Strojniški vestnik - Journal of Mechanical Engineering 61(2015)6, 392-398 © 2015 Journal of Mechanical Engineering. All rights reserved. D0l:10.5545/sv-jme.2014.2364 Original Scientific Paper Received for review: 2014-12-10 Received revised form: 2015-04-07 Accepted for publication: 2015-04-22 A Model for the Estimation of Brake Interface Temperature Aleksandar Grkic ^-Davorin Mikluc1 - Slavko Muždeka1 - Živan Arsenic2 - Čedomir Duboka3 1 University of Defence, Military Academy, Serbia 2 University of Belgrade, Faculty of Mechanical Engineering, Serbia 3 University of Belgrade, Serbia The temperature achieved at the contact surface of the disc and the pad of a friction brake during its operation has a significant impact on brake performance. Temperature measurement techniques, which are usually available under laboratory test conditions, enable obtaining relatively accurate values of the temperature at the friction surface. However, measuring the sliding surface temperature during the entire lifetime of the brake pad is very difficult due to the demanding operating conditions of the brakes, i.e. the appearance of wear, the presence of water, corrosion, and other immersive impacts. Purely mathematical models for the prediction of friction or contact surface temperature are often complex, and they are affected by a number of limitations. In this paper, an appropriate mathematical model was developed in order to enable estimation of the sliding surface temperature values between the brake disk and brake pads throughout the entire duration of brake application. This is achieved by using the results of the temperature measurement within the brake pad and its processing, by means of an originally developed mathematical model. Keywords: temperature estimation, braking, friction surface, measurement, modelling Highlights • Available temperature measurement techniques and mathematical models for prediction of contact surface temperature. • Measuring the temperature of the frictional surface and within the brake pad by using thermo couples. • The model for estimation of temperature on the contact surface of the disc and the pad. • Analysis of results and validation of the mathematical model. 0 INTRODUCTION The braking process is a complex stochastic tribological process by which the motion energy of vehicles is irrevocably transferred into heat and dissipated into the environment. Generally, the amount of heat is a time-related function, depending on the thermal characteristics of the parts enabling friction contact, as well as their size, shape, activation pressure, and sliding speed [1] and [2] . The temperature on the friction surfaces of automotive brakes can reach very high values. In this sense, it is an influential factor of the brakes' performance [3] to [7]. According to [8], the temperature distribution on the friction surfaces is generated by combined processes and complex phenomena that directly affect brake performance. High temperatures on the friction surface may cause the decrease in efficiency of braking, so called fading [9]. Moreover, extremely high temperatures can cause convex bending of the brake pads and an uneven distribution of pressure leading to uneven wear rate distribution [10]. In [11], it was shown that brake factor values differ significantly depending on the variation of brake interface temperature, which is quite uniform under the same initial brake temperature. This means that, depending on the initial brake temperature, deceleration and braking time significantly differ from one braking application to another. Taking into consideration that the initial brake rotational speed and control line pressure take predetermined and well-known values, knowing the temperature values of the contact surface enables estimating the coefficient of friction in automotive brakes [12]. Having knowledge of the main influencing values at the initiation of the braking process, and also during braking process, enables the prediction of the output brake parameters, i.e. brake performance can be predicted and thus managed. However, in order to ensure a reliable and efficient management of the braking process, it is necessary to continuously obtain information concerning the actual values of the braking influential parameters. Consequently, it is vital to have knowledge about the temperature on the contact surface of the disk and the brake pads throughout the braking application duration. It is very difficult to measure and predict the values and character of temperature changes in the brake. Temperature measurements on the contact surface are practically impossible over a longer period, due to the physics of the friction process. Apart from that, automotive brakes work in difficult operating conditions, which is reflected in the appearance of wear, the presence of water, corrosion and so on. Through this task, it is possible to apply several 392 *Corr. Author's Address: MilitaryAcademy, University of Defence in Belgrade, VeljkaLukica-Kurjaka 33, Serbia, iralex@eunet.rs Strojniški vestnik - Journal of Mechanical Engineering 61(2015)6, 392-398 different temperature non-contact measurement methods [13], such as optical and infrared methods, and contact type methods, as well as temperature measurement using thermo-couples or different temperature-sensitive materials. According to [14], the most effective way to determine the temperature on the contact surface of the disc and brake pads in the vehicle during braking is by applying thermocouples. In contrast, a number of authors used different mathematical methods to describe and present temperatures in the contact zone of the friction pair and the behaviour of the temperature field in the braking process, as well as their impact on wear and brake performance. The prediction of brake temperature in the contact surface can be realized in two ways: analytically and numerically [15] to [19]. The basis of the analytical method relies on the Fourier equation of temperature field [20], while the finite element method (FEM) [2] represents the most important numerical method. In recent years, the application of artificial intelligence (AI) methods (such as neural networks) has become a particularly interesting as a tool for predicting temperatures in automotive brakes [21]. All of the above-mentioned methods can provide satisfactory results in comparison the actual measurements. However, the application of any of these methods typically requires numerous simplifications and restrictions in order to offer solutions to the observed problem. Taking this into consideration, this paper investigates the possibilities of estimating both the character in changes and the values in the contact surface temperature between the disc and brake pads. The developed model is based on the results of temperature measurements in the vicinity of the contact surface and in the depth of a brake pad. A model for estimating the temperature on the contact surface requires continuous information about the temperature values within brake pads by means of measurement. This is possible during the entire working life of brake pads. 1 EXPERIMENTAL RESEARCH As previously stated, temperature measurement in the friction surfaces of a brake is a difficult task. This is due to numerous influencing factors specific to rubbing surfaces such as those in friction brakes, especially since it is necessary to provide temperature measurement with an appropriate accuracy and minimum delay. When comparing all the available techniques of temperature measurement, the method using thermocouples shows significant advantages over others; they are very effective for measuring the temperature in the contact of the friction pair. In this case, a so-called "hot end" or hot junction is located very close to the friction surface. However, it must be taken into consideration that the thermocouple should not at any time be exposed to direct rubbing over the friction surface in order to eliminate the potential impact on the quality of the measuring signal of the thermocouple sliding itself over the metal surface as much as possible. This kind of problems may be avoided if the thermocouple is positioned within the pad, very close to the sliding surface, e.g. 0.5 mm deep from it (SAE J843). In the present study, one temperature sensor was located in such a position, and it will be used to measure the temperature on the friction surface (7\). However, given the requirement that the temperature at the friction surface be measured throughout the lifespan of brake pads, this position is not satisfactory due to wearing phenomena. Hot junction 1 Disc Fig. 1. Position of thermocouples in brake pad Therefore, another thermocouple T2 will be positioned 12.5 mm deep from the contact surface, within the pad, as shown in Fig.1. The position of this thermocouple is close to the backing plate, and it is defined by the thickness of the brake lining material. This thermocouple is not exposed to the effects A Model for the Estimation of Brake Interface Temperature 393 Strojniški vestnik - Journal of Mechanical Engineering 61(2015)6, 392-398 of wearing, which ensures its use throughout the operating period. It is important to note that both thermocouples were placed at the friction radius of the pad. Typical test results of the temperature measurement are presented in Fig. 2; the solid line shows temperature measurement results at the sliding surface (i.e. 0.5 mm deep from the friction surface), while the dahed dot line shows temperature measurement results 12.5 mm deep from the friction surface of the disc pad. The measurement was carried out at the Frimeks laboratory of the Faculty of Mechanical Engineering, University of Belgrade, with a car disc brake tested at a single-ended full-scale inertia dynamometer [11]. Temperature measurements were carried out during 5 consecutive (or repeated) full-stop brake applications over a total time of 600 seconds, with an initial brake speed corresponding to linear vehicle speed of 60 km/h, and with the control line pressure of 60 bar, while the initial brake temperature at the beginning of the measurement cycle was 100 °C (±3 °C). The brake was subject to cooling by means of the fan operating throughout the measurement period. In each brake application, a brake disc was first accelerated until it reached the predetermined initial brake speed, and consequently braked to a full stop. After completing a single brake application, the brake disc remained at a standstill. Speeding up of the disc for the next brake application started a few moments before the brake attained a predetermined initial temperature of 100 °C. Ô140 <2_[ 120 100 80 60 brak[ng colling p hase I II speedin g up 0 100 200 A t 300 400 500 600 Time [s] Fig. 2. Temperatures measured in the disc pad for 5 consecutive brake applications This can also be seen in Fig. 2, where the change in the shape of the curve representing temperature measurement is evident in the area near the end of the cooling phase. This occurs because the brake temperature decreases significantly faster due to rotating disc during the speed build-up period. The delay in reaching the minimum temperature value at the depth of 12.5 mm from the sliding surface when compared to the minimum temperature "at the friction surface" is represented with the symbol At, as shown in Fig. 2. 2 TEMPERATURE MODELLING ON THE FRICTION SURFACE The model for estimation of temperature on the contact surface of the disc and the pad is based on the temperature ratio (k), which is determined experimentally as a rate between temperatures T1 and T2 at hot junctions 1 and 2, respectively, as shown in Fig. 1 above, by means of the test results from Fig. 2. The evaluation of k factor (temperature ratio) between temperatures T1 and T2 is shown in Fig.3. As shown in Fig. 3, the values of k factor vary between kmin=1.14 and kmax=1.32. It may be seen from both Figs. 2 and 3 that k factor certainly depends and varies on whether the brake was in the warming (brake application) or cooling (brake release) phase. 1.3 I1.2 1.1 0 100 200 300 400 500 600 Time [s] Fig. 3. k-factor between temperatures T1 and T2 Therefore, the k factor may be best represented by its mean value, which can be determined as follows: k = - 2 (1) The estimated value of the temperature TE, which represents the modelled values of the friction sliding surface temperature T1 can be obtained by multiplying the temperature value T2, which was measured in the depth of a pad with the mean value of the k factor. Variations of k factor also depend on the composition of the brake pad friction material, wear status, brake geometry and operating conditions, as well as the position of thermocouple T2 in the depth of friction material. It is important to emphasize that this model for prediction of temperature on the friction surface is limited to the brake under examination only, in addition to the given friction material characteristics and the position defined for T2 temperature measurement. 394 Grkič, A. - Mikluc, D. - Muždeka, S. - Arsenic, Ž. - Duboka, Č. Strojniški vestnik - Journal of Mechanical Engineering 61(2015)6, 392-398 The temperature Tj was not used in the model; it only represents control parameter in order to assess the quality of the model. Fig. 4 shows the results already presented in Fig. 2 in order to enable first approximation in resolving this situation with the help of a new dashed line for TE. This represents the results of continuous multiplication of the "pad inside temperature" T2 values (dashed dot line) by the mean value of the k factor, thus obtaining a "predicted" value of the temperature TE, which will correspond to the correct value of the temperature Tj (solid line) in the contact surface, as measured during the test. However, it is obvious that such an estimation of brake-sliding surface temperature is not only applicable to the given brake characteristics, including those related to the friction material used, but also to the given combination of the initial braking conditions (speed and pressure). The big question, in this case, would not be how to calculate the values of the sliding surface temperature accurately, but how to reach a universal relationship between the brake contact surface temperature and the temperature within the pad, i.e. at a given depth from the sliding surface. o 140 O 0 120 0 100 IF o 1— 80 60 -Ti \