An Integrated Model of a Fixture-Workpiece System for Surface Quality Prediction

Surface quality is a major factor affecting the performance of a component. The machined surface quality is strongly influenced by the external loads during the fixturing and machining processes. In machining process development, it is highly desirable to predict the quality of a machined surface. For this purpose, an integrated finite element analysis (FEA) model of the entire fixture–workpiece system is developed to investigate the influence of clamping preload and machining force on the surface quality of the machined workpiece. The effects of fixture and machine table compliance (from experimental data), and the workpiece and its locators/clamps contact interaction, and forced vibration, on the machined surface quality are taken into account. This simulation model provides a better understanding of the causes of surface error and a more realistic prediction of the machined surface quality. The deck face of a V-type engine block subjected to fixture clamping and a face milling operation is given as an example. A comparison between the simulation result and experimental data shows a reasonable agreement.     

Fixture layout optimization for flexible aerospace parts based on self-reconfigurable swarm intelligent fixture system

Based on the development demand of a novel intelligent fixture system, a self-reconfigurable intelligent swarm fixture system is presented. This paper deals with the fixturing layout optimization of a flexible aerospace workpiece. A new fixturing principle, “N-2-1-1,” is put forward. The optimization procedure for fixture layout combined with genetic algorithm and finite element analysis is developed and verified by case study simulation.     

基于线性不等式方程组解的存在性及其通解的工件可达/可离性分析算法

工件的可达/可离性反映了将工件安装到/脱离出夹具装夹布局的可能性,分析可达/可离性有助于在工件上正确选择装夹表面和装夹点。为此依据工件与装夹元件的实际接触或装配情况,利用泰勒定理提出了工件可达/可离性模型。通过将工件安装到/脱离出装夹布局的可能性等价于可达/可离性模型的解的存在性,借助任意数可表达为两个非负数之差这一数学技巧作为桥梁,将工件可达/可离性模型的解的存在性问题转化为线性规划问题,提出了工件可达/可离性的判断方法。尤其是在判断可达/可离性模型有解的情况下,继而考虑了工件安装到/脱离出装夹布局的方向性。在此基础上,进一步将可达/可离的方向性转化为可达/可离性模型的通解,由此构建了求解线性不等式方程组的Γ-算法。这个“先有解-再求解”的算法仅涉及到装夹元件在工件表面处的位置与单位法矢量信息,不仅适用于形状复杂的工件,而且避免了可达/可离性模型无解情况下依旧求解的局限性,同时也拓展和丰富了自动化夹具设计的理论基础。     

Automated fixture configuration using projective geometry approach

The geometric and topological specification of a workpiece boundary is usually represented in a specific data format in a CAD database. To retrieve a set of workpiece data, to analyse its shape in addition to the machining requirements, and to determine the proper fixture configuration accordingly, are not trivial tasks when a part has a complicated shape. The real challenge is to recognise and synthesise the shape of a workpiece from its data representation. Consequently, the decision for fixturing can be made when the shape of a workpiece and the relationship of the shape and the fixturing configuration can be derived by a systematic methodology. In this paper, a projective spatial occupancy enumeration (PSOE) approach is applied as a representational and manipulating scheme for developing algorithms in automatic fixture configuration. The workpiece is projected onto the working plane of the fixture baseplate. A 2D projection is defined as a matrix of cells which can represent a workpiece with an arbitrary shape. Using a discrete search based upon the matrix of cells, the fixture types and their locations are generated according to a set of heuristic algorithms. This work is a generalisation and extension of previous works for prismatic parts. The same methodology is equally applicable in general robot grasping.     

Development of Automated Fixture Planning Systems

Fixturing is an important manufacturing activity. The computeraided fixture design technique is being rapidly developed to reduce the lead time involved in manufacturing planning. An automated fixture configuration design system has been developed to select automatically modular fixture components and place them in position with satisfactory assembly relationships In this paper, an automated fixturing planning system is presented in which fixturing surfaces and points are automatically determined based on workpiece geometry and operational information. Fixturing surface accessibility, feature accuracy, and fixturing stability are the main concerns in the fixture planning. The system development, the fixture planning decision procedure, and an implementation example are presented in the paper.     

A Fast Interference Checking Algorithm for Automated Fixture Design Verification

Fixtures are tooling devices used to locate, support and hold workpieces during a manufacturing process. The major purpose of a computer-aided fixture design (CAFD) system is to provide a fixture design based on fixturing principles and workpiece information. Interference checking between the machining tool and fixture units, as well as between fixture units, is one of the important functions of automated fixture design. This paper presents a fast interference checking algorithm for automated modular fixture design validation. It is based on the study of the geometric characteristics of modular fixture components and the machining tool. The fixture component model is simplified into a 2D contour model with height information. The tool-path model is represented by a moving dot for 3-axis operations, or a moving line segment in 5-axis operations, as the fixture component model is different from the popular collision detection procedure using swept volume and is more efficient for fixturing verification. Application of this method will greatly reduce the computation complexity for fixturing interference checking. The method is implemented with a CAFD system. An example is given at the end of the paper.     

Computer-Aided Fixture Design Verification. Part 3. Stability Analysis

In fixture design, a workpiece is required to remain stable throughout the fixturing and machining processes in order to achieve safety and machining accuracy. This requirement is verified by a function of the computer-aided fixture design verification (CAFDV) system. This paper presents the methodologies of fixturing stability analysis in CAFDV. A kinetic fixture model is created to formulate the stability problem, and a fixture stiffness matrix (FSM) is derived to solve the problem. This approach not only verifies fixturing stability, but also finds the minimum clamping forces, fixture deformation, and fixture reaction forces. The clamping sequence can also be verified with this approach.     

Uncertainty analysis of deep drawing using surrogate model based probabilistic method

Deep drawing is an important manufacturing process in industry. In order to obtain high-quality products produced by deep drawing, the set of design variables used in forming operation is designed through deterministic optimization. However, in real forming process, the design variables show variability and randomness which will affect the product quality. These uncertainties are an inherent characteristic of nature and cannot be avoided. This paper focuses on uncertainty analysis of deep drawing with the consideration of uncertainties in material parameters and friction. An uncertainty analysis approach which combines the finite element method (FEM) simulation, surrogate modeling, and Monte Carlo simulation (MCS) is presented in this work. The constructed surrogate models are validated and compared by cross validation and error measures. Then Monte Carlos Simulation is conducted by the use of the constructed surrogate model. The surrogate model based probabilistic method used in this paper is an approach with high-efficiency and sufficient accuracy for uncertainty analysis in deep drawing.     

A model for evaluating the quality of the fixturing of the part from a machining process planning perspective

Achieving the required tolerance of positioning between two features is not obvious when features are produced in multiple set-ups where the fixture/workpiece interface plays a critical role. From a computer-aided process planning perspective, the suitability of a fixturing feature to achieve the required tolerances has to be evaluated. A model of an indicator for a locating quality is proposed here based upon the distribution of a small displacement of the workpiece compatible with the required tolerance onto the candidate fixturing surfaces.     

组合夹具结构设计自动化系统研究

在广义映射原理指导下,开发了支持“top-down”风范的组合夹具设计自动化软件系统。在对零件夹持特性分析基础上,提取夹具需求信息,建立了组合夹具的功能要求集合,并对组合夹具功－构映射关系进行了全面分析,对组合夹具概念结构实施多方案重构,并进行了实例验证。为夹具结构设计自动化软件系统的开发探索出一条新的途径。     

Fixture layout optimization for multi point respot welding of sheet metals

The high quality of welding in the automotive industry is achieved by proper positioning of the fixture elements. A new method, N-3-2-1 (N ≥ 1), is proposed for fixture layout optimization of sheet metals. The flexible nature of the sheet metals requires N+3 fixture elements to constrain it normal to the surface (primary plane), but 2-1 fixture elements for other two directions (secondary and tertiary). The objective function is to achieve high stiffness of the workpiece and is calculated in terms of strain energy. Finite element analysis (FEA) was combined with genetic algorithm. A method was also proposed to find the optimum fixturing position of the workpiece in multipoint respot welding operation. Two different kinds of case studies were solved and the performance of the proposed method was also tested in the industrial scenario by fixturing the workpiece and completing the respot welding operation with satisfactory results.

     

Design and optimization of machining fixture layout using ANN and DOE

In machining fixtures, minimizing workpiece deformation due to clamping and cutting forces is essential to maintain the machining accuracy. This can be achieved by selecting the optimal location of fixturing elements such as locators and clamps. Many researches in the past decades described more efficient algorithms for fixture layout optimization. In this paper, artificial neural networks (ANN)-based algorithm with design of experiments (DOE) is proposed to design an optimum fixture layout in order to reduce the maximum elastic deformation of the workpiece caused by the clamping and machining forces acting on the workpiece while machining. Finite element method (FEM) is used to find out the maximum deformation of the workpiece for various fixture layouts. ANN is used as an optimization tool to find the optimal location of the locators and clamps. To train the ANN, sufficient sets of input and output are fed to the ANN system. The input includes the position of the locators and clamps. The output includes the maximum deformation of the workpiece for the corresponding fixture layout under the machining condition. In the testing phase, the ANN results are compared with the FEM results. After the testing process, the trained ANN is used to predict the maximum deformation for the possible fixture layouts. DOE is introduced as another optimization tool to find the solution region for all design variables to minimum deformation of the work piece. The maximum deformations of all possible fixture layouts within the solution region are predicted by ANN. Finally, the layout which shows the minimum deformation is selected as optimal fixture layout.     

Measurement uncertainty evaluation of conicity error inspected on CMM

The cone is widely used in mechanical design for rotation, centering and fixing. Whether the conicity error can be measured and evaluated accurately will directly influence its assembly accuracy and working performance. According to the new generation geometrical product specification(GPS), the error and its measurement uncertainty should be evaluated together. The mathematical model of the minimum zone conicity error is established and an improved immune evolutionary algorithm(IIEA) is proposed to search for the conicity error. In the IIEA, initial antibodies are firstly generated by using quasi-random sequences and two kinds of affinities are calculated. Then, each antibody clone is generated and they are self-adaptively mutated so as to maintain diversity. Similar antibody is suppressed and new random antibody is generated. Because the mathematical model of conicity error is strongly nonlinear and the input quantities are not independent, it is difficult to use Guide to the expression of uncertainty in the measurement(GUM) method to evaluate measurement uncertainty. Adaptive Monte Carlo method(AMCM) is proposed to estimate measurement uncertainty in which the number of Monte Carlo trials is selected adaptively and the quality of the numerical results is directly controlled. The cone parts was machined on lathe CK6140 and measured on Miracle NC 454 Coordinate Measuring Machine(CMM). The experiment results confirm that the proposed method not only can search for the approximate solution of the minimum zone conicity error(MZCE) rapidly and precisely, but also can evaluate measurement uncertainty and give control variables with an expected numerical tolerance. The conicity errors computed by the proposed method are 20%-40% less than those computed by NC454 CMM software and the evaluation accuracy improves significantly.     

基于神经网络和遗传算法的智能夹具规划

提出基于Kohonen自组织神经网络的装夹面分组与选择算法和基于遗传算法的定位点优化算法,利用人工神经网络来处理装夹面选择中各种复杂的影响因素,选择最佳的装夹表面;在此基础上,参考夹具校验的一些结论,通过一些参数来模拟工件的稳定性与变形特性,利用遗传算法进行组合优化,确定最优定位点.最后用实例验证了算法的有效性.     

The application of the simulated annealing method and heuristic algorithms in the selection of fixture elements

This paper deals with the selection of suitable fixture element combinations and fixture allocation for a workpiece to allow for the different positions of the fixturing points, which are already given based on related theories. The advanced modelling extension (AME) of AutoCAD R12 was used as the 3D graphic interface. The function suitable for the AME environment was also controlled to obtain detailed data of the workpiece.First of all, the concept of group technology (GT) was used to categorise and encode the modular fixture elements with similar functions for cutting purposes. Next, the AME was combined with API (application programming interface) and Autolisp to establish the graphic illustration system for fixture elements. Then different heuristic algorithms for fixture element selection were developed to correspond to different requirements in fixture functions. The required fixture elements were then selected with the help of the simulated annealing calculation method to derive a suitable and economical number of fixture element combinations. The height of the fixture element combination derived may not match the height of the fixture point originally located. The workpiece shape also affects the allocated position of the fixture elements. Therefore, a number of heuristic algorithms were developed in this study to process all the factors involved and to obtain a desirable selection for fixture elements.     

基于主动寻位与状态记忆安装技术的工件位置精度研究

介绍了主动寻位与状态记忆（IL8-SM）安装技术的工作原理，提出并详细分析了工件在多工序转换过程中，IL＆SM夹具系统对工件加工特征位置精度影响的误差运动学原理；基于齐次坐标变换的方法研究了误差建模的规律，给出了描述工件位置误差的通用数学模型，为消除箱体（包括定位元件）原始误差对工件及其加工特征位置精度的影响提供了理论参考。研究结果对IL＆SM安装技术中采取误差补偿控制策略以提高工件加工精度等具有一定的参考价值。     

IDEF0 Model of the Measurement Planning for a Workpiece Machined by a Machining Centre

A comprehensive analysis of the entire measuring operation for a workpiece machined by a machining centre should be conducted systematically before the application of a planning technique. For this purpose, an IDEF0 model is used in this paper to plan the measuring sequence and operation of a coordinate measuring system for a workpiece machined by a machining centre. Generally speaking, a machining centre can machine workpieces having complicated shapes. Therefore, the planning of measurement procedures and operations on a workpiece machined by a machine centre requires consideration of issues such as the position and measuring sequence of the measurement points, how to avoid probe collision during measuring, which fixture elements are required for measuring fixtures, and where the support points of fixtures and position of fixture locations should be.     

Numerical simulation of the system “fixture–workpiece” for lever machining

In this article, the new configuration of fixture was proposed for ensuring the sufficient tool accessibility, which allows carrying out multiaxis machining of levers in one setup. The research based on numerical simulation was confirmed that the proposed fixture corresponds to all the accuracy parameters. Workpieces from steel, cast iron and aluminium alloy were investigated within the simulation. The values of displacements and stresses occurring during machining are less for proposed fixture in comparison with the existing fixtures that was confirmed by the deflected mode analysis. The modal analysis proved that the proposed fixture has much higher value of eigenfrequency than the other fixtures. To optimize the machining, the dependences for displacements and stresses on the cutting depth were determined. Oscillations of the system “fixture–workpiece” during machining were investigated for various manufacturing steps of levers machining of the fixtures from different fixture systems. The results of harmonic analysis showed that the dynamic stiffness of the proposed fixture was higher than that for the dedicated and modular fixtures. The oscillation amplitudes in the places of machined surfaces in the proposed fixture do not exceed the tolerance requirements for lever manufacturing.     

Adaptive Monte Carlo and GUM methods for the evaluation of measurement uncertainty of cylindricity error

Measurement uncertainty is one of the most important concepts in geometrical product specification (GPS). The “Guide to the expression of uncertainty in measurement (GUM)” is the internationally accepted master document for the evaluation of uncertainty. The GUM method (GUMM) requires the use of a first-order Taylor series expansion for propagating uncertainties. However, when the mathematical model of measurand is strongly non-linear the use of this linear approximation may be inadequate. Supplement 1 to GUM (GUM S1) has recently been proposed based on the basis of probability density functions (PDFs) using the Monte Carlo method (MCM). In order to solve the problem that the number of Monte Carlo trials needs to be selected priori, adaptive Monte Carlo method (AMCM) described in GUM S1 is recommended to control over the quality of the numerical results provided by MCM.The measurement and evaluation of cylindricity errors are essential to ensure proper assembly and good performance. In this paper, the mathematical model of cylindricity error based on the minimum zone condition is established and a quasi particle swarm optimization algorithm (QPSO) is proposed for searching the cylindricity error. Because the model is non-linear, it is necessary to verify whether GUMM is valid for the evaluation of measurement uncertainty of cylindricity error. Then, AMCM and GUMM are developed to estimate the uncertainty. The procedure of AMCM scheme and the validation of GUMM using AMCM are given in detail. Practical example is illustrated and the result shows that GUMM is not completely valid for high-precision evaluation of the measurement uncertainty of cylindricity error if only the first-order terms in the Taylor series approximation are taken into account. Compared with conventional methods, not only the proposed QPSO method can search the minimum zone cylindricity error precisely and rapidly, but also the Monte Carlo simulation is adaptive and AMCM can provide control variables (i.e. expected value, standard uncertainty and lower and higher coverage interval endpoints) with an expected numerical tolerance. The methods can be extended to the evaluation of measurement uncertainty of other form errors such as roundness and sphericity errors.     

薄壁件的装夹变形机理分析与控制技术

系统地提出一个分析与优选夹紧力大小、作用点以及夹紧顺序的通用方法.基于由摩擦力引起的接触力历史依赖性,定量地分析多重夹紧元件及其作用顺序对薄壁件变形的影响,并建立装夹方案的数学模型.同时提出基于最小总余能原理的有限元求解方法.另一方面,基于装夹方案的优化模型,提出装夹变形的控制技术以便获得最高的工件加工精度.以典型铝合金航空材料构件为例,模拟与分析夹紧力及夹紧顺序对其变形的影响过程.