Interface - The Journal of Wheel/Rail Interaction

CONTACT MECHANICS AND RAIL STRESSES

Understanding the Effects of Track Gauge, Wheel/Rail Geometry and Friction on Stresses at the Wheel/Rail Interface
By Jude Igwemezie, Ph.D., P.Eng. • April, 2009

Over the years, rail grinding has become more the norm than the exception as the rail industry has recognized that damaged materials on the rail and wheel contact surfaces must be addressed before they become a bigger problem. The art of rail grinding has also progressed to point that it has become a preventive rail maintenance tool that can extend rail life. In recent times, top of rail (TOR) lubrication has also been used to reduce TOR friction on the low rail and overall lateral forces, which are known to cause problems such as fastener fatigue, plate cutting on timber ties, and rail seat abrasion on concrete ties. An understanding of the fundamentals of contact mechanics, wheel and rail geometry and friction at the wheel/rail interface can help rail managers prolong rail and wheel asset life.

Contact Mechanics

Contact mechanics can be explained through the use of two axially aligned and rolling cylinders of equal diameter in contact, as shown in Figure 1. A plot of the transverse stress contour in both cylinders can be made under different contact friction conditions. If initially, the friction between the cylinders is zero (saturated lubrication), the maximum stress is subsurface (see Figure 2). In the case of the wheel and rail, maximum subsurface stresses could reach 300 ksi. This means that maximum damage will begin inside the rail and lead to spalling of the top of the low rail, or to gauge corner shelling in the case of the high rail. It also means that with saturation lubrication, initiation and propagation of fatigue damage is driven “underground” and starts inside the metal where they are not visible. As a result, spalls as deep as 1/4 inch (as shown in Figure 3) on the low rail, and shells of similar depth (as shown in Figure 4) are formed, requiring grinding to remove the excess material.

As friction increases, the maximum stress is drawn toward the surface, reaching it at approximately 0.5 friction coefficient (see Figure 5). This means that with significant friction, the damage starts where it is visible and progresses inwards. Also with friction, there is opportunity to wear away the material that is contact fatigue damaged. On the other hand, where there is friction, there is energy loss. The challenge for rail operators is to find a balance between rail wear, acceptable depth of subsurface crack initiation, and risk of detail fractures (DFs) and transverse defects (TDs) that are not visible until it is too late. The geometry of the wheel/rail contact and the friction between them becomes paramount.

Examination of the contact between the wheel and rail in curving action, as shown in Figure 6, shows that the wheel tread makes contact at the top of the high rail while the wheel flange applies curving and steering lateral forces at the gauge face. There is no flange contact on the low rail, resulting in both vertical and lateral forces being applied at the top-of-rail running surface. As a result, the moment arm of the overturning force on the low rail is higher than that on the high rail. The maximum lateral load that can be applied to the top of the low rail is the vertical load on the wheel multiplied by the coefficient of dynamic friction at the top of the low rail. This is why it is necessary to lubricate the top of the low rail in order to avoid low rail rollover derailments immediately after rail grinding.

Lowering the friction through the use of TOR lubrication reduces the lateral forces experienced by the low rail. The flange force on the high rail, which is determined by the lateral force on the low rail, is also reduced. Lowering the friction at the wheel/rail interface drives the fatigue defect formation subsurface, however. In order to keep the contact fatigue stresses to a minimum, maintenance managers must ensure that the rail makes contact with the best mating surface on the wheel for the entire length of the train. This is where the track gauge and positive gauge retention come into play.

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