Shield analysis and non-rigid match in positioning the actual interferogram on the tooth flank based on oblique incidence interferometry

When the oblique incidence interferometry is used to measure the form deviation of the tooth flank, because of the anamorphic distortion and image foreshortening, the collected interference fringe pattern (IFP) cannot be positioned on the tooth flank directly. Therefore a simulation tooth image (STI) is employed as a bridge to connect the collected IFP and the tooth flank. The exiting method is good enough to deal with the IFP of spur gear tooth flank, but it is inappropriate for the IFP of helical gear. This paper focuses on two improvements for positioning the IFP of helical gear on the tooth flank: (1) in the process of generating the STI, a mathematical model of helical tooth flank is proposed to judge the shielded situation of tooth flank; (2) in the process of matching the STI with the collected IFP, a non-rigid matching method is proposed to determine the relationship of the two images. The results of an experimental application are given to verify the feasibility and accuracy.