Accurate nonlinear modeling and computing of grinding machine settings modification considering spatial geometric errors for hypoid gears

• Function relationships between the grinding machine settings and SGEs are established.
• An accurate modeling for grinding machine settings modification considering SGEs.
• Measurement and compensation method for the SGEs.
• A trust region algorithm with dogleg step is proposed.
• Verification of accuracy and performance for hypoid gears.

The machine settings modification is a primary optimization stage in optimization design of the tooth form error flank. Spatial geometric errors (SGEs) as a main error source play an important role in affecting the precision of the actual CNC process, especially the grinding. Based on nonlinear analysis and application of computational algorithm, a new accurate grinding machine settings modification methodology considering the SGEs is proposed for manufacturing hypoid gears with a high level of accuracy. Firstly, the functional relationships between machine settings and SGEs of a six-axis CNC grinding machine tool are established. Then, an accurate modification objective function taking into account the residual tooth form error is investigated as a nonlinear least square problem, and a trust region algorithm with dogleg step is proposed to obtain accurate modification variations. After the SGEs are measured and compensated, the modification of grinding machine settings is accomplished. Finally, the practical application of a closed-loop modification process is presented to verify the good accuracy of the modification methodology by the proposed algorithm.