# 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  
In the present subsection, an assessment of [PERSON]'s model is featured, consisting in its identification and validation against the experimental data acquired on the brake dynamometer with a climatic chamber at the Technische Universitat Ilmenau. A general overview of the test rig is reported in Figure 3. This dynamometric brake stand is used to test the performance and NVH characteristics of brake systems under various and controlled conditions. The brake dynamometer is controlled through the manufacturer's software, which ensures a seamless control of the system actuators. The compressed air hydraulic actuator increases the pressure up to 21 MPa within the master cylinder. The system is equipped with a flow meter of the brake fluid and a pressure sensor that measures the actual pressure on the calliper. The brake torque is measured through a sensor positioned inside the inertial hub and corresponds to the output torque. The dynamometer allows a maximum operating regime of 2500 rpm and features a peak power of 186 kW and maximum torque of 5000 Nm. The test was conducted under the \"drag mode\" in order to ensure a constant sliding speed during oscillating input brake pressure. The brake pressure complies with a saw tooth signal with fixed frequency; therefore, the \(Nv(t)\) term in Equation (3) varies proportionally to the pressure law. In particular, the second test (Figure 4b) features an input frequency double that of the first one (Figure 4a). Moreover, during the test, the brake undergoes increasing temperature, a condition that affects the brake performance. In the first instance, the dynamic model in Equations (2) and (3) has been identified against the first set of experimental data and, in the second instance, validated against the second dataset, Figure 4. These manoeuvers emulate an extreme scenario of brake actuation that occurs in case of prolonged ABS intervention. For the model parameters identification, a minimization algorithm based on the [PERSON]'s method has been applied [52]. Within the optimization procedure, Equations (2) and (3) are computed for the whole time providing that \(\mu\) is set to zero when no pressure is applied on the callipers. In the following rows, the validation and identification results will be analysed by comparing the experimental and the model predicted braking torque. This latter can be easily calculated in compliance with the following:  
\[T_{b}=2\times\mu_{b}\times p_{b}\times A_{cl}\times R_{cl}, \tag{4}\]  
where \(T_{b}\) is the braking torque, \(\mu_{b}\) is the BLCF computed from Equation (2), \(p_{b}\) represents the actuated brake pressure, and \(A_{cl}\) and \(R_{cl}\) are geometric factors, namely the calliper area and the radial position  
Figure 4: Experimental measurements on the brake test rig performed at TU Ilmenau. Datasets (**a**) and (**b**) have been used for the identification and validation procedures, respectively. Top row: the oscillating braking pressure, as an input of the system. Middle row: brake speed profile. Bottom row: brake temperature profile. Figure 3: Brake dynamometer with climatic chamber, employed for experimental tests at the Technische Universität Ilmenau. 1—Drive Motor, 2—Flywheels, 3—Inertial hub, 4—Torque sensor, 5—Brake disc, 6—Brake calliper, 7—Brake pressure sensor, 8—Flow meter, 9—Master cylinder, 10—Compressed air hydraulic actuator, 11—Pressure accumulator. of the brake calliper application point. Figure 5a displays the outcome of the identification process conducted against the first dataset. This fitting was achieved by solving an optimization problem whose input variables are the parameters of the model, _a, b, c, e,_\(\gamma\)_.