*3.2. TSCS Analysis of Gear with ME*

In this paper, the ME is divided into two directions, and the ME in all directions can be decomposed into these two directions. As shown in Figure 16, point A and point C are the absolute center points of the two engaged gears. When the two gears are in the ideal engaged state, a 3D rectangular coordinate system is established with point A as the origin, where the AC direction is the X axis direction, the AB direction is the Y axis direction (which is the axial direction of gear 1), the Z axis direction is the radial direction of gear 1, plane V is the plane composed of the Y axis and Z axis, and plane S is the plane composed of the X axis and Y axis. Then, the first kind of ME is the rotation error around the Z axis in the S plane, and the amount of meshing error is <BAB2, which is <*a*, and the second kind of ME is the rotation error around the X axis in the V plane, and the amount of ME is <BAB1, which is <*b*.

**Figure 16.** Definitions of meshing errors (ME).

According to the actual measurement data from the gear factory, most of the range of the <*a* value is 0.1–0.7◦, and most of the range of the <*b* value is 0.02–0.15◦. Taking the counterclockwise rotation direction as the positive direction, selecting 0.2◦, 0.4◦ and 0.6◦ for <*a* respectively, and conducting the gear FEM contact analysis under the applied torque of 10 N·m, the analysis results are shown in Figure 17. Then, selecting <sup>−</sup>0.04◦, −0.08◦ and −0.12◦ for <sup>&</sup>lt;*b*, respectively, and conducting the gear FEM contact analysis under the applied torque of 10 N·m, the analysis results are shown in Figure 18.

(**c**) <ܽ ൌ ͲǤι

**Figure 17.** The TSCS nephograms of <*a* = 0.2◦, <*a* = 0.4◦ and <*a* = 0.6◦.

In Figure 17, from Figure 17a to Figure 17c are shown the TSCS nephograms of <*a* = 0.2◦, <*a* = 0.4◦ and <*a* = 0.6◦. It can be seen that the TSCS with an ME of <*a* is concentrated on the left side of the tooth surface, and with the increase in <*a* value, the gradient of the local TSCS increases gradually, and the maximum TSCS also increases accordingly.

In a similar situation, as can be seen from Figure 18, from Figure 18a to Figure 18c are the TSCS nephograms of <*b* = <sup>−</sup>0.04◦, <*b* = −0.08◦ and <*b* = <sup>−</sup>0.12◦. It can be seen that the TSCS with the ME of <*b* is concentrated on the right side of the tooth surface, and with the increase in <*b* value, the gradient of the local TSCS increases gradually, and the maximum TSCS also increases accordingly.

In addition, it can be seen from the figures that the TSCS of gears with an ME of <*a* is concentrated on the left side of the tooth surface, while the TSCS of gears with an ME of <*b* is concentrated on the right side of the tooth surface. There should be some interaction between the two kinds of ME, which needs further study.

In this paper, the FEM contact analysis is conducted under different torques for gears with different ME, and the results of the maximum TSCS are compared as shown in Table 7 and Figure 19. It can be seen that the influence of ME on the TSCS is very large, and the difference between the maximum TSCS corresponding to the different ME values is large. Within the set range for the ME value, the influence degree of <*a* is relatively greater. At the same time, it is found that with the increase in applied load, the ratio of the maximum TSCS of each gear a different ME to the ideal gear gradually decreases.

**Table 7.** The results of the maximum TSCS under different torques. Unit: MPa.


**Figure 19.** The results of the maximum TSCS under different torques.
