Optimal On-Machine Measurement of Position-Independent Geometric Errors for Rotary Axes in Five-Axis Machines with a Universal Head

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Abstract

This study proposes an optimal on-machine measurement method to measure position-independent geometric errors of five-axis machines, including machine tools and coordinate measuring machines, with a universal head. This measurement requires only a calibrated three-dimensional (3-D) probe and a precision sphere, which are fundamental components of on-machine measurement systems in general, to minimize measurement costs, including operator effort and operating time. Eight position-independent geometric errors are used to describe the coordinate systems of the two rotary axes through a kinematic analysis. The center of the precision sphere, which is stationary during the measurement, is measured at various angles of the rotary axes. Then, the linearized relationship between the measured positions of the precision sphere and the geometric errors is derived using an error synthesis model under rigid-body and small-value assumptions. The proposed method is tested through a simulation for validation. The geometric errors of a five-axis coordinate measuring machine with a universal head are measured with measurement uncertainty by applying the proposed method. Then, the measurement results are confirmed by comparing the measured positions of the precision sphere and calculated positions using the measured geometric errors at the other (i.e., the arbitrary, or not measured) angles of rotary axes.

Keywords

Five-axis machines Universal head Position-independent geometric errors Rotary axis On-machine measurement 

Nomenclature

a, c

command angle for rotary axes A, C

oia, sia

offset error and squareness error in the i-direction at rotary axis A (i = y, z)

oic, sic

offset error and squareness error in the i-direction at rotary axis C (i = x, y)

(mx, my, mz)

measured position of the precision sphere

(wx, wy, wz)

center of the precision sphere at reference coordinate system {R}

L

stylus length

{i}

coordinate system of axis i (i = X, Y, Z, A, C)

{S}

coordinate system at the stylus center

τij

4 × 4 transformation matrix from coordinate system {j} to coordinate system {i}

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Copyright information

© Korean Society for Precision Engineering and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Mechanical and Automotive EngineeringKyungil UniversityGyeongsangbuk-doRepublic of Korea
  2. 2.Division of Mechanical EngineeringYeungnam University CollegeDaeguRepublic of Korea
  3. 3.School of Mechanical EngineeringKyungpook National UniversityDaeguRepublic of Korea

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