Lei Liu

The prediction of load-dependent losses of gear pairs is a topic of constant concern, which depends largely on the modelling of friction coefficient in tooth meshing. Although the current load-sharing based models can handle the friction coefficient in mixed elastohydrodynamic lubrication regimes, dynamics behaviour of each tooth pair or the time variation of direction of normal contact load is not taken into consideration. This study proposes a new method for modelling efficiency of spur gear pairs in transient operating conditions by coupling the multi-tooth meshing model with the friction coefficient model. The friction coefficient is modelled through load-sharing function, and the gear dynamics model is established with regard to alternate meshing of single-double tooth pair and time variation of direction of normal load and mesh stiffness. The model is validated by comparing the calculated results of friction coefficients and load-dependent losses with experimental data in published literatures, showing good agreement. At the end, the efficiency model is applied to two types of gear pairs to investigate the influence of tooth shapes and operating parameters on the load-dependent losses of gear pairs.

Design of new tooth shapes have been the focus of gear researchers aimed at overcoming the defects of involute gears. For the spur gear drive with curved path of contact, normal contact loads between engaged teeth vary in direction and magnitude, which makes it difficult to build the dynamics model of the gear drive. The current models treat the curved path of contact as an equivalent straight line without considering directional variation of normal tooth loads. This paper presents an efficient tribo-dynamics integrated model for this type of gear drive including effects of alternate meshing of single-double tooth pairs. Directional variation of normal tooth loads is considered by invoking geometric parameters of meshing points instantly. And the transient lubrication properties in mixed elastohydrodynamic lubrication are also taken into account without extensive numerical simulations. The dynamics model of a gear drive with constant relative curvature (CRC gear drive) is given as an example. The model is verified with the results of the finite element model. The results indicate that the CRC gear drive has advantages over the involute gear drive in terms of lubrication performance and mechanical efficiency. The proposed model can be used to analyze dynamics features of gear drives with curved path of contact comprehensively.

This article presents a sphere–face gear pair by substituting the convex spherical gear for the pinion of a conventional face gear pair. The sphere–face gear pair not only maintains the advantages of the face gear pair with a longitudinally modified pinion but also allows variable shaft angles or large axial misalignments. Meshing characteristics of the proposed gear pair are studied in this article. The mathematical models of the sphere–face gear pair are derived based on machining principles. The tooth contact analysis (TCA) and curvature interference check are conducted for the sphere–face gear pair with variable shaft angles. The loaded TCA is also implemented utilizing the finite element method. The results of numerical examples show that proposed gear pair has the following features. Geometrical transmission error of constant shaft angle or varying shaft angle is zero; contact points of the sphere–face gear set with variable shaft angle are located near the centre region of face gear tooth surface; there is no curvature interference in meshing; and transmission continuity of the gear pair can be guaranteed in meshing.

The torus involute gear can compensate large axial misalignments and may possess good meshing characteristics without lead correction. In order to study its dynamic characteristics and verify its feasibility of the practical application, a new efficient rigid-elastic coupling dynamic model of multi-tooth is established which includes effects of lubrication oil film and tooth deformations directly in contact simulation of gears. In this model, each tooth is connected with the gearwheel by a rotatable spring-damper element whose stiffness is calculated through analysis of tooth deformation. The normal tooth contact force is determined via Lankarani and Nikravesh model. Variation of contact stiffness and rotatable spring stiffness with contact points are both taken into account. Combined with tooth contact analysis, the computation of friction coefficient is implemented with high efficiency by introducing the average lubrication oil film height. A three-dimension multi-body model of a torus involute gear pair is employed and verified by an impact experiment. The simulated results provide useful information about tooth impacts, dynamic transmission error and lubrication conditions like oil film heights and friction coefficients, and show that this type of gear can work with good meshing characteristics. The contributions in this paper lay theoretical basis for the application of the torus involute gear.