基于线性规划的工件稳定性建模及其应用

工件在实现定位后,在加工过程中将要受到工件重力和切削力等外力的作用。为使工件保持定位精度与生产安全性,必须保证工件在整个加工过程中具有稳定性。系统地讨论了工件稳定性建模及其求解方法,在摩擦锥线性近似以及变量非负转换的基础上,提出了工件稳定性的定量判断准则;利用线性规划方法对工件稳定性模型进行分析。结果表明,稳定性模型不仅能够验证工件的稳定性,而且还能够分析夹紧力大小、作用点以及夹紧顺序的合理性。这种方法既适用于夹具夹持稳定性分析,也适用于机械手的抓取稳定性分析。     

基于多重夹紧的工件-夹具间接触力的预测方法

在夹具设计过程中,工件-夹具之间的接触力是工件稳定性分析和加工精度估算的关键因素.为此,根据多重夹紧力对工件的作用过程,建立了接触力与多重夹紧力的大小、作用点以及夹紧顺序之间的接触力模型.基于总余能原理,提出了接触力模型的求解算法.最后通过典型实例,详细说明了接触力的分析预测过程.     

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.     

基于力的存在性与可行性的夹紧力变向增量递减规划算法

根据工件的静力平衡条件与工件-装夹元件之间接触力的方向约束,建立工件装夹方案的力学模型。进一步结合线性规划技术,构建力的存在性分析模型及其求解方法,实现夹紧力是否有解的判断。针对夹紧力有解这一条件,由装夹方案力学模型与线性规划技术推导出力的可行性分析模型及其判断标准,实现给定的夹紧力是否合理的判断。考虑夹紧力的取值范围,以一定步长正向从最小值开始取值,根据当前值与上一次取值之间可行性的差异,确定下一次取值的步长及其方向;若可行性相同则以相同步长继续正向取值,否则以一半步长、反向取值,直至步长的绝对值在阈值范围之内,构建夹紧力变向增量递减的规划算法。该算法将连续型的夹紧力设计问题转化为离散型,不仅利于计算机实现夹紧力的自动化设计,而且还适合于形状复杂的工件。     

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.     

Development of a finite element analysis tool for fixture design integrity verification and optimisation

Machining fixtures are used to locate and constrain a workpiece during a machining operation. To ensure that the workpiece is manufactured according to specified dimensions and tolerances, it must be appropriately located and clamped. Minimising workpiece and fixture tooling deflections due to clamping and cutting forces in machining is critical to machining accuracy. An ideal fixture design maximises locating accuracy and workpiece stability, while minimising displacements.The purpose of this research is to develop a method for modelling workpiece boundary conditions and applied loads during a machining process, analyse modular fixture tool contact area deformation and optimise support locations, using finite element analysis (FEA). The workpiece boundary conditions are defined by locators and clamps. The locators are placed in a 3-2-1 fixture configuration, constraining all degrees of freedom of the workpiece and are modelled using linear spring-gap elements. The clamps are modelled as point loads. The workpiece is loaded to model cutting forces during drilling and milling machining operations. Fixture design integrity is verified. ANSYS parametric design language code is used to develop an algorithm to automatically optimise fixture support and clamp locations, and clamping forces, to minimise workpiece deformation, subsequently increasing machining accuracy. By implementing FEA in a computer-aided-fixture-design environment, unnecessary and uneconomical “trial and error” experimentation on the shop floor is eliminated.     

A combined contact elasticity and finite element-based model for contact load and pressure distribution calculation in a frictional workpiece-fixture system

Contact forces between workpiece and fixture define fixture stability during clamping and influence workpiece accuracy during machining. In particular, forces acting in the contact region are important for understanding deformation of the workpiece at the contact region. This paper presents a model that combines contact elasticity with finite element methods to predict the contact load and pressure distribution at the contact region in a workpiece-fixture system. The objective is to determine how much clamp forces can be applied to generate adequate contact forces to keep the workpiece in position during machining. The model is able to predict the normal and tangential contact forces as well as the pressure distribution at each workpiece-fixture contact in the fixturing system. Model prediction is shown to be in good agreement with known industry practice on clamp force determination. The presented method has no limits on the types of materials that can be analyzed.     

铣削加工中最小夹紧力的计算

提出了一种计算铣削加工中夹紧工件所需最小夹紧力的简洁方法。首先,确定了工件与夹具元件之间的接触刚度;其次,建立了接触变形量与工件位移量的关系;然后,给出了工件的静态平衡方程。通过合并以上方程,建立了线性方程组计算工件与夹具元件之间的切向接触力,并根据最大切向接触力进一步计算出夹具元件与工件之间不发生相对滑动所需理论最小夹紧力。最后,通过算例验证了该方法的正确性。     

Improvement of flatness error in milling plate-shaped workpiece by application of side-clamping force

To improve flatness error of plate-shaped workpieces in milling under side clamp holding mechanisms, appropriate magnitudes of clamping forces and method of application are studied in this paper. The effect of side-clamping force on workpiece deformation is investigated by experimental and computational analyses for the case where the workpiece is clamped at a position higher than the neutral plane of bending of the plate-shaped workpiece. It is found that the thermal deformation and elastic deformation caused by clamping force are in two opposite directions. Then, an appropriate method is proposed to compensate for the workpiece thermal deformation caused by cutting heat with the opposite elastic deformation caused by the side-clamping force, so as to keep the machined top surface of the workpiece flat as much as possible. The proposed method has been confirmed through computational analyses and experiments. © 2000 Elsevier Science Inc. All rights reserved.     

Error Compensation of Thin Plate-shape Part with Prebending Method in Face Milling

Low weight and good toughness thin plate parts are widely used in modern industry, but its flexibility seriously impacts the machinability. Plenty of studies focus on the influence of machine tool and cutting tool on the machining errors. However, few researches focus on compensating machining errors through the fixture. In order to improve the machining accuracy of thin plate-shape part in face milling, this paper presents a novel method for compensating the surface errors by prebending the workpiece during the milling process. First, a machining error prediction model using finite element method is formulated, which simplifies the contacts between the workpiece and fixture with spring constraints. Milling forces calculated by the micro-unit cutting force model are loaded on the error prediction model to predict the machining error. The error prediction results are substituted into the given formulas to obtain the prebending clamping forces and clamping positions. Consequently, the workpiece is prebent in terms of the calculated clamping forces and positions during the face milling operation to reduce the machining error. Finally, simulation and experimental tests are carried out to validate the correctness and efficiency of the proposed error compensation method. The experimental measured flatness results show that the flatness improves by approximately 30 percent through this error compensation method. The proposed method not only predicts the machining errors in face milling thin plate-shape parts but also reduces the machining errors by taking full advantage of the workpiece prebending caused by fixture, meanwhile, it provides a novel idea and theoretical basis for reducing milling errors and improving the milling accuracy.     

弱刚度工件夹紧顺序与夹具布局的同步优化

针对弱刚度工件在定位、夹紧过程中易变形的问题,建立了夹紧顺序与接触力及节点位移增量之间关系的数学模型,给出了各夹紧步骤中工件夹具系统的静力平衡方程;在此基础上,根据最小余能原理及库仑摩擦定律,构建了装夹方案优化模型,提出了基于遗传算法的夹具布局与夹紧顺序同步优化方法。算例结果表明,该方法有效降低了由于装夹所引起的工件变形。提高了加工精度。     

Machining Fixture Verification for Nonlinear Fixture Systems

This paper presents a fixture configuration verification methodology for nonlinear fixture systems, which is developed on the basis of optimal clamping forces and total restraint. This method can be applied for validating the feasibility of a fixture with point, line and area contacts in two stages: fixturing and machining. The "∞-∞-∞" principle for nonlinear fixture location is proposed. The automatic fixture verification system is modelled as a nonlinear optimisation problem with respect to minimum clamping forces. The method provides a simple and effective means for: (a) verifying whether a particular fixturing configuration is valid with respect to locating stability, deterministic workpiece location, clamping stability and total restraint and (b) determining minimum variable clamping forces over the entire machining time. Two case studies are presented to demonstrate the effectiveness and the capabilities of the methodology. ID="A1"Correspondance and offprint requests to: Prof. D. R. Strong, Department of Mechanical and Industrial Engineering, The University of Manitoba, Winnipeg, Manitoba, Canada R3T 5V6. E-mail: strong@ms.umanitoba.ca     

Fixture Clamping Force Optimisation and its Impact on Workpiece Location Accuracy

Workpiece motion arising from localised elastic deformation at fixture-workpiece contacts owing to clamping and machining forces is known to affect significantly the workpiece location accuracy and, hence, the final part quality. This effect can be minimised through fixture design optimisation. The clamping force is a critical design variable that can be optimised to reduce the workpiece motion. This paper presents a new method for determining the optimun clamping forces for a multiple clamp fixture subjected to quasu-static machining forces. The method uses elastic contact mechanics models to represent the fixture-workpiece contact and involves the formulation and solution of a multi-objective constrained oprimisation model. The impact of clamping force optimisation on workpiece location accuracy is analysed through examples involving a 3-2-1 type milling fixture.     

Matrix-presentation linear least square error method of inverse elastic-plastic large deformation finite element model for upsetting

The main purpose of this paper is to develop the matrix presentation linear least square error method of inverse elastic-plastic large deformation finite element model for upsetting to obtain the friction coefficients during the upsetting process. This inverse model assumed the linear material and based on the modified experimental loading increments using the linear modified experimental upsetting loading standard proposed in this paper. Then the friction coefficients of contact boundary between the workpiece and the die at specific finite element analysis stages can be derived. Finally, using the cubic spline fitting, the history of friction coefficient during the upsetting process can be obtained. It is demonstrated that the workpiece profile of upsetting experiment is quite identical to the workpiece profile of simulation using the result obtained in this paper as the history of friction coefficient of contact boundary, and furthermore the distribution of stress and strain of the workpiece during upsetting process can be understood.     

Optimal Fixture Design Accounting for the Effect of Workpiece Dynamics

This paper presents a fixture layout and clamping force optimal synthesis approach that accounts for workpiece dynamics during machining. The dynamic model is based on the Newton– Euler equations of motion, with each fixture–workpiece contact modelled as an elastic half-space subjected to distributed nor-mal and tangential loads. The fixture design objective in this paper is to minimise the maximum positional error at the machining point during machining. An iterative fixture layout and clamping force optimisation algorithm that yields the "best" improvement in the objective function value is presented. Simulation results show that the proposed optimis-ation approach produces significant improvement in the work-piece location accuracy. Additionally, the method is found to be insensitive to the initial fixture layout and clamping forces.     

Machining fixture layout design using ant colony algorithm based continuous optimization method

In any machining fixture, the workpiece elastic deformation caused during machining influences the dimensional and form errors of the workpiece. Placing each locator and clamp in an optimal place can minimize the elastic deformation of the workpiece, which in turn minimizes the dimensional and form errors of the workpiece. Design of fixture configuration (layout) is a procedure to establish the workpiece–fixture contact through optimal positioning of clamping and locating elements. In this paper, an ant colony algorithm (ACA) based discrete and continuous optimization methods are applied for optimizing the machining fixture layout so that the workpiece elastic deformation is minimized. The finite element method (FEM) is used for determining the dynamic response of the workpiece caused due to machining and clamping forces. The dynamic response of the workpiece is simulated for all ACA runs. This paper proves that the ACA-based continuous fixture layout optimization method exhibits the better results than that of ACA-based discrete fixture layout optimization method.     

基于表面网格离散化与遗传算法的复杂工件装夹布局规划方法

装夹是工件加工过程中首先面临的问题,而稳定装夹则是保证工件加工质量与生产安全的必要条件。为此系统地提出了基于稳定性指标与稳定量度的工件装夹布局优化模型及其遗传算法求解技术。根据静力平衡条件与线性规划技术,提出装夹稳定性的判断依据及其解算方法,实现装夹时工件"稳不稳"的定量描述;依据力的超椭球方程,将超椭球体积定义为装夹稳定量度,用以描述工件装夹稳定时"有多稳"的问题;引入离散化思想,构建了以使装夹稳定量度达到最大为目标的复杂工件装夹布局规划模型,根据每一代的装夹稳定性,定义个体的适应度评价函数,提出装夹布局规划模型的遗传算法求解技术。提出的基于稳定性指标与稳定量度的装夹布局规划方法,由于只涉及接触点的坐标及其法矢量信息,不仅适用于具有复杂表面的工件,而且能够避免工件处于非稳定状态下优化模型的求解过程,提高了计算效率,为复杂工件装夹布局方案的合理设计提供了基础理论。     

夹紧方案的数学建模及夹紧力的优化设计

夹紧变形有两大产生原因:由夹紧副变形导致的工件位置误差以及由夹紧力导致的工件变形。本文主要建立了夹紧副变形与工件位置误差的关系模型;并基于该模型,以最小工件位置误差为目标,实现了夹紧力的优化设计。     

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.     

MPV车桥桥壳的定位夹紧分析

运用六点定位原则,分析在MPV车桥实际生产中利用双短V型块限定工件的自由度,使工件在批量加工过程中准确占据定位元件所规定的位置,并对工件进行受力平衡分析,计算所受的切削力大小,由此估算工件加工时所需的夹紧力,选择合适的夹紧机构,以保证生产顺利进行。