Numerical tooth contact analysis of a bevel gear set by using measured tooth geometry data

•We successfully fit the data points of the bevel gear by B-spline surface.•NTCA was developed to address the numerical instability of TCA.•The coordinate measuring machine and NTCA simulate TE with ease.

A numerical tooth contact analysis (NTCA) technique was developed to simulate the single flank test by the gear geometry data measured on a gear measuring center. The proposed NTCA uses only the position vector to calculate continuous transmission error (CTE) and the corresponding contact pattern. The proposed NTCA is very flexible since the tooth surface is measured from real gear and reconstructed as a B-spline free form surface, no mathematical model for specified gear type is required. The calculation speed of NTCA is fast for the multiple tooth contact since the structure of the proposed numerical algorithm is suitable for the parallel computing. The least rotation angle (LRA) method and the improved quad-tree (QT) search algorithm were used to determine the CTE and the tooth contact pattern. The validation of the proposed NTCA is verified by comparing the contact pattern and TE of test gear to the theoretical TCA results generated by the commercial TCA software.