 2. Measurement Process Characterization
2.3. Calibration
2.3.4. Catalog of calibration designs

## Roundness measurements

Roundness measurements Measurements of roundness require 360° traces of the workpiece made with a turntable-type instrument or a stylus-type instrument. A least squares fit of points on the trace to a circle define the parameters of noncircularity of the workpiece. A diagram of the measurement method is shown below.
The diagram shows the trace and Y, the distance from the spindle center to the trace at the angle.

A least squares circle fit to data at equally spaced angles gives estimates of P - R, the noncircularity, where R = radius of the circle and P = distance from the center of the circle to the trace. Low precision measurements Some measurements of roundness do not require a high level of precision, such as measurements on cylinders, spheres, and ring gages where roundness is not of primary importance. For this purpose, a single trace is made of the workpiece.
Weakness of single trace method The weakness of this method is that the deviations contain both the spindle error and the workpiece error, and these two errors cannot be separated with the single trace. Because the spindle error is usually small and within known limits, its effect can be ignored except when the most precise measurements are needed.
High precision measurements High precision measurements of roundness are appropriate where an object, such as a hemisphere, is intended to be used primarily as a roundness standard.
Measurement method The measurement sequence involves making multiple traces of the roundness standard where the standard is rotated between traces. Least-squares analysis of the resulting measurements enables the noncircularity of the spindle to be separated from the profile of the standard.
Choice of measurement method A synopsis of the measurement method and the estimation technique are given in this chapter for: The reader is encouraged to obtain a copy of the publication on roundness (Reeve) for a more complete description of the measurement method and analysis. 