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