Elsevier

Precision Engineering

Volume 34, Issue 1, January 2010, Pages 49-54
Precision Engineering

Multi-probe method for straightness profile measurement based on least uncertainty propagation (1st report): Two-point method considering cross-axis translational motion and sensor's random error

https://doi.org/10.1016/j.precisioneng.2009.01.009Get rights and content

Abstract

In the straightness profile measurement of a mechanical workpiece, hardware datums have been the traditional standard. However, error separation techniques of the surface profile from parasitic motions have been developed. These are known as software datums, which separate the surface profile from the parasitic motions using multiple sensors and/or multiple orientations and realize higher accuracy than that of the hardware datum. However, the conventional software datum cannot measure a large-scale workpiece because the large sampling number causes random error amplification. Furthermore, the conventional software datum assumes that sensor's random noise is small enough in comparison with the parasitic motions. But, the accuracy of the hardware datum has become high. Then, the accuracy of the sensor's random noise is not so small, relatively. In this paper, a next-generation software datum, the two-point method based on the least uncertainty propagation, is proposed. The proposed two-point method consists of weighting and inverse filtering, resulting in the least uncertainty of the estimated surface profile by choosing suitable weighting.

Introduction

In the straightness profile measurement of a mechanical workpiece, hardware datums have been the traditional standard. There are three conventional hardware datums: a straight edge, a level and an optical beam. The highly accurate straight edge has 0.15–0.5 μm straightness in the 1000 mm range. From the point of view of a surface profile measurement based on the hardware datum, the accuracy of the measurement result depends on the accuracy of the datum. For example, when the surface profile is measured using a displacement sensor scanning along the hardware datum, the output of the sensor includes information about the measured surface profile and the cross-axis translational motion of the scanning sensor.

However, error separation techniques of the surface profile from parasitic motions [1], [2], the software datums [3], have been developed. The software datums separate the surface profile from parasitic motions using multiple sensors and/or multiple orientations, and achieve higher accuracy than the hardware datum achieves.

In 1982, the sequential two-point method [4], which is the basic multiple sensor method for straightness profile measurement, was proposed. This method separates the measured surface profile from the cross-axis motion using two scanning sensors. In 1988, the characteristics of the integration method [5] were clarified from the point of view of the spatial frequency response, and the generalized two-point method was proposed [6]. Recently, there have been more studies on the software datum for straightness profile measurement [7], [8].

The surface profile measurement of a large-scale workpiece is in demand in science [9] and industry. The conventional software datum is inadequate since the large sampling number causes random error amplification. Furthermore, the conventional software datum assumes that sensor's random noise is small enough in comparison with the parasitic motions. But, the accuracy of the hardware datum has become high. Then, the accuracy of the sensor's random noise is not so small, relatively.

In this paper, the next-generation software datum, the two-point method based on the least uncertainty propagation, is proposed. The proposed two-point method consists of weighting and inverse filtering, and can determine the estimated surface profile with least uncertainty by choosing the suitable weight of the weighting addition.

Section snippets

Outline of conventional two-point method

Fig. 1 shows the principle of the conventional two-point method for the straightness profile measurement. Two displacement sensors are set on an X-stage to detect the measured surface profile f(x). The cross-axis translational motion of the X-stage, z(x), is the typical parasitic error and it corresponds to the accuracy of the hardware datum. The output of each sensor di(x) (i = 1, 2) can be described as follows:d1(x)=f(x+a1)+z(x)d2(x)=f(x+a2)+z(x)where ai is the sensor position from the sampling

Concept and principle

As shown in Fig. 5, the hardware datum for the straightness profile measurement includes cross-axis motion, but it does not amplify the sensor's random error. In contrast, the conventional software datum can eliminate the cross-axis motion, but it amplifies the random error, especially in the low spatial frequency domain.

Therefore, the compromise plan eliminates the cross-axis motion tolerably and controls the random error propagation. This compromise plan can be realized by the well-designed

Simulation example

Smith and Chetwynd [11] stated, “our experience with the micrometer-drive stage has invariably revealed slight variations in the pitch of the spindle (pitch error) and a larger perturbation from rectilinearity that is periodic with its rotation (spindle error).” This case will be good demonstration of the proposed method.

Fig. 13 shows the outline of the simulation example. A measured surface profile is assumed as a beam, 1000 mm in length with 0.5 μm bending, which is supported at Bessel points.

Conclusions

The concept, principle and fundamental characteristics of the software datum based on the least uncertainty propagation for straightness profile measurement are described. The proposed two-point method that consists of the weighting addition and inverse filtering can make the uncertainty of the estimated surface profile least. When kn, which is the ratio of the standard deviation of the sensor's random noise σn to the standard deviation of the cross-axis translational motion σz, is given, the

Acknowledgements

The author would like to acknowledge Professor S. Kiyono, Tohoku University, and Professor Y. Uda, Osaka Electro-communication University, for their helpful advice.

References (11)

  • C. Elster et al.

    Coupled distance sensor systems for high-accuracy topography measurement

    Precision Engineering

    (2006)
  • D.J. Whitehouse

    Some theoretical aspects of error separation techniques in surface metrology

    Journal of Physics E, Scientific Instruments

    (1976)
  • D.G. Chetwynd et al.

    Improving the accuracy of roundness measurement

    Journal of Physics E, Scientific Instruments

    (1976)
  • S. Kiyono et al.

    Measurement of step-wise profile of machined surface with software datum

    Journal of JSPE

    (1993)
  • H. Tanaka et al.

    Basic characteristics of straightness measurement method by two sequential points

    Transactions of the JSME (C)

    (1982)
There are more references available in the full text version of this article.

Cited by (0)

View full text