1. Actual meshing line length before trimming
The meshing transmission range of a pair of gears is limited, as shown in Figure 1. AE is the actual meshing line of the gear teeth, and the ratio of its length to the normal pitch of the gear tooth base circle is the coincidence degree of the gear transmission. Therefore, it is necessary to study the change of the actual meshing line of the gear teeth under different working conditions.
2. Actual meshing line length after trimming
With reference to the actual processing technology of the manufacturing enterprise, the linear shape modification is taken as the research object. During gear tooth meshing, the normal load direction is always consistent with the direction of the actual meshing line. After tooth top trimming, the load action direction will deviate from the direction of the theoretical meshing line due to the change of tooth profile shape, as shown in Figure 2. When the contact shape of gear pair is removed δ After that, there is a phase angle between the actual meshing line direction and the theoretical meshing line direction ω， The right-angle coordinate system is established based on the starting point of the trimming. The slope of the trimming contour can be obtained from the gear parameter relationship in the figure, and then the action direction of the actual load F ′ n can be obtained. The action direction of the theoretical load Fn can be obtained according to the pressure angle of the addendum circle. When the load acts on the tooth top, the actual meshing radius can be calculated according to the trigonometric function relationship as follows:
According to the angle between the actual meshing line and the theoretical meshing line ω And the actual meshing radius r ′ x of the meshing point can determine the distribution of the actual meshing line after trimming. Because the pressure angles of different meshing points on the involute are different, the included angle between the theoretical load direction and the actual load direction changes with the change of the meshing point.