Research on the influence on the addendum-shortened-coefficient of the first-last teeth of incomplete driving gear to avoid interference

Abstract

In order to ensure the normal transmission of incomplete gears without interference during the process of gear meshing. This research first establishes the theoretical model to explore the influence of the reference circle pressure angle (α), the addendum modification coefficient, and the number of teeth on the addendum-shortened-coefficient (σ) of the incomplete driving gear's first-last teeth, and then systematically explores the influence between the key factors and the decrease of σ. The results show that: (1) When the pressure angle of the driven gear addendum circle (αa2) and the maximum critical value of the addendum radius of the driving gear to avoid interference (ra1') increases with the increase of α, σ decreases with the increase of α; (2) In the cases of high-modification gear transmission and angular-modification gear transmission, there are five conditions in which σ decreases due to the addendum modification coefficient of driving gear (x1) and the addendum modification coefficient of driven gear (x2): 1) High-modification gear transmission with one case:① x1+x2=0, x1=−x2≠0 with the increase of x2, that is: x1 and x2 are opposite number; 2) Angular-modification gear transmission with other four cases: ② x1+x2<0, x1<0 with x2=0, that is: The driving and driven gears are negative-modified and standard gears, respectively; ③ x1+x2>0, x1=0 with x2>0, that is: The driving and driven gears are standard and positive-modified gears, respectively; ④ x1+x2<0, x1≠0, x2≠0 with the increase of x2, that is: The sum of x1 and x2 are negative and neither of them is zero, there exist three kinds of addendum modification gears for the driving and driven gear, which are positive-negative, negative-positive and negative-negative. ⑤ x1+x2>0, x1≠0, x2≠0 with the increase of x2, that is: The sum of x1 and x2 are positive and neither of them is zero, there exist three kinds of addendum modification gears for the driving and driven gear, which are positive-negative, negative-positive and positive-positive. (3) While exploring the influence of α, x1 and x2 on σ, the influence of the number of driven gear teeth (Z2) on σ is greater than that of the number of driving gear teeth (Z1). It contributes to the optimization design of incomplete gears to avoid transmission interference in the study and improve its gear strength, load-bearing capacity, and transmission efficiency without reducing, etc.