## 1 Introduction  
The phenomenon of train wheel polygons--that is, wheels with a certain degree of out-of-roundness (OOR)--is a well-known problem for high-speed railways [1].The term \"wheel polygon\" refers to periodic radial deviations from the ideal round shape of the circumference of the wheel. Figure 1 shows the shapes of typical polygonal wheels with different harmonic OOR orders. The technical term \"harmonic order\" refers to a sinusoidal radial deformation of the circumference with a specific period. The \"OOR amplitude\" is defined as the deviation of the radius from the nominal constant value. At present, there is no explicit conclusion regarding the mechanism whereby wheel polygons are generated. However, polygonal wheels produce a number of problems. For example, at speeds above 200 km/h, this phenomenon will cause considerable vibrations, which are transmitted to the train compartments via the wheels and from the rails to the track components, resulting in the deterioration of infrastructure, noise disturbance, and an increase in maintenance costs [2].  
There has been considerable research on the wear characteristics caused by this phenomenon and the dynamic responses. Early studies of wheel OOR were carried out in Germany, Sweden, Australia, and other developed regions using experimental studies and numerical simulations to analyze the mechanism of their occurrence and development [3; 4; 5].Most reported causes of the formation of wheel polygons involve the inhomogeneity of tread material, braking characteristics, wheel-rail rolling contact, axle bending modes, manufacturing errors, and misalignment during profiling [6; 7; 8]. Criteria for determining whether OOR wheels should be removed have been proposed in the United States, United Kingdom, and other countries in an attempt to reduce infrastructure maintenance costs and comply with noise legislation [9; 10].With the rapid development of high-speed railways in China, extensive field data show that polygonized wheels are very common in high-speed trains. This phenomenon has attracted the attention of researchers, and there is an economic incentive to detect and replace OOR wheels in good time. The causes and enlargement of wheel polygons [11; 12] and the effects of polygonal wheels on vehicle stability and train operational safety [13; 14; 15] have been discussed by researchers at various universities in China. In addition, a few studies [16; 17] focused on simulating the dynamics of high-speed railway vehicles on flexible tracks.  
Previous studies provide an initial insight into the origin of wheel polygons and their influence on vehicle dynamics. However, to the best of the authors' knowledge, little attention has been paid to the track dynamics resulting from wheel polygons in high-speed operations. The goal of this paper is to study the influence of the wheel polygon order, OOR amplitude, and train speed on the dynamic performance of a slab track. Our analysis is based on a co-simulation method using multi-body dynamics simulation software Universal Mechanism (V8.3, Laboratory of Computational Mechanics, Bryansk State Technical University, Bryansk, Russia) and finite element software ANSYS (R18.0, ANSYS Inc., Canonsburg, PA, USA). Our research results provide guidance on potential sensor locations for identifying polygonized wheels in-service before they fail through the application of a rail vibration monitoring system.