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 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.     

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。     

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.     

Optimized sequential design of two-dimensional tolerances

Tolerancing has great impact on the cost and quality of a product. Previous research essentially focussed on one-dimensional tolerancing where sized tolerances accumulate only in one direction. When sized and angular tolerances are considered simultaneously, tolerances accumulate, however, in two different directions in the given view plane. We utilize related tolerance zones to illustrate the accumulation processes of sized and angular tolerances. The orientational tolerances are converted into the equivalent sized or angular tolerances in terms of their engineering semantics. We establish the sequential linear optimization models to maximize the 2D sized, angular, and orientational working tolerances of a 3D machined part based on the process capabilities. At any completion stage of operations, we measure the processed sized dimensions and then substitute them into the dimensional chains to dynamically re-calculate the mean working dimensions for remaining operations. We also re-evaluate the working tolerances for remaining operations using sequential optimization models. This approach can release the working tolerances, reduce manufacturing costs, and enhance the acceptance rate of machined parts when we manufacture the complex, low-volume, and high-value-added parts. The approach is finally illustrated with a practical example.     

Tolerance control for dimensional and geometrical specifications

The development of tolerance charts has come a long way from the past manual methods to the current computer-aided models. As a result, many techniques have emerged over the years. However, the area of geometrical tolerance charting has not been given much attention. In view of this, this paper addresses both linear and geometrical tolerance control.The method proposed in this paper allows the user to construct a model directly from the process plan. The relevant process links between any two planes which are required to satisfy both the linear and geometrical requirements are easily obtained from the model. Having established all the appropriate constraints, the linear programming optimisation software is used for the determination of the unknown working dimensions and tolerances.In essence, this paper presents a new methodology for deriving the process links from the process plan and also highlights the significance of the use of linear programming in achieving the optimal tolerance mix or combination.     

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.     

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.     

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.     

Machining Planning for Tolerance Synthesis

The present paper deals with the preliminary study and the prototypical implementation of an expert system to quickly define an high level manufacturing sequence able to produce the assigned part tolerances. To do so, the expert system simulates the human reasoning process by applying specific knowledge and inferences. An assembly that is widely used to test the performances of different design methods represents the case study. This module belongs to a flexible and integrated environment that aims to automatically define both the tolerance specifications and the related process plan. Its aim is to support the designer during the definition of a functional project.     

Machining Planning for Tolerance Synthesis

The present paper deals with the preliminary study and the prototypical implementation of an expert system to quickly define an high level manufacturing sequence able to produce the assigned part tolerances. To do so, the expert system simulates the human reasoning process by applying specific knowledge and inferences. An assembly that is widely used to test the performances of different design methods represents the case study. This module belongs to a flexible and integrated environment that aims to automatically define both the tolerance specifications and the related process plan. Its aim is to support the designer during the definition of a functional project.     

面向制造的机床并行公差优化设计

运用并行公差优化设计方法对精密卧式加工中心线性轴进行公差分配.在保证机床现有精度条件下,综合分析机床各线性轴制造误差的敏感度和加工成本,优化了给定结构机床线性轴导轨选型和导轨基面工序公差的精度设计,节约了机床制造成本.     

Optimum manufacturing tolerance to selective assembly technique for different assembly specifications by using genetic algorithm

Tolerance on parts dimension plays a vital role as the quality of the product depends on sub components tolerance. Thus, precision products that are manufactured reflect at high manufacturing cost. To overcome this situation, sub components of an assembly may be manufactured with wider tolerance, measured (using latest technologies like image processing) and grouped in partition and corresponding group components may be mated randomly. This present work is to obtain an optimum manufacturing tolerance to selective assembly technique using GA and to obtain maximum number of closer assembly specification products from wider tolerance sub components. A two components product (fan shaft assembly) is considered as an example problem, in which the subcomponents are manufactured with wide tolerance and partitioned into three to ten groups. A combination of best groups is obtained for the various assembly specifications with different manufacturing tolerances. The proposed method resulted nearly 965 assemblies produced out of one thousand parts with 15.86% of savings in manufacturing cost.     

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.     

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.     

Manufacturing environment-oriented robust tolerance optimization method

Tolerance design has a great impact on the cost and quality of a product. Previous research focused on process tolerances or robust tolerance design with little consideration on real manufacturing context. This paper presents a nonlinear method for robust tolerance design based on the real manufacturing context in three stages. The objective function to be minimized is the total manufacturing cost. The constraint equations for the optimization model are also deduced, which select suitable manufacturing processes based on the manufacturing environment. Simulation annealing (SA) is used for the nonlinear optimization. The approach is finally illustrated by a practical example. The results of the comparison with different models indicate that the proposed approach is more effective with the manufacturing resource. The robust and reliable tolerance can be obtained.     

基于偏差传递的二维多工位装配夹具系统公差可行稳健设计

提出一种基于偏差传递的二维多工位装配夹具系统公差可行稳健设计方法。分析二维多工位装配尺寸偏差传递关系,建立由定位销和零件定位孔(槽)公差引起夹具定位偏差的偏差流状态空间模型。采用数论网格方法对定位销和零件定位孔(槽)公差进行采样,将得到的公差样本代入夹具定位偏差模型,求得夹具定位偏差样本空间,将夹具定位偏差作为状态空间模型的输入偏差,提出基于状态空间模型的二维多工位装配成功率计算方法。继而应用Taguchi正交试验直观分析方法,分析得到影响装配成功率的主要因素即夹具系统定位销副关键公差,运用回归正交组合设计拟合得到二维多工位装配成功率与夹具系统定位销副关键公差的响应面模型。以定位销、零件定位孔(槽)制造成本所构成的装配成本最小化为目标,二维多工位装配成功率为约束,建立二维多工位装配夹具系统定位销和零件定位孔(槽)公差可行稳健设计模型。以汽车车身地板二维三工位装配为例,建立其公差可行稳健设计模型并对该模型进行计算与分析,结果表明在装配成本增幅较小的情况下,采用稳健约束后可显著提高公差设计的可行稳健性。该方法为二维多工位装配夹具系统公差稳健设计提供了一种新途径。     

CAD系统中并行公差的建模方法

提出一种基于产品设计与制造、支持公差工程语义和并行公差的几何公差计算机辅助建模表示新方法。在CAD系统中，进行装配公差和零件制造公差建模，利用特征的几何公差结构块，求出各种公差带的空间表示函数，计算有关公差带在三维空间中相应自由度的允许变动量，为公差分析和综合提供实用的模型。用工程实例验证了所提出的方法。     

Rigorous Application of Tolerance Analysis in Setup Planning

Decades of computer-aided process planning research has resulted in techniques that automate portions of the process planning task such as operation sequencing and cutter path optimisation. Nonetheless, solutions to other areas such as setup planning and fixturing remain elusive. Setup planning research has received increased attention in recent years. The importance of tolerance analysis in setup planning has been recognised. However, due to the lack of a common measure for different types of tolerances, the analysis is carried out in an ad hoc fashion and often results in suboptimal setup plans. In this paper, a tolerance normalisation approach is presented to provide an accurate means for direct comparison of different types of geometric tolerances and dimensional tolerances. A normalised tolerance is an angle representing the maximum permissible rotation error when locating a component. It is calculated based on rigorous analysis of manufacturing errors involved in component setups. The formulae for tolerance normalisation are derived and the use of normalised tolerance in setup planning is illustrated.