One of the most powerful capabilities of CMM software is the ability to perform fitting calculations.  When an alignment is performed, the software fits the measured points to an XYZ coordinate system.  When characteristics like Flatness and Profile are evaluated, the software fits the measured points to theoretically exact feature geometry.  Most softwares have a selection of different algorithms or “fitting routines”, that fit the measured points in different ways.

 

Different fitting methods can be used for the following purposes:

• Alignments for Datum Reference Frame construction
• Alignments for manufacturing process troubleshooting
• Finding the best actual value
• Isolating “bad” areas

 

Datum Reference Frame Alignment

•  This alignment is for an ASME Y14.5 Datum Reference Frame •  Datum feature simulators and high point contact were used, in accordance with the applicable rules •  In this alignment, the features are displaced upward and slightly tilted •  The features just conform to a Profile tolerance of 0.8

 

Process Troubleshooting (Fixture) Alignment

•  This alignment has been constrained to locating points from the production process •  These points contacted the locators in the fixture used during machining •  In this alignment, the features are located properly •  The process issue is that the fixture does not contact the high points of the features

 

Some CMM softwares have algorithms that correspond to these functional alignments, as well as other algorithms that are optimized for stability or simplicity.  Many problems with CMM inspection results have a root cause in coordinate system alignment.  It is important that the programmer understands how the different algorithms in their software work, and how they should be applied for different types of alignments.  This may or may not be discussed in detail in the software user manual, and often requires additional investigation and research.

Fit for Best Actual Value

•  This fit is optimized to get the best (i.e. smallest) actual value for a Profile characteristic •  The worst extremities are made as good as possible •  This gives the feature the best chance of passing •  The surface appears to have variation everywhere, in different directions •  This doesn’t give much indication of what is really wrong with the feature or how to correct it

 

Fit for Problem Isolation

•  Another optimization is to get as much of the feature close to nominal as possible •  This tends to isolate the “good” and “bad” areas •  Part disposition and process correction is made easier •  In this case, only the large radius was bad and the rest of the feature was close to nominal

 

Other Alignments

 

Alignments can also be optimized for other purposes such as calculating adjustments to correct an overall process average, or calculating material removal for rework of molds and tooling.  These algorithms are generally not available in general-purpose CMM software, but are found in more advanced third-party point cloud processing packages.

 

Summary

 

Fitting of measured data points is a central concept in coordinate measuring machine software.  Proper application of fitting methods can be used to turn the CMM into an analysis and problem solving tool, and not just a quality control device.  Some fitting methods apply to optimizing the conformance of geometric tolerances, and others apply more to manufacturing process analysis.  It is important that the correct algorithm be applied for each purpose, or the results will not be optimal and may be very misleading.

 

Future articles will discuss the mathematics and optimization criteria involved in the different fitting algorithms.