UNCERTAINTY ANALYSIS AND QUALITY ASSURANCE FOR COORDINATE MEASURING SYSTEM SOFTWARE
Table Of Contents
<p> TABLE OF CONTENTS 1.</p><p> INTRODUCTION .................................................................................................... 1 1.1</p><p> Coordinate Measuring Systems .......................................................................... 1 1.2 </p><p>The Problem of Uncertainty................................................................................ 4 1.3 </p><p>The Problem of Software Uncertainty ................................................................ 6 1.4 </p><p>The NIST ATEP-CMS software testing program............................................. 11 2. </p><p>BACKGROUND INFORMATION AND LITERATURE SURVEY................... 14 2.1</p><p> NIST work ........................................................................................................ 14 2.2 </p><p>NIST Algorithm Information............................................................................ 17 2.3</p><p> NPL work.......................................................................................................... 21 2.4 </p><p>Other documentation......................................................................................... 24 3. </p><p>LEAST SQUARES FITTING ................................................................................ 26 3.1 </p><p>The Problem of Least Squares Fitting .............................................................. 26 3.2 </p><p>The Need for Least Squares Fitting .................................................................. 27 3.3</p><p> Issues involved in solving Least Squares Fitting Problems.............................. 27 3.4</p><p> An Approach to Least Squares Fitting.............................................................. 28 3.5</p><p> Implementation of the Approach ...................................................................... 28 3.6</p><p> Results of the Implementation .......................................................................... 29 3.7</p><p> An Application of Least Squares Fitting .......................................................... 29 4.</p><p> MINIMUM ZONE FITTING ................................................................................. 39 4.1 </p><p>The Problem of Minimum Zone Fitting............................................................ 39 4.2 </p><p>The Need for Minimum Zone Fitting ............................................................... 40 4.3 </p><p>Issues involved in solving Minimum Zone Fitting Problems........................... 42 4.4 </p><p>An Approach to Solving Minimum Zone Fitting ............................................. 43 4.5 </p><p>Implementation of the Approach ...................................................................... 44 4.6 </p><p>Reference vs. Commercial Algorithm Performance......................................... 46 4.7</p><p> Results of the Implementation .......................................................................... 48 5.</p><p> MAXIMUM INSCRIBED AND MINIMUM CIRCUMSCRIBED FITTING...... 49 5.1</p><p> The Problem of Maximum Inscribed and Minimum Circumscribed Fitting.... 49 5.2 </p><p>The Need for Maximum Inscribed and Minimum Circumscribed Fitting........ 51 5.3</p><p> Issues involved in solving Maximum Inscribed and Minimum Circumscribed Fitting Problems...................................................................................................... 52 5.4 An approach to Maximum Inscribed and Minimum Circumscribed Fitting .... 53 5.5 Implementation of the Approach ...................................................................... 59 5.6 Reference vs. Commercial Algorithms for Maximum Inscribed and Minimum Circumscribed Fitting ............................................................................................. 59 5.7 Results of the Implementation .......................................................................... 61 6. LEAST SQUARES FITTING OF COMPLEX SURFACES................................. 62 6.1 The Problem of Least Squares Fitting of Complex Surfaces............................ 62 6.2 The Need for Fitting of Complex Surfaces....................................................... 63 6.3 </p><p>Issues involved in solving Least Squares Fitting of Complex Surfaces Problems ................................................................................................................................. 64 6.4 </p><p>An Approach to Solving Least Squares Fitting of Complex Surfaces Problems ................................................................................................................................. 68 6.5 Implementation of the Approach ...................................................................... 69 6.6 </p><p>Results of the Implementation .......................................................................... 77 iv 7. </p><p>OTHER ISSUES AND FUTURE WORK ............................................................. 78 7.1</p><p> Other Issues Involved in CMS Fitting Software............................................... 78 7.2 </p><p>Future Work...................................................................................................... 79 8. Conclusions............................................................................................................. 81 </p><p>REFERENCES ........................................................................................................... 87 <br></p><p><br></p>
Project Abstract
AbstractCoordinate Measuring Machines (CMMs) are widely used in manufacturing for quality control and assurance of products. The software used in CMMs plays a critical role in ensuring accurate measurements and reliable inspection results. However, like any software, CMM software is subject to uncertainties that can affect the quality of measurements. Uncertainty analysis is essential for understanding and quantifying the potential errors and variations in measurement data. This research project focuses on uncertainty analysis and quality assurance for CMM software. The primary objective is to develop methodologies and tools to assess and manage uncertainties associated with CMM software. The study involves the identification of sources of uncertainty in CMM software, such as geometric errors, calibration uncertainties, and environmental factors. By quantifying these uncertainties, it is possible to improve the reliability and accuracy of measurements obtained from CMMs. Quality assurance for CMM software is another crucial aspect of this research. The goal is to establish robust procedures and protocols to ensure that CMM software meets predefined quality standards. This involves testing the software for accuracy, repeatability, and reproducibility. By implementing quality assurance measures, manufacturers can have confidence in the integrity of the measurement data generated by CMM software. The research methodology includes a combination of theoretical analysis, simulation studies, and experimental validation. Uncertainty propagation techniques will be used to assess the impact of different uncertainty sources on measurement results. Additionally, statistical methods will be employed to analyze the variability and consistency of measurements obtained from CMM software. Experimental validation will be conducted using real-world CMM systems to verify the effectiveness of the proposed uncertainty analysis and quality assurance methods. The outcomes of this research project are expected to benefit manufacturers and quality control professionals in various industries. By improving the understanding of uncertainty in CMM software and enhancing quality assurance procedures, manufacturers can reduce the risk of producing defective products and improve overall product quality. Ultimately, this research aims to contribute to the advancement of measurement technologies and quality control practices in manufacturing.
Project Overview
1. INTRODUCTION 1.1
Coordinate Measuring Systems Coordinate measuring systems (CMSs) are installed in factories, research and medical labs, as well as many other industrial and scientific facilities. The definition of a CMS is, "…any piece of equipment which collects coordinates (points) and calculates and displays additional information using the measured points," [8]. To find the dimensions of a part, a CMS measures point locations on the object’s surface. This coordinate data is then processed to determine the part’s dimensions and the types and locations of variations in the surface. Note that the raw coordinate data generally must be interpreted before the information gathered is of any real use. Specifically, once the coordinate data points are collected from the surface of the part by the CMS hardware, the information is processed by software, which usually performs a geometric fit to the gathered data. This fitting software, which is usually integrated as part of the CMS, uses the coordinate data to, for instance, determine a part’s location, orientation, concentricity, or deviation of the part from the corresponding perfect geometry. The software can apply appropriate processing of the data to determine if a part is within tolerances defined in specifications. Since a part is measured through only a sampling of points, its true surface can never be known exactly; instead, an approximation of the surface is known based on a finite sampling of coordinate points. The software will often be required to compute a “substitute geometry” based on the imperfect data. This substitute geometry is a perfect, theoretical, mathematical shape fit to the points. For example if a CMS samples points on a surface that is 2 nominally cylindrical, then the software can compute a fit to find the “best” perfect cylinder that is represented by the imperfectly measured points on the imperfect physical surface. Just how this substitute feature is determined can be complicated and is discussed in this paper. CMSs are used to measure everything from pistons and cylinders to gears and screw threads to airplane wings and car doors. Sometimes their uses go beyond manufactured parts to include, for example, bones and vertebrae alignment in the medical field. Many different types of coordinate measuring systems are in use today including theodolites, photogrammetry, optical systems, and coordinate measuring machines. Though such variation exists among CMSs, the software packages that they normally come equipped with are similar and share some basic problems and issues. Examples of several different types of systems are given1 in figure 1.1. Shown in the pictures are: 1) CMM: a measuring system with the means to move a probing system and capable of determining spatial coordinates on a workpiece surface, 2) theodolite: a small telescope mounted and moving on two graduated circles, one horizontal, the other vertical, while its axes pass through the center of the circles. The data points are found using triangulation, and 3) photogrammetry: this system works by taking pictures of the object being measured with a digital camera then inputting the image into the software to determine its part information. 1
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