It is well known that the optimum amount of tooth direction modification varies with the meshing tooth direction error and tooth force, but the law of variation is not clear. It is helpful to estimate the change trend and value of the optimum tooth profile modification amount under different load conditions or considering different assembly errors by studying the influencing factors and laws of the optimum tooth profile modification amount. Taking the limit meshing state of gear pair 2 under rated load as the standard value, the tooth alignment error and tooth force are changed in the range of 50% to 150% of the standard value (the increment is 25%), and a total of 25 groups of different meshing states are obtained. By using the method of tooth direction modification, the optimal amount of tooth direction modification is almost linear with the meshing tooth direction error and tooth force. As shown in the figure, 25 sets of results can be approximately fitted in a plane, and the maximum relative fitting error appears at the point (0.5,0.5), with a value of 3.3%.

It should be pointed out that the cutting part of the shearer operates under the condition of heavy load and low speed, and the tooth force in the simulation is not particularly low (or the meshing tooth direction error is not particularly large), so the 25 groups of simulation in the figure do not appear partial tooth surface separation in the direction of tooth width. Therefore, the approximate linear relationship between the optimal amount of tooth direction modification and the meshing tooth direction error and the tooth force is obtained when there is no partial tooth surface separation in the tooth width direction. When there is partial tooth surface separation in the direction of tooth width, the primary purpose of tooth modification is to increase the effective contact tooth width, which has not been discussed in this study.