scholarly journals Comparison of Analysis Line and Polytopes Methods to Determine the Result of a Tolerance Chain

2015 ◽  
Vol 15 (2) ◽  
Author(s):  
Laurent Pierre ◽  
Bernard Anselmetti
Keyword(s):  
Mechanical System ◽  
Tolerance Analysis ◽  
Functional Surface ◽  
Functional Tolerancing ◽  
The Face ◽  
Geometric Deviations ◽  
Minkowski Sums ◽  
Outer Bound ◽  
Analysis Line

Functional tolerancing must ensure the assembly and the functioning of a mechanism. This paper compares two methods of tolerance analysis of a mechanical system: the method of “analysis lines” and the method of “polytopes.” The first method needs a discretization of the ending functional surface according to various analysis lines placed on the outer-bound of the face and oriented along the normal of the surface. The second method uses polytopes. The polytopes are defined from the acceptable limits of the geometric deviations of parts and possible displacements between two parts. Minkowski sums and intersections polytopes are then carried out to take into account all geometric variations of a mechanism.

Fuzzy Sensitivity Analysis in the Context of Dimensional Management

2018 ◽  
Vol 5 (1) ◽  
Author(s):  
Thomas Oberleiter ◽  
Björn Heling ◽  
Benjamin Schleich ◽  
Kai Willner ◽  
Sandro Wartzack
Keyword(s):  
Tolerance Analysis ◽  
Design Stage ◽  
Special Focus ◽  
Total System ◽  
Early Design Stage ◽  
Technical Requirements ◽  
Geometric Deviations ◽  
Weak Points ◽  
Dimensional Management ◽  
The Impact

Real components always deviate from their ideal dimensions. This makes every component, even a serial production, unique. Although they look the same, differences can always be observed due to different scattering factors and variations in the manufacturing process. All these factors inevitably lead to parts that deviate from their ideal shape and, therefore, have different properties than the ideal component. Changing properties can lead to major problems or even failure during operation. It is necessary to specify the permitted deviations to ensure that every single product nevertheless meets its technical requirements. Furthermore, it is necessary to estimate the consequences of the permitted deviations, which is done via tolerance analysis. During this process, components are assembled virtually and varied with the uncertainties specified by the tolerances. A variation simulation is one opportunity to calculate these effects for geometric deviations. Since tolerance analysis enables engineers to identify weak points in an early design stage, it is important to know the contribution that every single tolerance has on a certain quality-relevant characteristic, to restrict or increase the correct tolerances. In this paper, a fuzzy-based method to calculate the sensitivity is introduced and compared with the commonly used extended Fourier amplitude sensitivity test (EFAST) method. Special focus of this work is the differentiation of the sensitivity for the total system and the sensitivities for the subsystems defined by the α-cuts of the fuzzy numbers. It discusses the impact of the number of evaluations and nonlinearity on sensitivity for EFAST and the fuzzy-based method.

Comparison of Different Sensitivity Analysis Methods in the Context of Dimensional Management

2017 ◽  
Author(s):  
Björn Heling ◽  
Thomas Oberleiter ◽  
Benjamin Schleich ◽  
Kai Willner ◽  
Sandro Wartzack
Keyword(s):  
Tolerance Analysis ◽  
Sensitivity Analyses ◽  
Design Stage ◽  
Fuzzy Arithmetic ◽  
Early Design Stage ◽  
Technical Requirements ◽  
Strongly Connected ◽  
Geometric Deviations ◽  
Comparison Of The Results ◽  
Dimensional Management

Although mass production parts look the same, every manufactured part is unique, at least on a closer inspection. The reason for this is that every manufactured part is inevitable subjected to different scattering influencing factors and variation in the manufacturing process, such as varying temperatures or tool wear. All these factors inevitably lead to parts, which deviate from their ideal shape. Products, which are built from these deviation-afflicted parts consequently show deviations from their ideal properties. To ensure that every single product nevertheless meets its technical requirements, it is necessary to specify the permitted deviations. Furthermore it is necessary to estimate the consequences of the permitted deviations, which is done via tolerance analysis. During this process the imperfect parts are assembled virtually and the effects of the geometric deviations can be calculated during a variation simulation. Since the tolerance analysis is to enable engineers to identify weak points in an early design stage it is important to know which contribution every single tolerance has on a certain quality-relevant characteristic, to restrict or increase the correct tolerances. In this paper two different approaches are shown and compared to represent the statistical behavior and the strongly connected sensitivity analyses. In particular a newly developed approach, which is based on fuzzy arithmetic, is compared to the established EFAST-method. The exemplary application of both methods and the comparison of the results are illustrated on a case study.

CAD-Based Tolerance Analysis in Preliminary Design Stages Enabling Early Tolerance Evaluation

2018 ◽  
Author(s):  
Stefan Goetz ◽  
Benjamin Schleich ◽  
Sandro Wartzack
Keyword(s):  
Tolerance Analysis ◽  
Design Stage ◽  
Preliminary Design ◽  
Design Changes ◽  
Preliminary Design Stage ◽  
Geometric Deviations ◽  
Set Up ◽  
Quality Of Products ◽  
Analysis Models

Associated with manufacturing and assembly processes, inevitable geometric deviations have a decisive influence on the function and quality of products. Therefore, their consideration and management are important tasks in product development. Moreover, to meet the demand for short development times, the front-loading of design processes is indispensable. This requires early tolerance analyses evaluating the effect of deviations in a design stage, where the product’s geometry has not yet been finally defined. Since such an early tolerance consideration allows quick and economic design changes seeking for robust designs, it is advisable that the design engineer, who is entirely familiar with the design, should take this step. For this purpose, this paper presents an easy-to-use CAD-based tolerance analysis method for skeleton models. The relevant part deviations are represented by varying geometric dimensions with externally driven family tables. The approach comprises the strength of vector-based methods but does not require an expensive set-up of tolerance analysis models. Particularly, the novelty of this method lies in the CAD-internal sampling-based tolerance analysis of simple geometries without the use of expensive CAT software. This enables designers to evaluate the effect of tolerances already at the preliminary design stage. Using a case study, the presented approach is compared with the conventional vector-based tolerance analysis.

Functional Tolerance Analysis of a Complex Mechanism Based on Analysis Line Method

2013 ◽  
Vol 373-375 ◽  
pp. 2078-2081
Author(s):  
Chun Li Li ◽  
Jian Xin Yang ◽  
Rui Li
Keyword(s):  
Tolerance Analysis ◽  
Complex Mechanism ◽  
Functional Feature ◽  
Manufacturing Costs ◽  
Line Method ◽  
Analysis Process ◽  
Functional Tolerance ◽  
Simple Assembly ◽  
Tolerance Accumulation ◽  
Analysis Line

Tolerance analysis plays an important role at the stage of product design and has great influences on the assembly quality and manufacturing costs. For each ending point on the functional feature, the displacement transfer relationship is influenced by the clearance between the two parts and the tolerances of each part. With regard to functional tolerance accumulation for the simple assembly, the tolerance analysis of a complex mechanism with three parts is conducted based on the analysis line method. The rules for the functional tolerance analysis process will be summarized in this paper.

Tolerance Analysis With Polytopes in HV-Description

2017 ◽  
Vol 17 (4) ◽  
Author(s):  
Santiago Arroyave-Tobón ◽  
Denis Teissandier ◽  
Vincent Delos
Keyword(s):  
Open Source ◽  
Open Source Software ◽  
Dual Space ◽  
Tolerance Analysis ◽  
Minkowski Sum ◽  
Duality Property ◽  
Finite Set ◽  
Minkowski Sums

This article proposes the use of polytopes in HV-description to solve tolerance analysis problems. Polytopes are defined by a finite set of half-spaces representing geometric, contact, or functional specifications. However, the list of the vertices of the polytopes is useful for computing other operations as Minkowski sums. Then, this paper proposes a truncation algorithm to obtain the V-description of polytopes in ℝn from its H-description. It is detailed how intersections of polytopes can be calculated by means of the truncation algorithm. Minkowski sums as well can be computed using this algorithm making use of the duality property of polytopes. Therefore, a Minkowski sum can be calculated intersecting some half-spaces in the dual space. Finally, the approach based on HV-polytopes is illustrated by the tolerance analysis of a real industrial case using the open source software politocat and politopix.

scholarly journals An Ideal Mating Surface Method Used for Tolerance Analysis of Mechanical System Under Loading

Procedia CIRP ◽  
2013 ◽  
Vol 10 ◽  
pp. 306-311
Author(s):  
Junkang Guo ◽  
Jun Hong ◽  
Yong Wang ◽  
Zhaohui Yang
Keyword(s):  
Mechanical System ◽  
Tolerance Analysis ◽  
Surface Method ◽  
Mating Surface

Geometric tolerance analysis through Jacobian model for rigid assemblies with translational deviations

2016 ◽  
Vol 36 (1) ◽  
pp. 72-79 ◽  
Author(s):  
Wilma Polini ◽  
Andrea Corrado
Keyword(s):  
Tolerance Analysis ◽  
Geometric Error ◽  
Functional Requirements ◽  
Content Type ◽  
Geometric Tolerances ◽  
Mechanical Assemblies ◽  
Geometric Deviations ◽  
2D And 3D ◽  
Practical Implications

Purpose – The purpose of this paper is to carry out a tolerance analysis with geometric tolerances by means of the Jacobian model. Tolerance analysis is an important task to design and to manufacture high-precision mechanical assemblies; it has received considerable attention by the literature. The Jacobian model is one of the methods proposed by the literature for tolerance analysis. The Jacobian model cannot deal with geometric tolerances for mechanical assemblies. The geometric tolerances may not be neglected for assemblies, as they significantly influence their functional requirements. Design/methodology/approach – This paper presents how it is possible to deal with geometric tolerances when a tolerance analysis is carried out by means of a Jacobian model for a 2D and 3D assemblies for which the geometric tolerances applied to the components involve only translational deviations. The three proposed approaches modify the expression of the stack-up function to overcome the shortage of Jacobian model that the geometric error cannot be processed. Findings – The proposed approach has been applied to a case study. The results of the case study show how, when a statistical approach is implemented, the Jacobian model with the three developed methods gives results very similar to those due to other models of the literature, such as vector loop and variational. Research limitations/implications – In particular, the proposed approach may be applied only when the applied geometrical tolerances involve translational variations in 3D assemblies. Practical implications – Tolerance analysis is a valid tool to foresee geometric interferences among the components of an assembly before getting the physical assembly. It involves a decrease of the manufacturing costs. Originality/value – The original contribution of the paper is due to three methods to make a Jacobian model able to consider form and geometric deviations.

A Comparison Study of Small Displacement Torsor and Analysis Line Methods for Functional Tolerance Analysis

2012 ◽  
Vol 605-607 ◽  
pp. 358-364
Author(s):  
Chun Li Li ◽  
Jian Xin Yang ◽  
Jun Ying Wang ◽  
Wen Xin Ma
Keyword(s):  
Computation Time ◽  
Tolerance Analysis ◽  
General Characteristic ◽  
Worst Case Analysis ◽  
Small Displacement ◽  
Worst Case ◽  
Small Displacement Torsor ◽  
Functional Tolerance ◽  
Tolerance Accumulation ◽  
Analysis Line

Tolerance analysis plays an important role in the stage of product design and has great influences on the product assembly quality and manufacturing costs. Two major methods are used for three-dimensional functional tolerance analysis, which are small displacement torsor and analysis line. A positioning mechanism with two parts is presented for tolerance accumulation calculation. Through the comparison of these two methods on computation processes and results, analysis line method can establish the explicit relationship between the functional requirement and the tolerances of the influential part, which allows finding the accumulation results in the worst-case and statistical conditions. However, it requires the determination of transfer relationship case by case. For small displacement torsor model, it permits a set of inequalities to express the tolerance zones, which yields a linear programming problem. It is applicable to different tolerance chains for its general characteristic. However it is adopted only for the worst-case analysis and requires more computation time.

scholarly journals Statistical Tolerance Analysis of 3D-Printed Non-Assembly Mechanisms in Motion Using Empirical Predictive Models

2021 ◽  
Vol 11 (4) ◽  
pp. 1860
Author(s):  
Paul Schaechtl ◽  
Benjamin Schleich ◽  
Sandro Wartzack
Keyword(s):  
Process Parameters ◽  
Predictive Models ◽  
Tolerance Analysis ◽  
Fused Deposition ◽  
Large Joint ◽  
Geometric Deviations ◽  
3D Printed ◽  
Statistical Tolerance ◽  
Joint Clearances ◽  
Statistical Tolerance Analysis

Fused Deposition Modelling (FDM) enables the fabrication of entire non-assembly mechanisms within a single process step, making previously required assembly steps dispensable. Besides the advantages of FDM, the manufacturing of these mechanisms implies some shortcomings such as comparatively large joint clearances and geometric deviations depending on machine-specific process parameters. The current state-of-the-art concerning statistical tolerance analysis lacks in providing suitable methods for the consideration of these shortcomings, especially for 3D-printed mechanisms. Therefore, this contribution presents a novel methodology for ensuring the functionality of fully functional non-assembly mechanisms in motion by means of a statistical tolerance analysis considering geometric deviations and joint clearance. The process parameters and hence the geometric deviations are considered in terms of empirical predictive models using machine learning (ML) algorithms, which are implemented in the tolerance analysis for an early estimation of tolerances and resulting joint clearances. Missing information concerning the motion behaviour of the clearance affected joints are derived by a multi-body-simulation (MBS). The exemplarily application of the methodology to a planar 8-bar mechanism shows its applicability and benefits. The presented methodology allows evaluation of the design and the chosen process parameters of 3D-printed non-assembly mechanisms through a process-oriented tolerance analysis to fully exploit the potential of Additive Manufacturing (AM) in this field along with its ambition: ‘Print first time right’.

scholarly journals Algorithm to Calculate the Minkowski Sums of 3-polytopes: Application to Tolerance Analysis

Procedia CIRP ◽  
2013 ◽  
Vol 10 ◽  
pp. 84-90
Author(s):  
Denis Teissandier ◽  
Vincent Delos ◽  
Lazhar Homri
Keyword(s):  
Tolerance Analysis ◽  
Minkowski Sums
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