Geometric dimensioning, tolerancing and inspection

In the functional design process of a mechanical component, the tolerance allocation stage is of primary importance to make the component itself responding to the functional requirements and to cost constraints. Present state-of-the-art approach to tolerance allocation is based on the use of Statistical Tolerance Analysis (STA) software packages which, by means of Monte Carlo simulation, allow forecasting the result of a set of user-selected geometrical and dimensional tolerances. In order to completely automate and optimize this process, this work presents a methodology to allow an automatic tolerance allocation, capable to minimize the manufacturing cost of a single part or assembly. The proposed approach is based on the Monte Carlo method to compute the statistical distribution of the critical to quality characteristics and uses an optimization technique based on Genetic Algorithms. The resulting procedure has been integrated in an off-the-shelf variation analysis software: eM-TolMate (by Siemens AG). Both the description of the optimization algorithm and some practical applications are presented in order to demonstrate the effectiveness of the proposed methodology. © 2012 Asian Network for Scientific Information.

Keywords: Functional design , Genetic algorithms , Monte carlo method , Tolerance allocation

When designing mechanical assemblies, assembly tolerance design is an important issue which must be seriously considered by designers. Assembly tolerances reflect functional requirements of assembling, which can be used to control assembling qualities and production costs. This paper proposes a new method for designing assembly tolerance networks of mechanical assemblies. The method establishes the assembly structure tree model of an assembly based on its product structure tree model. On this basis, assembly information model and assembly relation model are set up based on polychromatic sets (PS) theory. According to the two models, the systems of location relation equations and interference relation equations are established. Then, using methods of topologically related surfaces (TTRS) theory and variational geometric constraints (VGC) theory, three VGC reasoning matrices are constructed. According to corresponding relations between VGCs and assembly tolerance types, the reasoning matrices of tolerance types are also established by using contour matrices of PS. Finally, an exemplary product is used to construct its assembly tolerance networks and meanwhile to verify the feasibility and effectiveness of the proposed method. Copyright © 2012 Yi Zhang et al.

In this paper the authors present an original methodology aiming at the automation of the geometric inspection, starting from a high-density acquired surface. The concept of intrinsic nominal reference is herein introduced in order to evaluate geometric errors. Starting from these concepts, a new specification language, which is based on recognisable geometric entities, is defined. This work also proposes some surface differential properties, such as the intrinsic nominal references, from which new categories of form errors can be introduced. Well-defined rules are then necessary for the unambiguous identification of these intrinsic nominal references. These rules are an integral part of the tolerance specification. This new approach requires that a recognition process be performed on the acquired model so as to automatically identify the already-mentioned intrinsic nominal references. The assessable errors refer to recognisable geometric entities and their evaluation leaves the nominal reference specification aside since they can be intrinsically associated with a recognised geometric shape. Tolerance specification is defined based on the error categories which can be automatically evaluated and which are an integral part of the specification language. © 2011 Taylor & Francis.

Keywords: automated inspection , form error evaluation , GPS tolerancing

Variation analysis of assemblies is a strategic task in many industrial applications. Parts manufactured through plastic deformation processes exhibit appreciable shape deviations from the nominal geometry due mainly to spring-back phenomena. When these parts are assembled, initial shape deviations at part level highly influence the final assembly shape. This work focuses on the modeling and simulation of shape errors in order to perform variation analysis of compliant assemblies. The aim is to simulate variational shape of parts according to a small number of control points chosen on the part geometry through a morphing mesh procedure. These points are typically related to measurement or inspection points of manufactured parts. From the mesh model of parts, mesh nodes are moved by applying the morphing procedure. In particular, in order to assure control points belong to the "perturbed" shape, a linear-constrained approach is adopted. The so-morphed parts are used to accomplish the variational assembly analysis following the classical place, clamp, fasten, and release cycle. In order to achieve statistical results, Monte Carlo simulation is performed: a set of control points driving the perturbed parts is generated at each iteration; these parts are then assembled and results are stored. Numerical results are compared with ones coming from commercial software that uses a linear approach based on the sensitivity matrix.

Keywords: Geometric covariance , Monte Carlo FEA , Morphing mesh , Shape errors , Variational assemblies

The core of the paper is focused on the experimental characterization of four different 3D laser scanners based on Time of Flight principle, through the extraction of resolution, accuracy and uncertainty parameters from specifically designed 3D test objects. The testing process leads to four results: z-uncertainty, xy-resolution z-resolution and z-accuracy. The first is obtained by the evaluation of random residuals from the 3D capture of a planar target, the second from the scanner response to an abrupt z-jump, and the last two from direct evaluation of the image extracted by different geometric features progressively closer each other. The aim of this research is to suggest a low cost characterization process, mainly based on calibrated test object easy to duplicate, that allow an objective and reliable comparison between 3D TOF scanner performances. © 2011 SPIE-IS&T.

Keywords: Accuracy , Characterization , Precision , Range sensor , Resolution , Standardization , TOF laser scanner

The manufacturing process of freeform glass components for precision optics is usually based on contour CNC grinding and polishing operations. To predict the geometrical precision of the production process, a correlation between the geometrical error and the process parameters is required. This is even more important in the polishing operation which is the final stage of the process. In this work a model for material removal estimation in deterministic polishing of glass moulds is proposed and validated. The model is developed for CNC ball polishing of free-form surfaces, where the pad, made of a polyurethane layer superimposed to a rubber bulk, moves along a scanning path, in a suspension of cerium oxide. As many models in literature the removed material can be estimated by pressure and sliding velocity between polishing pad and workpiece. Adopting the Hertz theory these physical characteristics can be related to the CAD-CAM-CNC parameters, e.g. tool and workpiece shape, dimension and modulus of elasticity, feed rate, feed step, tool rotational speed and radial tool deformation. The model validation was performed on ground glass flat samples polished with different process parameters, measuring the removed material by a contact probe profilometer. The developed model shows a satisfactory estimation of removal material as a function of the process parameters.

Precision free-form components are functionally complex objects with very accurate surfaces. In the manufacturing of these parts the complete and correct characterization of geometrical errors is an important aspect since it allows the adoption of preventive actions to control errors causes such as the thermo-mechanic behaviour of the machine tool, the removal mechanism of the cutting operation, the wear of the tool, the lubricant action, etc. In this work an advanced method of geometry characterization has been adopted to investigate the various contributions of the geometric error, resulting from the machining of any free-form geometry. The method allows the effective estimation of the size contribution error as well as form, orientation and position deviation. The method consists in an iterative process that minimize the distance of the cloud of points measured to an optimized offset of the nominal model of the component. At the end of minimization process, optimal parameters are used for the complete shape characterization of the part.

The paper deals with the investigation of the influence of geometrical and dimensional errors on performance of the Tracta coupling. It is one of the most simple constant-velocity joints which has been used in front-wheel drive automobiles, all-wheel drive military vehicles, heavy vehicles and various other applications. The proposed study is based on building and simulating a parametric spatial multibody model of the full joint. Both kinematic and dynamic behaviour have been investigated. Five different linear and angular errors have been studied. The sensitivity of kinema-tics and dynamics irregularities to these errors has been computed and summarized in design charts. The results can be used in optimal toleran-ce allocation and accurate vehicle system simulation with the coupling joint sub-model.

Keywords: Mechanical error , Multibody model , Tolerance , Tracta joint

In this paper, a general methodology to do tolerance analysis of rigid assemblies is proposed. Firstly, tolerance specification sets, according to GD&T or ISO specifications, are translated into variational features by using 4∈×∈4 homogenous transformation matrices. In particular, planar and cylindrical features are considered. Then, once all variational features are modeled, assembly constraints among parts are introduced. To solve assembly constraints, an assembly transformation matrix is evaluated. By using point, line, and plane entities and their combinations, kinematic joints are modeled. A numerical procedure is proposed to solve fully and over-constrained assemblies. The best-fit alignment among variational mating features is performed by using optimization algorithms. The proposed method for tolerance analysis of rigid part assemblies allows to simulate different assembly sequences. Finally, in order to show the effectiveness of the proposed methodology, three case studies are described and analyzed. © 2009 Springer-Verlag London Limited.

Keywords: Assembly constraints , Assembly simulation , Feature modeling , GD&T/ISO specifications , Tolerance analysis , Variational features

The need for a designer to have a tool able to do motion and constraint analysis, to check for the under-constrained and/or over-constrained status of an assembly, is strategic in a design contest where several changes are made during the design process by using CAD. Traditional kinematic tools provide little information on over-constraints at 3D level. Screw theory has been already used in mechanical assemblies, in a top-down design, to do motion and constraint analysis. This theory is here used to analyze mechanical assemblies in the contest of a feature-based CAD system. The structure of the CAD assembly is captured and described as assembly graph, similar to Datum Flow Chain, through which the motion or constraint status of any part (in terms of twist and wrench matrices), can be obtained. The underlying algorithm is based on the Kirchoffs rules successfully applied by Davies to mechanisms. How to automatically create the assembly graph, detect the useful loops and then write the loop kinematic equations is described. Three case studies are presented related to CAD assemblies of mechanisms built up in SolidWorks® CAD system by Dassault Systèmes from which assembly constraints have been acquired. Copyright © 2010 by ASME.

In this paper we study the feasibility of developing a search engine capable of retrieving images from a granite image database based on a query image that is similar to the intended targets. The main focus was on the determination of the set of colour and/or texture features which yields highest retrieval accuracy. To assess the performance of the considered image descriptors we created a granite image database, formed by images recorded at our laboratory as well as taken from the Internet. Experimental results show that colour and texture features can be successfully employed to retrieve granite images from a database. We also found that improved accuracy is achieved by combining different colour and texture feature sets through classifier fusion schemes.

Keywords: CBIR , Colour , Granite , Image retrieval systems , Texture , Visual appearance

Often a designer has the problem to apply a suitable system of geometrical and dimensional tolerances to an assembly. The right solution is not unique, in fact it depends on the chosen parameters. If the tolerances have to be optimized, some important parameters have to be taken into account, e.g. the efficiency of each prescription, or if this last is reachable, or it can be verified and how much the realization costs. The authors opinion is that a statistical approach based on the Monte Carlo Method is very useful when the tolerances chains are complex. This paper shows an application of this method in order to verify the functional alignment between two assemblies and a critical analysis of the uncertainty in phase both of the component design and test. This study has been developed thanks to the strict requirements imposed by ESA (European Space Agency) on the components that Thales Alenia Space has to realize within the LISA Pathfinder experiment. The very critical aspect of this work is to reciprocally align two cylindrical elements of two different assemblies. The specifications require 100 μm as maximum linear displacement and 300 μrad as maximum angular displacement. Moreover this prescriptions have to be verified also when the two elements are independently moving. To be able to reach such strict accuracy level the components have been assembled in an ISO 100 class cleanroom and the work space was a 3D Coordinate-Measuring Machine (CMM). The cylindrical elements have a 10 mm diameter, so the value of the measurement uncertainty associated with the alignment check is fundamental. Starting from the different uncertainty sources, the measurability and verifiability of the alignment have been considered and evaluated. The overall uncertainty has been assessed by numerical simulations which have taken into account the dimensional, geometrical and form tolerances as well as the instrumental uncertainty of the 3D CMM. This estimation has been positively validated by a session of repeated measurements. Numerical simulations have also allowed performing a sensitivity analysis, in order to give information about which sources more contribute to the overall uncertainty. Copyright © 2010 by ASME.

The performance of 2D digital imaging systems depends on several factors related with both optical and electronic processing. These concepts have originated standards, which have been conceived for photographic equipment and bi-dimensional scanning systems, and which have been aimed at estimating different parameters such as resolution, noise or dynamic range. Conversely, no standard test protocols currently exist for evaluating the corresponding performances of 3D imaging systems such as laser scanners or pattern projection range cameras. This paper is focused on investigating experimental processes for evaluating some critical parameters of 3D equipment, by extending the concepts defined by the ISO standards to the 3D domain. The experimental part of this work concerns the characterization of different range sensors through the extraction of their resolution, accuracy and uncertainty from sets of 3D data acquisitions of specifically designed test objects whose geometrical characteristics are known in advance. The major objective of this contribution is to suggest an easy characterization process for generating a reliable comparison between the performances of different range sensors and to check if a specific piece of equipment is compliant with the expected characteristics. © 2010 by the authors.

Keywords: 3D measurement , Accuracy , Laser scanner , Metrological characterization , Pattern projection , Resolution , Uncertainty

The effect of the sintering temperature on the dimensional and geometrical precision of a 3%Cr-0.5%Mo- 0.5%C ring-shaped part produced in an industrial plant was studied. The part was compacted to 6.8 g/cm3 green density and sinter-hardened at 1120°C, 1250°C, 1300°C and 1350°C. Despite the large shrinkages (up to 1.24% at the highest temperature), dimensional and geometrical characteristics do not worsen noticeably on sintering, except for the dimensional tolerances on the diameter, which anyway keep a good precision level, from IT3 to IT4-IT5 (internal diameter) and from IT5 to IT6-IT7 (external diameter). According to the results, sintering at high temperature up to 1350°C does not seem to impair the most important characteristic of sintered parts, i.e. the precision. © 2010 Metal Powder Industries Federation.

The dimensional and geometrical characteristics of Charpy bars produced with two different steels were investigated to evaluate the effect of increasing the sintering temperature from 1120 °C (conventional sintering temperature) up to 1350 °C. The problem was approached from the Geometric Dimensioning and Tolerancing (GD&T) point of view, referring to the standard ASME Y14.5 (2009). The dimensional and geometrical characteristics were evaluated using a Coordinate Measuring Machine (CMM), measuring the surfaces by scanning mode. The work highlights that the increase in the sintering temperature, aimed at improving the mechanical properties, does not prevent the main benefit of this technology, i.e., the possibility of producing parts with good dimensional and geometrical precision. Moreover, a methodology establishing the measurement procedures and data processing, to be used in future work for the characterisation of more complex shapes, was defined. © 2010 Elsevier B.V.

Keywords: Geometric dimensioning and tolerancing , Powder metallurgy , Shrinkage

Purpose - The purpose of this paper is to investigate a method for comparing the scanning and reproducing accuracy of highly shaped objects like plaster casts used in dentistry. Design/methodology/approach - Theoretical considerations on errors introduced by the scanning systems and subsequent point clouds data elaboration have led to a method to estimate the accuracy of the whole process. Suitable indices have been chosen and computed at each stage. As a final result, the overall chain, scanning and reproducing systems can be assessed. In order to validate the proposed method casts have been scanned by means of commercial systems and then reproduced by using different rapid prototyping technologies, materials and parameters. Error indices have been computed and reported. Findings - Since it is not possible to define reliable and meaningful reference models for non-standard shapes, an absolute accuracy value for the scanning process cannot be stated. Anyway the proposed method, thanks to relative performance indices, allows the comparison of different acquisition systems and the evaluation of the most performing manufacturing chain. Practical implications - The study provides a method to assess the relative performance between commercial systems both in scanning and reproducing stage. Originality/value - In literature, some studies on the accuracy of scanning devices have been found but they are based on standard geometrical features. In this paper, the problem of complex shapes in absence of reference model is addressed instead. Copyright © Emerald Group Publishing Limited [ISSN 1355-2546].

Keywords: Accuracy , Dentistry , Rapid prototypes , Structural analysis

During last years, several numerical methods have been proposed to accomplish analysis and synthesis of 3D tolerance chains. These methods allow predicting final assembly variations, starting from tolerance specification set defined at part level. Nevertheless, few specific methodologies are available today to check the global consistency of a tolerance specification set, related to a mechanical assembly. In this work, an approach to validate the global consistency of a 3D tolerance specification set is proposed. The approach is mainly composed by two different analyses. The first analysis is aimed to verify, at assembly level, the adequacy of a tolerance specification set by determining the assembly subsets of parts which influence each assembly key characteristic. The second analysis is aimed to verify the consistency of the tolerance specification set by using rules, mainly based on the TTRS theory. In order to show the effectiveness of the methodology, two case studies are illustrated by using a friendly graphical user interface (GUI) developed in MatLab® environment. © 2009 Springer-Verlag.

Keywords: Global consistency , Tolerance graph , Tolerance specification , TTRS theory

The present paper deals with the manufacturing process of a railway carriage. In the first part of the paper, the authors focus on a "virtual railway factory" that uses a very innovative assembly cycle, if compared to the traditional manufacturing processes in the railway field. The case study refers to a railway carriage consisting of four modules, that are singularly set up of furnishings and other systems in dedicated workplaces. On one hand, the virtual simulation has highlighted several critical aspects to be improved, in order to achieve a greater feasibility and to reduce time and cost. On the other hand, the designers have been able to evaluate the movements of the parts and the assembly sequences of the components, by considering each geometric, functional and technological constraint and also some safety requirements. The second part of the paper deals with the simulation of the assembling operations and the analysis of tolerance chains, which have been performed through a Computer Aided Tolerancing system. In particular, the precision requirements have been also evaluated and we have compared the accumulation of dimensional and geometric deviations when using both rivets and traditional welds to fasten the modules. © 2009 Springer-Verlag.

Keywords: Computer Aided Tolerancing , Train design , Virtual manufacturing

While parallel kinematics micropositioners offer high repeatability in positioning with respect to their own reference frame, the accuracy of absolute positioning with respect to a second, fixed, reference frame largely depends on the knowledge of the relative position between the two. Here will be presented a method for a rapid estimation of these relative positions based on subsequent movements of a positioner under a CMM and evaluation of position uncertainty.

Keywords: Accuracy measurement , Hexapod , Positioning , Uncertainty

Resolution analysis represents a 2D imaging topic for the use of particular targets for equipment characterization. These concepts can be extended in 3D imaging through the use of specific tridimensional target object. The core of this paper is focused on experimental characterization of seven different 3D laser scanner through the extraction of resolution, accuracy and uncertainly parameters from 3D target object. The process of every single range map defined by the same resolution leads to different results as z-resolution, optical resolution, linear and angular accuracy. The aim of this research is to suggest a characterization process mainly based on resolution and accuracy parameters that allow a reliable comparison between 3D scanner performances. © 2009 SPIE-IS&T.

Keywords: 3D Scanner , Accuracy , Characterization , Resolution , SFR , Target Object