Abstract
Squareness measurements of the driving axes of a machine tool are very important in order to evaluate the performance of the machine. A laser interferometer measurement is one of the most reliable ways to measure squareness. However, a squareness measurement using a laser interferometer system with an optical square causes restrictions in the straightness interferometer setup, which results in the occurrence of Abbe’s offset. The Abbe’s offset combined with angular errors during the motion of an axis causes Abbe’s error. In addition, difficulty in the optical square setup causes restrictions on other optics and limitations of the measurable range. We present mathematical approaches that can be used to eliminate Abbe’s error and to estimate squareness over the full range by using the best fit of straightness data measured without an optical square. Experiments for squareness measurements of a threeaxis machine tool are conducted. The proposed techniques are used for squareness evaluation with the elimination of Abbe’s error and also for squareness estimation for the full travel range.
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Abbreviations
- a ij :
-
Abbe’s offset in i-direction of j-axis
- e ij :
-
Abbe’s error in i-direction of j-axis
- r ij :
-
straightness data measured with Abbe’s offset in i-direction of j-axis, i=x, y, z; j=x, y, z
- m ij :
-
straightness data with Abbe’s error eliminated from r ij in idirection of j-axis, i=x, y, z; j=x, y, z
- ɛ ij :
-
angular error in i-direction of j-axis, i=x, y, z; j=x, y, z
- s ij , s ij ′:
-
squareness of ij-plane for measurable and full travel range, respectively
- δ ij :
-
straightness error in i-direction of j-axis, i=x, y, z; j=x, y, z
- α,β :
-
inclination of representative line of measurement data from the X-axis and Y-axis, respectively
- Δα,Δβ :
-
difference in inclination of straightness representative lines for measurements with and without optical square at X-axis and Y-axis, respectively
- α′,β′:
-
inclination of straightness representative line (best fit curve) from X-axis and Y-axis, respectively
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Lee, DM., Lee, HH. & Yang, SH. Analysis of squareness measurement using a laser interferometer system. Int. J. Precis. Eng. Manuf. 14, 1839–1846 (2013). https://doi.org/10.1007/s12541-013-0246-0
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DOI: https://doi.org/10.1007/s12541-013-0246-0