A static analogy for 2D tolerance analysis

Purpose - This paper aims to present a method for the tolerance analysis of mechanical assemblies that is suitable to nonlinear problems where explicit functional equations are difficult or even impossible to write down. Such cases are usually modelled by linearised tolerance chains, whose coefficients (or sensitivities) are calculated from assembly data. Design/methodology/approach - The method is based on the free-body diagrams of force analysis, which are shown to be related to the sensitivities of linearised functional equations. Such an analogy allows the conversion of a tolerance chain into a corresponding static problem, which can be solved by common algebraic or graphical procedures. Findings - The static analogy leads to a correct treatment of tolerance chains, as the analysis of several examples has confirmed by comparison to alternative methods. Research limitations/implications - Currently, the method has only been tested on two-dimensional chains of linear dimensions for assemblies with nonredundant kinematic constraints among parts. Practical implications - The proposed method lends itself to ready application by using simple operations with minimal software assistance. This could make it complementary to current methods for calculating sensitivities, which are mathematically complex and require software implementation for deployment in industrial practice. Originality/value - Analogy with force analysis, which has not been previously highlighted in the literature, is a potentially interesting concept that could be extended to a wider range of tolerancing problems

An approach to collaborative assembly design modification and assembly planning

Ph.DDOCTOR OF PHILOSOPH

Key characteristic coupling and resolving key characteristic conflict

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 2003.Includes bibliographical references (p. 159-166).This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Real complex assemblies have to deliver large number of customer requirements. Assemblies in general have many parts which work together to deliver those requirements. The involvement of many parts and presence of many requirements to be delivered, results in the involvement of a part in the delivery chains of more than one requirement. As a result most of the requirements are not delivered independently. Coupling among the requirements makes it hard to achieve all the requirements with in their respective tolerance limits. The thesis gives classification of nature of relationships that can exist among various requirements. It discusses characteristic of each relationship and how it can affect the robustness of an assembly. When the requirements in the assembly are conflicting, i.e. reduction in variation in one of the requirements increases variation in conflicting requirement, it tends to become non-robust. Non-robust assemblies entail high manufacturing costs. Aim of the thesis is to identify the scenarios of conflict in the assembly. Screw theory can be used to find the presence of coupling among requirements in the assembly. It can also be used to identify the nature of coupling. If coupling suggests that requirements are coupled, we analyze the intensity of the conflict. Not all conflicts need to be solved. Only the conflicts that will make assembly miss tolerance limits on its requirements need to be solved. The thesis outlines some of the methods that can be used to either resolve conflict or reduce the amount of conflict in the assembly. Conflicts can be removed from the assembly by making suitable changes in design. Design changes will modify DFCs of the conflicting requirements. Use of appropriate assembly techniques can also remove conflicts from the assembly. An assembly without any conflicts is more robust and can be produced at a less cost as compared to the one having conflicts.by Jagmeet Singh.S.M

Stratégies de mise en oeuvre des polytopes en analyse de tolérance

In geometric tolerancing analysis area, a classical approach consists in handling polyhedrons coming from sets of linear constraints. The relative position between any two surfaces of a mechanism is determined by operations (Minkowski sum and intersection) on these polyhedrons. The polyhedrons are generally unbounded due to the inclusion of degrees of invariance for surfaces and degrees of freedom for joints defining theoretically unlimited displacements.In a first part are introduced the cap half-spaces to limit these displacements in order to transform the polyhedron into polytopes. This method requires controlling the influence of these additional half-spaces on the topology of calculated polytopes. This is necessary to ensure the traceability of these half-spaces through the tolerancing analysis process.A second part provides an inventory of the issues related to the numerical implementation of polytopes. One of them depends on the choice of a computation configuration (expression point and base, homogenization coefficients) to define a polytope. After proving that the modification of a computation configuration is an affine transformation, several simulation strategies are listed in order to understand the problems of numerical precision and computation time.En analyse de tolérances géométriques, une approche consiste à manipuler des polyèdres de R' issus d’ensembles de contraintes linéaires. La position relative entre deux surfaces quelconques d'un mécanisme est déterminée par des opérations (somme de Minkowski et intersection) sur ces polyèdres. Ces polyèdres ne sont pas bornés selon les déplacements illimités dus aux degrés d’invariance des surfaces et aux degrés de liberté des liaisons.Dans une première partie sont introduits des demi-espaces "bouchons" destinés à limiter ces déplacements afin de transformer les polyèdres en polytopes. Cette méthode implique de maîtriser l’influence des demi-espaces bouchons sur la topologie des polytopes résultants. Ceci est primordial pour garantir la traçabilité de ces demi-espaces dans le processus d’analyse de tolérances.Une seconde partie dresse un inventaire des problématiques de mise en oeuvre numérique des polytopes. L’une d’entre elles repose sur le choix d’une configuration de calcul (point et base d’expression, coefficients d’homogénéisation) pour définir un polytope. Après avoir montré que le changement de configuration de calcul est une transformation affine, plusieurs stratégies de simulations sont déclinées afin d’appréhender les problèmes de précision numérique et de temps de calculs

A unified approach to modeling, verifying, and improving the manufacturability of mechanical assemblies

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 2004.Includes bibliographical references (p. 247-256).This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.The goal of a design engineering organization is to design products that satisfy customers. Reaching this objective is dependent, among other things, on five parameters: the customer expectations, the target percentage of satisfied customers, the nominal performance of the design, the variability in the manufacturing processes, and the sensitivity of the design performance to such variability. This work presents a unified methodology that is amendable to computer implementation for modeling these five parameters for products that are primarily mechanical in nature. The validity of this methodology is subject to five major assumptions: the nominal performance of the design matches the performance expected by the customer, the set of customer expectations can be represented completely by a set of geometric relationships and tolerances between features in the assembly, the degradation in product performance is due solely to quantifiable variability or mean shift in the assembly geometry, the variability in each geometric relationship is independent of the variability in any other geometric relationship, and any compliant parts in the assembly can be accurately modeled as sets of rigid parts connected with linearly-compliant joints. The assembly model is developed using a combination of Screw Theory, Network Theory, Homogeneous Transformation Matrices, and Probability Theory. It is shown how this model can be used to verify the manufacturability of a mechanical assembly design. It is also shown how the model and the results obtained from it can be used to improve the level of manufacturability of a design if it is found to be unacceptably low. To validate the effectiveness and accuracy of the methodology, an automated version written for Matlab®(cont.) was used to model and analyze the manufacturability of an engine valvetrain. The results of this case study are presented and compared to results using existing industry-standard tools. Several suggestions for improving the manufacturability of the valvetrain are also proposed and discussed.by J. Michael Gray.S.M