## 1 Introduction
The longitudinal creepage occurs when the wheel does not cover its entire perimeter on the rail and is given as a percentage. The creep force is calculated by multiplying the normal force by the creepage. Thus, for positive longitudinal slip, with an increase in tension, the slip region increases and the non-slip region decreases, resulting in rolling and slipping contact. The traction-creep curve can be affected by the presence of a third body in the wheel-rail contact. This can be formed by a substance applied to increase or decrease friction (friction modifier or lubricant) or a natural substance acting to decrease friction (water, leaves, etc.) [7]. Lateral slip occurs due to the existence of an angle of attack \(\alpha\): the angle between the track radial line and the center line of the wheelset axle. Wheel flange wear occurs due to slippage between the wheel-rail contacts. This interaction results in the loss of material from the solid. To correlate the creepage with mass loss and wear, Ref. [7] performed an experiment known as twin disc. Two cylindrical samples, one extracted from the wheel and the other from the rail, were applied and placed in contact with each other with parallel axes. The tests were configured to represent a given pressure and percentage of longitudinal slip. Figure 1 shows the test. Figure 1 can be used to identify the sizes of specimens extracted from the wheel and rail for applications in the test. This test is recommended in the [9] AAR M-107/M-208 standard as a requirement for class D wheel development. The creepages were represented in the form of a variable \(T\gamma\), divided by the contact patch area. Figure 2 demonstrates the different behaviors obtained in the test, in which the function relating wear (loss of mass of specimens) to the indicator \(T\gamma\) is not linear. The behavior can be divided into three levels: medium, severe, and catastrophic [10]. The bogies are directly related to wheel wear [11]. Thus, understanding the vehicle's dynamic behavior during wheel-rail contact, which determines wheel performance, is only possible when analyzed simultaneously with the performance of railway bogies. Brazilian freight railways adopted a three-piece bogie model containing two side frames and a bolster. Factors such as simplicity and low cost made bogie suspension, known as the three-piece bogie, the main choice for American freight railroads [12]. In this type of bogie, the friction wedge is the main element used to dissipate the energy from vibration. This element provides dry friction damping between the friction wedge surface and the bogie side wear plate. The increase in wedge wear can reduce the damping. Therefore, the wedge height limit is defined through manual and rule standards. It is desirable for a bogie to allow for the wheelsets to steer effectively in curves and have an adequate amount of warp stiffness [13]. Warp stiffness is the rotational stiffness that resists the moments generated by the suspension [14]. An insufficient warp stiffness could lead the bogie to warp. This occurs when the side frame position forms a parallelogram. When a bogie is in warp, the wheelsets are both sharply misaligned with the turn rail at a severe angle of attack [15]. New bogie designs according to [16] AAR M-976 specifications should meet the following requirements: increase warp stiffness through improvements in friction wedges; use pads to allow a greater degree of freedom for the wheelsets to position themselves radially; and reduce the angle of attack and, consequently, rolling resistance [17]. The  
Figure 1: Twin disc test design [8]. Figure 2: Twin disc results [7]. increase in warp stiffness allowed for the use of pads due to the elastomeric elements not performing well in bogies without such features. In addition, the increase in warp resistance is directly related to the reduction in hunting [18]. When the bogie steers in a curve, certain moments occur. The steering moment occurs when longitudinal forces developed at the wheelset conicity of wheels.