Effective Product Lifecycle Management: the role of uncertainties in addressing design, manufacturing and verification processes

The aim of this thesis is to use the concept of uncertainty to improve the effectiveness of Product Lifecycle Management (PLM) systems. Uncertainty is a rather new concept in PLM that has been introduced with the new technical language, drawn by ISO, to manage Geometrical Product Specification and Verification (GPS) in the challenging environment of modern manufacturing. GPS standards regard in particular design and verification environments, and want to guarantee consistence of information through a technical language which define both specification and verification on sound logical and mathematical bases. In this context, uncertainty is introduced as the instrument that measures consistency: between the designer intentions (specifications) and the manufactured artefact (as it is observed through measurement) as well as between the measurand definition provided by designers (the specification again) and that used by metrologists. The implications of such an approach have been analyzed through a case study dealing with flatness tolerance and paying particular attention to the verification processes based on Coordinate Measuring Machines (CMM). A Design of Experiment (DoE) has been used and results have been analyzed and used to build a regression model that allows generalization in the experiment validity domain. Then, using Category Theory, a categorical data model has been defined which represents the operation based structure of GPS language and uses the flatness research results in order to design a software able to concretize the GPS vision of geometrical product specifications management. This software is able to translate specification requirements into verification instructions, estimate the uncertainty introduced by simplified verification operations and evaluate costs and risks of verification operations. It provides an important tool for designers, as it allows a responsible definition of specifications (designer can simulate the interpretation of specifications and have an idea of the costs related with their verification), and for metrologist, as it can be a guide for designing GPS compliant verification missions or handling the usual verification procedures according to the GPS standards. However, during the study, it has been matured the consciousness that this approach, even if correct and valuable, was not the most suitable to fully exploit the real potential of CMM. Then, aside the GPS oriented work, an adaptive sampling strategy, based on Kriging modelization, has been proposed with very encouraging result

An effective dimensional inspection method based on zone fitting

Coordinate measuring machines are widely used to generate data points from an actual surface. The generated measurement data must be analyzed to yield critical geometric deviations of the measured part according to the requirements specified by the designer. However, ANSI standards do not specify the methods that should be used to evaluate the tolerances. The coordinate measuring machines employ different verification algorithms which may yield different results. Functional requirements or assembly conditions on a manufactured part are normally translated into geometric constraints to which the part must conform. Minimum zone evaluation technique is used when the measured data is regarded as an exact copy of the actual surface and the tolerance zone is represented as geometric constraints on the data. In the present study, a new zone-fitting algorithm is proposed. The algorithm evaluates the minimum zone that encompasses the set of measured points from the actual surface. The search for the rigid body transformation that places the set of points in the zone is modeled as a nonlinear optimization problem. The algorithm is employed to find the form tolerance of 2-D (line, circle) as well as 3-D geometries (cylinder). It is also used to propose an inspection methodology for turbine blades. By constraining the transformation parameters, the proposed methodology determines whether the points measured at the 2-D cross-sections fit in the corresponding tolerance zones simultaneously

Modeling of 2D and 3D Assemblies Taking Into Account Form Errors of Plane Surfaces

The tolerancing process links the virtual and the real worlds. From the former, tolerances define a variational geometrical language (geometric parameters). From the latter, there are values limiting those parameters. The beginning of a tolerancing process is in this duality. As high precision assemblies cannot be analyzed with the assumption that form errors are negligible, we propose to apply this process to assemblies with form errors through a new way of allowing to parameterize forms and solve their assemblies. The assembly process is calculated through a method of allowing to solve the 3D assemblies of pairs of surfaces having form errors using a static equilibrium. We have built a geometrical model based on the modal shapes of the ideal surface. We compute for the completely deterministic contact points between this pair of shapes according to a given assembly process. The solution gives an accurate evaluation of the assembly performance. Then we compare the results with or without taking into account the form errors. When we analyze a batch of assemblies, the problem is to compute for the nonconformity rate of a pilot production according to the functional requirements. We input probable errors of surfaces (position, orientation, and form) in our calculus and we evaluate the quality of the results compared with the functional requirements. The pilot production then can or cannot be validated

Development of an intelligent geometry measurement procedure for coordinate measuring machines

A Coordinate Measuring Machines (CMM) is a highly accurate electronic scale for the automatic measurement of 2 and 3 dimensional geometries. In a typical operation the CMM measures a set of user defined points, and then utilizes some internal logic to ascertain whether the inspected part meets the specifications. CMMs have received widespread acceptance among the manufacturing community, and in many instances are required as per supplier contract. Applications of CMMs vary from the measurement of simple 2D parts to complex 3D spatial frames (as for example in their use to measure the integrity of automobile frames). The primary objective of the proposed research is to investigate procedures for the efficient use of CMMs. Two of the key parameters in CMM usage are the number of points measured, and the relative location of the points measured. In this thesis we firsts show that when these two inspection parameters are varied, for the same part, then different conclusions with regard to the part\u27s geometry may be drawn. Next we investigate the relationship between these two parameters and the reliability of the concluded data. Specifically we focus on a 2D circle, a 2D rectangle, and a 2D plane. The experiments were conducted on the Brown & Sharpe\u27s Coordinate Measuring Machine

Design of optimal measurement strategies for geometric tolerances control on coordinate measuring machines

This study is concerned with a vast industrial problem: the inspection of physical components and subsystems for checking their conformance to dimensional and geometric tolerance specifications. Although a number of non contact optical devices are being currently developed for such a task, Coordinate Measuring Machines (CMM) are still universally adopted thanks to their superiority in terms of accuracy in the measurement of point coordinates. However, their unsurpassed metrological quality for this basic operation is counterbalanced by a fundamental problem that is plaguing practitioners in the sector of industrial metrology. The problem is usually referred to as methods divergence and can be stated as follows. On one hand, the machines probe the part surface point-wise and economic constraints force the point sample to be small. On the other end, geometric errors, as defined by tolerance standards, depend heavily on extreme values of the form deviations over the related surface so that a full-field inspection is virtually required. For example, straightness error is the minimum distance between two parallel lines enclosing the actual feature. Thus extreme points are more important than the others in determining the straightness error. This problem, translated in statistical terms, means using a small sample of form deviations to make inference on a quantity dependent on extreme values of the population, thereby unlikely to be in the sample. Thus sample-based evaluation of geometric errors is naturally prone to be substantially biased and uncertain, especially when the surfaces exhibit systematic form deviations. In spite of this, common practice in industry is to probe very few points according to very simple sampling strategy (uniform, random, stratified). The software packages sold with the machines contain algorithms of computational geometry which are selected by purely economic criteria (easy to implement, fast to compute) regardless of their implications on measurement quality. Moreover, user awareness of the importance of evaluating measurement uncertainty in the inspection of geometric tolerances is exceedingly limited. This is no wonder if we consider that the ISO committees have been working for several years on different four methods for uncertainty evaluation in CMM measurement tasks (ISO 15530 family) and still now only one standard has been officially delivered (ISO 15530-3, march 2004). Uncertainty calculation using calibrated objects)

Analysis of Characteristics of Non-Commercial Software Systems for Assessing Flatness Error by Means of Minimum Zone Method

As far as machine parts are concerned, accuracy can be defined in many aspects. In order for a workpiece to be functional, dimensional and surface roughness requirements are not enough. Accuracy of geometric elements and position tolerances is necessary information. The notation, definitions, interpretations and general values of geometric tolerances are defined by standards. Nevertheless, there are several mathematical methods of calculating values based on data measured by means of coordinate measuring machines. Standards demand the use of the minimum zone method in assessing form deviation without mentioning the way of obtaining it. In this paper, the minimum zone method, which is an iterative algorithm, was investigated. Thus, the result of flatness measurement was calculated by continuous approximation. There are various methods of defining the steps of iteration, affecting the length of time and accuracy of the flatness value. The aim of the research was to examine the characteristics of two non-commercial software solutions for assessing the minimum zone in comparison with the commercial CMM software. Based on the analysis, it can be concluded that the developed software solutions are efficient in assessing flatness error and that the differences between these and the commercial software are negligible

An effective dimensional inspection method based on zone fitting

Coordinate measuring machines are widely used to generate data points from an actual surface. The generated measurement data must be analyzed to yield critical geometric deviations of the measured part according to the requirements specified by the designer. However, ANSI standards do not specify the methods that should be used to evaluate the tolerances. The coordinate measuring machines employ different verification algorithms which may yield different results. Functional requirements or assembly conditions on a manufactured part are normally translated into geometric constraints to which the part must conform. Minimum zone evaluation technique is used when the measured data is regarded as an exact copy of the actual surface and the tolerance zone is represented as geometric constraints on the data. In the present study, a new zone-fitting algorithm is proposed. The algorithm evaluates the minimum zone that encompasses the set of measured points from the actual surface. The search for the rigid body transformation that places the set of points in the zone is modeled as a nonlinear optimization problem. The algorithm is employed to find the form tolerance of 2-D (line, circle) as well as 3-D geometries (cylinder). It is also used to propose an inspection methodology for turbine blades. By constraining the transformation parameters, the proposed methodology determines whether the points measured at the 2-D cross-sections fit in the corresponding tolerance zones simultaneously

High-order adaptive methods for computing invariant manifolds of maps

The author presents efficient and accurate numerical methods for computing invariant manifolds of maps which arise in the study of dynamical systems. In order to decrease the number of points needed to compute a given curve/surface, he proposes using higher-order interpolation/approximation techniques from geometric modeling. He uses B´ezier curves/triangles, fundamental objects in curve/surface design, to create adaptive methods. The methods are based on tolerance conditions derived from properties of B´ezier curves/triangles. The author develops and tests the methods for an ordinary parametric curve; then he adapts these methods to invariant manifolds of planar maps. Next, he develops and tests the method for parametric surfaces and then he adapts this method to invariant manifolds of three-dimensional maps