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Identification and measurement of geometric errors for a five-axis machine tool with a tilting head using a double ball-bar

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Abstract

Geometric errors are one of the primary potential sources of error in a five-axis machine tool. There are two types of geometric errors: position-dependent geometric errors and position-independent geometric errors. A method is proposed to identify and measure the position-independent geometric errors of a five-axis machine tool with a tilting head by means of simultaneous multi-axis controlled movements using a double-ball bar (DBB). Techniques for identifying position-independent geometric errors have been proposed by other researchers. However, most of these are based on the assumption that position-dependent geometric errors (such as linear displacement, straightness, and angular errors) are eliminated by compensation, once the position-independent geometric errors have been identified. The approach suggested in this paper takes into account the effect of position-dependent geometric errors. The position-dependent geometric errors are first defined. Path generation for circle tests with two or three simultaneous control movements is then carried out to measure the position-independent geometric errors. Finally, simulations and experiments are conducted to confirm the validity of the proposed method. The simulation results show that the proposed method is sufficient to accurately identify position-independent geometric errors. The experimental results indicate that the technique can be used to identify the position-independent errors of a five-axis machine tool with a tilting head.

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Abbreviations

{i}:

local coordinate, i=X, Y, Z, B, C

{F}:

reference coordinate of five-axis machine tool

is, js, ks :

unit orientation vectors of the local coordinate, s=X, Y, Z, B, C

δji :

translational error component of the i-axis in the j direction, where j is x, y, z, b, c

ɛji :

rotational error component of the i-axis about the j direction, where j is x, y, z, b, c

eji :

offset error component of the i-axis in the j direction, where j is x, y, z, b, c

sji :

squareness error component of the i-axis about the j direction, where j is x, y, z, b, c

Eri :

radial deviation of the ith DBB measurement

X, Y, Z:

points on the circular tool path

X0, Y0, Z0 :

center position of the circular tool path

ΔX, ΔY, ΔZ:

position errors at point (X, Y, Z)

x, y, z:

movement in the x, y, z directions

lxb, lzb :

distance between coordinate systems {B} and {Z}

P j i :

position vector of i in coordinate {j}

τ j i :

transformation matrix from {i} to }j}

D i :

matrix containing position-independent geometric errors, i=X, Y, Z, B, C

E i :

matrix containing position-dependent geometric errors, i=X, Y, Z, B, C

N i :

matrix expressing the nominal motion, i=X, Y, Z, B, C

O ZB :

matrix expressing the distance between coordinate systems {B} and {Z}

θ:

rotation angle of the rotary table

ϕ :

angular position of a measurement point strip

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Authors and Affiliations

  1. School of Mechanical Engineering, Kyungpook National University, 1370, Sangyeok-dong, Buk-gu, Daegu, South Korea, 702-701

    Dong-Mok Lee, Zankun Zhu, Kwang-Il Lee & Seung-Han Yang

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  1. Dong-Mok Lee
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  2. Zankun Zhu
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  3. Kwang-Il Lee
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  4. Seung-Han Yang
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Correspondence to Seung-Han Yang.

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Lee, DM., Zhu, Z., Lee, KI. et al. Identification and measurement of geometric errors for a five-axis machine tool with a tilting head using a double ball-bar. Int. J. Precis. Eng. Manuf. 12, 337–343 (2011). https://doi.org/10.1007/s12541-011-0044-5

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  • DOI: https://doi.org/10.1007/s12541-011-0044-5

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