Tolerance Analysis Of Mechanical Assemblies Research Articles

Including material conditions effects in statistical geometrical tolerance analysis of mechanical assemblies

Including material conditions effects in statistical geometrical tolerance analysis of mechanical assemblies

Direct tolerance analysis of mechanical assemblies with normal and non-normal tolerances for predicting product quality

ABSTRACT Tolerance analysis, as an effective tool for predicting the effects of geometrical and dimensional deviations on the key characteristics, plays an essential role in increasing the functionality and quality of mechanical products. The conventional methods in the literature have been developed based on this main assumption that the assembly function is available in an explicit form. However, in most industrial applications, deriving an assembly function in an explicit form may be difficult if not impossible. On the other hand, one of the major weaknesses of the conventional tolerance analysis methods in the literature is that all effective dimensions should be varied under the normality assumption. To overcome these weaknesses, in this paper, a new tolerance analysis approach is developed based on the univariate DRM and Pearson system concepts. The proposed method can analyze directly without the need to define any assembly function and also the rejected product rate can be easily predicted using evaluations of the assembly dimension at the limited number of special points. Finally, for verification of the proposed method, some illustrative case studies are considered and results are compared to obtained results of the Monte-Carlo Simulations and the improved Hassofer-Lind and Rack-Fizzler reliability index methods.

Automated Tolerance Analysis of Mechanical Assemblies from a CAD Model with PMI

Computer-Aided Design and Applications is an international journal on the applications of CAD and CAM. It publishes papers in the general domain of CAD plus in emerging fields like bio-CAD, nano-CAD, soft-CAD, garment-CAD, PLM, PDM, CAD data mining, CAD and the internet, CAD education, genetic algorithms and CAD engines. The journal is aimed at all developers and users of CAD technology to ptovide CAD solutions for various stages of design and manufacturing. The journal publishes all about Computer-Aided Design and Computer-Aided technologies.

Statistical Tolerance Analysis of Over-Constrained Mechanical Assemblies With Form Defects Considering Contact Types

Tolerance analysis aims toward the verification impact of the individual tolerances on the assembly and functional requirements of a mechanism. The manufactured products have several types of contact and are inherent in imperfections, which often causes the failure of the assembly and its functioning. Tolerances are, therefore, allocated to each part of the mechanism in purpose to obtain an optimal quality of the final product. Three main issues are generally defined to realize the tolerance analysis of a mechanical assembly: the geometrical deviations modeling, the geometrical behavior modeling, and the tolerance analysis techniques. In this paper, a method is proposed to realize the tolerance analysis of an over-constrained mechanical assembly with form defects by considering the contacts nature (fixed, sliding, and floating contacts) in its geometrical behavior modeling. Different optimization methods are used to study the different contact types. The overall statistical tolerance analysis of the over-constrained mechanical assembly is carried out by determining the assembly and the functionality probabilities based on optimization techniques combined with a Monte Carlo simulation (MCS). An application to an over-constrained mechanical assembly is given at the end.

Tolerance analysis of mechanical assemblies based on the product of exponentials formula

Many existing tolerancing models deal with the tolerance analysis of mechanical assemblies using linear stack-up function, which will cause truncation errors for nonlinear assembly problem. This article proposes a new method for describing the variation propagation based on the product of exponentials formula. Both the length deviations and the angle deviations are uniformly represented by twist coordinates. Accordingly, the nonlinear stack-up functions relating the assembly functional requirements to the manufacturing variations can be derived, and no truncation errors generated. A three-dimensional assembly case is studied exploiting the proposed method and the direct linearization method, respectively. It appears that the product of exponentials formula can bring consistent tolerance analysis results with the exact geometric solutions, whereas there are some small errors in the analysis results of direct linearization method. The precision of tolerance estimation via the product of exponentials formula is improved by 0.52% at the most compared with that by the direct linearization method. Due to the elimination of local datum reference frames, the product of exponentials formula can also lead to a more concise description of tolerance accumulation than the direct linearization method.

A comprehensive fuzzy feature-based method for worst case and statistical tolerance analysis

Tolerance analysis is an analytical tool for the estimation of accumulating effects of the individual part tolerances on the functional requirements of a mechanical assembly. This article presents a comprehensive feature-based method for tolerance analysis of mechanical assemblies with both dimensional and geometric tolerances. In this method, dimensional and geometric tolerance zones are described by the combination of fuzzy modelling and small degrees of freedom (SDOF) concept. In this model, the uncertainty in dimensions and geometric form of features is mathematically described using fuzzy modelling, and the kinematic effects of tolerances in assemblies are expressed by SDOF concept. In the proposed method, complicated GD&T concepts such as various material modifiers (maximum material condition, least material condition and regardless of feature size), envelope requirement, bonus tolerances and Rule No. 1 (Taylor principle) in several conditions are accurately modelled. Compatible with the proposed model, a procedure for modified worst case and statistical tolerance accumulation analysis is introduced. An algorithm is laid out that describes the steps and the procedure of tolerance analysis. The application of this method is demonstrated through an example, and the results are compared with experimental results.

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.

Tolerance analysis of mechanical assemblies based on small displacement torsor and deviation propagation theories

Construction of the quality tolerances (Q-T) function is a key step in assembly tolerance analysis process. This paper presents a new feature-based tolerance analysis method for mechanical assemblies with GDT (2) the analysis process and acquired Q-T function is relatively concise to the other feature-based method; (3) the integrated assembly information is more intact. A case study is provided to illustrate the proposed method.

On the role of form defects in assemblies subject to local deformations and mechanical loads

Tolerancing activity is usually based on the traditional assumptions that surfaces have no form defects and are rigid under external loads. These assumptions tend to simplify the tolerance analysis of mechanical assemblies and hence the allocation of geometrical specifications. The present paper proposes an original procedure to systematically analyze and quantify the assembly of parts with form and position defects and deformable contact surfaces. Based on this procedure, stochastic simulations are performed by modifying the ratio between the position defects and form defects of surfaces. Even if the form defects are limited, they can lead to a non-compliant assembly. Clearly, the engineer's traditional approach, where form defects are assumed to have no influence, is generally not appropriate if we are to ensure that the expected performance is to be achieved on assembly.

Visualized Equivalent Variational Modeling in Tolerance Analysis of 3D Mechanical Assemblies

This paper introduces a new, visualized approach for including all the geometric feature variations in the tolerance analysis of mechanical assemblies. It focuses on how to characterize geometric feature variations in vector-loop-based assembly tolerance models. The characterization will be used to help combine the effects of all variations within an assembly in order to perform tolerance analysis of mechanical assemblies by employing commercial 3D kinematic software (e.g. ADAMS). Equivalent variational modeling, based on TAKS method, has been developed for modeling variations in 3D mechanical assemblies. Create a library of Equivalent Variational Joints (EVJs) to allow inclusion all kinds of variations in analysis, and allow the kinematic model to include both geometric and dimensional variation in a velocity analysis. EVJ, for use in tolerance analysis, was developed for commonly used 3D kinematic joint types, and was implemented with examples to explain their use to form Equivalent Variational Mechanisms (EVMs).

Fuzzy-small degrees of freedom representation of linear and angular variations in mechanical assemblies for tolerance analysis and allocation

Abstract Tolerances naturally generate an uncertain environment for design and manufacturing. In this paper, a novel fuzzy based tolerance representation approach for modeling the variations of geometric features due to dimensional tolerances is presented. The two concepts of fuzzy theory and small degrees of freedom are combined to introduce the fuzzy-small degrees of freedom model (F-SDOF). This model is suitable for tolerance analysis of mechanical assemblies with linear and angular tolerances. Based on the fuzzy concept, a new index (called the assemblability index) is introduced which signifies the fitting quality of parts in the assembly. Graphical and numerical representations of tolerance allocation by this method are presented. The goal of tolerance allocation is to adjust the tolerances assigned at the design stage so as to meet a functional requirement at the assembly stage. The presented method is compatible with the current dimensioning and tolerancing standards. The application of the proposed methodology is illustrated through presenting an example problem.

Tolerance analysis of assemblies with asymmetric tolerances by unified uncertainty–accumulation model based on fuzzy logic

In mechanical assemblies, individual components are placed together to deliver a certain function. The performance, quality, and cost of the mechanical assembly are significantly affected by its tolerances. Toleranced dimensions inherently generate an uncertain environment in a mechanical assembly. This paper presents a proper method for tolerance analysis of mechanical assemblies with asymmetric tolerances based on an uncertainty model. This mathematical approach is based on fuzzy logic and tolerance accumulation models such as worst-case and root-sum-square methods. A fuzzy-based tolerance representation is developed to model uncertainty of tolerance components in the mechanical assemblies. According to this scheme, toleranced components are described as fuzzy numbers with their membership functions constructed using the statistical distributions of manufactured variables. In this way, the uncertainty of assembly requirements and accumulation of tolerances are represented in the form of fuzzy number. In this paper, a new factor, the fuzzy factor, is introduced that helps converting the membership functions into fuzzy intervals that can be used for modal interval analysis. Equations for estimation of percent contributions of individual tolerances are introduced in terms of uncertainty parameter. These equations yield percent contributions of upper and lower bounds of independent variables (manufactured dimensions) on the upper and lower bounds of dependent variables (assembly dimensions). The proposed method is applied to an example, and its results are discussed.

Tolerance analysis of mechanical assemblies based on modal interval and small degrees of freedom (MI-SDOF) concepts

Tolerance analysis is a key analytical tool for estimation of accumulating effects of the individual part tolerances on the design specifications of a mechanical assembly. This paper presents a new feature-based approach to tolerance analysis for mechanical assemblies with geometrical and dimensional tolerances. In this approach, geometrical and dimensional tolerances are expressed by small degrees of freedom (SDOF) of geometric entities (faces, feature axes, edges, and features of size) that are described by tolerance zones. The uncertainty of dimensions and geometrical form of features due to tolerances is mathematically described using modal interval arithmetic. The two concepts of modal interval analysis and SDOF are combined to describe the tolerance specifications. The algorithm is presented which explains the steps and the procedure of tolerance analysis. The proposed method is compatible with the current GD&T standards and can incorporate GD&T concepts such as various material modifiers (maximum material condition, least material condition, and regardless of feature size), envelope requirement, and bonus tolerances. This method can take into account multidimensional effects due to geometrical tolerances in tolerance analysis. The application of the proposed method is illustrated through presenting an example problem and comparing results with tolerance charting method.

Concurrent design for nominal and tolerance analysis and allocation of mechanical assemblies using DE and NSGA-II

Tolerance analysis of mechanical assemblies promotes concurrent engineering by bringing engineering requirement, manufacturing cost and quality together in a common model. To improve the tolerance design, the designer could first try to decrease the sensitive components by moving the nominal values to a less sensitivity portion. Second, the cost-based optimal machining tolerances are allocated. Differential Evolution (DE) and Non-dominated Sorting Genetic Algorithm (NSGA-II) are used for minimising the critical dimensions deviation and manufacturing cost with optimal machining tolerances. A numerical example (Stacked blocks assembly) shows the superior nature of DE and NSGA-II algorithms.

Tolerance Analysis with eM-TolMate

This article presents a review of a commercial computer-aided tolerance analysis tool, eM-TolMate, which is embedded in four major CAD systems (Catia [1], UG [2], Pro/E [3], SDRC [4]). eM-TolMate combines the Monte Carlo statistical simulation techniques with an internal tolerance management system and identifies the key characteristics (i.e. dimensions/clearances of interest) of nominal component models that are critical to proper assembly. Features and tolerances are directly created in CAD models and both single component or multi component analyses are available. For assemblies, eM-TolMate offers the capability to apply user-defined assembling rules or to automatically detect mating conditions. Actual features are varied within the specified tolerance range, and standard or user-defined statistical distributions are used in simulation runs to determine variations of key characteristics. It also offers the capability to rank tolerances based on contribution to the variation, so the user can identify where tolerances need to be tightened or can be loosened. eM-TolMate [5] represents a useful tool in tolerance analysis of mechanical assemblies.

Worst-Case Tolerance Design and Quality Assurance via Genetic Algorithms

In many engineering designs, several components are often placed together in a mechanical assembly. Due to manufacturing variations, there is a tolerance associated with the nominal dimension of each component in the assembly. The goal of worst-case tolerance analysis is to determine the effect of the smallest and largest assembly dimensions on the product performance. Furthermore, to achieve product quality and robustness, designers must ensure that the product performance variation is minimal.Recently, genetic algorithms (GAs) have gained a great deal of attention in the field of tolerance design. The main strength of GAs lies in their ability to effectively perform directed random search in a large space of design solutions and produce optimum results. However, simultaneous treatment of tolerance analysis and robust design for quality assurance via genetic algorithms has been marginal.In this paper, we introduce a new method based on GAs, which addresses both the worst-case tolerance analysis of mechanical assemblies and robust design. A novel formulation based on manufacturing capability indices allows the GA to rank candidate designs based on varying the tolerances around the nominal design parameter values. Standard genetic operators are then applied to ensure that the product performance measure exhibits minimal variation from the desired target value. The computational results in the design of a clutch assembly highlight the advantages of the proposed methodology.

Generalized 3-D tolerance analysis of mechanical assemblies with small kinematic adjustments

The direct linearization method (DLM) for tolerance analysis of 3-D mechanical assemblies is presented. Vector assembly models are used, based on 3-D vector loops which represent the dimensional chains that produce tolerance stackup in an assembly. Tolerance analysis procedures are formulated for both open and closed loop assembly models. The method generalizes assembly variation models to include small kinematic adjustments between mating parts. Open vector loops describe critical assembly features. Closed vector loops describe kinematic constraints for an assembly. They result in a set of algebraic equations which are implicit functions of the resultant assembly dimensions. A general linearization procedure is outlined, by which the variation of assembly parameters may be estimated explicitly by matrix algebra. Solutions to an over-determined system or a system having more equations than unknowns are included. A detailed example is presented to demonstrate the procedures of applying the DLM to a 3-D mechanical assembly.

Including Geometric Feature Variations in Tolerance Analysis of Mechanical Assemblies

Geometric feature variations are the result of variations in the shape, orientation or location of part features as defined in ANSI Y14.5M-1982 tolerance standard. When such feature variations occu...

Review of statistical approaches to tolerance analysis

The review paper describes the technique of applying statistical methods to tolerance analysis of mechanical assemblies. It states the problem, and reviews the various approaches proposed for statistical tolerance analysis. It also considers the important case of a nonideal probability distribution of component tolerances. Lastly, it reviews and assesses the application of these methods to solid modelling systems and to the geometric tolerancing standard, and makes recommendations about possible directions to be taken in future research on the subject.