# Research on Wheel Flat Recognition Based on Wayside Wheel-Rail Force
## 1 Introduction  
Due to uneven braking forces, wheels may experience locking and skidding, leading to the formation of wheel flats (as shown in Figure 1). A wheel flat causes the wheel to generate continuous and regular impacts on the rail, inducing abnormal rail vibrations. In extreme cases, the wheel-rail force can even reach 10-20 times the normal value [1]. Meanwhile, these impacts increase axle stress: the equivalent stress at the axle's critical section can double compared to normal conditions, potentially causing axle fractures and posing significant safety hazards to train operations. Wheel flat defects are prevalent in China's railway transportation industry, particularly in heavy-haul railways. Owing to heavy loads and the need to connect multiple carriges, trains are prone to uneven braking forces, which facilitate wheel flat formation. Additionally, the enormous axle loads further amplify the damage caused by wheel flats to both rails and vehicles. Currently, the inspection and diagnosis of wheel flats--especially detailed parameters such as flat length and depth--still rely on manual daily maintenance and overhaul, consuming substantial human and material resources. Therefore, leveraging intelligent equipment to diagnose wheel flats and monitor their development offers significant economic benefits for modern railway freight transportation. Using wayside detection equipment, wheel-rail forces of all vehicles traversing the test section can be monitored to diagnose wheel faults. While wheel-rail impact patterns derived from these forces can directly identify the presence of wheel flats, they cannot discriminate specific fault characteristics such as flat length and depth. To obtain precise fault parameters of wheel flats, in-depth research is required to establish a mapping relationship between wheel-rail forces and fault features through analyzing the interaction mechanism between wheel defects and wheel-rail impacts. This relationship enables the acquisition of detailed wheel flat information--such as dimension parameters--by detecting real-time wheel-rail force variations. In recent years, scholars have conducted extensive research on wheel flattening and its effects on vehicle-track systems. As early as the late 1960s, Japanese researchers theoretically analyzed the impact mechanism of wheel flats, deriving the fundamental impact force formula and initiating successive studies on its dynamic effects [2; 3; 4]. Over the past two decades, investigations into wheel flat impacts and their influences on vehicle-track dynamics have seen significant advancements. In 2002, [PERSON] et al. [5] developed a numerical model to predict wheel-rail dynamic interactions under flat-induced excitations. [PERSON] [6] (2007) proposed an analytical model using [PERSON]'s function to simulate wheel-rail interactions, simultaneously introducing a time-domain analysis method for impact forces. Based on these approaches, the study explored how rail wear--within rigid contact frameworks--affects wheel-rail contact force variations. [PERSON] [7] (2008) validated a high-frequency coupled vehicle-track vibration model through field tests, analyzing vertical forces using measured wheel flat data. That same year, [PERSON] [8; 9] conducted in-depth research on wheel-rail impacts, deriving criteria for speed-related contact loss and investigating the speed-flat length relationship. [PERSON] et al. [10] (2013) used ANSYS to study how flat length influences impact loads, while [PERSON] et al. [11] analyzed axle stress responses under wheel-rail elastic models. [PERSON] et al. [12] investigated three-dimensional wheel-rail dynamic contact loads and lateral vehicle responses with wheel flats. [PERSON] et al. [13] (2014) established a time-domain model incorporating a three-dimensional non-Hertzian contact framework  
Figure 1: The wheel flat caused by skidding. (based on [PERSON]'s variational principle), analyzing dynamic interactions and quantifying flat impacts on conventional force modeling. [PERSON] et al.