Reliability design and sensitivity analysis of cylindrical worm pairs

• Novel method to evaluate the higher order moments of the state function.
• New formula to compute the reliability by using the Edgeworth series.
• New revised formula to assess the reliability based on the Edgeworth series method.
• Developed approach to compute the reliability sensitivity.
• A practical technique to appraise the reliability and sensitivity for worm drives.

The reliability and the reliability sensitivity of a cylindrical worm drive are considered in the present paper. To estimate them, some new mathematical methods are proposed. Depending on these approaches, a practical and simple technique to perform the estimation is taken shape. The application of such technique does not require knowing the probability distributions of the basic design parameters. The evaluation can be implemented so long as the mean values and the variances of the basic design arguments are known. In the bargain, the situation that the standardized random variable obeys an arbitrary probability distribution can be handled by taking advantage of the technique suggested as well. The numerical results show that the traditional excogitation methodology can in general give a favorable outcome with higher reliability. Generally speaking, as for an enclosed cylindrical worm gearing, the contact fatigue reliability is usually, more or less, higher than the bending fatigue reliability. In addition increasing the center distance and the module is beneficial to improve the reliability. Meanwhile the greater variance of the design parameters may lead to lower reliability as to a worm gear pair.