Abstract

Background: More and more noncircular gears are reported in various relevant patents and papers. The Pascal limacon gear is one kind of noncircular gears and widely used in many mechanisms. The pitch curve is a key accuracy index for the noncircular gears and influenced by many errors, included worktable errors.

Objective: The goal of this paper is to analyze the influence of worktable errors on the Pascal limacon gear’s pitch curve.

Methods: Firstly, according to the mathematical model for hobbing Pascal limacon gear, a vector expression for the Pascal limacon gear pitch curve errors caused by the worktable rotary angle error and the center distance error was derived. Then, with consideration of the above errors, a comprehensive method was proposed, and the Pascal limacon gear pitch curve errors were calculated. The concept of the sensitivity degree of the errors of the Pascal limacon gear pitch curve to the center distance was proposed. Thirdly, the influence of the center distance errors on the pitch curve could be assessed.

Results: Using one Pascal limacon gear as an example, the results show that the worktable rotary angle error has a slight effect on the Pascal limacon gear pitch curve, and the center distance error has a great effect on the Pascal limacon gear pitch curve.

Conclusion: The Pascal limacon gear pitch curve error is highly sensitive to the center distance error near the polar angles of π/ 2 and 3π / 2.

Keywords: Hobbing, noncircular gear, pitch curve, sensitivity, the center distance, the worktable rotary angle.