# Transmission error of hypoid gear under small load

It can be seen from the calculation model of gear mesh stiffness that before calculating the gear mesh stiffness under load, the transmission error of the gear under no load is calculated first. In this paper, small load is used instead of no load. The main reason for applying small rotating moment load here is that the current meshing analysis model is mostly based on the geometric meshing relationship of the gear. At this time, the loading moment of the gear is not considered. In order to compare the analysis results, no force should be applied in the gear contact analysis, but in the finite element contact analysis of the gear wheel, a force should be applied to keep the contact between the gear teeth, This torque can be very small. Here it can be taken as one percent of the maximum working torque of the gear. Under the action of this small moment, the finite element contact analysis can basically simulate the contact process of the gear under the action of no load, which can ensure that there is only one tooth contact in the process of finite element analysis, and can approximate the transmission error of the gear under no load.

Apply 10 N · m resistance torque at the output end of the big gear, as shown in the figure, during the gear rotation, the change course of the normal meshing force at the equivalent meshing point of the contact surface of three pairs of meshing teeth, the contact surface is expressed as suf ˊ I, where I = 1, 3, 5 is the gear surface of the big gear, I = 2, 4, 6 is the gear surface of the small gear, suf ˊ 1 of the big gear and suf ˊ 2 of the small gear are the meshing gear pairs, and so on, The normal force on the tooth surface of large and small gears is the force and reaction force, so this paper only gives the force on the tooth surface of large gears. From the figure, it can be seen that the normal meshing force of each tooth does not overlap, and the gear is always in single tooth meshing state, and the value of meshing force is small at this time. After processing the mesh analysis results of large and small gears, we can get the transmission error in the process of gear mesh, as shown in Figure 9. It can be seen from the figure that the transmission error of gears under small load is approximately parabola, which is consistent with the actual transmission error of hypoid gears under small load measured in the literature, This is to reduce the contact impact of gears in the process of meshing. The transmission error of gears without load is designed as parabola shape in gear design.

The most widely used method of hypoid gear mesh simulation is gear geometric contact analysis (TCA), which can obtain the instantaneous mesh point of the tooth surface. Through the gear contact analysis, the position of the mesh midpoint and the normal vector of the mesh midpoint can be obtained quickly. Compared with the TCA analysis results and the finite element calculation results under small load, the finite element analysis results are basically consistent with the TCA analysis results, The results show that the finite element simulation has high accuracy. 