Integrated tolerance optimisation with simulated annealing

Tolerance is one of the most important parameters in design and manufacturing. The allocation of design and machining tolerances has a significant impact on manufacturing cost and product quality. This article presents an analytical model for simultaneously allocating design and machining tolerances based on the least-manufacturing-cost criterion. In this study, tolerance allocation is formulated as a non-linear optimisation model based on the cost-tolerance relationship. A new global optimisation algorithm, simulated annealing, is employed to solve the non-linear programming problem. An example for illustrating the optimisation model and the solution procedure is provided.     

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.     

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.     

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.     

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.     

Concurrent process tolerance design based on minimum product manufacturing cost and quality loss

In a concurrent design environment, a robust optimum method is presented to directly determine the process tolerances from multiple correlated critical tolerances in an assembly. With given distributions of multiple critical assembly dimensions, the Taguchi quadric quality loss function is first derived. The quality loss is then expressed as the function of pertinent process tolerances. A nonlinear optimal model is established to minimize the summation of manufacturing costs and product quality loss. An example illustrates the proposed model and the solution method .     

Optimal Process Tolerance Balancing Based on Process Capabilities

An optimal approach for process tolerance balancing is presented. The new approach is based on process capabilities and is to be used in the stage of process planning. A nonlinear programming model is used to simultaneously optimise process tolerances of required operations. In the optimisation model, the objective function is to minimise the total manufacturing cost with different weighting factors. Using the estimated standard deviations of the dimensions and the manufacturing cost-tolerance functions, the constraint equations for the process tolerance chains and the manufacturing capability indices are established, together with a model for the economical tolerance bounds of machine tools. A practical example was used to verify the usefulness of the proposed approach. The results of the comparative study show that the proposed approach is more advantageous in relaxing tolerance requirements and in reducing scrap rates generally, compared with the existing methods. ID="A1"Correspondance and offprint requests to: Dr Y. Gao, Department of Mechanical Engineering, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong. E-mail: meygao@ust.hk     

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.     

Optimal Parameter and Tolerance Design with a Complete Inspection Plan

The need to remain competitive has led manufacturing sectors to consider tolerances as the key to achieving low cost and high quality. To produce quality products at low cost in today’s manufacturing industry, an integration of product design and process planning is essential. Process tolerance is one of the most important parameters that link product design and process planning. The process mean is also a critical parameter for further quality improvement and cost reduction under the permissible process setting adjustment within design tolerance limits. This study discusses an approach to integrate the product and process design via the optimisation of process mean and process tolerance.     

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。     

Algorithms for computer-aided generative process planning

Process planning is the function within a manufacturing facility that establishes the machining processes and parameters to be used so as to convert a piece-part from its initial form to the final form predetermined on an engineering drawing. Computer-aided process planning (CAPP) has become a major focus of manufacturing automation as it forms the interface between computer-aided design (CAD) and computer-aided manufacturing (CAM). Issues in CAPP include part representation, process selection, alternative process-plan generation, intermediate surface and tolerance determination, and operation sequencing. This paper focuses on quantitative models for determining cutting dimensions and tolerances for intermediate surfaces, and on a heuristic for sequencing cutting operations.     

Concurrent Optimisation of Parameter and Tolerance Design via Computer Simulation and Statistical Method

This study optimises component parameters and component tolerances simultaneously via computer simulation and response surface methodology (RSM). The approach first generates a set of experimental data through computer simulation, then the data are converted to a total cost as a response value before applying RSM for statistical analysis and mathematical optimisation. The response value (total cost) includes quality and related costs which reflect the combined effect of the parameter and tolerance values being assigned. The results provide designers with the optimal component design values, the critical components, and the response function of a product or process design, which are very important to know during design activities as they give designers information about repeated applications, accurate feedback and appropriate suggestions, particularly under uncertain design conditions. Three examples are provided: They are mechanical assembly design, machining process planning, and electronic circuit design.     

An improved tolerance charting technique using an analysis of setup capability

The tolerance charting method enables the calculation of working tolerances in machining process planning. The method has been used as a basic tool for analysing process plans for many decades. Process capability in tolerance charting is modelled using the tolerances of the working dimensions. The literature shows that machining process capability can be analysed from the point of view of surface position errors. During setups, it is possible to perform decomposition into two surface position tolerances: a datum surface position tolerance and a machining surface position tolerance. This type of analysis has the advantage of producing simplified tolerance chains. This paper provides an adaptation of the tolerance charting technique that uses a capability model based on datum and machining surface position tolerance. The results show an improvement in the working tolerance stackup that reduces the capability required for productive resources. As a result, reductions in manufacturing costs can be achieved. The proposal is valid for manual or computer-assisted techniques.     

Nonlinear optimisation in tolerance charts — A study of objective functions

One of the main objectives in tolerance charting is to determine the working dimensions and tolerances at the lowest cost without violating the blueprint specifications. It is with this objective in mind that the authors present a comprehensive study of the effect of the choice of an objective function on the final manufacturing cost. Optimisation of the objective functions has been done using PROFORT (nonlinear optimisation). The paper deals with a single example, solved using two linear and a nonlinear objective function.     

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 .     

Sensitivity-based conceptual design and tolerance allocation using the continuous ants colony algorithm (CACO)

In an assembly, there are two ways to control the deviation of critical dimensions. One is by keeping the deviation of the critical dimension small by tightening manufacturing tolerances and controlling aging and environmental effects. This approach is traditional and expensive, as it requires tighter manufacturing tolerances and protection from aging and the environment. The second is by moving the nominal values of the non-critical dimensions to a less sensitive portion. This approach is very helpful in improving the quality with no additional cost. One can analyze any number of designs very early in the concept development stage of a project. After the concept design the cost-based optimal tolerances for the corresponding dimensions are allocated. The continuous ants colony algorithm, a kind of meta-heuristic approach, is used as an optimization tool for minimizing the critical dimension deviation and allocating the cost- based optimal tolerances.     

On-machine measurement using a noncontact sensor based on a CAD model

Once a machining process is finished, an inspection process is carried out to check whether the part is within dimensional tolerances. A coordinate measuring machine (CMM) is a general metrological device for assessment of dimensions on the shop floor. It cannot be ignored, however, that CMM measurements require significant resources in operating time and cost, which has led to many studies into on-machine measurement (OMM) systems. This study aims to develop an OMM system with a noncontacting laser displacement sensing apparatus and a computer-aided design (CAD) model for ease of operation, improved operating speed, and free form profiling. The system is composed of two software modules, one for sensor alignment with the machine tool and the other for measurement based on CAD/CAM (computer-aided machining). Consequently, the system was verified on the shop floor at a numerical control (NC) machining center.     

Dimensional and geometrical tolerance balancing in concurrent design

In conventional design, tolerancing is divided into two separated sequential stages, i.e., product tolerancing and process tolerancing. In product tolerancing stage, the assembly functional tolerances are allocated to BP component tolerances. In the process tolerancing stage, the obtained BP tolerances are further allocated to the process tolerances in terms of the given process planning. As a result, tolerance design often results in conflict and redesign. An optimal design methodology for both dimensional and geometrical tolerances (DGTs) is presented and validated in a concurrent design environment. We directly allocate the required functional assembly DGTs to the pertinent process DGTs by using the given process planning of the related components. Geometrical tolerances are treated as the equivalent bilateral dimensional tolerances or the additional tolerance constraints according to their functional roles and engineering semantics in manufacturing. When the process sequences of the related components have been determined in the assembly structure design stage, we formulate the concurrent tolerance chains to express the relations between the assembly DGTs and the related component process DGTs by using the integrated tolerance charts. Concurrent tolerancing which simultaneously optimizes the process tolerance based on the constraints of concurrent DGTs and the process accuracy is implemented by a linear programming approach. In the optimization model the objective is to maximize the total weight process DGTs while weight factor is used to evaluate the different manufacturing costs between different means of manufacturing operations corresponding to the same tolerance value. Economical tolerance bounds of related operations are given as constraints. Finally, an example is included to demonstrate the proposed methodology.