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Three-axes Squareness Evaluation of Coordinate Measuring Machines Using a Telescopic Ball-bar
Test & Measurement 2019
Poloko Kuduntwane (Metrologist)
NMISA Pretoria 16 September 2019
Introduction
Background
• Generally, CMMs have twenty-one geometric error parameters related to scale errors and three out-of-squareness between axes and the three planes XY, XZ and YZ.
• Among those geometric errors, inaccurate or out-of-squareness between these axes of a multi-axis machine is a significant source of measurement error affecting the positioning accuracy.
• How the squareness error between two linear axes of motion is calculated
Method 1: Squareness Evaluation Using A Step-Gauge
• This method has been widely used in the past and currently for CMM performance evaluation as step gauges are a popular and easily commercially available artefacts.
• The out-of-squareness is determined by measurements of the displacement of the stylus tip along face diagonals of the three planes XY, XZ and YZ.
• the artefact to be placed at positions of 90⁰ to each other or 45⁰ to the twoaxes (β is 45⁰).
• A formula can be given as:
𝜃 ≈𝑂𝐵2 − 𝐴𝐶2
𝑂𝐵2 + 𝐴𝐶2[rad]
• 𝜃 is the squareness error, OB and AC are measured values of the same artefact at positions O-B and A-C.
Step-Gauge Setup on the CMM
Planes Squareness
Error (rad)
XY 33,666x10-6
XZ 9,000x10-6
YZ -31,335x10-6
Method 2: Squareness Evaluation Using A Telescopic Ball-bar
• This method is based on a renishaw QC20 ball bar system as used in quantifying errors on CNC milling machines. The advantage of the ball bar test is that it is quick and simple
• The system consists of two spheres where the centre distance can be adjusted and be measured by a LVDT.
• The CMM stylus/probe is set at different positions on a circular arc and the ball bar LVDT and its software records the position and length of the ball-bar as seen below.
Ball-bar Setup on the CMM
Semi partial arcs Full circle
Planes
Squareness
Error
(µm/m)
Squareness
Error
(µm/m)
Squareness
Error
(µm/m)
200 mm ø 300 mm ø 600 mm ø
XY 23,8 16,5 7,6
XZ 13,6 5,2 11,3
YZ -56,5 -40,5 -25,7
The squareness error formula is given as:
Squareness error (arc seconds)
= 206 𝑥𝐷1−𝐷2
Circle diameter
Comparison and Conclusion
• The squareness error of the step-gauge and the telescopic ball-bar compare fairly well for the XZ- and YZ- planes, where they both give a negative squareness error for the YZ plane.
• There is a vast difference on the XY plane, and this needs to be investigated further by redoing the measurements and by further verifying both the methods’ results with a third method which uses a laser tracer
Planes
Squareness
Error
(arc sec)
Squareness
Error
(arc sec)
Step-gauge Ball-bar
XY 6,9 1,6
XZ 1,9 2,3
YZ -6,5 -5,3