## 1 Introduction  
Friction brakes convert a vehicle's kinetic energy to predominantly thermal energy [1, 2]. The frictional force is caused by the brake pads' force applied on the brake discs. There are many demands placed on them all, sometimes contradictory. Brake discs are un-sprung parts of a vehicle, and are rotating masses which act against inertia in the rotary direction when the vehicle is accelerating and decelerating [3]. Thus, the weight of disc brakes affects the driving and operational vehicle performance, and it should be as low as possible. In order to lower their weight, traditional materials used for their production are replaced by lightweight ones. In addition to grey cast iron and steel, lighter materials are used for the production of disc brakes, which do not excessively increase the price of the product and also meet strength, frictional and thermal requirements [4]. Criteria for materials to be used for a brake disc are also mentioned in the publication [5]. To have a lower weight brake disc as well as to keep its strength at the required level, a combination of aluminium and alloy can be used. The publication [6] describes how the weight of a brake disc is lowered by 20% by using aluminium in the assembling section, and how grey iron is applied in the friction surface section to maintain braking performance. Materials are combined either by casting or by a bolted joint [7]. The reliability and contributions of lightweight brake discs have been verified by the brake dynamometer [6]. Brake pads must withstand high temperatures and pressures while maintaining an adequate coefficient of friction as well [8]. Their lifetime must be as long as possible while at the same time retaining their original performance and having minimal wear [9]. The production of friction lining most often uses mineral, metal or ceramic organic materials in powder or fibre forms. These materials are bound by vitreous, metal or carbon fibres [10,11]. There are also biomaterials used, mainly from agricultural production, as mentioned in the publications [12, 13, 14]. Brake discs and pads must create such a pair which is able to generate intense brake forces in a short moment. The intensity of brake force is affected by the force of the brake cylinder that is applied on the brake pads, and by the coefficient of friction between the brake pads and a brake disc [15,16]. If the brake pads are made of material that is too lightweight, this will first lead to their deformation and, after that, to the activation of required braking force [17]. That would mean that the time for brake activation as well as stopping distance will be prolonged [18]. The heat accumulated in the brake disc and brake pads can to some extent increase the coefficient of friction. Higher temperatures can cause an increase in the coefficient of friction. After exceeding a certain temperature, usually 350 \({}^{\circ}\)C continuously and 800 \({}^{\circ}\)C at peak time, it can lead to permanent adverse modifications [19,20]. The overheating of brake discs and brake pads can occur due to various reasons [21]. High temperatures can be caused by intense and long-lasting braking when a vehicle is driving downhill [22]. This problem is predominantly connected to heavy vehicles, as also described in the publications [23, 24, 25]. However, mostly due to bad braking strategy, the risk of brakes overheating may occur in passenger vehicles as well [26, 27, 28]. Overheating can also happen even when braking normally, if the brake disc or brake pads are made of improper material with the wrong value of thermal conductivity [29,30]. Overheating may occur due to the wrong material combination of a brake disc with brake pads as well, which is also seen in the publications [31,32]. The publications [33,34] pay attention to overheating of brake discs and pads as a result of their insufficient thickness.