Effects of interval friction coefficients on the differential mechanism dynamics

The presence of a differential mechanism is fundamental in most automotive applications. Its importance stems from allowing a vehicle to take a curve. The differential should be well-lubricated to ensure its smooth operation and mitigate its vibration level. With lubrication conditions deteriorating over time, the sliding friction coefficient becomes difficult to predict its accurate value. Thus, scrutinizing the dynamic performance of the mechanism with deterministic sliding friction can be misleading. This paper aims to investigate the dynamic performance of the automotive differential with the presence of interval sliding friction. To this end, a 3D dimensional model of automotive differential with time-varying mesh stiffness (TVMS) and bearing flexibility is proposed. The influence of sliding friction on TVMS for straight bevel gear is revealed. The Newton-Euler formulation is used to derive the dynamic equations governing the motions of the automotive differential with friction. The Chebyshev inclusion function and the least square method are used to deal with the interval mathematical formulation of the model. The scanning method is used as a reference method in this paper. There are quite similarities between the results derived by the scanning method and that of the interval process method. The reliability analysis of the differential is conducted. The outcome of this research shows that any variation of the sliding friction can alter the dynamic performance of the differential significantly. The differential is more sensitive to the friction coefficient between the ring gear and the drive pinion and between the left-side gear and two planets. The findings should make an important contribution to the analysis of the differential mechanism.

A revised method to calculate time-varying mesh stiffness of helical gear

Time-varying mesh stiffness (TVMS) of gear plays vital role in analysing dynamic characteristic of gear transmission. So accurately evaluating the TVMS is important and essential. In this paper, a revised method to calculate the TVMS of helical gear is proposed. Based on slice method, the helical gear is sliced into pieces along the tooth width direction. The proposed method corrects the fillet foundation stiffness within multi-tooth in contact and considers the non-linearity and load-dependence of the Hertzian contact stiffness. The effect of the axial mesh force is considered. Finally, an equivalent helical gear model is established in ANSYS to study the mesh stiffness. The results show the proposed method has high effectiveness compared with FEM (finite element method).

Analytical calculation models for mesh stiffness and backlash of spur gears under temperature effects

The temperature has a great contribution to the mesh stiffness and backlash of the gear pair. Presence of thermal deformation caused by temperature will complicate the gear teeth interaction. In this paper, the thermal time-varying stiffness model and thermal time-varying backlash model are proposed with the consideration of tooth profile error and total thermo-elastic deformation consists of the teeth deformation, teeth contact deformation, and gear body-induced deformation. The key parameters of thermo-elastic coupling deformation affected by temperature are calculated. Based on the proposed models, the influencing mechanism of temperature on the tooth profile error, mesh stiffness, total deformation, and backlash are revealed. The effects of shaft radius and torque load on the thermal stiffness and thermal backlash are studied. The proposed thermal stiffness and backlash calculation model are proven to be more comprehensive and the correctness is validated.

Dynamic Characteristic Analysis of Spur Gear System Considering Tooth Contact State Caused by Shaft Misalignment

Shaft misalignment will change the gear contact state, and then leads to the variation of the internal stiffness excitation of the gear pair, and finally the dynamic characteristics of the gear system will be affected. However, the influence of the gear contact state change on stiffness is usually neglected in the traditional stiffness calculation model for misaligned gears, and the underlying influence mechanism of the gear contact state changes aroused by the shaft misalignment on the dynamic characteristics of gear system is still unclear. To address these shortcomings, traditional loaded tooth contact analysis (LTCA) model is improved with the influences of fillet foundation deformation taken into consideration. Combined with the improved LTCA model, a new mesh stiffness calculation model for misaligned gear considering the tooth contact state is proposed, and then the effects of the contact state changes aroused by the shaft misalignment on the mesh stiffness excitation are studied. Moreover, a dynamic model of misaligned gear system with 8 degree of freedom (DOF) is established, and the dynamic characteristics of the system are simulated and finally verified by experiment. The results show that the proposed model can be used to evaluate the dynamic characteristics of the misaligned gear system with the change of gear tooth contact state taken into consideration. This study provides a theoretical method for the evaluation and identification of the shaft misalignment error.