Tolerance Synthesis Research Articles

ISO manufacturing tolerancing: three-dimensional transfer with analysis line method

Functional tolerancing described in definition drawing of mechanical parts constitutes a contract to be respected by manufacturers. Process engineers have to choose process plans able to manufacture part respecting functional requirements and have to determine manufacturing specifications for each phase. Tolerance zone transfer method offers a three-dimensional algorithm of manufacturing specifications generation with International Organization for Standardization (ISO) standards. Analysis line method, developed in this article, establishes the calculus relation of the results of the tolerance chains according to the tolerances of manufacturing specifications to allow the tolerance synthesis. In this paper, the analysis line method is presented using an example. The aim is to show the hypotheses made during transfers in the context of ISO standards of tolerancing and to define accurately the datum reference frames used and deviations between these frames at particular points named analysis points.

A new method for automatic synthesis of tolerances for complex assemblies based on polychromatic sets

In computer-aided tolerance design (CAT), integrated design of dimensional and geometric tolerances is still one of the research hotspots. Polychromatic sets theory (PST) is a new mathematic tool, which is especially suitable for formal hierarchical structure models. Based on PST, in this article, a new hierarchical representation model for tolerance synthesis is presented to realise integrated design of dimensional and geometric tolerances. According to the inference relations between unified and individual colours of PST, the synthesis matrices of variational geometric constraints (VGC) are established in the VGC tier of the model, and the synthesis matrices of tolerance types are established in the tolerance type tier of the model. On this basis, the synthesis processes from the feature tier to the VGC tier and from the VGC tier to the tolerance type tier can be realised. VGCs, which are achieved by the synthesis matrices of VGCs, can be combined together to establish a well-constrained VGC network (VGCN). Tolerance types, which are achieved by the synthesis matrices of tolerance types, can be added to the well-constrained VGCN to construct a well-constrained tolerance network. An application example is given in the article to illustrate the synthesis steps.

Thermal dilatation in functional tolerancing

Functional tolerancing is classically based onto dimension chains to respect functional requirements. Tolerance synthesis deals with dimensions optimization in order to maximize tolerances. This method is classically used taking into account only geometrical defaults. Mechanisms concerned with significant variation of temperature in different stages of functioning, require taking into account thermal expansion. This expansion has a direct impact onto clearances and dimensions of the mechanism. The purpose of this paper is to consider thermal expansion of parts integrated within functional tolerancing. In particular, this paper will compare the effects of tolerancing, thermal expansion and uncertainties of temperature in order to know if uncertainties must be included in the tolerance chain or can be neglected as second order. A basic experimental mechanism is used to show this method and the differences between the two approaches. ► New method of tolerance synthesis. ► Thermal influence. ► Meshing analysis possible.

Concurrent Conceptual Evaluation of Tolerances’ Synthesis in Mechanical Design

Taking into account the global competitive environment and the impact of collaborative engineering environments on Small and Medium-sized Enterprises, it has now become necessary to develop new models and tools that can keep helping the designers and engineers in the decision-making processes related to the product design lifecycle. The tolerance synthesis purpose is to provide a rational basis for assigning tolerances to dimensions, and it has become an important subject in the product design process. The aim of this research work is to present an approach to support a concurrent conceptual tolerance synthesis evaluation process in a mechanical design within a collaborative engineering environment context, for example, Virtual Enterprise. The reference model proposed was developed and refined through a set of mechanical design study cases. The analysis and reflections of the study case presented in this manuscript are described in detail to show an example of how the different study cases were used to develop an understanding of how the reference model proposed can stimulate the conceptual synthesis evaluation of tolerances in the product design process.

Simultaneous Tolerance Synthesis for Manufacturing and Quality using Evolutionary Algorithms

Tolerance plays a major role in the manufacturing industry, as it affects product design, manufacturing, and quality of the product. This paper considers product design, manufacturing, and quality simultaneously, and introduces a concurrent approach for tolerance allocation using evolutionary algorithms. A non-linear model that minimizes the combination of manufacturing cost and quality loss simultaneously, in a single objective function has been considered. In the proposed work, evolutionary algorithms (that is, Genetic Algorithms (GA), Differential Evolution (DE), and Particle Swarm Optimization (PSO)) have been used to determine the optimal tolerances at the minimum manufacturing and quality loss cost. The application of the proposed methodology has been demonstrated on a simple mechanical assembly.

Rational method for 3D manufacturing tolerancing synthesis based on the TTRS approach “R3DMTSyn”

During the production of new part in an industrial environment, it results in a high percentage of scrap if manufacturing planning is not carried out properly. One of the major factors responsible for this phenomenon is tolerance synthesis. In this paper, we deal with tolerance synthesis, and especially tolerance type identified after transfer. An algorithmic Rational method for 3D Manufacturing Tolerancing Synthesis (R3DMTSyn), which is based on the use of the Technologically and Topologically Related Surface (TTRS) rules, is developed. The TTRS concept helps to generate only the necessary manufacturing specification needed to guarantee the respect of the functional specification studied. The manufacturing project is modeled by a graphical representation called the SPIDER GRAPH. With the SPIDER GRAPH, all active surfaces can be detected (machined and positioning surfaces), so it is possible to identify the location of the functional surfaces used in each functional specification. The construction or the determination of the tolerancing torsor, belonging to each active surface, contributes to the selection of the adequate case of associations. A semantic study is already done to identify all possible combinations or associations needed to locate surfaces during each phases. Finally, referring to the developed TTRS_Cars_Process and in every phase, one or more manufacturing specifications are generated until finishing the treatment of all surfaces (surface belonging to the functional condition, or intermediate surfaces).

Tolerance Synthesis Modeling Based on Degree of Freedom of Geometric Variations of Features

A tolerance synthesis model is established based on degree of freedom of geometric variations of features in this paper. The method allows a designer to analyze the relationship between geometric variations of features of a part and functional requirement of assembly (FRA). Firstly, tolerance is modeled with DOFs of geometric variations of features and the tolerance zone is expressed with six kinematic DOFs in three-dimensional (3D) space. Secondly, the stack-up of geometric variations of features is formulated as explicit tolerance analysis equations using kinematical coordinate systems associated with each feature. To express mathematically the relationship between given FRA values and the corresponding DOFs of geometric variations of features, the reverse synthesis equations are obtained using a matrix inversion scheme of the tolerance analysis equations. Finally, a case study is used to illustrate the proposed method.

104 組立現場での工夫を考慮した公差設計に関する一考察(OS1-1 デジタル設計・製造支援I)

In recent product design, there have been increased troubles caused by inappropriate tolerance allocations, and therefore tolerance design has become an important issue. Independently of many academic and commercial works concerning to tolerance analysis and tolerance synthesis, manufacturing and assembly divisions have their own devices to satisfy requirements for assembled shape accuracy, which have been developed empirically. This paper discusses effects of the devices from the point of view of tolerance design, toward establishment of integrated tolerance synthesis which consideres such devices taken in manufacturing divisions.

Tolerance optimisation problem using a near-to-global optimum

An algorithm is developed to deal with the discrete optimisation problem. The algorithm approximates any design continuous domain with finite number of discrete points and employs single and multi-level search to reach near-to-global optimum. Global optimisers are often expensive techniques. In single level search, one orthogonal array is used to model any given search domain. In multi-level search, two or more orthogonal arrays are coupled in series and used to model the search domain. The number of design levels are increased with the number of arrays via different coefficients. The tolerance synthesis problem with optimum process combination is revisited to compare our method with well-established algorithms such as simulated annealing (SA) and sequential quadratic programming (SQP). The effect of algorithm parameters: different structure combinations, reducing move factors, weighing factors and column assignments on optimum for single and multi-level search are investigated. Results indicate the capability of the approach to reach near-to-global optimum in about 5.20%–19.5% of time taken by other methods which justifies the use of the developed algorithms unless global optimisers are specially needed.

An alternative to Monte Carlo simulation method

Tolerance analysis usually complements tolerance synthesis; however, analysis algorithms, especially the Monte Carlo method proves highly expensive. This study offers an alternative to the Monte Carlo method. The huge sample sizes are replaced by small orthogonal experiments. The mean and variance of critical design requirements are calculated via the two methods. Preliminary results indicate the need for larger size orthogonal arrays to conform to results by Monte Carlo simulation (MCS). Two new modifications are introduced and their effects on the optimum tolerances and process combinations are studied. Results indicate the potential of the algorithm for further future developments. This study claims two important things: a not all variables are of the same importance in their domains b there is a reasonable alternative to Monte Carlo simulation method subject to use of larger size arrays.

Simultaneous optimal selection of design and manufacturing tolerances with alternative manufacturing process selection

Tolerance specification is an important part of mechanical design. Design tolerances strongly influence the functional performance and manufacturing cost of a mechanical product. Tighter tolerances normally produce superior components, better performing mechanical systems and good assemblability with assured exchangeability at the assembly line. However, unnecessarily tight tolerances lead to excessive manufacturing costs for a given application. The balancing of performance and manufacturing cost through identification of optimal design tolerances is a major concern in modern design. Traditionally, design tolerances are specified based on the designer’s experience. Computer-aided (or software-based) tolerance synthesis and alternative manufacturing process selection programs allow a designer to verify the relations between all design tolerances to produce a consistent and feasible design. In this paper, a general new methodology using intelligent algorithms viz., Elitist Non-dominated Sorting Genetic Algorithm (NSGA-II) and Multi Objective Particle Swarm Optimization (MOPSO) for simultaneous optimal selection of design and manufacturing tolerances with alternative manufacturing process selection is presented. The problem has a multi-criterion character in which 3 objective functions, 3 constraints and 5 variables are considered. The average fitness factor method and normalized weighted objective functions method are separately used to select the best optimal solution from Pareto optimal fronts. Two multi-objective performance measures namely solution spread measure and ratio of non-dominated individuals are used to evaluate the strength of Pareto optimal fronts. Two more multi-objective performance measures namely optimiser overhead and algorithm effort are used to find the computational effort of NSGA-II and MOPSO algorithms. The Pareto optimal fronts and results obtained from various techniques are compared and analysed.

New cost–tolerance model for mechanical part design

At first sight, the establishment of cost–tolerance relations for manufacturing processes may seem to be a fully developed topic. Nevertheless, many real cases in industry have made it clear that a solution that satisfies the practical requirements in this field has not yet been reached. The applicability of the developments of this topic depends greatly on the validity of the cost–tolerance relation values of each specification in a mechanical part, which is subject to tolerances. Nevertheless, none of the studies carried out thus far that consider suppositions of former developments to be valid have made a careful study of this relation. The current study puts forth a new method for establishing the cost–tolerance relation of a manufacturing process based on the variability of the equipment involved in the process. In other words, the proposed method is based on the ability of a specific process to achieve performance within the assigned tolerances at the materialised magnitude. It makes it possible to obtain practical results directly linked to the production process at every time. Furthermore, this method is a key for future developments related to tolerance synthesis or analysis.

Effect of calcium ions on the Hsp104 synthesis and heat tolerance of Saccharomyces cerevisiae

Effect of calcium ions on heat tolerance of Saccharomyces cerevisiae and on the induction of Hsp104 synthesis by this microorganism was studied. Short-term (30 min) treatment with CaCl2 at 30°C enhanced the heat tolerance to the lethal heat shock (50°C); the synthesis of Hsp104 was induced as well. The effect of Ca2+ on the heat tolerance and Hsp104 synthesis was shown to be ion-specific and was inhibited by LaCl3, which is known to block calcium ion channels on the cytoplasmic membrane. The effect of Ca2+ depended on the potential of the inner mitochondrial membrane. When the cells were treated with sodium azide, which reduced the electrochemical potential, the effect of calcium both on heat tolerance and Hsp104 synthesis was suppressed. Depending on the concentration of exogenous Ca2+ and the ambient conditions, calcium ions may either induce or inhibit the expression of the stress genes and cell viability.

A Neural Network Approach to Tolerance Synthesis and Cost Optimisation in Assembly

A Neural Network Approach to Tolerance Synthesis and Cost Optimisation in Assembly

Parametric Tolerance Analysis of Mechanical Assembly by Developing Direct Constraint Model in CAD and Cost Competent Tolerance Synthesis

The objective of tolerance analysis is to check the extent and nature of variation of an analyzed dimension or geometric feature of interest for a given GD & T scheme. The parametric approach to tolerance analysis is based on parametric constraint solving. The accuracy of simulation results is dependent on the userdefined modeling scheme. Once an accurate CAD model is developed, it is integrated with tolerance synthesis model. In order to make it cost competent, it is necessary to obtain the costtolerance relationships. The neural network recently has been reported to be an effective statistical tool for determining relationship between input factors and output responses. This study deals development of direct constraint model in CAD, which is integrated to an optimal tolerance design problem. A backpropagation (BP) network is applied to fit the costtolerance relationship. An optimization method based on Differential Evolution (DE) is then used to locate the combination of controllable factors (tolerances) to optimize the output response (manufacturing cost plus quality loss) using the equations stemming from the trained network. A tolerance synthesis problem for a motor assembly is used to investigate the effectiveness and efficiency of the proposed methodology.

Parametric Tolerance Analysis of Mechanical Assembly Using FEA and Cost Competent Tolerance Synthesis Using Neural Network

Tolerance design plays an important role in the modern design process by introducing quality improvements and limiting manufacturing costs. Tolerance synthesis is a procedure that distributes assembly tolerances between components or distributes final part design tolerances between related tolerances. Traditional tolerance design assumes that all objects have rigid geometry, overlooking the role of inertia effects on flexible components of assembly. The variance is increasingly stacked up as components are assembled without considering deformation due to inertia effects. This study deals with the optimal tolerance design for an assembly simultaneously considering manufacturing cost, quality loss and deformation due to inertia effect. An application problem (motor assembly) is used to investigate the effectiveness and efficiency of the proposed methodology.

Part optimization and tolerances synthesis

A tolerance synthesis provides the distribution of tolerances on the functional specifications of parts for a mechanism, with the objective of satisfying a set of functional requirements. This approach involves adjusting the nominal dimensions of parts. The present article offers a six-step solution within an Excel solver environment. The designer is able to control the optimization process using a dashboard. The initial steps detect conflicting requirements and suggest compromises, while the subsequent steps optimize the nominal part dimensions in order to maximize mechanism quality with minimum tolerance. The final steps then seek to maximize tolerances with the aim of minimizing costs. The proposed method can also manage specifications with both maximum and minimum material requirements.

Activity-Based Tolerance Allocation (ABTA) – driving tolerance synthesis by evaluating its global cost

This paper deals with tolerance allocation driven by an activity-based approach. Its main objective is to rationally give a good indicator of the relevance of tolerance values fixed by designers. Taking into consideration the impacts of tolerance allocation on the manufacturing process and so the production cost, several examples are given to illustrate this concept. Moreover this paper deals with how the geometrical analysis can be carried out in this activity framework, illustrated by several industrial cases. In addition, this paper explains how, coupled with an optimisation algorithm, this method can generate the best compromise between cost and high performance. To illustrate the efficiency of this approach and its realisation, models and user interfaces based on an industrial case are given.

Important issues in tolerance design of mechanical assemblies. Part 2: Tolerance synthesis

Tolerance design has become a very sensitive and important issue in product and process development because of increasing demand for quality products and the growing requirements for automation in manufacturing. It is an interactive process between design and manufacturing decision making. A systematic approach to tolerance design involves repeated computation following two alternate approaches, tolerance analysis and tolerance synthesis. A detailed discussion on tolerance analysis has been presented in Part 1 of this paper. The focus of this part of the paper is on tolerance synthesis, i.e. the allocation of assembly tolerance among the individual dimensions. A brief discussion on the relevant background terminology has been presented. Details of research carried out and theories developed over the decades on different aspects of tolerance synthesis have been discussed.

Important issues in tolerance design of mechanical assemblies. Part 1: Tolerance analysis

Tolerance design has become a very sensitive and important issue in product and process development because of increasing demand for quality products and the growing requirements for automation in manufacturing. It is an interactive process between design and manufacturing decision making. A systematic approach to tolerance design involves repeated computation following two alternate steps: (a) tolerance analysis and (b) tolerance synthesis. The focus of this part of the paper is on tolerance analysis. A brief discussion on the relevant background terminology has been presented. Details of research carried out and theories developed over the decades on different aspects of tolerance analysis have been discussed.