Contact ratio analysis of the Rzeppa joint based on full-static modeling

- The concept of the contact ratio is introduced for the Rzeppa joint.
- A full-static analysis procedure is developed for calculating the contact ratio.
- Increase in the joint force can be explained in terms of the contact ratio.
- Geometric gap between the tracks can explain the shape of the contact force curve.

Ball-type constant-velocity joints (also known as the Rzeppa ball joints) are widely used for transmitting rotational motion between two misaligned shafts. Due to their geometrical complexity, most methods for analyzing such systems employ a certain degree of simplifying assumptions. In the present study, the problem is formulated with essentially no simplifying assumptions. The concept of the contact ratio commonly used as a performance index of the gear teeth is similarly defined here as the average number of balls actually in contact with the race tracks during power transmission. Many sample cases demonstrate that the contact ratio can be used as a useful performance index for Rzeppa joint systems to estimate the maximum contact force between the balls and tracks. For example, the decrease in the contact force with an increase in the number of balls can be explained in terms of an increase in the contact ratio. The size of the gap between the ball and the tracks was analyzed to explain the asymmetry in the contact force curve.