Three-wire measurement calculation method for pitch diameter of external threads in planetary roller screws

To improve the measurement accuracy of the external thread diameter in planetary roller screw mechanisms (PRSM) and to mitigate the influence of machining errors on the results of the traditional three-point measurement method, a contact equation between the measured thread and the measuring needle is established, using a set of calculation equations for the external thread diameter that incorporate machining errors, which are then solved. By considering the critical factors, including pitch deviation, half-thread thickness deviation and thread side angle deviation, contact points are predicted by using the assembly relationship between the thread and the measuring needle. The contact equation between the measured thread and the measuring needle is derived by using the principle of continuous surface tangency. The calculated values of the thread diameter in the three-point method, with and without considering machining errors, are solved separately, and the impact of thread machining errors on the correction values of the external thread diameter is investigated. The results reveal the following correlation between thread machining errors and the correction values of the diameter: the increase in pitch deviation results in a monotonically decreasing correction value; the increase in half-thread thickness deviation leads to a monotonically increasing correction value; under the simultaneous deviation of both thread side angles, the correction value exhibits a non-linear trend of initially decreasing and then increasing with the increasing of deviation angle; in asymmetric deviation conditions on one side, while maintaining a similar non-linear variation trend, the variation amplitude is significantly reduced.