A Measurement Approach for Radius Gauge Based on Telecentric Backlight Projection

As an important gauge for measuring incomplete arc components in aero-engines, the measurement accuracy of standard radius gauges is crucial. To improve the accuracy and efficiency of radius gauge with short arc contour, this paper proposes a radius gauge arc contour dimension measurement approach based on telecentric backlight projection. A radius gauge arc contour dimension measurement system is designed, and projection images of the measured radius gauges are captured using an area scan camera equipped with a bilateral telecentric lens. A systematic calibration method is introduced to determine the coordinate transformation parameters, lens distortion parameters, and camera installation tilt angle. These calibrated parameters are used to compensate the arc profile image coordinates. Additionally，to address the issue of low arc fitting accuracy for small central angles in traditional arc fitting algorithms, an improved Kasa arc fitting algorithm based on the Huber loss function is proposed, which is used to fit and obtain the curvature radius of the radius gauge. Numerical simulations were conducted to validate the accuracy of the proposed algorithm. The proposed method was applied to measure a standard ring gauge with a reference radius of 10.000 mm, yielding a measured radius of 10.001 mm with a standard deviation of 0.001 mm. Eight different standard radius gauges were also measured, and the measurement deviations of all the tested radius gauges were within 0.02 mm, with standard deviations less than 0.003 mm. The proposed measurement approach can be extended to the radius parameter measurement of other components containing incomplete arcs.