# Transmission error of hypoid gear under small load

According to the gear meshing stiffness calculation model, before calculating the gear meshing stiffness under loading, the transmission error of the gear under no load is calculated first. In this paper, small load is used to replace no load. The application of small rotating torque load here is mainly due to the fact that most of the current meshing analysis models are obtained based on the geometric meshing relationship of the gear. At this time, the gear loading torque is not considered. In order to compare the analysis results, no force should be applied during the gear contact analysis, but a force needs to be applied during the finite element contact analysis of the gear wheel in order to keep the gear pair in contact, This torque can be very small. Here, one percent of the maximum working torque of the gear can be taken. Under the action of this small torque, the finite element contact analysis can basically simulate the contact process of the gear under no-load, ensure that there is always only one tooth contact in the process of finite element analysis, and approximate the gear 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 Figure 1, the change process of normal meshing force at the equivalent meshing point of the contact surface of three pairs of meshing teeth during gear rotation is shown, and the contact surface is expressed as suf_ i. Where I = 1, 3 and 5 represent the tooth surface of large gear, I = 2, 4 and 6 represent the tooth surface of pinion and suf of large gear_ 1 suf with pinion_ 2 is the meshing gear pair, and so on. The normal force on the tooth surface of large and small gears is the acting force and reaction force. Therefore, this paper only gives the acting force on the tooth surface of large gears. It can be seen from the figure that the normal meshing force of each tooth does not overlap, the gear is always in the single tooth meshing state, and the meshing force value is small at this time. After processing the meshing analysis results of large and small gears, the transmission error in the gear meshing process can be obtained, as shown in Figure 2. It can be seen from the figure that the transmission error of the gear under small load is approximately parabola, which is consistent with the actual transmission error of the hypoid gear under small load measured in the experiment, This is to reduce the contact impact of the gear in the meshing process. In the gear design, the transmission error of the gear without load is designed as a parabola shape.

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

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