I have a concept about rolling friction which someone might be able to confirm for me. Let's say there is a steel ball rolling on a steel surface. It seems to me that the rolling friction force would be proportional to the rolling object's velocity. My understanding is rolling friction is caused by deformation of the rolling ball or deformation of the surface or both. As a ball rolls in one direction if there is a "ploughing" effect of the surface, for example, then it makes sense that a faster moving ball would compress or deform the surface deeper in front of the moving ball, thereby generating greater elastic restoring forces, than a slower moving ball which would compress or deform the surface less, and therefore, would generate a smaller elastic restoring force. Therefore, the rolling friction force would be less. I cannot imagine a ball rolling at a mere .5 cm/sec about ready to come to a stop having the same rolling friction force as a ball rolling at 1 m/sec. I visualize a graph with the horizontal line being velocity and the vertical line being the rolling friction force, and that the line would begin at the origin and slope up. Am I basically right about this concept?