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

Article

## 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.

## Keywords

Five-axis machine tool Position-dependent geometric errors Position-independent geometric errors Double ball-bar

## Nomenclature

{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}

Pji

position vector of i in coordinate {j}

τji

transformation matrix from {i} to }j}

Di

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

Ei

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

Ni

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

OZB

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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© Korean Society for Precision Engineering and Springer-Verlag Berlin Heidelberg 2011

## Authors and Affiliations

• Dong-Mok Lee
• 1
• Zankun Zhu
• 1
• Kwang-Il Lee
• 1
• Seung-Han Yang
• 1
Email author
1. 1.School of Mechanical EngineeringKyungpook National UniversityDaeguSouth Korea