Data-driven operation and compensation approaches to tooth flank form error measurement for spiral bevel and hypoid gears

In the actual design and manufacturing of spiral bevel and hypoid gears, the real tooth flank form geometry inevitably deviate from their theoretical or master target one, due to machine tolerances and systematic flexibility, heat treatment distortions, variation of cuttings forces and other noise factors. This deviation in normal direction is tooth flank form error which can cause some detrimental effects on tooth contact performances. Particularly, once the edge contact or highly concentrated stresses occurs, it will result in noisy operation and premature failure. This paper presents an accurate systematic CMM measurement method to prescribe and data-driven control the tooth flank form error. Firstly, the accurate measurement positioning is developed as an important step in whole measurement. And then, a data-driven programming is performed to prescribe a flank grid in CMM measurement. Where, this programming includes: (i) UMC machine settings are used to establish a universal tooth flank model, (ii) NURBS fitting and stitching approach is employed to accurate explicit flank expression, and (iii) flank parameterization using the steepest descent method with Newton step is proposed to identify flank grid points. Moreover, to distinguish with the conventional methods, a high-order machine setting modification considering residual tooth flank form error is proposed to get a flexible compensation of tooth flank form error. Given numerical test can verify the proposed methods.