# Survey on Modelling and Techniques for Friction Estimation in Automotive Brakes
## 1 Introduction  
### General Remarks  
The tightening up of regulations on driving safety [1] and emissions has pushed researchers to develop outperforming solutions aimed at reducing environmental impact and energy consumption. It is evident that, in accordance with this trend, in a few years the non-exhaust emissions from vehicles will also be regulated. Indeed, a review of the Institute for Energy and Transport of the European Commission reports PM10 brake wear emission rates up to 8.8 mg/km and PM2.5 rates up to 5.5 mg/km for passenger cars [2]. Bearing in mind that the last regulations for diesel engines set a limit of 5 mg/km for PM10 from exhaust, it is clear that friction brakes and tires are nowadays considered the main emitters of micro- and nanoparticles in road vehicles next to internal combustion engines [3]. Therefore, wear and emissions estimations, along with brake enhancement, require the development of a reliable model of brake linings' coefficient of friction (BLCF). Unfortunately, analytical representation of the pad-disc tribological contact is challenging, which in turn influences the brake operation by varying the BLCF: fading [4; 5]; bedding [6]; hysteresisagainst the pressure [7]; hysteresis against the speed [8], wear [9; 10], and aging [6]; and variation in the environmental conditions [11]. The behaviour of a pad-disc coupling is also dependent on the chemical composition and mechanical properties of each component [12]. In addition to the abovementioned, there are also other phenomena that must be taken into consideration when studying the brake tribology: (i) thermally induced deformation of the brake pad due to non-uniform temperature distribution; (ii) non-uniform pressure distribution over the pad surface owing to calliper deformation, especially for low-pressure applications; (iii) the presence of residual grinding torque even without brake application; (iv) chemical contamination processes of the contact plateaus owing to oxidation or inclusion of re-suspended road dust particles. It therefore seems clear that when creating a model capable of predicting the real BLCF by taking into account the abovementioned phenomena, is important to monitor the brake operation and optimize its actuation. A thorough experimental analysis is still demanded in the field of optimal control of automotive brakes. Actually, just a few analytical models have been employed for modelling the BLCF in automotive brakes. The reason is that many of the proposed models are only suitable to describe the common pin-disc contact in a controlled environment [13; 14; 15]; therefore, they are not suitable to depict the automotive brake pad-disc interface. The latter problem involves dry sliding contact, although the pads could be unintentionally lubricated, e.g., due to rain. Most of the time the sliding occurs at high speed and high forces and consequently implies high temperatures: during hard brake manoeuvres, the kinetic energy dissipated into the brake pad can easily exceed 30 kW [6]. With reference to the pad-disc tribological contact, it is experimentally assessed that the BLCF is linked to the number of contact plateaus between the pad and the disc [6; 16], constituting approximately 20% of the pad area. The contact plateaus can grow or decay in relation to processes that involve agglomeration and compaction of the wear debris around the nucleation sites [17]. These phenomena are influenced by the contact temperature, the humidity [18] and the local pressure [19]. Therefore, in relation to the plateaus in birth-growth-destruction dynamics [17], the BLCF can range between 0.3 and 0.6 [12; 20], with peaks up to 0.8 and down to 0.1 [4; 17]. Among the recorded instances in the literature, it is also possible to encounter extreme values of the BLCF with special specimens, e.g.,: a lower value of 0.04 for polyamide linings reinforced with glass fibres and an upper value of 2.0 for polyamide/steel linings [21].