# Calculation of load ratio and normal load of meshing contact stiffness of gear tooth surface

According to the semi empirical formula model, the contact stiffness is related to the contact load. According to the description of the meshing process of spur gear pair, there is single double meshing alternating action along the meshing tooth profile. Therefore, in the single double alternating action period, there is a pair of gear teeth in the single meshing area to bear the normal contact load completely, while in the double meshing area, there is a method of two pairs of gear teeth sharing the normal contact load As shown in Fig. 1. In the relevant standards, agma925-a03 “effect of pollution on gear surface density” and ISO / ts6336-22

The calculation of load capacity of spur and hydraulic gears-part22: Calculation of micropitting load capacity lists the distribution diagram of load ratio, as shown in Figure 2.

It can be seen from Fig. 2 (a) that the end face load ratio of unmodified gear pair obeys the jump mode, that is, the double meshing increases or decreases with a certain slope, the single meshing area is flat, and the load jump suddenly occurs at the moment of double single alternation. In the same way, after tooth surface modification, the load jumping distance can be reduced, and the range length of single double meshing area can be changed (Fig. 2 (b)). If the tooth surface modification can be optimized, the perfect load distribution of seamless connection will appear as shown in Fig. 2 (c), which indicates that the tooth surface modification can realize smooth load curve distribution and meshing operation Dynamic smooth transition effect. However, in the actual meshing process, the load ratio distribution mode is still in the form shown in Fig. 2 (a) and 2 (b). Sanchez et al. Studied and proposed the load ratio formula considering Hertz contact effect for spur gear pair with coincidence degree of L < ε < 2. Considering different geometric effects and influencing factors, the derivation formula and application of load ratio are studied. In this paper, Sanchez’s formula is used to calculate the normal load calculation and distribution, such as the formula.

According to the analytical equation of torsional load and combined formula, the normal load of contact point can be further deduced as follows:

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