The precise mathematical model for the tooth surface and transition surface of spiral bevel gears is derived. Taking a pair of spiral bevel gears of a heavy vehicle as an example of calculation and analysis, a finite element model of spiral bevel gears transmission system is established. Through the finite element tooth contact analysis under quasi-static loading and high loading condition, the influences of torque on the root stress distribution, contact stress, and transmission error are discussed, and the results are compared with the empirical formula results. Finally, a contact performance test bench of spiral bevel gear pair is developed, then the root bending stress, contact pattern, and transmission error tests are carried out. These experiment results are compared with analyzed ones, which showed a good agreement.

Aiming at the problems of poor tracking accuracy, low convergence speed, weak robustness of a 6-DOF electro-hydraulic suspension test system under system uncertainties and external disturbance, this article proposes double closed-loop control scheme. In the outer loop controller, this article designs a new decoupled adaptive fast nonsingular terminal sliding mode (DAFNTSM) control to achieve fast convergence rate, high accurate and adaptive disturbances estimation during trajectory tracking. Additionally, a coupling force compensator based on RBF neural network is employed, which can reduce online calculation quantity and guarantee accuracy. For six inner loop controllers, each hydraulic actuator can precisely follow the required force solved by outer loop controller. The hard-in-loop experiment results reveal that the control approach we proposed in this paper realize superior trajectory tracking characteristics in comparison with the conventional nonsingular terminal sliding mode (CNTSM) method.

In a planetary gear set with an elastic ring gear, there are several pairs of flexible internal meshing simultaneously. The interactions between them are often ignored when considering their mesh stiffness. This study is devoted to investigating the effect of the number of equally spaced planets and the number of fixed supports of ring gear on mesh force and loaded-static transmission error (LSTE) as well as related mesh stiffness through a 2D system-level finite element model. This model is first validated by the comparison with the traditional potential energy method (PEM) when the ring gear is fully fixed. Then taking the number of planets and fixed supports as variables, 16 sets of analyses are conducted. Mesh force and LSTE extracted from the model, together with the mesh stiffness derived by them, are analyzed and concluded in the time domain and/or frequency domain. It is demonstrated that the number of planets has a certain impact on the ring-planet mesh stiffness. In terms of the number of planets and fixed supports, planetary gear systems can be classified into three categories according to the distinctive behaviors of mesh force and LSTE in the time domain and frequency domain.

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