12.15 DYNAMIC CONTACT STRESSES

The equations presented above for contact stresses assume that the load is pure rolling. When rolling and sliding are both present, the stress field is distorted by the tangential loading. Figure 12-18 shows a photoelastic study of a cam-follower pair[15] loaded (a) statically and (b) dynamically with sliding . The distortion of the stress field from the sliding motion can be seen in part b . This is a combination of rolling contact with relatively low-velocity sliding. Increased sliding causes more distortion of the stress field.

Effect of a Sliding Component on Contact Stresses

Smith and Lui[14] analyzed the case of parallel rollers in combined rolling and sliding, and developed the equations for the stress distribution beneath the contact point. The sliding (frictional) load has a significant effect on the stress field. The stresses can be expressed as separate components, one set due to the normal load on the rolls (denoted by a subscript n ) and the other set due to the tangential friction force (denoted by a subscript t ). These are then combined to obtain the complete stress situation. The stress field can be two-dimensional in a very short roll, such as a thin plate cam or thin gear, assumed to be in plane stress. If the rolls are long axially, then a plane strain condition will exist in regions away from the ends, giving a three-dimensional stress state.

The contact geometry is as shown in Figure 12-11 b (p. 353) with the x axis aligned to the direction of motion, the z axis radial to the rollers, and the y axis axial to the rollers. The stresses due to the normal loading pmax are:

and those due to the frictional unit force fmax are:

The tangential unit force fmax is found from the normal load and a coefficient of friction