# The influence of the modification quantity on the dynamic load of the involute spur gear under different modification types

The modification length is 2.8mm, the change range of modification amount is [0, 0.05mm], and the value interval is 0.02mm. Among them, when the modification amount is 0, it means that the gear has no modification. Four different types of modification are used for comparative study, which are linear modification, parabola modification, exponential modification and conic modification. Among them, the expressions of exponential modification and conic modification are respectively:

Figure shows the change trend of dynamic load coefficient with the amount of shape modification under the above four types of shape modification. See the formula for the definition of dynamic load coefficient. It can be seen from the figure that with the increase of the modification amount, the dynamic load coefficient changes in a “V” shape, that is, there is an optimal modification amount to minimize the dynamic load coefficient, and the optimal modification amount is less than the deformation amount of the highest point of single tooth meshing under the average torque of the engine by 0.022mm. Among them, the optimal shape modification amount of linear shape modification is 0.014mm, and the corresponding dynamic load coefficient is 1.87; the optimal shape modification amount of quadratic curve is 0.016mm, and the corresponding dynamic load coefficient is 2.1; the optimal shape modification amount of parabola shape modification is 0.016mm, and the corresponding dynamic load coefficient is 1.95; the optimal shape modification amount of exponential shape modification is, and the corresponding dynamic load coefficient is.

The minimum dynamic load coefficients of the four modified types are 23%, 18.6%, 19.4% and 13.2% lower than those of the unmodified type 2.42, respectively, which shows that the linear modification has the best damping effect. However, with the increase of the modification amount, the range of the dynamic load coefficient of the linear modification is the largest, followed by the exponential modification and the quadratic curve modification, and the parabola modification. It is defined that when the dynamic load coefficient of the modified gear exceeds that of the non modified gear, the corresponding modification amount is the critical modification amount. From the figure, it can be seen that there are critical modification amount in all four modification types, indicating that the modification amount of the tooth profile modification should be less than the critical modification amount, otherwise the effect of vibration reduction cannot be achieved.

Among them, the maximum value of parabola modification is 0.04mm, the second value of exponential modification and conic modification is 0.036mm, and the minimum value of linear modification is 0.032mm. 