Many hundreds of thousands of measurements are made every year to check that components meet specification. Many of these measurements are made using co-ordinate measuring machines (CMMs). Decision rules in international standard ISO 14253  state that to demonstrate conformance with a specification, the measurement result has to have an associated measurement uncertainty. If you are going to claim that your results are traceable, a requirement of ISO 9001, then an uncertainty needs to be associated with the result. But how do you calculate an uncertainty for measurements made on a CMM?
The ISO Guide to the expression of uncertainty in measurement gives some general guidance on calculating measurement uncertainties. However, for a CMM, except in the most trivial cases, the calculations are complex. A simpler method is needed.
One option that is widely used, but not necessarily recommended, is to use the CMM manufacturer’s specified value for the maximum permissible error of length measurement, EL, MPE. This error is usually expressed as A + L/K, where A and K are constants and L is the measured length. If no other information is available use of EL, MPE is a start, but you have to bear in mind that the machine specification is not an uncertainty and that it only applies for a particular case, i.e. determining the length between two points with a particular stylus system. However, this method does not apply when determining inter-feature distances and angles, when reporting geometric form or when using long styli.
A better alternative is to use the methods described in ISO 15530 part 3  and to use the method of substitution. This method works well, but relies on suitable reference standards being available and meeting the similarity conditions listed in clause 5.2. To quote the standard: The aim of this part of ISO 15530 is to provide an experimental technique for simplifying the uncertainty evaluation of CMM measurements. In this experimental approach, measurements are carried out in the same way as actual measurements, but with calibrated workpieces or measurement standards of similar dimension and geometry instead of the unknown objects to be measured.
The preferred technique to establish the uncertainty of measurement is the use of uncertainty evaluating software (UES) that makes use of Monte Carlo methods. Monte Carlo methods are a class of computational algorithms that rely on repeated random sampling to compute their results. In affect you are running the CMM programs many times on a Virtual CMM. There are several commercial implementations of UES including those that are optional extras for Zeiss Calypso and Leitz Quindos, and the stand-alone package Metrosage Pundit. The technique for calculating task specific measurement uncertainties using simulation is outlined in ISO 15530 part 4 . At NPL, scientists have access to the Leitz and Calypso implementations of UES both of which are based around previous work by PTB and NPL .
So how is a Virtual CMM implemented in practice on a typical CMM? The first thing that has to be done is to measure the residual error field; this measurement is usually performed by the manufacturer. This task is performed using an artefact such as a hole plate. Next, temperature gradients are measured around the machine. Finally the kinematic chain of the machine has to be described. This information describes the real CMM to the simulation software. In use, further input parameters are needed. The first input parameter takes the form of a special probe qualification routine. Other input parameters are required relating to the uncertainty in the thermal expansion of the component and the component’s surface texture.
Once all these input parameters are known, the software repeatedly simulates collecting individual points with a Gaussian spread and propagates these values through all the calculations necessary to produce the desired result. You effectively run the CMM program repeatedly (100 to 200 times) on a Virtual CMM varying the input parameters slightly each time. The output is all the characteristics requested, each printed out with an associated measurement uncertainty.
The beauty of this method is that, as long as the conditions do not change, the Monte Carlo simulation only has to be performed once for a particular component.
A further advantage of the technique is that it allows ‘what-if’ calculations to be performed. That is to say, before receiving a component you can see what effect varying the number of points and stylus configurations will have on the quality of your measurements. You can, in some cases, even allow the software to help you choose which CMM you are going to use for a particular component.
The Virtual CMM goes part of the way to achieve traceability in co-ordinate metrology and work is on-going to include scanning and rotary tables.
The Virtual CMM is a technique that originated in research laboratories and is now readily available to end users. NPL has experience in using a number of commercial packages. l
For further information contact David Flack, at the NPL.
1 BS EN ISO 14253-1:1999 Geometrical product specifications (GPS). Inspection by measurement of workpieces and measuring equipment. Decision rules for proving conformance or non-conformance with specifications
2 BS EN ISO 15530-3:2011 Geometrical Product Specifications (GPS) -- Coordinate measuring machines (CMM): Technique for determining the uncertainty of measurement -- Part 3: Use of calibrated workpieces or measurement standards
3 ISO 15530-4:2008 Geometrical Product Specifications (GPS) -- Coordinate measuring machines (CMM): Technique for determining the uncertainty of measurement -- Part 4: Evaluating task-specific measurement uncertainty using simulation
4 Trapet, E., Franke, M., Härtig, F., Schwenke, H., Wäldele, F., Cox, M., Forbes, A., Delbressine, F., Schellekens, P., Trenk, M., Meyer, H., Moritz, G., Guth, Th., Wanner, N.: Traceability of Coordinate Measurements According to the Method of the Virtual Measuring Machine, Final Project Report MAT1-CT94-0076, PTB-report F-35, Part 1 and 2, ISBN 3-89701-330-4, 1999