Tolerance Analysis Of Assemblies Research Articles

Design and Manufacture of 30-Degree Projection Lens for Augmented Reality Waveguide.

A projection lens with a 30-degree field of view is developed for use in augmented reality (AR) glasses, including a waveguide combiner designed for a 0.35-inch LCoS panel. The entrance pupil diameter of the lens is 14 mm and the lens has an effective focal length of 16.443 mm; an F-number of 1.175. This paper has four key issues: optical projection lens design, lens manufacturing and assembly tolerance analysis, projection lens resolution testing, and AR glasses system resolution testing of panel images projected by the projection lens. After lens manufacture, the lens was tested, achieving a central field image quality of 57 cycles/mm, an angular resolution of 33 pixels per degree (PPD), a 0.7 field image quality of 40.3 cycles/mm, and an angular resolution of 23 pixels per degree (PPD). Imaging performance testing based on a diffraction-type waveguide shows a resolution of 57 cycles/mm in the center area and an angular resolution of 33 PPD.

3D stack-up assembly tolerance analysis for sealing optimization of PEMFCs

As elastic rubber seals are in contact with rigid metal bipolar plates (BPPs), multi-layer stack seals are critical to PEMFC safety. The precision of rigid-flexible seals is significantly affected by assembly errors. To reveal the transformation mechanism from BPPs manufacturing tolerances to PEMFC sealing, this study adopted semi-analytical modeling and numerical simulation. A deviation transfer model with three parameters (deviation size |r→|, deviation direction φr, rotation angle θr) was constructed on the basis of manufacturing tolerances to evaluate BPPs deviation. Numerical simulations were further conducted to obtain rubber-metal contact status. The effect of varying deviations on leakage was also investigated. It is found that: 1) φr causes various sealing behaviors in various sealing zones; 2) θr slightly affects leakage rates; 3) |r→| is crucial for optimizing the BPPs tolerance. The proposed method investigates the effect of 3D stack-up assembly errors on sealing performance and provides a theoretical foundation for the tolerance design and optimization of PEMFCs.

A novel assembly tolerance analysis method considering form errors and partial parallel connections

A novel assembly tolerance analysis method considering form errors and partial parallel connections

A Computer-Aided Design-Based Tolerance Analysis of Assemblies With Form Defects and Deformations of Nonrigid Parts

Abstract Product assemblability and functional behavior are affected by geometric deviations. These deviations consist of manufacturing errors and part deformation defects caused by external loads. Taking the sources of deviations into account in tolerance analysis yields not only to more precise and reliable results but also to more complex tasks. In this context, the modeling of assembly parts with defects in a Digital MockUp (DMU) is quite promising. In this article, an integrated decision support tool is proposed to consider the causes of multiple defects, such as tolerances and external mechanical loads, in the tolerancing process. The worst-case concept and the small displacement torsor (SDT) are used to model rigid parts with orientation and positional defects. To model the part with form defects, random positions of each toleranced face points are determined using the Gaussian perturbation method (GPM) and considering the tolerance zone limits. A computer-aided design (CAD) method based on the B-spline interpolation allows the reconstruction of realistic surfaces of parts with form defects. Realistic configurations of nonrigid components subjected to external mechanical loads are determined using the finite element analysis (FEA). The realistic assembly configurations are performed by updating the mating constraints between planar and cylindrical parts. The proposed method considers all tolerance types on CAD models (positional, orientation, and form defects) and part deformations. The tolerance analysis is performed to check the compliance with the functional requirement (FR) and to correct the initial tolerance values. An industrial case study is used to validate the steps of the proposed tolerancing method.

T-Maps-Based Tolerance Analysis of Composites Assembly Involving Compensation Strategies

Abstract Clamping force and shimming are two important compensation processes in the composite assembly. Their effects on variation propagation should be investigated in tolerance analysis. The paper presents a tolerance analysis method for composites assembly based on the T-Maps method, mainly concerning the anisotropic variations accumulation and propagation where there is the clamping force modification and the shimming. Variations of the composite parts in different directions are represented by the T-Maps. Since the different axial deviations are represented in the same Euclidean point-space, the T-Maps-based tolerance analysis of the composite parts assembly provides more accurate and reliable results. Compensation processes, the clamping force, and the shimming, on assembly tolerance synthesis of the composite parts, are analyzed clearly in the T-Map. This procedure is found to be effective for the anisotropy-oriented assembly tolerance analysis, especially concerning about effect of the clamping force and the shimming on variations accumulation and propagation. The assembly of an aircraft composite elevator is considered to demonstrate the effectiveness of the T-Maps-based method. The procedures outlined in the paper are quite general and can be used for assembly tolerance analysis of anisotropic parts.

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.

A generic integrated approach of assembly tolerance analysis based on skin model shapes

Nowadays, assembly tolerance analysis has become a challenging problem to predict the accuracy of a final assembly and examine whether specified tolerances satisfy assembly functional requirements (AFRs) for ensuring product assembly performance. Skin model shapes can be addressed to represent part geometric tolerances with manufacturing defects, thereby providing high fidelity surfaces that can replace nominal or ideal surfaces and significantly improve the accuracy and reliability of assembly tolerance analysis. However, their application in easy-to-use assembly simulation is limited by the level of detail required for manufacturing defect simulation and the complicated calculation process for integrating these defects into the tolerance analysis. Therefore, to overcome these issues in predicting assembly deviations in the early design stage, we propose a generic integrated approach of assembly tolerance analysis based on skin model shapes. First, two methods are introduced for modelling and generating skin model shapes according to different mate types of assembly key features. Second, a calculation method of assembly deviation propagation is developed by the integration of skin model shapes and stream-of-variation theory with accuracy and efficiency guarantees. Besides, a slightly modified relative contact positioning method is presented, based on different surface and progressive contact method, to obtain deterministic contact points and contact positioning errors between key mating joint surfaces. And then, the deviation values of AFRs are calculated, considering the inevitable manufacturing and assembly process errors. Finally, a typical mechanical assembly on assembly tolerance analysis is used as a case study to demonstrate the effectiveness of the proposed approach.

An Automated Method for Assembly Tolerance Analysis

Abstract This paper proposes an automated method for assembly tolerance analysis. The input of the method is an assembly model, the assembly information is stored in the assembly model, and the tolerance annotation is marked in the solid part model. The output of the method is the probability statistical results of the analyzed objective and the lists of the sensitivity and contribution of the tolerance factors. The variation in the geometric features is simulated by the control point variation model, the location of the analyzed objective is calculated based on the contact conditions of the actual geometry of the assembly model, and the analysis results are obtained based on the Monte Carlo method. To structuralize the calculation procedure of the location of the geometric features, first, the error propagation graph of the assembly model is established according to the assembly information and tolerance annotation. Subsequently, the hierarchy of the coordinate system of the geometric features is established, and the homogeneous transformation matrices between the coordinate systems are obtained. In this manner, the process to calculate the location of the geometric features can be automated. The prototype software of an automated assembly tolerance analysis is introduced, and the application of the prototype software is demonstrated.

Matrix-based tolerance analysis for multi-component selective assembly with geometric and dimensional features using genetic algorithm

Tolerance analysis (TA) is a method of investigating how the geometric and dimensional tolerance (GDT) deviations in each component propagate and affect the functional requirements of the product. Total deviation in an assembly fit can be controlled by selecting the components of the assembly through a purposeful strategy, called selective assembly (SA). In this paper, the matrix model of TA is applied in SA. The surface-based and shape closure analyses are done using the principles of TTRS and MGDE, and the assembly fit is modelled in terms of displacement matrices. The conventional method of dividing the components into groups only by the deviation on dimensional tolerance (DT) alone is replaced by integrated GDT. The effect of rotational displacements in component features on assembly fit is verified. A two-dimensional, worst case, rigid TA in SA is demonstrated. The best combinations of assembly components are obtained through genetic algorithm.

Comparison among different tools for tolerance analysis of rigid assemblies

Comparison among different tools for tolerance analysis of rigid assemblies

Comparison among different tools for tolerance analysis of rigid assemblies

Tolerance analysis is an important task to design and to manufacture high-precision mechanical assemblies; it has received considerable attention in the literature. Actually there are some different tools used or proposed by the literature to make the tolerance analysis of an assembly, but no one of them is completely and univocally accepted. A comparison between a Computer Aided Tolerancing (CAT) tool for geometry assurance and some methods proposed in the literature is discussed in this work. Therefore, the aim of this work is to solve by a CAT software five case studies that were already solved by different methods. The potentialities and the limits of using a CAT technique for geometry assurance are highlighted.

Tolerance–reliability analysis of mechanical assemblies for quality control based on Bayesian modeling

PurposeThe purpose of this paper is to present a new efficient method for the tolerance–reliability analysis and quality control of complex nonlinear assemblies where explicit assembly functions are difficult or impossible to extract based on Bayesian modeling.Design/methodology/approachIn the proposed method, first, tolerances are modelled as the random uncertain variables. Then, based on the assembly data, the explicit assembly function can be expressed by the Bayesian model in terms of manufacturing and assembly tolerances. According to the obtained assembly tolerance, reliability of the mechanical assembly to meet the assembly requirement can be estimated by a proper first-order reliability method.FindingsThe Bayesian modeling leads to an appropriate assembly function for the tolerance and reliability analysis of mechanical assemblies for assessment of the assembly quality, by evaluation of the assembly requirement(s) at the key characteristics in the assembly process. The efficiency of the proposed method by considering a case study has been illustrated and validated by comparison to Monte Carlo simulations.Practical implicationsThe method is practically easy to be automated for use within CAD/CAM software for the assembly quality control in industrial applications.Originality/valueBayesian modeling for tolerance–reliability analysis of mechanical assemblies, which has not been previously considered in the literature, is a potentially interesting concept that can be extended to other corresponding fields of the tolerance design and the quality control.

Analysis Line Approach for Assembly Tolerance Analysis

This work presents the analysis line approach for assembly tolerance analysis. Firstly, the product functional requirements and geometric variations of part positioning features can be converted into small displacements of a series of analysis points along the specified analysis directions. The small displacement torsor (SDT) theory is employed to establish the mathematical relations between the displacements of these analysis points. And then, the variation transfer relations and tolerance accumulation calculations of various orthogonal joints between different parts are studied to determine the maximum displacement of the analysis points on the functional surface. The final displacement accumulation results of the functional surface are compared with the geometric functional requirements of the product, so as to judge whether the product functional requirements are met. Finally, an example is given to demonstrate the effectiveness of the proposed analysis line approach.

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.

A Novel Model for the Tolerancing of Nonrigid Part Assemblies in Computer Aided Design

In the design step, the realistic modeling of the product represents an industrial requirement and a digital muck up (DMU) improvement. Thus, the tolerance integration in the computer aided design (CAD) model with the neglect of important physical factors, such as the components’ deformations during the mounting and assembly operation, causes a deviation between the numerical and the realistic models. In this regard, this paper presents a new model for the tolerance analysis of CAD assemblies based on the consideration of both manufacturing defects and deformations. The dimensional and geometrical tolerances are considered by the determination of assemblies’ configurations with defects based on the worst case tolerancing. The finite elements (FEs) simulation is realized with realistic models. An algorithm for updating the realistic mating constraints, between rigid and nonrigid parts, is developed. The case study of an assembly with planar and cylindrical joints is presented.

Assembly tolerance analysis based on the Jacobian model and skin model shapes

Purpose The purpose of this paper is to carry out an assembly tolerance analysis by means of a combined Jacobian model and skin model shape. The former is based on small displacements modeling of points using 6 × 6 transformation matrices of open kinematic chains in robotics. The latter easily models toleranced features with all kinds of geometric deviations. Design/methodology/approach This paper presents the procedure of performing tolerance analysis by means of the Jacobian model and skin model shape for assemblies. The point cloud-based discrete representative is able to model the actual toleranced surfaces instead of the ideal or associated ones in an assembly, which brings the simulation tools closer to reality. Findings The proposed method has the advantage of skin model shape which is suitable for geometric tolerances management along the product life cycle and contact analysis of kinematic small variations, as well as, with the Jacobian, enabling transformation of locally expressed parts deviations to globally expressed functional requirements. The result of the case study shows the accuracy of the method. Research limitations/implications The proposed approach has not been developed fully; other functional features such as the pyramid are still ongoing challenges. Practical implications It is an effective method for supporting design, manufacturing and inspection by providing a quantitative analysis of the effects of multi-tolerances on the final functional key characteristics and for predicting the quality level. Originality/value The paper is original in taking advantages of both Jacobian model and skin model shape to consider all geometric tolerances in assembly.

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.

Research on tolerance modeling method and 3D tolerance analysis technology based on STD

The description methods of various tolerance zones and kinematic links based on SDT are discussed. The surfacemodels are applied to describe an assembly, and SDT is used to express the relative position between any two surfaces of anassembly; According to the effect of each functional element on the whole functional requirements of products, the 3-1; dimension-chain is created, and 3-D dimensional and geometrical tolerance analysis for assembly is realized. The engineering example involving 3-D tolerance analysis is given to test the proposed method.

Incorporation of form deviations into the matrix transformation method for tolerance analysis in assemblies

Mathematical models for tolerance representation are used to assess how the geometrical variation of a specific component feature propagates along the assembly, so that tolerance analysis in assemblies can be carried out using a specific tolerance propagation method. Several methods for tolerance analysis have been proposed in the literature, being some of them implemented in CAD systems. All these methods require modelling the geometrical variations of the component surfaces: parametric models, variational models, DoF models, etc. One of the most commonly used models is the DoF model, which is employed in a number of tolerance analysis methods: Small Displacement Torsor (SDT), Technologically and Topologically Related Surfaces (TTRS), Matrix Transformation, Unified Jacobian–Torsor model. However, none of the DoF-based tolerance analysis methods incorporates the effect of form deviations. Among the non DoF-based methods, there are two that include form tolerances: the Vector Loop or Kinematic method and the Tolerance Map (T-Map) model, although the latter is still under development. In this work, a proposal to incorporate form deviations into the matrix transformation method for tolerance analysis in assemblies is developed using a geometrical variation model based on the DoF model. The proposal is evaluated applying it to a 2D case study with components that only have flat surfaces, but the proposal can be extrapolated to 3D cases.