A variational model for 3D tolerance analysis with manufacturing signature and operating conditions

2018 ◽  
Vol 38 (1) ◽  
pp. 10-19 ◽  
Author(s):  
Andrea Corrado ◽  
Wilma Polini ◽  
Giovanni Moroni ◽  
Stefano Petrò
Keyword(s):  
Three Dimensional ◽  
Reference Value ◽  
Tolerance Analysis ◽  
Geometrical Model ◽  
Operating Conditions ◽  
Variational Model ◽  
Assembly Process ◽  
Functional Requirements ◽  
Content Type ◽  
Mechanical Assemblies

Purpose The purpose of this work is to present a variational model able to deal with form tolerances and assembly conditions. The variational model is one of the methods proposed in literature for tolerance analysis, but it cannot deal with form tolerances and assembly conditions that may influence the functional requirements of mechanical assemblies. Design/methodology/approach This work shows how to manage the actual surfaces generated by the manufacturing process and the operating conditions inside the variational model that has been modified to integrate the manufacturing signature left on the surfaces of the parts and the operating conditions that arise during an actual assembly, such as gravity and friction. Moreover, a geometrical model was developed to numerically simulate what happens in a real assembly process and to give a reference value. Findings The new variational model was applied to a three-dimensional case study. The obtained results were compared to those of the geometrical model and to those of the variational model to validate the new model and to show the improvements. Research limitations/implications The proposed approach may be extended to other models of literature. However, its limitation is that it is able to deal with a sphere–plane contact. 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 in the manufacturing costs. Originality/value The main contributions of the study are the insertion of a systematic pattern characterizing the features manufactured by a process, assembly operating conditions and development of a geometrical model to reproduce what happens in a real assembly process.

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.

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

2019 ◽  
Vol 19 (2) ◽  
Author(s):  
Edoh Goka ◽  
Lazhar Homri ◽  
Pierre Beaurepaire ◽  
Jean-Yves Dantan
Keyword(s):  
Tolerance Analysis ◽  
Optimization Methods ◽  
Optimization Techniques ◽  
Behavior Modeling ◽  
Functional Requirements ◽  
Mechanical Assembly ◽  
Mechanical Assemblies ◽  
Statistical Tolerance ◽  
The Individual ◽  
Statistical Tolerance Analysis

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.

scholarly journals A static analogy for 2D tolerance analysis

2014 ◽  
Vol 34 (2) ◽  
pp. 182-191 ◽  
Author(s):  
Antonio Armillotta
Keyword(s):  
Functional Equations ◽  
Nonlinear Problems ◽  
Tolerance Analysis ◽  
Static Problem ◽  
Alternative Methods ◽  
Force Analysis ◽  
Correct Treatment ◽  
Content Type ◽  
Mechanical Assemblies ◽  
Free Body

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.

Application of a Unified Jacobian—Torsor Model for Tolerance Analysis

2003 ◽  
Vol 3 (1) ◽  
pp. 2-14 ◽  
Author(s):  
Alain Desrochers ◽  
Walid Ghie ◽  
Luc Laperrie`re
Keyword(s):  
Three Dimensional ◽  
Tolerance Analysis ◽  
Small Displacement ◽  
Manufacturing Processes ◽  
Functional Requirements ◽  
Tolerance Zone ◽  
Kinematic Chains ◽  
Final Assembly ◽  
Novel Method ◽  
Assembly Constraints

Because of uncertainties in manufacturing processes, a mechanical part always shows variations in its geometrical characteristics (ex. form, dimension, orientation and position). Quality then often reflect how well tolerances and hence, functional requirements, are being achieved by the manufacturing processes in the final product. From a design perspective, efficient methods must be made available to compute, from the tolerances on individual parts, the value of the functional requirement on the final assembly. This is known as tolerance analysis. To that end, existing methods, often based on modeling of the open kinematic chains in robotics, are classified as deterministic or statistical. These methods suppose that the assembled parts are not perfect with regard to the nominal geometry and are rigid. The rigidity of the parts implies that the places of contacts are regarded as points. The validation or the determination of a tolerance zone is therefore accomplished by a series of simulation in specific points subjected to assembly constraints. To overcome the limitations and difficulties of point based approaches, the paper proposes the unification of two existing models: the Jacobian’s matrix model, based on the infinitesimal modeling of open kinematic chains in robotics, and the tolerance zone representation model, using small displacement screws and constraints to establish the extreme limits between which points and surfaces can vary. The approach also uses interval algebra as a novel method to take tolerance boundaries into account in tolerance analysis. The approach has been illustrated on a simple two parts assembly, nevertheless demonstrating the capability of the method to handle three-dimensional geometry. The results are then validated geometrically, showing the overall soundness of the approach.

Projection-based augmented reality system for assembly guidance and monitoring

2020 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Chengjun Chen ◽  
Zhongke Tian ◽  
Dongnian Li ◽  
Lieyong Pang ◽  
Tiannuo Wang ◽  
...  
Keyword(s):  
Augmented Reality ◽  
Three Dimensional ◽  
Assembly Process ◽  
Pixel Classification ◽  
Content Type ◽  
Depth Images ◽  
Augmented Reality System ◽  
Customized Production ◽  
Assembly Guidance ◽  
Randomized Decision Forests

Purpose This study aims to monitor and guide the assembly process. The operators need to change the assembly process according to the products’ specifications during manual assembly of mass customized production. Traditional information inquiry and display methods, such as manual lookup of assembly drawings or electronic manuals, are inefficient and error-prone. Design/methodology/approach This paper proposes a projection-based augmented reality system (PBARS) for assembly guidance and monitoring. The system includes a projection method based on viewpoint tracking, in which the position of the operator’s head is tracked and the projection images are changed correspondingly. The assembly monitoring phase applies a method for parts recognition. First, the pixel local binary pattern (PX-LBP) operator is achieved by merging the classical LBP operator with the pixel classification process. Afterward, the PX-LBP features of the depth images are extracted and the randomized decision forests classifier is used to get the pixel classification prediction image (PCPI). Parts recognition and assembly monitoring is performed by PCPI analysis. Findings The projection image changes with the viewpoint of the human body, hence the operators always perceive the three-dimensional guiding scene from different viewpoints, improving the human-computer interaction. Part recognition and assembly monitoring were achieved by comparing the PCPIs, in which missing and erroneous assembly can be detected online. Originality/value This paper designed the PBARS to monitor and guide the assembly process simultaneously, with potential applications in mass customized production. The parts recognition and assembly monitoring based on pixels classification provides a novel method for assembly monitoring.

A framework for tolerance design considering systematic and random uncertainties due to operating conditions

2019 ◽  
Vol 39 (5) ◽  
pp. 854-871
Author(s):  
S. Khodaygan
Keyword(s):  
Operating Conditions ◽  
Tolerance Allocation ◽  
Manufacturing Cost ◽  
Tolerance Design ◽  
Element Analysis ◽  
Content Type ◽  
Multi Objective ◽  
Mechanical Assemblies ◽  
Conflicting Objectives ◽  
Random Uncertainties

Purpose The purpose of this paper is to present a novel Kriging meta-model assisted method for multi-objective optimal tolerance design of the mechanical assemblies based on the operating conditions under both systematic and random uncertainties. Design/methodology/approach In the proposed method, the performance, the quality loss and the manufacturing cost issues are formulated as the main criteria in terms of systematic and random uncertainties. To investigate the mechanical assembly under the operating conditions, the behavior of the assembly can be simulated based on the finite element analysis (FEA). The objective functions in terms of uncertainties at the operating conditions can be modeled through the Kriging-based metamodeling based on the obtained results from the FEA simulations. Then, the optimal tolerance allocation procedure is formulated as a multi-objective optimization framework. For solving the multi conflicting objectives optimization problem, the multi-objective particle swarm optimization method is used. Then, a Shannon’s entropy-based TOPSIS is used for selection of the best tolerances from the optimal Pareto solutions. Findings The proposed method can be used for optimal tolerance design of mechanical assemblies in the operating conditions with including both random and systematic uncertainties. To reach an accurate model of the design function at the operating conditions, the Kriging meta-modeling is used. The efficiency of the proposed method by considering a case study is illustrated and the method is verified by comparison to a conventional tolerance allocation method. The obtained results show that using the proposed method can lead to the product with a more robust efficiency in the performance and a higher quality in comparing to the conventional results. Research limitations/implications The proposed method is limited to the dimensional tolerances of components with the normal distribution. Practical implications The proposed method is practically easy to be automated for computer-aided tolerance design in industrial applications. Originality/value In conventional approaches, regardless of systematic and random uncertainties due to operating conditions, tolerances are allocated based on the assembly conditions. As uncertainties can significantly affect the system’s performance at operating conditions, tolerance allocation without including these effects may be inefficient. This paper aims to fill this gap in the literature by considering both systematic and random uncertainties for multi-objective optimal tolerance design of mechanical assemblies under operating conditions.

Comparing ANSYS Fluent® and OpenFOAM® simulations of Geldart A, B and D bubbling fluidized bed hydrodynamics

2019 ◽  
Vol 30 (1) ◽  
pp. 93-118 ◽  
Author(s):  
Cesar Martin Venier ◽  
Andrés Reyes Urrutia ◽  
Juan Pablo Capossio ◽  
Jan Baeyens ◽  
Germán Mazza
Keyword(s):  
Fluidized Bed ◽  
Volume Fraction ◽  
Three Dimensional ◽  
Operating Conditions ◽  
Internal Diameter ◽  
Ansys Fluent ◽  
Content Type ◽  
Current State ◽  
Bubbling Fluidized Bed ◽  
Bubble Sizes

Purpose The purpose of this study is to assess the performance of ANSYS Fluent® and OpenFOAM®, at their current state of development, to study the relevant bubbling fluidized bed (BFB) characteristics with Geldart A, B and D particles. Design/methodology/approach For typical Geldart B and D particles, both a three-dimensional cylindrical and a pseudo-two-dimensional arrangement were used to measure the bed pressure drop and solids volume fraction, the latter by digital image analysis techniques. For a typical Geldart A particle, specifically to examine bubbling and slugging phenomena, a 2 m high three-dimensional cylindrical arrangement of small internal diameter was used. The hydrodynamics of the experimentally investigated BFB cases were also simulated for identical geometries and operating conditions using OpenFOAM® v6.0 and ANSYS Fluent® v19.2 at identical mesh and numerical setups. Findings The comparison between experimental and simulated results showed that both ANSYS Fluent® and OpenFOAM® provide a fair qualitative prediction of the bubble sizes and solids fraction for freely-bubbling Geldart B and D particles. For Geldart A particles, operated in a slugging mode, the qualitative predictions are again quite fair, but numerical values of relevant slug characteristics (length, velocity and frequency) slightly favor the use of OpenFOAM®, despite some deviations of predicted slug velocities. Originality/value A useful comparison of computational fluid dynamics (CFD) software performance for different fluidized regimes is presented. The results are discussed and recommendations are formulated for the selection of the CFD software and models involved.

Thermomechanical stress analysis for gas turbine blade with cooling structures

2018 ◽  
Vol 14 (4) ◽  
pp. 722-734 ◽  
Author(s):  
Fujuan Tong ◽  
Wenxuan Gou ◽  
Lei Li ◽  
Wenjing Gao ◽  
Zhu Feng Yue
Keyword(s):  
Stress Analysis ◽  
Gas Turbine ◽  
Radial Displacement ◽  
Three Dimensional ◽  
Mechanical Effect ◽  
Operating Conditions ◽  
Tip Clearance ◽  
Three Dimensional Model ◽  
Content Type ◽  
Thermomechanical Effect

Purpose Blade tip clearance has always been a concern for the gas turbine design and control. The numerical analysis of tip clearance is based on the turbine components displacement. The purpose of this paper is to investigate the thermal and mechanical effects on a real cooling blade rather than the simplified model. Design/methodology/approach The coupled fluid-solid method is used. The thermal analysis involves solid and fluid domains. The distributions of blade temperature, stress and displacement have been calculated numerically under real turbine operating conditions. Findings Temperature contour can provide a reference for stress analysis. The results show that temperature gradient is the main source of solid stress and radial displacement. Compared with thermal or mechanical effect, there is a great change of stress magnitude for the thermomechanical effect. Large stress gradients are found between the leading and trailing edge of turbine cooling blade. Also, the blade radial displacement is mainly attributed to the thermal load rather than the centrifugal force. The analysis of the practical three-dimensional model has achieved the more precise results. Originality/value It is significant for clearance design and life prediction.

Fractal modeling of elastic-plastic contact between three-dimensional rough surfaces

2018 ◽  
Vol 70 (2) ◽  
pp. 290-300 ◽  
Author(s):  
Rufei Yu ◽  
Wei Chen
Keyword(s):  
Rough Surfaces ◽  
Fractal Theory ◽  
Three Dimensional ◽  
Geometrical Model ◽  
Contact Model ◽  
Radial Clearance ◽  
Content Type ◽  
Elastic Plastic ◽  
Fractal Roughness ◽  
Conformal Contact

Purpose This paper aims to propose a semi-analytical model to investigate the elastic-plastic contact between fractal rough surfaces. Parametric studies have been performed to analyze the dependencies between the contact properties and the scale-independent fractal parameters. Design/methodology/approach A modified two-variable Weierstrass-Mandelbrot function has been used to build the geometrical model of rough surfaces. The computation program was developed using software MATLAB R2015a. The results have been qualitatively validated by the existing theoretical and experimental results in the literature. Findings In most cases, a nonlinear relation between the load and the displacement of the rigid plane is found. Only under the condition of larger loads, an approximate linear relation can be seen for great D and small G values. (D: fractal dimension and G: fractal roughness). Originality/value The contact model of the cylindrical joints (conformal contact) with radial clearance is constructed by using the fractal theory and the Kogut-Etsion elastic-plastic contact model, which includes purely elastic, elastic-plastic and fully plastic contacts. The present method can generate a more reliable calculation result as compared with the Hertz contact model and a higher calculation efficiency as compared with the finite element method for the conformal contact problem.

Three-dimensional tolerance analysis of discrete surface structures based on the torsor cluster model

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Chuanyuan Zhou ◽  
Zhenyu Liu ◽  
Chan Qiu ◽  
Jianrong Tan
Keyword(s):  
Mathematical Model ◽  
Cluster Model ◽  
Three Dimensional ◽  
Tolerance Analysis ◽  
Analysis Method ◽  
Discrete Elements ◽  
Content Type ◽  
Dimensional Tolerance ◽  
Discrete Surfaces ◽  
Discrete Surface

Purpose The purpose of this paper is to propose a novel mathematical model to present the three-dimensional tolerance of a discrete surface and to carry out an approach to analyze the tolerance of an assembly with a discrete surface structure. A discrete surface is a special structure of a large surface base with several discrete elements mounted on it, one, which is widely used in complex electromechanical products. Design/methodology/approach The geometric features of discrete surfaces are separated and characterized by small displacement torsors according to the spatial relationship of discrete elements. The torsor cluster model is established to characterize the integral feature variation of a discrete surface by integrating the torsor model. The influence and accumulation of the assembly tolerance of a discrete surface are determined by statistical tolerance analysis based on the unified Jacobian-Torsor method. Findings The effectiveness and superiority of the proposed model in comprehensive tolerance characterization of discrete surfaces are successfully demonstrated by a case study of a phased array antenna. The tolerance is evidently and intuitively computed and expressed based on the torsor cluster model. Research limitations/implications The tolerance analysis method proposed requires much time and high computing performance for the calculation of the statistical simulation. Practical implications The torsor cluster model achieves the three-dimensional tolerance representation of the discrete surface. The tolerance analysis method based on this model predicts the accumulation of the tolerance of components before their physical assembly. Originality/value This paper proposes the torsor cluster as a novel mathematical model to interpret the tolerance of a discrete surface.

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