Paper:

# Square Layout Four-Point Method for Two-Dimensional Profile Measurement and Self-Calibration Method of Zero-Adjustment Error

## Hiroki Shimizu^{†}, Ryousuke Yamashita, Takuya Hashiguchi, Tasuku Miyata, and Yuuma Tamaru

Kyushu Institute of Technology

1-1 Sensui-cho, Tobata-ku, Kitakyushu-shi, Fukuoka 804-8550, Japan

^{†}Corresponding author

An on-machine measurement method, called the square-layout four-point (SLFP) method with angle compensation, for evaluating two-dimensional (2-D) profiles of flat machined surfaces is proposed. In this method, four displacement sensors are arranged in a square and mounted to the scanning table of a 2-D stage. For measuring the 2-D profile of a target plane, height data corresponding to all measuring points are acquired by means of the raster scanning motion. At the same time, pitching data of the first primary scan line and rolling data of the first subsidiary scan line are monitored by means of two auto-collimators to compensate for major profile errors that arise out of the posture error. Use of the SLFP method facilitates connection of the results of straightness-measurements results obtained for each scanning line by using two additional sensors and rolling data of the first subsidiary scan line. Specifically, the height of a measuring point is calculated by means of a recurrence equation using three predetermined height data for adjacent points in conjunction with data acquired by the four displacement sensors. Results of the numerical simulation performed in this study demonstrate higher efficiency of the SLFP method with angle compensation. During actual measurement, however, it is difficult to perfectly align inline the origin height of each displacement sensor. With regard to the SLFP method, zero-adjustment error is defined as the relative height of a sensor’s origin with respect to the plane comprising origins of the other three sensors. This error accumulates in proportion to number of times the recurrence equation is applied. Simulation results containing the zero-adjustment error demonstrate that accumulation of the said error results in unignorable distortion of measurement results. Therefore, a new self-calibration method for the zero-adjustment error has been proposed. During 2-D profile measurement, two different calculation paths – the raster scan path and orthogonal path – can be used to determine the height of a measurement point. Although heights determined through use of the two paths must ideally be equal, they are observed to be different because accumulated zero-adjustment errors for the two paths are different. In view of this result, the zero-adjustment error can be calculated backwards and calibrated. Validity of the calibration method has been confirmed via simulations and experiments.

*Int. J. Automation Technol.*, Vol.12 No.5, pp. 707-713, 2018.

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