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The book takes the subject from an introductory level through advanced topics needed to properly design, model, analyze, specify, and manufacture cam-follower systems.
Cam Design and Manufacturing Handbook
(Cam Systems Failure - Cylindrical Contact)

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   by Robert L. Norton
Published By:
Industrial Press Inc.
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12.13 CYLINDRICAL CONTACT

Cylindrical contact is common in machinery. A non-crowned cylindrical roller follower running against a face cam is one example. Roller bearings are another application. The mating cylinders can be both convex, one convex and one concave (cylinder-in-trough), or, in the limit, a cylinder-on-plane. In all such contacts there is the possibility of sliding as well as rolling at the interface. The presence of tangential sliding forces has a significant effect on the stresses compared to pure rolling. We will first consider the case of two cylinders in pure rolling and later introduce a sliding component.

Photoelastic analysis of contact stresses under a cam-follower (Source: V. S. Mahkijani, Study of Contact Stresses as Developed on a Radial Cam Using Photoelastic Model and Finite Element Analysis. M.S. Thesis, Worcester Polytechnic Institute, 1984) [15]

 

Contact Pressure and Contact Patch in Parallel Cylindrical Contact

When two cylinders roll together, their contact patch will be rectangular as shown in Figure 12-11 b (p. 353). The pressure distribution will be a semi-elliptical prism of halfwidth a . The contact zone will look as shown in Figure 12-13 (p. 355). The contact pressure is a maximum pmax at the center and zero at the edges as shown in Figure 12-14 (p. 357). The applied load F on the contact patch is equal to the volume of the half-prism:

 

where F is the total applied load and L is the length of contact along the cylinder axis. This can be solved for the maximum pressure:

 

The average pressure is the applied force divided by the contact-patch area:

 

Substituting equation 12.14c in 12.14b gives

 

We now define a cylindrical geometry constant that depends on the radii R 1 and R 2 of the two cylinders, (Note that it is the same as equation 12.9b (p. 356) for spheres.)

 

To account for the case of a cylinder-on-plane, R 2 becomes infinite, making 1/ R 2 zero. For a cylinder-in-trough, R 2 becomes negative. Otherwise R 2 is finite and positive, as is R 1. The contact-patch half-width a is then found from

 

where m 1 and m 2 are material constants as defined in equation 12.9a (p. 355).

 

The pressure distribution within the semi-elliptical prism is

 

which is an ellipse, as shown in Figure 12-11 (p. 353).

 

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