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.     

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.     

Tolerancing of parts using an expert system

Tolerancing of parts is an important aspect involving both the designer and the manufacturer. The designer has a tendency to specify tolerances tighter than those required by the function of a part in order to increase its reliability. But tolerances greatly influence manufacturing costs. Tolerance specification of parts should therefore consider the manufacturing cost alongise the functional requirement of the part. A good tolerance specification strikes an appropriate balance between these two. The paper presents a rational approach to tolerance specification of parts, considering functional requirements as well as manufacturing costs. The approach is implemented using the expert system EXDEM developed on the ICL 2960 computer at IIT, New Delhi. This system assigns tolerances to dimensions of mechanical parts automatically.     

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.     

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.     

Using economic criteria to establish manufacturing tolerances

In this article, we propose an approximate, but easily applicable, method that uses economic criteria to determine where to establish manufacturing tolerances when 100% inspection is performed. The method considers the Taguchi loss function and the relation between cost and manufacturing tolerance. The method we propose moves away from the usual approach in that it deals explicitly with the dependence of manufacturing costs of the products sold with respect to the manufacturing tolerance .     

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.     

工业机器人位姿误差的计算

机器人连杆的加工误差、温度变化以及机械传动误差等诸多因素会导致机器人抓手的位置和姿态产生误差。本文以机器人运动学及误差理论为基础 ,推导出了在各种位姿描述情况下机器人位置和姿态误差的计算公式。该方法可以作为对各种工业机器人的位姿精度进行分析的基础     

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。     

Geometric Deviation Modeling by Kinematic Matrix Based on Lagrangian Coordinate

Typical representation of dimension and geometric accuracy is limited to the self-representation of dimension and geometric deviation based on geometry variation thinking, yet the interactivity affection of geometric variation and gesture variation of multi-rigid body is not included. In this paper, a kinematic matrix model based on Lagrangian coordinate is introduced, with the purpose of unified model for geometric variation and gesture variation and their interactive and integrated analysis. Kinematic model with joint, local base and movable base is built. The ideal feature of functional geometry is treated as the base body; the fitting feature of functional geometry is treated as the adjacent movable body; the local base of the kinematic model is fixed onto the ideal geometry, and the movable base of the kinematic model is fixed onto the fitting geometry. Furthermore, the geometric deviation is treated as relative location or rotation variation between the movable base and the local base, and it's expressed by the Lagrangian coordinate. Moreover, kinematic matrix based on Lagrangian coordinate for different types of geometry tolerance zones is constructed, and total freedom for each kinematic model is discussed. Finally, the Lagrangian coordinate library, kinematic matrix library for geometric deviation modeling is illustrated, and an example of block and piston fits is introduced. Dimension and geometric tolerances of the shaft and hole fitting feature are constructed by kinematic matrix and Lagrangian coordinate, and the results indicate that the proposed kinematic matrix is capable and robust in dimension and geometric tolerances modeling.     

一种含平行四边形支链的3自由度并联机构姿态精度综合与装配工艺设计

以含平行四边形支链的3平动自由度并联机构主模块为对象,通过误差建模揭示出影响这种机构末端姿态精度因素。利用灵敏度分析结果,将精度综合归结为一类有约束线性规划问题,并据此提出两种可以有效抑制末端姿态误差的装配工艺方案。     

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.     

Optimum tolerance synthesis for complex assembly with alternative process selection using Lagrange multiplier method

Any part cannot be manufactured to the required nominal dimensions due to inherent variations in workmanship, material, and machine. The specification of tolerance on part dimensions plays a major role on performance, quality, and cost of the product. Distribution of tolerance among the components of an assembly is known as tolerance allocation. The selection of alternative processes for tolerance allocation also plays a vital role in reducing manufacturing cost. Near-optimal allocated tolerances are obtained using nontraditional optimization techniques in which the solutions are achieved randomly. Also, there is a chance for omitting the better process for allocation. The results of successive run of the program based on these techniques will not yield consistent results. An attempt has been made in this work to solve the above problem using Lagrange multiplier method for complex assemblies with univariate search method. The methodology has been demonstrated on wheel mounting assembly. The example product after implementing the proposed method would yield 1.4% savings in manufacturing cost as compared with the cost obtained by Singh.     

Design and accuracy analysis of a metamorphic CNC flame cutting machine for ship manufacturing

The current research of processing large size fabrication holes on complex spatial curved surface mainly focuses on the CNC flame cutting machines design for ship hull of ship manufacturing. However, the existing machines cannot meet the continuous cutting requirements with variable pass conditions through their fixed configuration, and cannot realize high-precision processing as the accuracy theory is not studied adequately. This paper deals with structure design and accuracy prediction technology of novel machine tools for solving the problem of continuous and high-precision cutting. The needed variable trajectory and variable pose kinematic characteristics of non-contact cutting tool are figured out and a metamorphic CNC flame cutting machine designed through metamorphic principle is presented. To analyze kinematic accuracy of the machine, models of joint clearances, manufacturing tolerances and errors in the input variables and error models considering the combined effects are derived based on screw theory after establishing ideal kinematic models. Numerical simulations, processing experiment and trajectory tracking experiment are conducted relative to an eccentric hole with bevels on cylindrical surface respectively. The results of cutting pass contour and kinematic error interval which the position error is from –0.975 mm to +0.628 mm and orientation error is from –0.01 rad to +0.01 rad indicate that the developed machine can complete cutting process continuously and effectively, and the established kinematic error models are effective although the interval is within a ‘large' range. It also shows the matching property between metamorphic principle and variable working tasks, and the mapping correlation between original designing parameters and kinematic errors of machines. This research develops a metamorphic CNC flame cutting machine and establishes kinematic error models for accuracy analysis of machine tools.     

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.     

Influence of manufacturing errors in a metal-cutting machine with parallel kinematic structure on its machining precision

Possible manufacturing and assembly errors in a metal-cutting machine with parallel kinematic structure that affect its kinematic model are analyzed. On the basis of the manufacturing tolerances for the metal-cutting machine, the equations of the direct and inverse kinematic transformations are refined. An algorithm is derived for simulating the influence of geometric errors on the positioning precision of the actuator in the metal-cutting machine.     

Evaluation and uncertainty analysis of vectorial tolerances

Recently, the integration of coordinate measuring machines (CMMs) and computer-aided design (CAD) systems has promoted a new approach to the evaluation of workpiece geometry; namely, vectorial dimensioning and tolerancing. This new approach is promising, because it defines process-related dimensions and tolerances clearly and distinctly. Therefore, it enables proper manufacturing control and process diagnosis. However, current proposal of vectorial tolerancing has several limitations. First, the current orientation vector is inadequate for representing true three-dimensional (3D) orientation. As a result, the orientation of a free-form surface cannot be properly established. Second, there has been little discussion of vectorial tolerance evaluation. This paper proposes a new rotation vector that provides a more general mathematical basis for representing vectorial tolerances. A nonlinear, best-fit algorithm has been developed to evaluate vectorial tolerances for both analytical geometric elements and free-form surfaces. To study the uncertainty of the best-fit result caused by sampling strategy and dimensional errors, sensitivity analysis of the evaluated parameters was investigated. Simulation and experiment showed that the developed model can predict the uncertainty of the evaluated parameters accurately.     

基于Web的可重构制造资源优化配置平台研究

针对网络化制造中的资源动态快速重组问题，提出了基于物理制造单元的制造资源信息建模，以该模型建立了网络化、分布式制造资源库；研究了面向CAPP的制造资源预配置及其实现方法；研究了以时间、质量、成本为约束的制造资源优化配置及其实现方法。     

弧面凸轮廓面误差的研究

通过对包络法加工弧面凸轮基本原理的研究，找出了产生凸轮廓面误差的因素；利用矢量法分析了弧面凸轮廓面的各项原始加工误差，为提高弧面凸轮廓面的加工精度提供了一定的理论依据。