On-Machine Measurement of the Straightness and Tilt Errors of a Linear Slideway Using a New Four-Sensor Method

Abstract

Although there are some multi-sensor methods for measuring the straightness and tilt errors of a linear slideway, they need to be further improved in some aspects, such as suppressing measurement noise and reducing precondition. In this paper, a new four-sensor method with an improved measurement system is proposed to on-machine separate the straightness and tilt errors of a linear slideway from the sensor outputs, considering the influences of the reference surface profile and the zero-adjustment values. The improved system is achieved by adjusting a single sensor to different positions. Based on the system, a system of linear equations is built by fusing the sensor outputs to cancel out the effects of the straightness and tilt errors. Three constraints are then derived and supplemented into the linear system to make the coefficient matrix full rank. To restrain the sensitivity of the solution of the linear system to the measurement noise in the sensor outputs, the Tikhonov regularization method is utilized. After the surface profile is obtained from the solution, the straightness and tilt errors are identified from the sensor outputs. To analyze the effects of the measurement noise and the positioning errors of the sensor and the linear slideway, a series of computer simulations are carried out. An experiment is conducted for validation, showing good consistency. The new four-sensor method with the improved measurement system provides a new way to measure the straightness and tilt errors of a linear slideway, which can guarantee favorable propagations of the residuals induced by the noise and the positioning errors.