Basic conditions of cylindrical gear biting

Cylindrical gear biting is a very complex process. The specific biting model is shown in Figure 1. In the figure, the driving roller rotates around the O1 axis and the core roller rotates around the O2 axis. R1 and R2 are the radius of the driving roller and the core roller respectively, α 1、 α 2 is the contact angle between the driving roller, the core roller and the cylindrical gear, P1 and P2 are the pressure of the driving roller and the core roller on the cylindrical gear, t is the friction between the driving roller and the cylindrical gear, l is the projection length of the contact arc length, H0 and H are the width before and after the biting of the cylindrical gear respectively, Δ H is h0-h, indicating the reduction of the ring wall of the cylindrical gear every revolution.

The friction coefficient between the blank and the ring rolling die is μ，β Is the friction angle between the blank and the die, and its relationship is μ= tan β， Basic conditions for biting of ring parts:

Generally, the friction angle is very small, which can be replaced by the ratio of the biting arc length of cylindrical gear and die to the corresponding radius α 1=L/R1， α 2=L/R2。 According to the relevant formula, the maximum feed rate per revolution when a blank enters the drive roll is:

This formula shows that the maximum feed rate of the blank entering the driving roller for each rotation cycle cannot exceed Δ Hmax, which must be within the range of this value to ensure the smooth rolling of the ring, i.e Δ h ≤ Δ hmax。 From the numerical relationship of the formula, it can be seen that the feed rate satisfied by the ring rolling at the beginning is the smallest, i.e Δ Hmax is the minimum value during ring rolling.

Because the cylindrical gear is not set to rotate by itself during machining, the phenomenon of stationary will appear in the process of ring rolling. This situation is mainly due to the fact that the feed rate of each rotation of the ring rolling can not meet the basic conditions of the biting hole pattern of the cylindrical gear. During the rotation of the driving roller, the friction between the driving roller and the cylindrical gear can not drive the cylindrical gear to rotate and slide relatively. The cylindrical gear can not produce plastic deformation, so the continuous deformation process is interrupted. In order to avoid this phenomenon in ring rolling, the feed rate per revolution must be adjusted to make it within the maximum allowable range of cylindrical gear biting hole. Increasing friction and wall thickness will help to improve this situation.

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