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.     

螺旋铣孔主轴单元的精度分配

基于螺旋铣孔的加工原理设计了螺旋铣孔专用主轴单元,为提高整个单元的精度,对主轴单元的关键部件在设计阶段早期进行了精度分配。对影响孔精度的主要因素进行了分析,分别使用改进的统计方法和遗传算法建立了精度分配模型,统计模型中考虑了权重影响系数和精度储备系数,从刀尖的位置和定位误差角度对主轴单元进行了精度分配。     

基于粒子群算法的装配公差优化分配

装配公差分配是产品公差设计的重要组成部分.目前装配公差优化分配主要使用遗传算法.为了提高收敛速度,避免早熟收敛,提出了基于粒子群算法的装配公差优化分配方法.采用了基于实数的编码表示方法,以装配公差分配的优化目标函数作为评价函数,利用罚常数将约束条件并入评价函数中.一个实例的优化结果表明所提方法的收敛性、稳定性和算法效率均优于基于遗传算法的方法.     

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.     

再制造机床可修复零部件精度分配研究

研究可修复零部件精度参数的分配是关系到再制造机床性能和再制造成本的重要问题。本文提出了用BP+GA的混合算法优化分配可修复零部件精度参数的方法。首先利用BP神经网络建立零部件精度参数与再制造机床空间几何误差之间的正向映射模型,然后用正交设计法得到训练样本数据并训练网络,最后再用BP+GA的混合算法逆向确定零部件的精度参数。仿真结果表明了混合算法是解决复杂精度分配问题的一种理想方法,优化结果可用于指导零部件精度的修复。     

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.     

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 .     

离散变量优化设计的改进斐波那契遗传算法

根据工程实际,充分考虑规范规定的约束条件和各项技术标准要求,建立离散变量结构优化模型。针对遗传算法在迭代过程中经常出现未成熟收敛、振荡、随机性太大和迭代过程缓慢等缺点,提出一种新的遗传算子——转基因算子,用于对遗传算法的改进;提出一种离散变量结构优化设计的斐波那契算法,并与遗传算法结合在一起解决问题。优化设计结果表明,这种改进斐波那契遗传算法的收敛特性得到很好的改善,即发挥了斐波那契算法省时、局部搜索能力强的特点,又发挥了遗传算法全局性好的特点,是有效的工程结构优化设计方法。     

Tolerance design optimization of machine elements using genetic algorithm

An important problem that faces design engineers is how to assign tolerance limits. In practical applications, tolerances are most often assigned as an informal compromise between functionality, quality and manufacturing cost. Frequently, the compromise is obtained iteratively by trial and error. A more scientific approach is often desirable for better performance. In this paper, a genetic algorithm (GA) is used for the design of tolerances of machine elements to obtain the global optimal solution. The objective is to design the optimum tolerances of the individual components to achieve the required assembly tolerance, zero percentage rejection of the components and minimum cost of manufacturing. The proposed procedure using GA is described in this paper for two tolerance design optimization problems: gear train and overrunning clutch assemblies. Results are compared with conventional techniques and the performances are analyzed.     

螺钉联接的可靠性优化设计

在鱼雷大段联接中,螺钉联接是一种广泛采用的方法.鱼雷壳体结构设计和强度分析过去一直采用以最大载荷、最小强度给出的安全系数来保证结构的可靠性,这里则提出使用可靠性理论和优化设计方法对螺钉联接进行再设计,并建立了相应的数学模型,利用遗传算法进行优化计算,经过计算取得了很好的成果.     

Genetic-algorithm-based optimal tolerance allocation using a least-cost model

Conventional tolerance analysis is tedious and time consuming, which makes engineers resist doing it. Complex assembly problems are generally beyond the capabilities of most design and manufacturing engineers. In this paper, genetic algorithm, a kind of non-traditional optimization technique is used as the basic foundation for optimal tolerance allocation to help design and manufacturing engineers to overcome the shortcomings in the conventional tolerance stack analysis and allocation system.     

Integrated setup planning and operation sequencing (ISOS) using genetic algorithm

Process planning is an essential component for linking design and manufacturing process. Setup planning and operation sequencing are two most important functions in the implementation of CAD/CAPP/CAM integration. Many researches solved these two problems separately. Considering the fact that the two functions are complementary, it is necessary to integrate them more tightly so that performance of a manufacturing system can be improved economically and competitively. This paper presents a generative system and genetic algorithm (GA) approach to process plan the given part. The proposed approach and optimization methodology analysis constraints such as TAD?(tool?approach?direction), tolerance relation between features and feature precedence relations to generate all possible setups and operations using workshop resource database. Tolerance relation analysis has a significant impact in setup planning for obtaining the part accuracy. Based on technological constraints, the GA algorithm approach, which adopts the feature-based representation, simultaneously optimizes the setup plan and sequence of operations using cost indices. Case studies show that the developed system can generate satisfactory results in optimizing the integrated setup planning and operation sequencing in feasible condition.     

FORM ERROR EVALUATION OF CIRCLES BASED ON A FINELY-DESIGNED GENETIC ALGORITHM

A genetic algorithm(GA)-based new method is designed to evaluate the circularity error of mechanical parts. The method uses the capability of nonlinear optimization of GA to search for the optimal solution of circularity error. The finely-designed GA (FDGA) characterized dynamical bisexual recombination and Gaussian mutation. The mathematical model of the nonlinear problem is given. The implementation details in FDGA are described such as the crossover or recombination mechanism which utilized a bisexual reproduction scheme and the elitist reservation method; and the adaptive mutation which used the Gaussian probability distribution to determine the values of the offspring produced by mutation mechanism. The examples are provided to verify the designed FDGA. The computation results indicate that the FDGA works very well in the field of form error evaluation such as circularity evaluation.     

基于模拟退火遗传算法的拆卸路径规划

针对现存拆卸路径规划图论方法中的组合爆炸问题和遗传算法的早熟现象,给出模拟退火和遗传算法相结合的拆卸路径规划方法.在拆卸路径规划模型中,以拆卸效率最优作为优化目标,给出了算法流程.该算法对拆卸路径的全面寻优提供了一种新的思路.通过实例验证该算法的可行性,最后提出了进一步的研究方向.     

A Genetic Algorithm Approach to the Scheduling of FMSs with Multiple Routes

Usually, most of the typical job shop scheduling approaches deal with the processing sequence of parts in a fixed routing condition. In this paper, we suggest a genetic algorithm (GA) to solve the job-sequencing problem for a production shop that is characterized by flexible routing and flexible machines. This means that all parts, of all part types, can be processed through alternative routings. Also, there can be several machines for each machine type. To solve these general scheduling problems, a genetic algorithm approach is proposed and the concepts of virtual and real operations are introduced. Chromosome coding and genetic operators of GAs are defined during the problem solving. A minimum weighted tardiness objective function is used to define code fitness, which is used for selecting species and producing a new generation of codes. Finally, several experimental results are given.     

一种基于D-H参数的7自由度机械臂机构精度综合方法研究

提出了一种基于最佳精度模型的机械臂机构精度综合的方法,利用遗传算法对D-H参数公差优化分配,为机械臂的精度设计提供理论依据。以一种基于双电机伺服驱动关节的7自由度协作机械臂为研究对象,机械臂的几何定位精度的设计目标为1.4 mm,建立该型机械臂末端执行器的几何定位误差模型;对参数误差进行敏感性分析,找出对机械臂末端执行器几何定位误差影响相对较大的参数误差;根据最佳精度数学模型,利用遗传算法对D-H参数公差优化分配;经过对误差仿真计算分析,机械臂的最大几何定位误差为1.226 7 mm,均值为0.485 9 mm,方差为0.216 5 mm,满足设计要求。为该机械臂的制造装配提供了理论参考依据。与基于最小成本模型的精度综合法相比,提出的精度综合方法不需要统计加工制造成本信息,能够确保机械臂的设计精度满足设计要求,可用于单个或者小批量生产制造机械臂的精度设计。     

基于模糊理论的机械串联系统可靠性分配方法

提出了一种新的可靠性分配方法,比较适用于产品设计的初期分配。在产品设计初期,可靠性分配大多数参数在不确定的条件下进行,分配过程面对很多不确定的模糊因素。应用基于模糊理论的可靠性加权分配方法,对于参数不确定的情况有比较好的效果,应用算例证明此方法合理可行。     

A Hybrid Search Algorithm for Porous Air Bearings Optimization

The study deals with the development of a hybrid search algorithm for efficient optimization of porous air bearings. Both the compressible Reynolds equation and Darcy's law are linearized and solved iteratively by a successive-over-relaxation method for modeling parallel-surface porous bearings. Three factors affecting the computational efficiency of the numerical model are highlighted and discussed. The hybrid optimization is performed by adopting genetic algorithm (GA) for initial search and accelerated by simplex method (SM) for refined solution. A simple and useful variable transformation is presented and used to convert the unconstrained SM to a constrained method. In this study, the hybrid search algorithm for a multi-variable design exhibits better efficiency compared with the search efficiency by using the SM. The proposed hybrid method also eliminates the need of several trials with random initial guesses to ensure high probability of global optimization. This study presents a new approach for optimizing the performance of porous air bearings and other tribological components.     

Efficient warpage optimization of thin shell plastic parts using response surface methodology and genetic algorithm

During the production of thin shell plastic parts by injection molding, warpage depending on the process conditions is often encountered. In this study, efficient minimization of warpage on thin shell plastic parts by integrating finite element (FE) analysis, statistical design of experiment method, response surface methodology (RSM), and genetic algorithm (GA) is investigated. A bus ceiling lamp base is considered as a thin shell plastic part example. To achieve the minimum warpage, optimum process condition parameters are determined. Mold temperature, melt temperature, packing pressure, packing time, and cooling time are considered as process condition parameters. FE analyses are conducted for a combination of process parameters organized using statistical three-level full factorial experimental design. The most important process parameters influencing warpage are determined using FE analysis results based on analysis of variance (ANOVA) method. A predictive response surface model for warpage data is created using RSM. The response surface (RS) model is interfaced with an effective GA to find the optimum process parameter values.     

An application of possibilistic programming to the fuzzy location–allocation problems

This paper considers location–allocation problem in the real uncertain world and develops a possibilistic non-linear programming model to deal with this problem. Fuzzy decision making in fuzzy environment concept is used to determine possibility distribution of location and allocation variables. To solve this model, a novel approach based on genetic algorithm structure is developed. As the proposed model includes both deterministic (location) and uncertain (allocation) parameters, the developed solution algorithm uses a hybrid chromosome structure. Also, to cover continuous nature of the problem and prevent GA from early convergence, a new crossover operator is introduced. Finally, performance of the developed algorithm is evaluated by an example.