An active tooth surface design methodology for face-hobbed hypoid gears based on measuring coordinates

• An active tooth surface design method used in the phase of trial-manufacture is proposed.
• Need only one time of correction for pinion tooth surface.
• Tooth surface deviations of both gear and pinion are considered.
• Meshing performances of a certain side can be selectively guaranteed.
• Predesigned meshing performances can be obtained.

An active tooth surface design methodology is proposed for face-hobbed hypoid gears based on fitting the measuring coordinates of real tooth surface that includes the flank deviations caused by machine errors and the deformation of heat treatment. Firstly, non-uniform rational B-spline (NURBS) is used as a tool to fit the discrete measuring coordinates of gear and pinion, then real tooth surface equations are obtained. Secondly, the pinion auxiliary tooth surface that is in line contact with the gear real tooth surface and has a parabolic transmission error (TE) is obtained by using the gear as a virtual cutter to generate the pinion under a predesigned motion function, then the pinion target tooth surface is obtained by modifying the pinion auxiliary tooth surface along the contact line with a predesigned contact pattern (CP). Thirdly, an optimization model is proposed to solve the adjustments of pinion machining parameters, this model is solved by using sequence quadratic program (SQP). The feasibility of this methodology is demonstrated by using a numerical example of a Klingelnberg–Oerlikon's Spirac hypoid gear set; the results are in line with the preconditions. This proposed methodology provides a new approach for meshing performances control of face-hobbed hypoid gears in the phase of trial-manufacture.

As the figure shows, firstly, an auxiliary tooth surface of pinion Σt is generated by using the gear real tooth surface as a virtual cutter, Σt is in line contact with gear real tooth surface under a predesigned transmission error (TE), then the target tooth surface of pinion Σ1 is obtained by modifying Σt along the contact lines according to the predesigned contact pattern (CP), thus the predesigned meshing performances are satisfied. Finally, the adjustments of pinion machining parameters are solved via an optimization model.Figure optionsDownload as PowerPoint slide