Effect of manufacturing tolerances on indexing accuracy and synthesis of the Geneva Mechanism

Machine tools used for batch and mass production are generally equipped with the Geneva Mechanism for indexing. One of the factors affecting the machining accuracy in these machine tools is the positional accuracy of the tools with respect to the work which, in turn, is affected by the indexing accuracy of the indexing mechanism. This paper discusses the effect of manufacturing tolerances on indexing accuracy. It is observed that indexing accuracy is different for constrained and unconstrained designs corresponding to the same value of tolerance. Results regarding indexing accuracy for different values of tolerances in constrained designs are recorded and suggest that, in the case of constrained designs, careful allocation of tolerances on design parameters is needed. The method of tolerance allocation suggested by Choubey and Atluri⁸ is followed. Synthesis of a six-slot Geneva Mechanism incorporating manufacturing tolerances and following stochastic non-linear programming and the exterior penalty function method is carried out to study these effects. Practical implications of the effects of manufacturing tolerances on indexing accuracy and synthesis of Geneva drives are discussed, giving suitable examples     

Optimal tolerance design of assembly for minimum quality loss and manufacturing cost using metaheuristic algorithms

Tolerance allocation is a design tool for reducing overall cost of manufacturing while meeting target levels for quality. An important consideration in product design is the assignment of design and manufacturing tolerances to individual component dimensions so that the product can be produced economically and functions properly. The allocation of tolerances among the components of a mechanical assembly can significantly affect the resulting manufacturing costs. In this work, the tolerance allocation problem is formulated as a non-linear integer model by considering both the manufacturing cost of each component by alternate processes and the quality loss of assemblies so as to minimise the manufacturing cost. Metaheuristics techniques such as genetic algorithm and particle swarm optimisation are used to solve the model and obtain the global optimal solution for tolerance design. An example for illustrating the optimisation model and the solution procedure is provided. Results are compared with conventional technique and the performances are analysed.     

Computer-aided geometrical dimensioning and tolerancing for process-operation planning and quality control

This paper describes an extension of a model which determines an optimum set of dimensions and tolerances for machining processes at minimum manufacturing cost. This optimisation minimizes the cost of scrap, which is a function of manufacturing tolerances, as the objective function. Requirements of design sizes, geometrical tolerances (including both form and position) and machining allowances are expressed mathematically as constraints for the optimisation. A computerised trace method has been extended to determine the relationships between geometrical tolerances and associated relevant manufacturing dimensions and tolerances. In addition to the manufacturing cost, the model takes into account manufacturing sequence, distribution of manufacturing dimensions, process capabilities, tolerances, design sizes, geometrical tolerances, machining allowances and optimum scrap level. The resulting computerized interactive system can be used not only in process planning, but also in quality control.     

Simultaneous optimal selection of design and manufacturing tolerances with different stack-up conditions using scatter search

The allocation of design and manufacturing tolerances directly influences the manufacturing cost and functionality of a product. Traditionally, it is carried out in two phases; CAD and CAPP, in a sequential manner. This approach has the drawbacks of more lead-time and sub-optimality. The present work reports on a procedure to simultaneously allocate both design and manufacturing tolerances based on minimum total manufacturing cost. The optimization model for tolerance design is a non-linear multivariable problem. Since such a problem may have a noisy surface, there is a need to apply an efficient global optimization technique. In the present work, scatter search, one of the recently emerged optimization techniques in the area of metaheuristics, is applied successfully to determine the optimal tolerances at the minimum manufacturing cost. An example is taken from the literature to explain the proposed methodology. The results exhibit the effectiveness of the proposed algorithm over other methods.     

基于多重相关特征质量损失函数的并行公差设计

基于多变量质量损失函数,推导了多重相关特征产品的质量损失与有关零件工序公差的函数关系,建立了基于制造成本-质量损失的并行公差设计的优化综合模型,其目的是寻求制造成本和质量损失之间的平衡,以实现相关特征产品的设计公差与工序公差并行优化分配,达到提高产品质量和降低成本的目的。圆锥齿轮装配的并行公差设计实例验证了所提方法的有效性。     

Study on the tolerance allocation optimization by fuzzy-set weight-center evaluation method

The tolerance allocation optimization method by fuzzy-set weight-center evaluation is used to derive the manufacturing difficulty coefficient, through quantifying the manufacturing condition factors which all affect the manufacturing cost, including the forming means of the blank, element size, machining surface features, operator’s skills, and material’s machinability. The coefficient is then converted into a weight factor used in the inversed square model representing the relationship between the cost and tolerance, a cost-objective function model based on optimal tolerance allocation according to the manufacturing conditions is thus established for optimizing and allocating the tolerances. Integrating this model into computer-aided-tolerance-allocation makes it more convenient, accurate, and feasible.     

尺寸公差与形位公差混合优化分配

为解决尺寸公差与形位公差混合优化分配问题,提出了一种公差优化分配方法.根据成本-公差函数和尺寸公差与形位公差的关系,建立了以最小制造总成本为目标的非线性公差混合优化分配模型.该模型的约束包括装配尺寸链的功能要求和加工能力.求解该模型能同时得到优化的尺寸公差和形位公差.最后,分别用公差混合优化分配法和传统方法对一个实例进行公差分配,结果表明所提方法比传统方法更优越.     

Compatibility of tolerancing

Tolerances are assigned to a mechanical engineering design either on the basis of functional and/or manufacturing requirements (toleranced dimensions, geometrical tolerances) or on the basis of the general categories—fine, medium, coarse—of the international standards or the designer's knowledge and experience (untoleranced dimensions). Conventional dimensions of the currently applicable dimensioning rules and implicit dimensions, including those attributed to geometrical tolerances, thus create four groups of tolerances which may or may not be compatible. In addition, any tolerance compromise, however tedious and difficult, not achieved systematically may well lead to accuracies which cannot be produced by the available machine tools. In the paper, a systematic approach to the above problems is presented. A methodology is demonstrated for the verification of the tolerance compatibility and for the assignment of compatible, producible and cost optimum tolerances.     

Optimal Tolerance Allocation Based on Fuzzy Comprehensive Evaluation and Genetic Algorithm

It is very important to know how to allocate tolerances economically for parts in a CAD/CAM system because this directly affects the machining costs of the parts. A new approach based on fuzzy comprehensive evaluation (FCE) and a genetic algorithm (GA) is presented to obtain a rational tolerance allocation for the parts. First, the current methods for tolerance allocation are reviewed in detail. Then, FCE is used to evaluate the machinability of a part; a new optimal model, which can fully exploit DFA (design for assembly) and DFM (design for manufacturing), is established by combining the functional sensitivity factors and machinability factors of parts. A genetic algorithm (GA) is developed and used to verify the feasibility of the above method; the computed result shows that the method can produce tolerance allocations economically and accurately.     

Automatic feature recognition from engineering drawings

Recognising features from 2D engineering drawings is one of the most important issues facing advanced integrated design and manufacturing. Although the problem of recognising features from a solid model has been extensively studied, most existing product models are expressed as engineering drawings. Moreover, the solid model can only provide complete 3D topological and geometrical data. Some essential machining information cannot be retrieved. In this study, an automatic transfer system is proposed with the capability of recognising linear swept features from engineering drawings. The swept profiles are first extracted from drawing views, then features can be identified from the swept profiles using a set of recognition rules. In addition to the feature types and their geometry, some annotations of drawings, e.g. dimensions and geometric tolerances, can also be recognised and attached to the recognised features by this approach.     

Computer-Aided Tolerance Charting for Products with Angular Features

This paper describes a process by which computer-aided design methods are used for the tolerance charting of products with angular features. If a product contains one or more angular features, such as chamfers and tapered surfaces, radial or normal machining of the features will result in axial dimension changes. In this paper, basic trigonometric formulae are first presented to explain the phenomenon of tolerance accumulation. In the process of tolerance charting, dummy cuts are included to reflect the corresponding dimensional changes due to indirect machining. With the assistance of flags and linked lists, the system proposed can automatically identify all dimensional chains which are associated with either regular cuts or dummy cuts. Moreover, optimisation techniques are recommended to allocate the allowable tolerances as specified by blueprints. In the search for an optimal design, the total manufacturing cost defined by the working tolerances is the objective function to be minimised.     

Selection of machining datum and allocation of tolerance through tolerance charting technique

Tolerance charting is an effective tool to determine the optimal allocation of working dimensions and working tolerances such that the blueprint dimensions and tolerances can be achieved to accomplish the cost objectives.The selection of machining datum and allocation of tolerances are critical in any machining process planning as they directly affect any setup methods/machine tools selection and machining time.This paper mainly focuses on the selection of optimum machining datums and machining tolerances simultaneously in process planning.A dynamic tolerance charting constraint scheme is developed and implemented in the optimization procedure.An optimization model is formulated for selecting machining datum and tolerances and implemented with an algorithm namely Elitist Non-Dominated Sorting Genetic Algorithm(NSGA-II).The computational results indicate that the proposed methodology is capable and robust in finding the optimal machining datum set and tolerances.     

Using tolerance maps to validate machining tolerances for transfer of cylindrical datum in manufacturing process

Process planers typically utilize different datum features than designers use when specifying tolerances. Datum features used in process plans are chosen to simplify setups and achieve desired geometric accuracy. Meanwhile, proper machining tolerances are required to be reassigned to satisfy design requirements. However, existing methods to transfer geometric tolerances directly and accurately are still missing due to incompatible mathematical models of tolerances. Also, the affection of material conditions on datum and partial constraint situations have not been deeply considered yet. Since cylindrical features are often used as datum features, this paper describes the use of tolerance maps (T-Maps) (patent no. 6963824) and manufacturing maps (M-maps) to establish analytical relationship among all relevant design and machining tolerances for transfer of cylindrical datum. Firstly, a parametric model of datum transfer is proposed to describe factors involving the process. Next, based on spatial and geometric parameters, as well as tolerances information, variation analysis among features is implemented to formulate transformed T-Maps, sum of which constructs M-Map. Then, distinct bounding boxes of cross-sections in M-Map are extracted through computing vertex coordinates of their boundaries due to complete and partial constraint scenarios. Thereafter, by virtue of bounding boxes, relationship among design and machining tolerances are obtained through fitting M-Maps into T-Maps. Finally, an example is introduced to verify feasibility of the proposed model and method.     

Computerised trace method for establishing equations for dimensions and tolerances in design and manufacture

A computerised trace method has been developed for determining the relationships of assembly requirements with design dimensions and tolerances of the components in an assembly, and the relationships of design specifications and machining allowance requirements with manufactured dimensions and tolerances of the component in a process plan. This method traces from the proposed components or planned operations only the dimensions and tolerances that affect the given requirement, and therefore the equations for design or for manufacture can be established simultaneously and accurately. Hence it is possible to establish constraints for the optimisation of dimensions and tolerances for design or for manufacture.     

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

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 chart balancing with a complete inspection plan taking account of manufacturing and quality costs

This paper introduces a mathematical model of tolerance chart balancing for machining process planning under complete inspection. The criteria considered in this study are based on the combined effects of manufacturing cost and quality loss, under constraints such as process capability limits, product design specifications, and product quality requirements. Manufacturing costs include the machining cost, part cost, inspection cost, reworking cost, and replacement cost. The machining cost is expressed in geometrical decreasing functions, which represent tolerances to be assigned. Process variability is expressed in quadratic loss functions, which represent the deviation between the part measurement and the target value. An example is presented to demonstrate the proposed model. A comparison made with previous methods shows that the proposed model minimizes the total cost of manufacturing activities and quality-related issues in machining process planning, particularly in the early stages. Moreover, the applications are not be limited to machining process planning but can also be used in other forms of production planning.     

Extraction/conversion of geometric dimensions and tolerances for machining features

It is important for a feature-based system to preserve feature integrity during feature operation, especially when feature interaction occurs. The paper presents a feature conversion approach to convert design features used in a design model into machining features for the downstream applications. This process includes both form features (geometric information) and non-geometric features conversion. Most researchers have concentrated on geometric information extraction and conversion without tackling the important problem of non-geometric feature information. This paper focuses on the extraction and conversion of feature geometric dimensions and tolerances (GD&T) for downstream machining application.The main barrier to the integration of a feature-based CAD/CAPP/CAM system – feature interaction – is discussed in this paper, which alters design features in their geometries and non-geometric information. How to identify and validate these feature dimensions and tolerances is one of the key issues in feature interaction conversion. The development of robust methodologies for preserving feature integrity for use in process planning application is the main thrust of the work reported in this paper.     

Accuracy analysis and design of A3 parallel spindle head

As functional components of machine tools, parallel mechanisms are widely used in high efficiency machining of aviation components, and accuracy is one of the critical technical indexes. Lots of researchers have focused on the accuracy problem of parallel mechanisms, but in terms of controlling the errors and improving the accuracy in the stage of design and manufacturing, further efforts are required. Aiming at the accuracy design of a 3-DOF parallel spindle head(A3 head), its error model, sensitivity analysis and tolerance allocation are investigated. Based on the inverse kinematic analysis, the error model of A3 head is established by using the first-order perturbation theory and vector chain method. According to the mapping property of motion and constraint Jacobian matrix, the compensatable and uncompensatable error sources which affect the accuracy in the end-effector are separated. Furthermore, sensitivity analysis is performed on the uncompensatable error sources. The sensitivity probabilistic model is established and the global sensitivity index is proposed to analyze the influence of the uncompensatable error sources on the accuracy in the end-effector of the mechanism. The results show that orientation error sources have bigger effect on the accuracy in the end-effector. Based upon the sensitivity analysis results, the tolerance design is converted into the issue of nonlinearly constrained optimization with the manufacturing cost minimum being the optimization objective. By utilizing the genetic algorithm, the allocation of the tolerances on each component is finally determined. According to the tolerance allocation results, the tolerance ranges of ten kinds of geometric error sources are obtained. These research achievements can provide fundamental guidelines for component manufacturing and assembly of this kind of parallel mechanisms.     

Particle swarm optimization (PSO) algorithm for optimal machining allocation of clutch assembly

Nowadays tolerance optimization is increasingly becoming an important tool for manufacturing and mechanical design. This seemingly, arbitrary task of assigning dimension tolerance can have a large effect on the cost and performance of manufactured products. With the increase in competition in today’s market place, small savings in cost or small increase in performance may determine the success of a product. In practical applications, tolerances are most often assigned as informal compromises between functional quality and manufacturing cost. Frequently the compromise is obtained interactively by trial and error. A more scientific approach is often desirable for better performance. In this paper particle swarm optimization (PSO) is used for the optimal machining tolerance allocation of over running clutch assembly to obtain the global optimal solution. The objective is to obtain optimum tolerances of the individual components for the minimum cost of manufacturing. The result obtained by PSO is compared with the geometric programming (GP) and genetic algorithm (GA) and the performance of the result are analyzed .     

基于DFA和DFC的综合公差优化

公差是机械设计和制造过程中最重要的参数之一,其对加工成本和产品质量有很大的影响。本文采用 DFA和DFC的综合方法对制造过程中的装配精度进行分析和综合,建立了以公差为主的成本信息模型,对设计公 差和加工公差进行了系统分析,以最低制造成本为目标,根据成本 公差间的函数关系,建立了非线性的公差优化模 型,并采用遗传算法使这一问题得到了很好的解决。实例证明该方法是可行的。并为并行工程实施中其他的DFX 与DFC结合实现制造成本最低提供了良好的解决方案。