###### Abstract  
Railway track maintenance services aim to shorten the time of removing failures on the railways. One of the most important element that shorten the repair time is the quick access to the failure site with an appropriate equipment. The use of road-rail vehicles is becoming increasingly important in this field. In this type of constructions, it is possible to use proven road vehicles such as self-propelled machines or trucks running on wheels with tires. Equipping these vehicles with a parallel rail drive system allows for quick access to the failure site using both roads and railways. Steel rail wheels of road-rail vehicles are designed for specific applications. Since the total weight of vehicle is a crucial parameter for roadworthiness, the effort is made to minimize the mass of rail wheels. The wheel under consideration is mounted directly on the hydraulic motor. This method of assembly is structurally convenient, as no shafts or intermediate couplings are required. On the other hand, it results in strict requirements for the wheel geometry and can cause significant stress concentration. Therefore, the problem of wheel geometry optimization is discussed. Consideration is given to the use of ER8 steel for railway application and 42 CrMo4 high-strength steel. Finite element analysis within Ansys software and various optimization tools and methods, such as random tool, subproblem approximation method and first-order method are applied. The obtained results allow to minimize the rail wheel mass with respect to the used material. Moreover, computational demands and methods leading to the best results are compared. Keywords:rail wheel; rail-road vehicle; parametric optimization; finite element analysis +
Footnote †: journal: Applied  
optimization of railway wheels. Fatigue strength, mass minimization and rolling noise were considered. Self-adaptive genetic optimization algorithms were applied to solve the problem. In the study [4], ([PERSON] et al., 2013) presented the problem of multi-objective optimization of wheel profile to minimize both flange wear and surface fatigue. The optimization was carried out using a genetic algorithm. Whereas the problem concerning optimization of both the geometry of wheel and rail profile in order to improve tractive and braking forces was discussed in the study [5]([PERSON] et al., 2016). ([PERSON] et al., 2014) [6] developed an innovative new rail wheel profile optimized to improve wear and stability. The study on optimization of the rail profile for heavy haul railways was presented by ([PERSON] et al., 2016) in the paper [7]. An innovative method for reverse design of rail wheel profiles was presented in study by ([PERSON] et al. 2018) [8]. The method was based on mapping the differences in the rolling radius and allowed to reduce the stress in contact between the wheel and the rail. ([PERSON] et al., 2019) [9] presented the study on a tired rail wheel with the web made of austempered ductile iron including casting simulation as well as static and fatigue strength assessment. The wheel was designed to operate in a diesel multiple unit. Whereas a numerical evaluation of the fatigue load capacity of the cylindrical crane wheel was presented by ([PERSON], 2017) in the article [10]. The application of multiaxial high-cycle fatigue criteria for the analysis of the subsurface rolling contact fatigue of structures working in contact conditions was discussed. The multiaxial fatigue analysis is applied when the equivalent fatigue stress for complex loading is investigated. In turn, various examples of applying the finite element numerical analysis in optimal design of structures were presented in works [11; 12; 13; 14; 15; 16; 17], and those using Ansys software in papers [18; 19; 20; 21]. Nevertheless, all of the studies on rail wheels mentioned above concerned the use for railcars and locomotives, but not for road-rail vehicles as referred to in herein.