Research on Tribological Features of Brake Friction Materials - Comparison of the Results Obtained with the Pin-On-Disc and Ball-Cratering Methods

are one of the most important systems in each vehicle. For this reason, numerous studies are carried out in many scientific institutions that allow for better un-derstanding of friction and wear phenomenon. Therefore, the correctness of the obtained results is of great importance. Hence, the choice of the research method is not without significance. In this paper, it was decided to check how the choice of the method will affect the quality of the obtained results. The chosen methods were Ball-cratering and Pin-on-disc. Six groups of samples taken from three different types of pads were tested. The pads were both brand new and used. The analysis of the results was performed using the chi-square concordance test. It was established that at the significance level of 0.95, the choice of the research method was not statistically significant. Both methods pro-vide similar high-quality results.


Introduction
Brakes are one of the most important vehicle systems as they are closely related to safety. However, the correct design of the working elements (pads and discs) is not easy [1,2]. The friction materials currently used are composites of about 20 different materials for different purposes. During operation, they are subjected to very extreme factors -mainly changing temperature and humidity [3].
The friction elements of brake systems are subject to various types of wear. The most important is abrasive wear, i.e. destruction of the top layer of cooperating parts that move relative to each other. Loss of the pad material is caused by the separation of material particles as a result of scratching, micro-cutting and grooving [4]. It is this type of wear that was focused on later in the work. The most important criterion according to which research methods can be divided into the determination of abrasive wear parameters is the macrogeometry of the contact between the sample and the counter-sample. It is an important design feature of machines for measuring the value of the friction coefficient and the intensity of wear. The most common solutions are [5][6][7]: a) point contact (ball-disk), e.g. Ball-cratering; b) line contact (cylinder-disk), e.g. Pin-on-disc; c) surface contact (plane-plane), e.g. inertial stations.
Two of the above research methods, Ball-cratering and Pin-on-disc, were used in this work. The aim of the study is to compare the obtained results and check whether these methods can be used interchangeably.

Materials and research methods description
Two test stands were used for the research, which are at the disposal of the Faculty of Mechanical Engineering of the Białystok University of Technology. They were: 1) based on point contact and using the Ball -cratering method. It is a method in which the friction pair is a cylindrical sample (1 "diameter and 10 mm high) and a ball (also 1" diameter) [8]. Fig. 1 shows a diagram of one of them, namely the T-20 test rig manufactured in Poland. In this device, the test sample 1 is mounted in a holder on the vertical arm of the rotary lever, and its mass is balanced by a counterweight 7 located at one end of the horizontal arm of the lever. At the other end, there is a pan on which a load 5 is placed, which presses the sample against the countersample 2. The length of the swivel lever arms is the same, so the pressing force is identical to the gravity force resulting from the pressure of the given load on the pan. The counter-sample is mounted on the shaft of the electric motor 8 (with adjustable rotational speed). The strain gauge 4, located above the sample holder, allows direct measurement of the friction force during the test. As the ball rotates, it rubs against the sample, the vertical position of which allows the material to fall freely, thus it does not interfere with the measurement [9]. As a result of friction, a crater is formed, the measurement of which in two planes allows to determine the average diameter and then the frictional wear intensity factor Kc in accordance with the Archard equation [10] (examples of craters and the method of measuring their diameter are shown in Fig. 4). The stand allows to measure the friction force in real time, thanks to which you can easily calculate the friction coefficient of the friction pair. The research problem may be the point nature of the contact -different than in the vehicle braking system, but it may be compensated by a properly designed experiment.
2) T11 -Using the Pin-on-disc method. It allows for the implementation of linear macrogeometry of the contact between the sample and the counter-sample. This method can be used both for testing dry friction, as well as under the operating conditions of a lubricant [11,12]. The Pin-on-disc method enables the determination of the average coefficient of friction of the node and the examination of the wear intensity of the friction surfaces. The first parameter is measured directly during the tests as a function of time or number of disk revolutions, while the second is determined on the basis of the mass lost by the sample. The necessary data is obtained by weighing the sample before and after the test. In the vast majority of solutions, the disk rotates in the horizontal plane, although there are devices in which the disk is positioned vertically [13]. Due to the similarity to the disc brake system, the stands with the horizontal axis of rotation of the disc are good for testing brake discs and pads. As in the case of the Ball-cratering method, the horizontal positioning of the disc causes the pin to slide over loose fragments of the sample torn off during the test. For this reason, the same material tested several times may give different final results each time [14]. Despite this, the Pinon-disc method in this configuration is commonly used to test samples taken from brake pads [15][16][17][18][19]. Fig. 2 shows a diagram of the Polish production stand used for the tests.
The test samples were taken from brake pads intended for passenger cars. Three types of brand new pads were used and in about 50 % of the wear. Few of samples used (before grinding) are presented on Fig. 3. This gave a total of 6 groups of samples. Four samples were cut from each group of pads, giving a total number of 24. This number allowed for testing each group of samples three times (three samples were Pin-on-disc, one Ballcratering by rotating it around its axis). Samples and experiments were prepared as described in previous articles [21,22]. where: z is COF value. Results and calculations are compiled in Table 1.  The chi-square test [24][25][26] was used to determine the influence of the research method on the obtained results. In this test, we compare the observed values with the expected values. The formula for this test is as follows:

Results and their analysis
( ) where: k is number of research methods; r is number of measurements; n is total number of observations; n is expected values; i is test method number; j is measurement number.
The mean values of the measurements were used for the analysis. Ultimately, the data used for the analysis is presented in Table 2. For the test purposes, the following hypotheses were adopted: H0the test method does not affect the obtained result (Pin-on-disc results = Ball-cratering results); H1the test method influences the obtained results (Pin-on-disc results ≠ Ball-cratering results); The calculation results allowed for the determination of the following values: 2 13.86294.  = (4) To correctly interpret the results, it was necessary to calculate the degrees of freedom: which after substitution gave: Then using the inverse chi-square distribution and assuming the confidence level: 0.05, value read [27]: there is no reason to reject the H0 hypothesis. Therefore, it should be stated that the influence of the applied research method on the obtained results at the confidence level of 0.95 is not statistically significant.

Conclusions
Six groups of samples taken from three types of brake pads were tested in the study. Each pads group was in two different degrees of wear: brand new and 50 % worn. A series of tests were made with the use of two tribotesters: Ball-cratering and Pin-on-disc. Statistical analysis of the results allowed to establish that: 1. The value of the chi-square function is much lower than the critical value, which refuted the H1 hypothesis.
2. No statistical significance was found, proving that the quality of the results depends on the choice of the research method when testing the friction materials of brake pads.
3. Appropriate (correct) design of the experiment allows the above research methods to be used interchangeably while maintaining their high quality. 4. The above methods, due to their interchangeability, can be used as a way to validate empirical results.