There are three ways of tooth profile modification: cutting or grinding a part near the top of the tooth, which is called top profile modification; cutting or grinding a part near the root, which is called root profile modification; and simultaneous top and root modification is called full profile modification.

In order to ensure the strength of the tooth roots, only the top of the gear teeth is modified in the profile modification design, and the root modification is equivalent to the top of the meshing gear teeth. Therefore, only the top modification is considered in this paper.

The main task of profile modification is to determine three elements: the amount, length and type of profile modification.In the research of tooth profile modification, two methods are usually used to express the corresponding modification quantity of the tooth profile modification position: one is to express the modification quantity of the tooth profile position as a function of the curvature radius of the tooth profile or the involute spread angle of the point, which is convenient for gear machining; the other is to express the modified position of the tooth profile as a function of the length of the engagement line on the meshing line of the gear pair.It is more convenient to analyze the influence of tooth modification on gear meshing transmission.

For the sake of dynamic analysis, the modification gauge is expressed as a function of the engagement line length. As shown in the figure, L is the modification length, Cmax is the maximum modification quantity for the top position of the teeth, and the modification function can be expressed as: