1 What is 3D volumetric positioning accuracy and
How to define
and measure it Charles
Wang Optodyne, Inc
1180 Mahalo Place
Compton, CA 90220
310-635-7481
optodyne@aol.comI.Introduction
20 years ago, the largest machine
tool positioning errors are lead screw pitch error and thermal expansion error. Now, most of the
above errors have been reduced by linear
encoder and compensation. Hence, the largest machine tool
positioning errors become squareness errors
and straightness errors. Hence, to achieve higher 3D volumetric positioning accuracy, the
measurement and compensation of the
squareness and straightness errors are very important. II.Machine tool
positioning errors For a 3-axis
machine, there are 6 errors per axis or a total of 18 errors plus 3
squareness errors. These
21 rigid body errors can be expressed
as the followings [1].
Linear
displacement errors: Dx(x), Dy(y), and Dz(z) Vertical straightness errors: Dy(x), Dx(y), and Dx(z)
Horizontal straightness errors: Dz(x),
Dz(y), and Dy(z) Roll angular errors:
Ax(x), Ay(y), and Az(z) Pitch angular
errors: Ay(x),Ax(y), and Ax(z) Yaw angular
errors: Az(x), Az(y), and Ay(z) Squareness
errors: Øxy, Øyz, Øzx, where, D is the
linear error, subscript is the error direction and the position
coordinate is inside the parenthesis, A is
the angular error, subscript is the axis of
rotation and the position coordinate is inside the parenthesis.
III.Existing definition of volumetric accuracy For a 3 axes machine, if the dominate positioning errors
are the 3 displacement errors of each axis, Dx(x), Dy(y), Dz(z),
then the volumetric error is the root-mean-square sum of all these
displacement errors. That is. Volumetric error = sqrt {[Max Dx(x)-Min Dx(x)]²
+ [Max Dy(y)-Min Dy(y)]² + [Max Dz(z)- Min Dz(z)]²}.
This definition is okay as long as the dominate errors are the
3 displacement errors (or lead screw pitch
errors). However, for current machine tools, the Click
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