# Application test of positive displacement gear

When no external error is considered in gear hobbing, that is, the center distance installation error of gear hob is zero. If the installation error of gear hob center distance is considered, at this time, the center distance α Installation error e α Not zero. Given the basic parameters of gear hob and gear tooth surface, the center distance between gear hob and gear is taken from the formula α Installation error e α= 0.05mm, center to center α：

Axis intersection angle error E Σ = 0mm. At this time, the processed gear is a positive displacement gear, and the displacement XM = 0.05mm.

As shown in Figure 1, it is the error between the simulated tooth profile of the gear end face and the theoretical involute tooth profile when the displacement XM = 0.05mm.

As can be seen from Figure 1, when the installation center distance error e between gear hob and gear α= When 0.05mm, that is, the displacement XM = 0.05mm, the error between the simulated tooth profile and the theoretical involute tooth profile is 23.29 μ m~23.35 μ m 。

Take the center distance between gear hob and gear α Installation error e α= 0.5mm, center to center distance α ：

At this time, the processed gear is a positive displacement gear, and the displacement XM = 0.5mm. Based on Mathematica software, the gear end face profile and theoretical involute profile of gear hobbing are simulated, as shown in Figure 2. The black solid line is the theoretical involute tooth profile, and the blue discrete points are the end tooth profile obtained by simulation.

As shown in Figure 3, it is the error between the simulated tooth profile of the gear end face and the theoretical involute tooth profile when the displacement XM = 0.5mm.

It can be seen from Figure 3 that when the installation center distance error e between gear hob and gear α = When it is 0.5mm, that is, the displacement XM = 0.5mm, the error value between the simulated tooth profile and the theoretical involute tooth profile is 233.2 μ m~233.7 μ m 。

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