Non-contact R-test with laser displacement sensors for error calibration of five-axis machine tools

► A prototype non-contact R-test using laser displacement sensors is developed. ► A new algorithm to calculate sphere displacement from sensor displacements is proposed. ► Its application to static and dynamic error calibration for a rotary axis is presented. ► Its measuring performance is experimentally compared to conventional contact-type R-test. The R-test is an instrument to measure three-dimensional displacement of a precision sphere attached to a spindle relative to a work table by using three displacement sensors. Its application to error calibration for five-axis machine tools has been studied in both academia and industry. For the simplicity in calculating the sphere center displacement, all conventional R-test devices use contact-type displacement sensors with a flat-ended probe. Conventional contact-type R-test may be potentially subject to the influence of the friction or the dynamics of supporting spring in displacement sensors particularly in dynamic measurement. This paper proposes a non-contact R-test with laser displacement sensors. First, a new algorithm is proposed to calculate the three-dimensional displacement of sphere center by using non-contact displacement sensors. The compensation of measurement error of a laser displacement sensor due to the curvature of target sphere is incorporated. Then, the measurement uncertainty of four laser displacement sensors with different measuring principles is experimentally investigated in measuring the geometry of a sphere in order to select the laser displacement sensor most suitable for the application to a non-contact R-test. A prototype non-contact R-test device is developed for the verification of the proposed algorithm for non-contact R-test. Experimental case studies of error calibration of (1) static and (2) dynamic error motions of rotary axes in a five-axis machine tool with the developed non-contact R-test prototype are presented. Its measurement performance is compared to the conventional contact-type R-test device.