Microgeometry optimization has become an important phase of gear design that can remarkably enhance gear performance. For spiral bevel and hypoid gears, microgeometry is typically represented by ease-off topography. The optimal ease-off shape can be defined as the outcome of a process where generally conflicting objective functions are simultaneously minimized (or maximized), in the presence of constraints. This matter naturally lends itself to be framed as a multi-objective optimization problem. This paper proposes a general algorithmic framework for ease-off multi-objective optimization, with special attention given to computational efficiency. Its implementation is fully detailed. A simulation model for loaded tooth contact analysis is assumed to be available. The proposed method is demonstrated on a face-hobbed hypoid gear set. Three objectives are defined: maximization of gear mesh mechanical efficiency, minimization of loaded transmission error, minimization of maximum contact pressure. Bound constraints on the design variables are imposed, as well as a nonlinear constraint aimed at keeping the loaded contact pattern inside a predefined allowable contact region. The results show that the proposed method can obtain optimal ease-off topographies that significantly improve the basic design performances. It is also evident that the method is general enough to handle geometry optimization of any gear type.

In this paper, we set out to investigate the performances of some algorithms proposed in the gear literature for identifying the machine-tool settings required to obtain predesigned gear tooth surface topographies, or needed to compensate for flank form deviations of real teeth. For ease of comparison, the problem is formulated as a nonlinear least squares problem, and the most widely employed algorithms are derived as special cases. The algorithms included in the analysis are (i) one-step methods, (ii) iterative methods, and (iii) iterative methods with step control. The performance index is devised in their ability of returning practical solutions in the presence of (i) strong model nonlinearities, (ii) ill-conditioning of the sensitivity matrix, and (iii) demanding topographic shapes. Instrumental here is an original classification of topographic modifications as either “simple” or “complex,” based on the singular value decomposition (SVD) analysis of the sensitivity matrix. Some selected numerical examples demonstrate that iterative techniques with step control are the most convenient in terms of reliability and robustness of the obtained solutions. The generation process considered here is face-milling of hypoid gears, although the methodology is general enough to cope with any gear cutting/grinding method.

The steady-state cornering behaviour of rear-wheel drive vehicles fitted with locked differential is critically analysed by means of simple, albeit carefully formulated, vehicle models, which allow for a rigorous theoretical analysis. Results obtained for some classical manoeuvres, with either constant forward speed, steer angle or turning radius, clearly show that, in the case of locked differential, the vehicle cornering behaviour is strongly affected by the manoeuvre. As an important consequence, the handling diagram is not unique and the understeer gradient is no longer dependent only upon the lateral acceleration, as in vehicles equipped with an open differential. Accordingly, this study shows that some typical tools and concepts of vehicle dynamics are indeed inadequate in the case of locked differential.