Fixturing analysis methods for calculating the contact load distribution and the valid clamping regions in machining processes

In the present work, two analysis methods for analysing fixturing systems in machining processes are presented in order to determine the most suitable clamping regions. The first involves calculating the contact load at the fixture-workpiece interface using a simple and direct mathematical tool, which simplifies the deformation minimisation problem. The second method starts from the contact load data obtained and solves several cases in which the clamping position varies. From these data, it is possible to ascertain the interpolating equations, where the load contact is defined as a function of the clamping position. Then, the border curves which limit the valid clamping regions are calculated by imposing two fixturing conditions on the interpolating equations.     

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.     

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。     

Microclamping principles from the perspective of micrometrology – A review

This paper gives an overview of the field of clamping and gripping principles from the viewpoint of sample fixturing for dimensional metrology for microobjects. The requirements for clamping microcomponents that allow dimensional measurements are therefore explained before principles and solutions of microclamps as found in literature are reviewed and evaluated on basis of these requirements. Results show that there is no single superior clamping principle or method of implementation but rather several effective solutions for specific applications. The core value of this paper is the link between requirements for sample fixturing in dimensional micrometrology and the many approaches already investigated in the field of microclamping. A radar chart and a decision tree summarize and visualize the major aspects of this review. Finally, directions of future key research areas are suggested.     

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     

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。     

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.     

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.     

Development of a novel coordinate transposing fixture system

A novel quick action flexible fixture for two-dimensional clamping is fitted with sensors for automatically measuring the positions of the clamping surfaces and the vice opening. An algorithm is proposed to determine the location and orientation of the workpiece on the fixture. The NC codes preprogrammed with a given origin and orientation can then be modified with these data to appropriately transposed coordinates, which can then be downloaded to the NC controller for NC machining. With this system, the time and cost of fixturing will be greatly reduced.     

The structural variation of the gas diffusion layer and a performance evaluation of polymer electrolyte fuel cells as a function of clamping pressure

Interfacial contact resistance between gas diffusion layers (GDLs) and bipolar plates (BPs) has a substantial effect on the performance loss of polymer electrolyte fuel cells (PEFCs). Particularly during the final manufacturing process of a fuel cell stack, an externally applied clamping load determines the extent of electrical contact between those two solid components. In order to have the least electrical contact loss, it is highly necessary to keep all PEFC components close each other without causing structural failure of fuel cell stacks. In the present work, we investigated the effect of the clamping pressure on extrinsic properties such as porosity and permeability, which is closely related to mass transfer of reactants. Also, the variance of interfacial electrical resistance was analyzed as a function of the stack clamping pressure or the compressed GDL thickness, which reflects the external clamping load. Then with these experimentally obtained material properties of GDL, computational efforts were made to account for the effect of the clamping pressure on the fuel cell performance.     

An expert system for fixturing design for face milling using modular fixture

The research objective of this paper is to develop an expert system for a modular fixture. We provide a complete fixturing procedure analysis for workpieces with different shapes such as L, I, T, and U types. In this system AutoCAD is used to draw the workpiece; then the data for points, lines, and faces are dealt with. Using the knowledge presentation method, the clamping position of the modular fixtures, the kinematics constraint balance and the fixture and cutting forces are determined. Integer programming is used to arrive at an optimal arrangement. In addition, the system provides a learning concept incorporating knowledge from experience and heuristic rules to enable repeated self-learning to compensate for the lack of knowledge. Finally, some examples are demonstrated.     

FIX-DES: A computer-aided modular fixture configuration design system

This paper presents a computer-aided modular fixture configuration design system: FIX-DES. When fixturing requirements are specified as locating/clamping surfaces and points, a fixture configuration will be automatically generated by

1. Selecting fixture elements from a fixture element database to form fixture units based on fixture element assembly relationships.
2. Placing the fixture units and elements into position on a baseplate while the fixturing requirements and assembly relationships (e.g. hole alignments) are maintained.

The fixture element assembly relationships can be established automatically when the geometric models and fixturing functions of the fixture elements are specified so that the FIX-DES system can be applied easily to different fixture systems. The system also provides the interactive design and design modification functions for human expert involvement. The system was developed with core programs in C and C++ and interface programs in a specific CAD environment. The system has been successfully applied in industry and can be transferred easily to other CAD systems. The overall structure of the FIX-DES system is introduced in the paper. The development of the automated fixture configuration design (AFCD) functions are presented in detail. Finally a fixture configuration design example is given to illustrate the application of the system.     

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。     

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。     

NOMEX蜂窝芯高速铣削加工工艺的优化

为了解决NOMEX蜂窝芯高速铣削加工过程中固持可靠性差和加工效率低以及加工表面质量差的问题，提出一种新的基于强磁场和摩擦学原理的蜂窝芯高速加工固持方法。该方法利用灌入蜂窝孔中的铁粉自重以及强磁场平台对铁粉产生的吸引力，在铁粉与蜂窝孔侧壁之间以及蜂窝、铁粉与固持平台之间产生摩擦力，实现对蜂窝底部的全约束和固定。建立了NOMEX蜂窝芯高速铣削加工的铣削力模型，进行了以铣削力最小为目标的铣削参数的优化。通过铣削参数的优化，保证了加工过程中蜂窝的固持稳定性，同时保证了蜂窝加工效率和加工质量。     

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.     

Characterization of fretting wear behavior of Cu–Al coating on Ti–6Al–4V substrate

Fretting wear and fretting fatigue are two commonly observed material damages when two contacting bodies with a clamping load are under the oscillatory motion. In this study, fretting wear damage of Cu–Al coating on titanium alloy, Ti–6Al–4V substrate was investigated using the dissipated energy approach. Fretting tests were conducted with either no fatigue load or the maximum fatigue load of 300 MPa and stress ratio of 0.1 on the substrate (specimen). In order to investigate the effect of contact load and contact size, different pad sizes and contact loads were used in the tests. Accumulated dissipated energy versus wear volume data showed a linear relationship regardless of fatigue loading condition on specimen with the smaller pad size. However, two separate linear relationships were observed based on the fatigue loading condition with the larger pad size, such that a relatively more dissipated energy was required for a certain amount of wear with fatigue load on the specimen. The linear relationship between the accumulated dissipated energy and wear volume for both pad sizes extended from partial to gross slip regimes and was not affected by the applied contact load. Further, fretting tests with and without fatigue load resulted in different shapes of fretting loops when the larger pad size was used.     

Experimental investigation of the performance of a reconfigurable fixturing system

A reconfigurable fixturing system has been developed for computer-integrated assembly environments. The fixturing system employs a number of fixture modules that are set-up, adjusted and changed automatically by the assembly robot without human intervention. A commercially available computer-aided design (CAD) package with the help of a dedicated software program is used for the design, analysis, and verification of the fixture layout. The robot program for setting-up, adjusting, and dismantling the designed fixture is generated automatically. This paper presents and discusses the accuracy of such a reconfigurable fixturing system in view of the off-line programming techniques. The experimental techniques to measure the accuracy and repeatability for setting-up the fixture are presented. The measured results of the robot positioning various types of locating fixture modules are presented and compared with the intended position settings. From the comparison, the accuracy that is to be expected from such an approach to fixturing and measures for improvement are discussed. The cycle times involved in setting-up the fixture modules are also presented and analysed. These results provide an initial guide for manufacturing industries interested in employing such systems in their computer-integrated assembly environment.