena affecting the tribological contact, with the aim of monitoring the brake operation and its actuation for safety and environmental purposes. As surveyed, the ad hoc models for disc brakes are not capable of accurately predicting the BLCF for every operating condition. Indeed, it is noticeable that the brake operation is affected by several phenomena that make the friction hard to describe through conventional analytical models. In this regard, an auxiliary tool, the so-called cellular automata, is able to depict the correlation between the patch dynamics and wear particle stream and temperature has been presented. This model sets out to provide a guess of the frictional behaviour at the pad-disc contact and to find correlations between characteristics of friction and properties of the contacting materials and loading conditions. The integration of the cellular automata model with a friction law allows for offsetting the gap between the patch dynamics and the macroscopic phenomena. The great advantage of the cellular automata is that the complexity between the processes occurring on different time scales can be handled without complicating the employed model. This kind of simulation is very helpful to comprehend the particle flow on the small scale but, as remarked in the dedicated Section 2.3, conclusions about global friction behaviour are not possible. Nonetheless, the brake wear [9] requires the inclusion of time dependence in the analytical form; the brake fading [5] demands the inclusion of a temperature-dependent term; the brake hysteresis [7] implies the use of a dynamic set of equations for the friction modelling. Owing to this complexity, the neural network has earned recent attention from the tribology community as an alternative approach to the achievement of a branched correlation between the friction and influencing factors such as pad composition, environmental conditions and operating conditions [7]. As evidenced, the approaches based on analytical correlations present several drawbacks that make them unsuitable for online applications:  
* both the model-based approach and the neural networks require a high experimental burden for parameter characterization and the training/learning processes, respectively;
* both cause a high computational burden when augmented with differential equations modelling the brake disc temperature or the hysteresis behaviour;
* both become unreliable when the plant characteristics change due to brake wear itself or in the case of replacement with aftermarket brake linings and owing to a variation in the weather conditions. Once it is clarified that an accurate modelling of all the friction phenomena is unknot likely to be achieved, from the literature it emerges that the design of an observer for the vehicle states has given rise to considerable interest among the control community, aimed at developing robust control strategies for brake enhancement during service operation. The state observation technique is expected to be a promising solution because:  
* it uses measurements coming directly from the vehicle sensors by avoiding an analytical description of the brake phenomenology;
* it guarantees robustness since it does not need an ad hoc identification for the specific plant;
* it does not require the implementation of models that cause a high computational burden, such as brake temperature distribution models;* finally, it can be used to predict the wheel torque as a supporting tool for the enhancement of the vehicle stability control systems. Considering all the mentioned drawbacks and the achieved results, it appears clear that a state observer could be a very powerful tool for the online observation of BLCF.