# Survey on Modelling and Techniques for Friction Estimation in Automotive Brakes
## 2 Techniques for the Estimation of BLCF in Automotive Disc Brakes
### An Extension of the Model-Based Approach--The Cellular Automata Model
Although they have diverse purposes, each work puts forth the potentialities of the cellular automata employed to analyse the disc brake interface behaviour. For a better comprehension of the transition functions among the cells, see [55]. The authors of [55] believe that a model that encompasses the dynamic on a mesoscopic scale is a promising tool to provide a qualitative description of the patch life cycle, which is responsible for  
Figure 8: Characteristic times for the multi-scale problem in analysis [56]. Figure 7: Cellular automata discretization and portrayal of the patch structures in black [54]. the variation in the surface topography. In other words, it is a suitable approach to obtain insight into the pad-disc interface. The authors of [57] propose a simulating tool based on 2D cellular automata that can be used to determine the concentration of airborne wear particles generated from disc brakes. To achieve this goal, a model able to describe the physical behaviour of the contact situation in disc brakes is sought. In [56], the cellular automata model is extended to render the surface topography in three dimensions in order to comprehend the tribological behaviour under different load conditions. In [58] cellular automata are used to investigate the behaviour of the hard patches on a nanoscale length under the influence of different pad chemical compositions. Another technique that has been recently applied in the considered tribology field is the Movable cellular automata (MCA). The concept of the MCA is based on the conventional concept of cellular automata but, in addition to the basic postulates, the elementary object is also characterized by translational and rotational degrees of freedom. This tool is suitable for the visualization of friction processes on the nanometre scale, such as topography modification, film degradation and mass mixing. In [58; 59] the frictional behaviour against the local contacts in an automotive brake system has been analysed on the basis of computer simulation by means of the MCA. This technique has been applied with satisfactory results, showing a good qualitative correspondence between the model results and the experimental evidence. The cellular automata method renders the particle flow and the interaction between the patches and the particle motion [54]. Indeed, upon reaching a patch, the particles are either deflected or agglomerated. For this reason, the wear particle density beside and in front of these regions is maximal; instead, within the wakes of the patches, the number of wear particles is rather low. As it arises from the literature, the results are stable, and thus the set of rules is consistent in each timescale. The information obtained by the cellular automata simulation on the contact surfaces' topography could be used as an input for a macroscopic model. The choice of inner variables, rules, and boundary conditions allows for determining the tribological properties of the system. This includes the heat flux, the wear particle stream, patch growth and patch destruction. As has been explained and itemized, these processes occur on different timescales. This kind of simulation is very helpful to comprehend the particle flow on a very small scale but, due to the reduced particle sizes and time steps that cause a high computational burden, conclusions towards a global friction behaviour are not possible.