# Railcar Dynamic Response during Braking Maneuvers Based on Frequency Analysis
## 1 Introduction  
During braking, tangential forces developed in the wheel-rail contact area have a direct effect on the dynamic response of the railway vehicle. As a result, the vehicle's dynamic response exhibits different frequencies depending on the friction coefficient. Large tangential forces may threaten the stability of the railway vehicles if the braking torque is not applied properly [1], and even damage the train's wheels, engine, and rails, if applied abruptly [2]. If vibrations caused by braking are very strong, they can be transferred to the vehicle's body. Railway vehicle vibrations can cause discomfort to passengers and even cause harmful vibrations in railway structures [3]. [PERSON] [4] addresses this issue by proposing a linear actuator adapted to the secondary suspension to reduce vibrations caused by the train-bridge interaction. Vibration monitoring is used to find faults in railway components. Accelerometers were installed on the axle-box and bogie by [PERSON] et al. [5] to detect lateral and vertical track irregularities. [PERSON] [6] uses a machine-learning-based algorithm to classify rail failures as either vertical, lateral alignment, or cross-level. [PERSON] et al. [7] installed accelerometers on the vehicle bogies to monitor lateral and vertical vibrations, thereby determining track alignment. [PERSON] et al. [8] used a technique based on empirical mode decomposition (EMD) to find a transfer function, which converts vehicle accelerations into track deformations. Their proposal aims to visualize the evolution of damage in the track and substructures. The rolling tangential forces that cause vibrations to the vehicle are generated in a relatively small contact area (ellipse-shape) of 1 cm\({}^{2}\) size [9]. The contact area is separated into traction and sliding regions. The ratio between these two regions determines theoverall dynamic behavior of the wheel and is dependent on a number of factors, including the coefficient of friction, creep, and the lateral position of the wheel in relation to the rail. As with out-of-round wheels [10; 11; 12] and rail corrugations [13], the behavior of tangential forces can be monitored from the vehicle's body using in-service-vehicle devices, with remarkably promising results. Applying the same principle, vibration analysis may detect changes in the wheel-rail friction coefficient. Wheel-rail friction is approximately 0.3 under dry, clean conditions [14]. This value, however, is not constant and depends on the nature of the contaminants on the rails. Some common contaminants are water, snow, leaves, and even grease. Since the rails and wheels are exposed to the outside environment, it is impossible to maintain ideal friction conditions for optimal performance. In this case, friction modifiers are needed to improve traction when starting off is difficult due to contaminants on rails [15]. Friction modifiers have been studied by many researchers to find the best performance on wheel traction [16; 17; 18]. It has been reported that the increase in the friction coefficient results in an improvement in the dynamic performance of the locomotives. On the other hand, it has been observed that the rear wheels have better traction because the front wheels sweep away some of the dirt from the track [19]. However, this only improves the performance of the rear wheels by 20%, compared to 32% when friction modifiers such as sand dust are used. Therefore, friction modifiers are preferred to improve acceleration or braking, and even to prevent skidding on hills. Vibrations are utilized in the aforementioned works in order to identify track anomalies; however, none of these studies have performed vibration analysis in order to identify variations in the coefficient of friction. This paper proves how varying the wheel-rail friction coefficient affects the dynamic response of railway vehicles during braking. The experimental data from a 1:20 scale-down railcar is used for studying the effects of severe braking.