8.18:
Rolling Resistance
Consider a tire rolling at a constant speed. Forces acting on it are its weight and the normal force.
The contact surfaces deform, creating a finite contact area. This results in a distribution of normal forces at each contact point.
The front section of this area experiences deformation, which retards the rolling motion.
In contrast, the rear section undergoes a relatively smaller restoration that pushes the tire forward.
The resultant normal force acting at A is the sum of these forces.
To keep the tire rolling at a constant speed and balance the moment of the weight about A, a horizontal driving force must be applied to the center of the tire. Here all the forces must be concurrent.
The moment equilibrium condition at point A gives the driving force in terms of the coefficient of rolling resistance.
The weight multiplied by the coefficient of rolling resistance upon the radius is usually smaller than the coefficient of kinetic friction times the weight.
So, the rolling frictional force is smaller than the sliding force.
8.18:
Rolling Resistance
When a solid cylinder rolls steadily on a rigid surface, the normal force applied by the surface on the cylinder is perpendicular to the tangent at the contact point. However, since no materials are entirely rigid, the surface's reaction to the cylinder involves a range of normal pressures.
For instance, imagine a hard cylinder rolling on a comparatively soft surface. The cylinder's weight compresses the surface beneath it. As the cylinder moves, the material in front of it slows down due to deformation while the material behind it recovers from its deformed state, pushing the cylinder forward. The normal pressures acting on the cylinder in this way are depicted by their resulting forces, Nd and Nr. The deformation force (Nd) and its horizontal component are consistently larger than the restoration force (Nr), necessitating a horizontal driving force to be exerted on the cylinder to maintain its motion.
Rolling resistance primarily occurs due to this effect, although it is also influenced, to a lesser extent, by surface adhesion and relative micro-sliding between the contact surfaces.
To further explain this concept, consider a tire rolling at a constant speed. The main forces acting on it are its weight, acting vertically downward, and the normal force exerted by the ground, acting vertically upward. As the tire rolls, the front section of the contact area experiences deformation, which retards the rolling motion of the tire. In contrast, the rear section undergoes a relatively smaller restoration that pushes the tire forward. The net effect is that the resultant normal force acting at point A (the center of the contact area) is the sum of these opposing forces.
To keep the tire rolling at a constant speed and balance the moment of the weight about point A, a horizontal driving force (F) must be applied to the center of the tire. For equilibrium, all the forces acting on the tire must be concurrent. Using the moment equilibrium condition at point A, we can determine the driving force needed to maintain constant speed in terms of the rolling resistance coefficient (a).
This driving force is usually smaller than the product of the coefficient of kinetic friction and the tire's weight.
This relation implies that the rolling frictional force is typically smaller than the sliding force experienced when a tire skids over a surface. As a result, rolling resistance is generally less detrimental to a vehicle's performance than sliding friction.
Suggested Reading
- Hibbeler, R.C. (2016). Engineering Mechanics ‒ Statics and Dynamics. Hoboken, New Jersey: Pearson Prentice Hall. pp 452 ‒ 439.
- Meriam, J.L.; Kraige, L.G. and Bolton, J.N. (2020). Engineering Mechanics ‒ Statics. Hoboken, New Jersey: John Wiley. pp 372.
- Beer, F.P.; Johnston, E.R.; Mazurek, D.F; Cromwell, P.J. and Self, B.P. (2019). Vector Mechanics for Engineers ‒ Statics and Dynamics. New York: McGraw-Hill. pp 469.