The study of cost-tolerance model by incorporating process capability index into product lifecycle cost

To reduce the cost of manufacturing systems, many studies of cost minimization have been performed. Since tolerance design significantly affects the manufacturers’ cost, the optimization of cost-tolerance allocation will be an important issue for reducing these costs. Costs incurred in a product life-cycle include manufacturing cost and quality loss. However, most cost-tolerance optimization models frequently ignore the concept of quality loss and may not lead to an accurate analysis of the tolerance. Until now, process capability analysis has been the tool used to evaluate the adequacy of a production tool in meeting a quality target. Hence, the concept of process capability analysis should be included into the cost-tolerance optimization model. In this study, a flexible cost-tolerance optimization model will be constructed by integrating the process capability index into the product life-cycle cost function. The constructed cost-tolerance optimization model simultaneously considers the manufacturing cost of the components, the process capability of the manufacturing operations, and the quality loss of products. The decision-maker can apply the proposed cost-tolerance optimization model to determine a reasonable tolerance with minimum total cost including consideration of the process capability .     

Minimum-Loss Assembly Tolerance Allocation by Considering Product Degradation and Time Value of Money

In the optimisation of tolerance allocation for a mechanical assembly, much work has concentrated on the minimum cost– tolerance allocation without considering the quality of the final assembly. Cheng and Maghsoodloo combined the cost– tolerance function and quality loss function, to determine the optimal tolerances for individual components, so that the total assembly cost (including both tolerance cost and quality loss) might be minimised. The objective of this paper is to propose a model for optimal tolerance allocation by considering both tolerance cost and the present worth of quality loss such that the total assembly cost/loss is minimised. The proposed model takes into account the time value of money for quality loss and product degradation over time, and includes two new parameters: the planning horizon and the product user’s discount rate. From the result of this study, a longer planning horizon results in an increase in both tolerance cost and quality loss; however, a larger value of discount rate yields a decrease in both tolerance cost and quality loss.     

Functional tolerance theory in incremental growth design

The evolutionary tolerance design strategy and its characteristics are studied on the basis of automation technology in the product structure design. To guarantee a successful transformation from the functional requirement to geometry constraints between parts, and finally to dimension constraints, a functional tolerance design theory in the process of product growth design is put forward. A mathematical model with a correlated sensitivity function between cost and the tolerance is created, in which the design cost, the manufacturing cost, the usage cost, and the depreciation cost of the product are regarded as control constraints of the tolerance allocation. Considering these costs, a multifactor-cost function to express quality loss of the product is applied into the model. In the mathematical model, the minimum cost is used as the objective function; a reasonable process capability index, the assembly function, and assembly quality are taken as the constraints; and depreciation cost in the objective function is expressed as the discount rate—terminology in economics. Thus, allocation of the dimension tolerance as the function and cost over the whole lifetime of the product is realized. Finally, a design example is used to demonstrate the successful application of the proposed functional tolerance theory in the incremental growth design of the product. __________ Translated from Chinese Journal of Mechanical Engineering, 2006, 42(10): 73–79 [译自: 机械工程学报]     

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.     

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.     

Tolerance evolutionary model and algorithm in product growth design

To guarantee the successful transformation from product functional requirement to geometry constraints and finally to dimension constraints between components in a product, an evolutionary tolerance design strategy is proposed on the basis of automation technology in product structure design. In the first part of this paper, the theory of the growth design and the process of tolerance evolutionary design are introduced. Following the evolution of product structure, product tolerance grows from its initial state, defined by accuracy requirements, to its final state, defined as dimension tolerance and geometric tolerance. In this growing process, the basic units in the product growth design, known as functional surfaces and their nominal features, are used as evolutionary carriers. With the help of these basic units, the method for the construction of a two-layer correlation network is proposed. In the second part, the tolerance assertions to assist tolerance evolutionary design are given, based on which the basic process for an evolutionary design of dimensions chain and geometric tolerance are presented. In order to optimize the allocation of the dimension tolerance, a mathematical model is developed in which a correlated sensitivity function between the cost and the tolerance is created. In the model, the design cost, the manufacturing cost, the usage cost, and the depreciation cost of the product are used as constraints to the tolerance allocation. Considering these costs, a multifactor cost function to express quality loss of the product is developed and is applied into the model. The minimum cost is used as the objective function, and the depreciation cost in the objective function is expressed by the discount rate—terminology in economics. The aim was to achieve a final and ideal balance around assembly, manufacturing, and usage through the control of product precision. In the last part, the successful usage of the proposed tolerance evolutionary strategy in the incremental growth product design is demonstrated through a design example.     

Concurrent optimization of machining process parameters and tolerance allocation

With the advent use of sophisticated and high-cost machines coupled with higher labor costs, concurrent optimization of machining process parameters and tolerance allocation plays a vital role in producing the parts economically. In this paper, an effort is made to concurrently optimize the manufacturing cost of piston and cylinder components by optimizing the operating parameters of the machining processes. Design of experiments (DoE) is adopted to investigate systematically the machining process parameters that influence product quality. In addition, tolerance plays a vital role in assembly of parts in manufacturing industries. For the selected piston and cylinder component, improvements efforts are made to reduce the total manufacturing cost of the components. By making use of central composite rotatable design method, a module of DoE, a mathematical model is developed for predicting the standard deviation of the tolerance achieved by grinding process. This mathematical model, which gives 93.3% accuracy, is used to calculate the quality loss cost. The intent of concurrent optimization problem is to minimize total manufacturing cost and quality loss function. Genetic algorithm is followed for optimizing the parameters. The results prove that there is a considerable reduction in manufacturing cost without violating the required tolerance, cutting force, and power.     

基于有限元模型的汽车薄板焊装公差分配研究

当前的汽车车身薄板覆盖件焊装公差分配方法,通过收紧装配公差以期达到车身焊装高的质量要求,而公差过小不仅提高了制造成本,还往往超出了装配件制造能力。本文提出一种基于有限元模型的公差分配方法用于薄板装配,利用该方法可在装配前确定满足产品整体质量要求的最大允许加工公差,这样既可以降低装配件制造成本,又可以保证车身焊装的质量。此方法为汽车薄板件冲压工艺设计提供了依据。     

生长型设计中的功能公差设计理论

在产品结构设计自动化技术基础上,研究生长型设计中公差进化设计的策略与原则,提出将产品功能要求转化成零部件之间的几何约束关系,并最终表达为对功能尺寸约束的功能公差设计理论。建立成本—公差敏感函数的数学模型,将产品设计、制造、使用以及技术折旧成本作为公差分配的控制约束,并在其中引入产品使用磨损模型,以经济学中的贴现率来表征技术折旧成本,以成本最低为目标函数,以合理的工艺能力指数、装配功能、装配质量作为约束条件,实现基于功能与成本的面向产品全生命周期的尺寸公差分配。最后,设计实例说明所提出的功能公差设计理论能够在生长型设计中成功应用。     

Inspection Allocation Planning for a Multiple Quality Characteristic Advanced Manufacturing System

Producing products with multiple quality characteristics is always one of the concerns for an advanced manufacturing system. To assure product quality, finite automatic inspection systems should be used. Inspection planning to allocate inspection stations should then be performed to manage the limited inspection resource. Except for finite inspection station classes, in this work, the limited number of inspection stations, of each inspection station class, is considered for solving the inspection allocation problem in a multiple quality characteristic advanced manufacturing system. Since the product variety in batch production or job shop production increases to satisfy the changing requirements of the various customers, the tolerances specified will vary from time to time. This inspection allocation problem is solved using a unit cost model in which the manufacturing capability, inspection capability, and tolerance specified are concurrently considered for a multiple quality characteristic product. The situation of unbalanced tolerance design is also considered. The inspection allocation problem can then be solved according to customer requirements. Since determining the optimal inspection allocation plan seems to be impractical, as the problem size becomes large, two decision criteria (i.e. sequence order of workstation and tolerance interval) are employed separately to develop two different heuristic solution methods in this work. The performance of each method is measured in comparison with the enumeration method that generates the optimal solution. The result shows that a feasible inspection allocation plan can be determined efficiently. ID="A1"Correspondance and offprint requests to: Dr Yau-Ren Shiau, Department of Industrial Engineering, Feng-Chia University, 100 Wenhwa Road, Seatwen, PO Box 25–097, Taichung 407, Taiwan     

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.     

基于NSGA-Ⅱ算法的车身薄板零件公差优化

在汽车制造工业产品开发过程中,需要同时考虑质量与成本之间的矛盾。盲目提高质量要求,将使产品制造成本增加;随意降低成本,则有可能影响质量,导致客户投诉和返修率上升。首先建立概念设计阶段的装配偏差分析模型,用来分析车身装配质量;并选取指数函数作为公差成本函数,以此为基础建立多目标优化模型,然后采用NSGA-II算法优化各个零件的公差。最后利用车身侧围框架案例阐述零件公差分配过程,获得了多目标函数的Pareto解集,取得了较好的优化效果。     

Effect of ultrasonic impact treatment on the ultra high cycle fatigue properties of SMA490BW steel welded joints

This paper presents bi-criteria formulation of a tolerance allocation model for an interchangeable assembly to simultaneously evolve suitable combination of manufacturing facility in multiple facility shaft-hole production environments of medium- and large-scale industries and tolerances to complement the need of customers. An Exhaustive Search Procedure is used to obtain the optimal solution for small and medium size problems and simulated annealing algorithm is used for large size problems. The usefulness of the Pareto front in manufacturing tolerance allocation decisions is demonstrated with three case study problems. The effect of process capability of shaft-hole assembly manufactured from alternative manufacturing machines and the optimality is analyzed in three cases to understand their criticality in decision-making. The models discussed in this paper could be useful for medium- and large-scale manufacturing industries, where there will be a variety of manufacturing facilities (specifications, capabilities, models, and types) for making both shaft-hole assembly and play a key role to meet the tolerance and cost requirements of different customers. This paper further discusses how this formulation and methodologies can be used for two hole and two shaft assemblies and multiple shaft-hole assemblies. Finally, the paper ends with highlighting directions of future research avenues in the shaft-hole assembly.     

基于粒子群算法的公差分配优化方法

基于成本—公差模型和质量损失模型,以加工能力和装配尺寸链的功能约束条件为标准,以制造成本最低、质量损失最小为优化目标,建立兼顾产品成本和质量的公差分配的多目标函数优化模型。基于粒子群优化算法,按照从全局到局部的寻优策略,用线性调节方法来确定其参数的变化规律,进而应用MATLAB软件对建立的函数模型进行优化计算,得到产品的生产成本和质量损失之间的关系曲线,可为公差分配提供更多的解决方案和更可靠的理论依据。     

基于工序加工能力的并行公差优化设计

提出一种基于工序加工能力的并行工序公差优化设计方法。在产品的初步结构设计阶段，通过相配零件的加工工艺规划把装配功能公差表示为零件的工序公差，建立以加权制造总成本最小为目标，以并行公差链、标准化的工序公差系数、机床最大经济极限公差为约束的非线性并行公差优化设计模型，求解该模型得到最佳的工序公差。最后给出了并行公差优化设计的一个工程实例，结果表明，所提的方法具有比传统串行等精度方法更合理、工序公差数值更大的优点。     

Formulation of Manufacturing Strategy

With customers demanding high quality, low cost and shorter lead time, the manufacturing function plays a vital role in attaining a competitive advantage. Thus, to compete effectively, it is important to formulate and implement the appropriate manufacturing strategy. This paper presents the author’s experience and the resulting generic methodology which has been successfully used in several organisations.     

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 .     

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.     

Primary deviations of mechanism links with sliding and revolute pairs

The problem of how to secure the needed “volumetric” accuracy of a precision five coordinate machines during its manufacturing and operation is important for modern machinery manufacturing. One way to increase a machine’s accuracy is to compensate the primary deviations of machine mechanism with numerical control. The models describing the deviations of actuators’ disposition are a powerful way to investigate the accuracy of compensative algorithms. To generate the matrix model, it is necessary to have the information on primary deviations for the links of mechanisms with sliding and revolving pairs. In the present work, the primary deviations of the links that enter into sliding and revolute pairs are determined in terms of standard of accuracy. The term of a load-carrying system of the machine is specified. It is suggested to separate the load-carrying system into subsystems with one kinematic pair and this is the basis for generating the model that describes the deviations of actuators’ disposition for a multicoordinate machine.     

Investigating optimal capacity scalability scheduling in a reconfigurable manufacturing system

Responsiveness to dynamic market changes in a cost-effective manner is becoming a key success factor for any manufacturing system in today’s global economy. Reconfigurable manufacturing systems (RMSs) have been introduced to react quickly and effectively to such competitive market demands through modular and scalable design of the manufacturing system on the system level, as well as on the machine components’ level. This paper investigates how RMSs can manage their capacity scalability on the system level in a cost-effective manner. An approach for modeling capacity scalability is proposed, which, unlike earlier approaches, does not assume that the capacity scalability is simply a function of fixed increments of capacity units. Based on the model, a computer tool that utilizes a genetic algorithm optimization technique is developed. The tool aids the systems’ designers in deciding when to reconfigure the system in order to scale the capacity and by how much to scale it in order to meet the market demand in a cost-effective way. The results showed that, in terms of cost, the optimal capacity scalability schedules in an RMS are superior to both the exact demand capacity scalability approach and the approach of supplying all required capacity at the beginning of the planning period, which is adopted by flexible manufacturing systems (FMSs). The results also suggest that the cost-effective implementation of an RMS can be realized through decreasing the cost of reconfiguration of these new systems.