# The Analysis of Pneumatic Wheel Rim Deformation While Hitting an Obstacle
## 1 Introduction  
Road wheels of vehicles should be treated as a fundamental factor influencing the level of active safety. They transfer not only the torque generated by the propulsion system, but also all the forces that result in a reduction in speed and maintenance of directional stability. Along with the suspension system, the wheels are also the first element reacting to the forces caused by moving on the surface and damping vibrations related to its unevenness. It often happens that the wheels are one of the first elements transmitting destructive forces--during collisions and road accidents. Many studies on vehicle traffic safety have shown that the tire road friction coefficient (TRFC) is correlated with the accident probability [1; 2; 3; 4]. According to the report on road safety in Poland [5], in 2020 the share of road accidents due to technical reasons was 17.1%. However, excessive speed of vehicles is still the main cause of road accidents. This factor is also widely discussed in the literature [6; 7; 8], examples of studies from the Czech Republic are presented in [9] and from Hungary in [10]. The issues of road transport safety are widely discussed in the literature, for example in [11; 12; 13; 14; 15; 16]. Many authors pay attention to vehicle safety systems: braking systems, including Anti-lock Braking System (ABS) and Electronic Stability Program (ESP) [17; 18; 19; 20; 21; 22], vehicle suspension systems [23; 24; 25; 26], tires [27; 28; 29; 30], tire pressure monitoring systems (TPMS) [31; 32], and other systems [33; 34; 35; 36]. In [37], tests mapping the damage to the wheel of a tire on a vehicle on a special test stand are described. The problem of studying the phenomena occurring between the elements of road wheels and the ground is complex. Due to this fact, the analysis of damage to these elements is not used to recreate the course and assess the causes of incidents, collisions, and road accidents. Damage to road wheels--rims in particular--is a common phenomenon that experts in this field deal with. It occurs as a result of driving into a hole in the road surface, hitting an obstacle, or as a result of a collision with another vehicle. One of the key problems in the analysis of this type of event is determining the speed value--regardless of whether the problem concerns \"only\" the payment of compensation for damage (e.g., resulting from the road condition) or determining the details of the course of a road accident and determining its cause. In recent times, experts dealing with this subject have less and lesspossibilities in terms of the methods of analysis used. This is due to the use of more and more modern technological solutions in vehicles, which make the known and used so far \"tools\" useless. Attempts to use traces in the form of damage to wheel elements--despite the fact that the description of the phenomena may be problematic--should be considered a justified and necessary direction. Due to road safety, the wheels are subjected to endurance tests [38]. The scope of the tests includes the measurements of stresses during the simultaneous action of bending and torsional moments as well as fatigue tests [39; 40; 41]. The next laboratory tests that the wheels are subjected to are impact tests. Their methodology is described by international standards or by standardized test procedures directly defined by vehicle manufacturers. Impact tests are mandatory for newly designed car rims and their assigned tires. The tests are designed to simulate a collision with an obstacle hitting the side surface of the wheel [42; 43] and in the radial direction [44]. The test results are intended to identify the stresses arising in the tire and rim, and to measure the energy at which the internal structure of the tire is broken. During the impact tests, the wheel is attached to the supporting structure and the beater hits the side of the wheel or the tire tread. The weight of the hammer and the height of the fall depend on the size of the wheel.