Statistical Engineering Division, ITL
Precision Engineering Division, MEL
Mathematical and Computational Sciences Division, ITL
Department of Mechanical Engineering, George Washington University
Coordinate Measuring Machines (CMMs) are used to measure the physical dimensions of manufactured parts. Their ability to measure almost an endless variety of geometrically complex parts in a rapid and accurate manner has led to their widespread use in industry. However, the sophistication and flexibility of the CMM make assessment of the measurement uncertainty difficult. Developing reliable uncertainty methodology for CMMs would (1) promote improvement in quality and efficiency through better determination of part dimensions and (2) facilitate international trade that requires ISO 9000 compliance.
Basically, a CMM is a robotic machine that positions a sensing probe in its working volume. The probe contacts a sample of locations on the part surface and the CMM records corresponding three-dimensional point coordinates. The measurement process contains many sources of uncertainty. Some of the largest sources are the geometric distortions of the machine frame, the systematic effect of the probe, and the thermal and mechanical effects of the operating environment. In the first two years of the project, our group developed a reliable model for real-time correction of the systematic effect of the probe. The result is an improved system without significant added costs. The papers ``Error Compensation for CMM Touch Trigger Probes'' and ``Practical Aspects of Touch Trigger Probe Error Compensation'' in Precision Engineering summarize the results. The latter paper includes a detailed uncertainty analysis.
Presently, based on three years of experience in the area, our group is working on several problems related to CMMs. First, we are continuing to quantify the major sources of uncertainty by examining sampling strategies to measure the geometric distortions of the machine frame. Second, we are developing a computer simulation model that produces uncertainty estimates on an arbitrary CMM measurement based on a small set of performance measures. Finally, using Bayesian methodology, we have derived superior decision rules for accepting or rejecting parts based on engineering tolerance and measurement uncertainty. The accompanying figure displays the results of a sensitivity analysis of the ISO standard versus the proposed Bayesian rule. In the figure, 100% corresponds to the correct estimate. Note that the ISO rule does not make use of prior uncertainty. Under various estimates of the uncertainties, the Bayesian rule results in lower cost than the ISO rule.
Figure 9: Costs of Part Acceptance Rules.
Date created: 7/20/2001