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Machine tool analyzer: a device for identifying 13 position-independent geometric errors for five-axis machine tools

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Abstract

We introduce a prototype “machine tool analyzer” (MTA), consisting of a nest of five displacement sensors and a dual-ball system with two centering structures, designed to identify 13 position-independent geometric errors (PIGEs) in five-axis machine tools. The 13 PIGEs include three squareness errors in the three linear axes, two squareness errors and two offset errors in the rotary/tilting axis, and two squareness errors in the spindle axis. The MTA completes four circular paths, during which an identification algorithm identifies thirteen possible PIGEs and set-up errors. The MTA was applied to a commercial five-axis machine tool with a swivel head/rotary table and verified experimentally. Cost-effective measurements were achieved using a single set-up of the nest and associated system. In addition, a circular test using a double ball-bar was used to test the volumetric accuracy of the five-axis machine tool and verify the identified PIGEs. The maximum deviation, minimum deviation, and PV values in the circular test were 109, 55, and 55 μm, respectively, without compensation for errors imparted by the PIGEs, and 38, 5, and 33 μm, respectively, with compensation. This demonstrated the validity of the proposed method.

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Abbreviations

b ij, c ij :

j-th rotation angles at i-th measurements of a B-axis and a C-axis, respectively (i = 1, …, 4; j = 1, …, ni), rad

l nominal :

Nominal tool length between the origin of the B-axis and the UB center of a dual-ball system, mm

l offset :

Offset between the UB center and LB center of a dual-ball system, mm

ΔL i,j,k :

Deviation in the k-direction based on the j-th measured deviation at the i-th measurement (i = 1, …, 4; j = 1, …, ni; k = radial, axial), mm

m i :

i-th displacement sensor (i = 1, …, 5)

n i :

Sampling number at the i-th measurement (i = 1, …, 4)

o ij :

Offset error of the j-axis relative to the i-direction (i = x, y, z; j = b, c, s), mm

s ij :

Squareness error of the j-axis around the i-direction (i = x, y, z; j = x, y, z, b, c, s), rad

(d, 0, h i):

Nominal coordinate of a ball in coordinate system {C} for the i-th measurement (i = 1, …, 4), mm

(w xi, w yi, w zi):

Set-up errors of measuring sensors in the x, y, and z directions at the i-th measurement (i = 1, …, 4), mm

(x ij, y ij, z ij):

j-th nominal coordinate of X, Y, and Z axes at the i-th measurement (i = 1, …, 4; j = 1, …, ni), mm

(Δx ij, Δy ij, Δz ij):

j-th measured deviations in the x, y, and z directions at the i-th measurement (i = 1, …, 4; j = 1, …, ni), mm

{ i } :

Coordinate system of axis i {i = X, Y, Z, B, C, S}

{ R }, { W }, { T } :

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

\( {\boldsymbol{\uptau}}_i^j \) :

4 × 4 homogeneous transformation matrix from j coordinate system to i coordinate system

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The software used in the present study is authorized.

Funding

This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (Nos. 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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  1. Seung-Han Yang
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Contributions

S.H.Y.: methodology, resources, data curation, writing (original draft), writing (review and editing), visualization, and funding acquisition. K.I.L.: conceptualization, methodology, software, validation, writing (original draft), writing (review and editing), visualization, supervision, and funding acquisition.

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Correspondence to Kwang-Il Lee.

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Yang, SH., Lee, KI. Machine tool analyzer: a device for identifying 13 position-independent geometric errors for five-axis machine tools. Int J Adv Manuf Technol 115, 2945–2957 (2021). https://doi.org/10.1007/s00170-021-07341-7

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