Optimization of tooth profile modification for helical gears to reduce impact of meshing

1 Construction of modified tooth surface

The modified tooth surface is constructed by superposition of theoretical tooth surface and modified surface.As shown in Figure 7, the modified curve consists of two quadratic parabolas and a straight line.

In the figure, Y1 is the root modification quantity, Y2 is the top modification quantity, Y3 is the root modification length, Y4 is the top modification length, Y5 is the tooth modification quantity, y6 is the tooth modification length, B is the tooth width, H is the effective tooth height.

2 Optimization of tooth profile modification

The basic reason for impact is the relative speed difference between large and small wheel teeth at the rodent point. If there is no relative speed difference, there is no impact. Therefore, this paper optimizes the impact force by optimizing the relative speed difference at the rodent point.

When the tooth surface is optimally modified, the optimum model can be expressed as:

Optimum variables: y1, y2, y3, y4, y5, y6

Target function:



S.s. t.{δmin≤y1,y2,y5≤δmaxhmin≤y3,y4≤hmax0

In the formula, the values of delta min and delta Max are correlated with gear module, which are 0.001 Mn and 0.015mn (mn is modular), 0.1 Mn and 0.8 Mn respectively for Hmin and hmax, and 0.5B for Lmax (B is tooth width).

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