A measurement datum is crucial in measuring a gear tooth flank by laser interferometry. Manufacturing a physical reference tooth flank as a measurement datum has many drawbacks: many different reference tooth flanks are needed with the changing of the measured gear’s parameters; the reference tooth flank’s manufacturing error lowers the measurement precision; the installation error between the measured and referenced tooth flank lowers the measurement precision also. The drawbacks restrain the practical use of measuring gear by laser interferometry. A construction method of a virtual measurement datum has been proposed to solve the problem. First, a virtual error-free model of the measured tooth flank is built according to its parameters and actual measurement position. Subsequently, the interferogram of the virtual tooth flank is simulated as a measurement datum through the ray tracing. To harvest the actual measurement position of the measured tooth flank, a compensation approach for optical system error and a tracing algorithm for actual installation position are developed. Experimental results prove that a virtual measurement datum can be constructed and used in measuring a gear tooth flank. Furthermore, this research verifies that ray tracing can be used to construct a virtual measurement datum in the relevant comparative measurements processes by laser interferometry.
The installation position errors of a measured gear are unavoidable when measuring gear tooth flank form deviation with laser interferometry, causing mistakes when using the simulated phase difference as a measurement reference to calculate the form deviation. In order to avoid manufacturing many standard gears as measurement references, a compensation method for the installation errors of the measured gear has been developed. In this process, the actual installation position of the measured gear can be traced by modifying the theoretical position parameters using the ray-tracing method. Experimental results show that this method is feasible. Thus, the simulated phase difference that compensate for installation errors can be utilized as a measurement reference in calculating the form deviation of the measured gear.
Segmenting the valid measuring region from an interferogram is an important step in the grazing incidence interferometry, which is related to the accuracy of the measurement result. For the spurious fringes which are generated by the diffuse reflection of the chamfering in the edge of the object surface, we propose a method-spin segment to correct the result of the image segment. First, a phase schematic diagram whose stripe feature is clearer than the original interference fringe patterns is generated. Next, the difference of the gray gradient between the fringe's local normal direction and local tangent direction is calculated to judge the valid measurement region. The principles of selecting some parameters are summarized and the calculation steps are shown. To examine the correction method, the results of an experimental application of spin segment are given to verify the feasibility and accuracy.