Non-Newtonian mixed thermo-elastohydrodynamics of hypoid gear pairs

Transmission efficiency is the main objective in the development of vehicular differential systems, comprising hypoid gear pairs. The overall aim is to contribute to improved vehicle fuel efficiency and thus levels of harmful emissions for modern desired eco-drive axles. Detailed predictive analysis plays an important role in this quest, particularly under realistic operating conditions, comprising high contact loads and shear rates. Under these conditions, the hypoid gear pairs are subject to mixed non-Newtonian thermo-elastohydrodynamic conditions, which is the approach undertaken in this paper. Such an approach for hypoid gear pair has not hitherto been reported in the literature.

Dynamic Analysis of Automotive Hypoid Gears

The dynamics of differentials in rear wheel drive vehicles are of major importance for the automotive industry. Hypoid transmissions — forming the motion transfer mechanism from the driveshaft to the wheels — often suffer from severe vibrations, which could lead to Noise, Vibration and Harshness (NVH) issues. The latter are often attributed to improper mesh between the mating gear flanks due to misalignments, variation of contact load and shifting of the effective mesh position. A new modelling approach on the torsional dynamics of hypoid gear pairs is presented in this work. This is characterised by an alternative expression of the Dynamic Transmission Error (DTE), which accounts for the variation of the effective mesh position. Numerical results indicate the enriched dynamic behaviour that can be predicted using the new formulation. A solution continuation method is employed to follow the response branches over the operating range of the differential under examination. The ensuing parametric studies convey the importance of the main system parameters on the dynamic behaviour of the differential, yielding suggestions for design guidelines.

Evaluation System of Tooth Contact Patterns of Hypoid Gears Using Artificial Intelligence

Tooth contact inspection is one of the most common methods for checking qualities of hypoid gear pairs. A change in machine setting parameters for cutting and lapping processes of a hypoid gear pair enables a tooth contact pattern of a hypoid gear pair to be varied. The deviation of the pattern from the target one is represented by a grade point. In the inspection, the qualities of hypoid gear pairs are usually classified into only two grades; OK or NG. However, in order to conduct a follow-up survey on problems of the products and to be useful to be trouble shooting tasks of the end products, finer classifications and more quantitative evaluations of tooth contact patterns could be effective. Such approaches have been tried, however, only experienced and well-trained technicians for the inspection of hypoid gear pairs can determine the point of each tooth contact pattern. And it is difficult to make this evaluation method automatic. To overcome this problem, an application of artificial intelligence system must be useful. The present paper describes a computer evaluation system using the neural network, which is a kind of the artificial intelligence systems, for tooth contact patterns of hypoid gear pairs which can evaluate the results of the inspections instead of experienced hypoid gear technicians. This system with the neural network has a capability to learn relationships between evaluation grade points of tooth contact patterns given by the hypoid gear technicians and graphics of tooth contact patterns of hypoid gear pairs. Moreover, it can return the evaluation grade points when a tooth contact pattern is input into the system. The evaluation performance of the developed system was discussed. And a quality of normative tooth contact patterns, which were used as the teacher signals for training the neural network system, greatly affected its performance. The comparison of evaluated grade points obtained from developed system with the technician’s ones showed that the correct answer ratio obtained from the developed system was about 90% in the best case.

An Investigation of Root Stresses of Hypoid Gears with Misalignments

In this study, the impact of misalignments on root stresses of hypoid gear sets is investigated experimentally and theoretically. An experimental set-up designed to allow operation of a hypoid gear pair under loaded quasi-static conditions with various types of tightly controlled misalignments is introduced. These misalignments include the position errors (V and H) of the pinion along the vertical and horizontal directions, the position error (G) of the gear along its axis, and the angle error (γ) between the two gear axes. For example, face-hobbed hypoid gear pair from an automotive axle application is instrumented via a set of strain gauges positioned at the roots along the faces of multiple teeth to measure root strains within a range of input torque. These root strain measurements at different V, H, G, and γ values are presented. A computational model is also proposed to predict the root stresses of face-milled and face-hobbed hypoid gear pairs under various loading and misalignment conditions. The model employs an automated finite elements mesh generator based on a predefined template for a general and computationally efficient treatment of the problem. Model predictions are compared to measurements at the end to assess the accuracy of the model and describe the measured sensitivities.

Prediction of friction-related power losses of hypoid gear pairs

A model to predict friction-related mechanical efficiency losses of hypoid gear pairs is proposed in this study. The model includes a gear contact model, a friction prediction model, and a mechanical efficiency formulation. The friction model uses a friction coefficient formula obtained by applying multiple linear regression analysis to a large number of elastohydrodynamic lubrication analyses covering typical ranges of key parameters associated with surface roughness, geometry, load, kinematics, and the lubricant. Formulations regarding the kinematic and geometric properties of the hypoid gear contact are presented. The load and friction coefficient distribution predictions are used to compute instantaneous torque/power losses and the mechanical efficiency of a hypoid gear pair at any given position. Results of a parametric study are presented at the end to highlight the influence of key operating conditions, surface finish, and lubricant properties on mechanical efficiency losses of hypoid gears.