## 1 Introduction  
In order to achieve an adequate level of driving comfort and safe-vehicle handling, the vibrations induced in the vehicle structure must be dampened. The basic mechanisms for the dissipation of vibration energy in vehicles include dry friction (which occurs at the interface between interacting components) and viscous resistance forces (in fluids). Dry friction damping is mainly used in vehicles with multi-leaf spring suspension. However, in the course of vehicle operation, the conditions of interaction between the leaf spring plates change; thus, the coefficient of friction [1] changes significantly. It then affects the dynamics of the car body and, for example, changes the exposure of people to vibrations in vehicles [2]. For this reason, modern vehicles usually use hydraulic shock absorbers, selected to interact with the spring elements of the suspension. Obviously, vibration damping methods are still being developed. These are mainly related to the active control of the damping force and its adaptation to actual requirements. Mostly, they are oriented towards magnetorheological fluids, although electromagnetic shock absorbers are also being increasingly used. In this case, an important aspect is the possibility of recovering energy from vibration motion [3]. Damping force adjustment is also possible in modern friction damper solutions [4]. In addition, advanced materials and their composites characterised by high dissipation properties and ageing resistance can be applied to the construction of viscoelastic dampers [5]. Typical automotive shock absorbers are characterised by different resistance forces being evident at the compression stroke (bringing the wheel closer to the car body) and the expansion stroke (rebound). The value of the resistance forces is a function of the parameters of the working fluid (hydraulic oil) and the valves throttling fluid flow between the shock absorber chambers. The shock absorber converts the mechanical energy of movement into the thermal energy produced by pumping the fluid through the throttle valves. It is then transmitted to the external environment. Important requirements for hydraulic shock absorbers include the invariability of the damping characteristics throughout their lifetime, low sensitivity to environmental factors (e.g., temperature, humidity), as well as high mechanical strength and shock resistance. The permissible operating temperature ranges of shock absorbers, as specified by their manufacturers, mostly lie between \(-40\) and \(130\)\({}^{\circ}\)C [6]; however, in specific applications (e.g., all-terrain vehicles), the highest allowable temperature may be as high as \(180\)\({}^{\circ}\)C. This property depends, among other things, on the kind of oils, type of sealing system, and their thermal resilience. The temperature also influences changes of oil viscosity; therefore, it changes the characteristics of the shock absorber itself. In extreme cases, decreasing oil viscosity with increasing temperatures can result in leaks, performance degradation, or damage. Mineral oils are most commonly used in passenger car shock absorbers. More heavily loaded shock absorbers use synthetic oils, which have greater resistance and less viscosity variation along with the temperature. On one hand, the high oil viscosity can lead to undue resistance forces at low ambient temperatures. However, its low value increases the susceptibility to oil foaming, reduces damper resistance, and degrades lubricating properties. A simple linear relationship to changes in viscosity is often assumed for minor changes in temperature values. However, this approach is inappropriate for the entire range of temperature changes assumed by manufacturers. Issues related to stand and numerical testing of shock absorbers are presented in a number of scientific papers. These are mainly associated with the identification of damper characteristics, car vibration studies [7], or mathematical modelling issues.