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A Dual Difference Method for Identification of the Inherent Spindle Axis Parallelism Errors of Machine Tools

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Abstract

It is essential to identify spindle axis parallelism errors because such errors trigger volumetric errors when tools of different lengths are used. However, only a few works have addressed this issue. Thus, we identified the inherent spindle axis parallelism errors of machine tools relative to the end-point reference straight line of the Z-axis (according to ISO 230-1) using a dual difference method. Here, “inherent” refers to parallelism errors of the spindle axis that are not affected by the geometric errors of other axes controlled during the measurements, and “dual difference” refers to the difference in the differences of measuring data. The dual difference method uses two pairs of circular tests performed with the aid of a double ball-bar (DBB); the tool lengths differ during each test and the DBB set-up is shared by the pairs. Parallelism errors are then identified based on the dual differences within and between the two pairs. Experimentally, the maximum peak-to-valley (PV) values were 54.5 and 48.7 μm for differences in radial deviations within the two pairs when the parallelism errors were not compensated. After tool-center-point compensation by the identified errors, the PV values improved to 8.0 and 9.2 μm, respectively, showing that compensation was successful. In addition, the concentricity of two holes machined using tools of different lengths improved from 31.2 μm without compensation to 15.9 μm with compensation, further demonstrating the effectiveness of the method.

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Abbreviations

l i :

Offset (i = 1, …, 3), mm.

n i :

Number of samples during the i-th circular test (i = 1, …, 4).

s ij :

Squareness error of the j axis around the i direction (i, j = x, y, z), rad.

p xs, p ys :

Parallelism errors of the spindle axis around the x and y directions, respectively, rad.

δ ij :

Positional error of the j axis in the i direction (i, j = x, y, z), mm.

εij :

Angular error of the j axis around the i direction (i, j = x, y, z), rad.

θ j :

Rotation angle during the circular test (j = 1, …, ni), rad.

R :

Nominal length of the double ball-bar, mm.

ΔR ij :

j- th measured radial deviation during the i-th circular test (i = 1, …, 4; j = 1, …, ni), mm.

(w xi, w yi, w zi):

Set-up errors of a ball on a workpiece table in the x, y, and z directions, respectively, during the i-th circular test, (i = 1, …, 4), mm.

(0, 0, t i):

Nominal coordinate of a ball at the tool nose in the spindle coordinate system {S} during the i-th circular test, (i = 1, …, 4), mm.

(0, 0, h i):

Nominal coordinate of a ball on a workpiece table in the workpiece coordinate system {W} during the i-th circular test, (i = 1, …, 4), mm.

(x, y, z):

Nominal commands of the X, Y, and Z axes, respectively, mm.

{ i } :

Coordinate system of axis i, (i = X, Y, Z).

{ R }, { W }, { S }, { t } :

Coordinate systems of the reference, workpiece, spindle, and tool, respectively.

\({{\varvec{\uptau}}}_{i}^{j}\) :

4 × 4 Homogeneous transformation matrix from the j coordinate system to the i coordinate system.

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Acknowledgements

This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (Nos. 2020R1C1C100330011, 2019R1A2C2088683).

Funding

This work was supported by the National Research Foundation of Korea(NRF) grant funded by the Korea government(MSIT) (No. 2020R1C1C100330011, 2019R1A2C2088683).

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Authors and Affiliations

  1. School of Mechanical Engineering, Kyungpook National University, 80, Daehak-ro, Buk-gu, Daegu, 41566, Republic of Korea

    Seung-Han Yang

  2. School of Mechanical and Automotive Engineering, Kyungil University, 50, Gamasil-gil, Hayang-eup, Gyeongsan-si, Gyeongbuk, 38428, Republic of Korea

    Kwang-Il Lee

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Correspondence to Kwang-Il Lee.

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Yang, SH., Lee, KI. A Dual Difference Method for Identification of the Inherent Spindle Axis Parallelism Errors of Machine Tools. Int. J. Precis. Eng. Manuf. 23, 701–710 (2022). https://doi.org/10.1007/s12541-022-00653-y

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