# Analysis on the coincidence degree of bevel gears without backlash

The linear gear can also improve the transmission stability by increasing the degree of coincidence. The calculation formula of line gear coincidence is:

Where, Δ φ 1 is the corresponding angle of a tooth on the driving wheel from the beginning of engagement to the end of engagement; N1 is the number of driving teeth.

According to the formula, there are three ways to increase the coincidence degree:

(1) Increase the number of teeth;

(2) Increase the corresponding angle from entering to exiting the engagement, that is, increase the value range of parameter variable t;

(3) At the same time, increase the number of teeth and the range of parameters.

This paper mainly discusses how to increase the coincidence degree by increasing the number of teeth.

When increasing the number of teeth, it is necessary to consider the space occupation of the teeth to the cone, as shown in Figure 1. Take the cross section of driving wheel I as shown in Figure 2. Each tooth occupies a part of the circumference of the cone top circle, and the sum of the circumference of the cone top circle occupied by all teeth shall satisfy the relationship

Where, R is the top circle radius of cone; R is the section circle radius of gear; m is the spiral radius of driving wheel center line; n is the number of teeth.

According to the linear gear mechanism constructed in this paper, when the value range of parameter t is constant, the coincidence degree can be increased by increasing the number of teeth, but the increase of the number of teeth should meet the relationship shown in the formula. 