Test of the Rotary Head (MTR) in the OGP Vision Machine

Test of the Rotary Head (MTR) in the OGP vision machine

The MTR was set up in the CMM with the calibration plate and 8 mm tooling ball projection. The rotary head was set at 5 different locations, 45 deg apart and the tooling ball positions were measured in the machine coordinate frame. The positions are shown below:

units in mm.

A 3D circle was fit through the 5 points. A summary of the results is contained in this document.

A pdf of the code results:

http://www-rnc.lbl.gov/~wieman/Mathcad%20-%20circle%20fit%203D%20brief.pdf

A pdf of full code listing:

http://www-rnc.lbl.gov/~wieman/Mathcad%20-%20circle%20fit%203D%20full.pdf

A copy of the code and data:

http://www-rnc.lbl.gov/~wieman/circle%20fit%203D%20mathcad%20with%20data%20file.zip

As shown above the circle fit to the 5 measured points is tilted a bit from the x axis. This is not of concern because it is easy to transform. This is just a matter of aligning the axis of rotation with the x axis. Of more concern is the deviation of the data points from the plane of the circle which can be seen in the edge views of the circle with a magnified x scale. This deviation, assuming no measurement errors is due to wobble in the rotation axis of the rotary stage. This can result in significant errors at the end of the sector.

A quantitative summary of the results:

best fit circle center (units in mm)

normal vector of the plane of the best fit circle

radial distance of the 5 measured points from the best fit circle

Radial errors:

standard dev of measured points from the circle in the radial direction: 1.5 mm

the equivalent window width: 5.4 mm

or: ± 2.7 mm

actual width of the window to include the 5 measured points 3.7 mmc

These errors are acceptable; they would not compromise the sector measurement.

Errors normal to the circle plane, i.e. rotation axis wobble:

These errors indicate rotation axis wobble which will affect the measurement resolution at the end of the sector.

standard deviation of measured points from the circle plane: 6.9 mm

equivalent window width: 24 mm

resultant axis wobble, standard deviation: 180 mrad

equivalent window width: 630 mrad, or 130 arcsec

This axis wobble translates into a position error at the end

of the 300 mm sector at

position window width, from axis wobble: 190 mm

Rotary head angle errors:

The angle of the measured points about center of the fit circle relative to the first point:

relative measured angles: degrees

the values set for the rotary: 0, 90, 45, 45 90 degrees

discrepancy between measured and set values: degrees

angle error window width 400 arcsec

This is a surprisingly large number. The spec for the rotary head is ± 5 arcsec

This is just the first measurement of this type and should not be considered definitive until further measurements are made with more points.