Finite element modeling of fixture–workpiece contacts: single contact modeling and experimental verification

Knowledge of workpiece elastic deformation and reaction forces are essential for machining surface error prediction and stability analysis of the fixture–workpiece system. A finite element (FE) model of the fixture–workpiece system is well-suited for predicting workpiece elastic deformation and reaction forces as it can easily account for all sources of compliance in the system. However, the reaction forces and workpiece elastic deformations predicted by the FE model are known to be very sensitive to the boundary conditions used to model the fixture–workpiece contact interface. In this paper, the effects of different FE boundary conditions on the deformation and reaction force predictions for a single fixture–workpiece contact are analyzed. Specifically, frictional contact elements, and nodal force and displacement boundary conditions applied to spherical–planar and planar–planar locator and clamp contact geometries are considered. The effects of workpiece compliance on the prediction accuracy are also evaluated. Based on this study, specific guidelines for FE modeling of locator–workpiece/clamp–workpiece contacts are developed and verified through experiments.     

A model to predict minimum required clamp pre-loads in light of fixture–workpiece compliance

The determination of minimum required clamp pre-loads is an important process in the design of machining fixtures. This paper presents a linear, clamp pre-load (LCPL) model that can be applied to fixture–workpiece systems whose compliance is load invariant. The model considers the static deformation of the fixture–workpiece system in response to the clamping process and the machining process. Sources of compliance throughout a fixture–workpiece system are considered. The model computes the minimum required pre-loads necessary to prevent workpiece slip at the fixture–workpiece joints throughout the machining process.This paper also describes an experimental study that was used to characterize the accuracy of the LCPL model with regard to the application of a ramping external load to a fixture–workpiece system. Over the contact conditions tested, the LCPL model was observed to overestimate the minimum required clamp pre-loads by an average of 7%. This experimental study also revealed the sensitivity of the computed pre-loads to the relative compliance of the fixture elements as well as the coefficient of friction.     

Improved workpiece location accuracy through fixture layout optimization

Inaccuracies in workpiece location lead to errors in position and orientation of a machined feature on the workpiece. The ability to accurately locate a workpiece in a machining fixture is strongly influenced by rigid body displacements of the workpiece caused by elastic deformation of loaded fixture–workpiece contacts. This paper presents a model for improving workpiece location accuracy in fixturing. A discrete elastic contact model is used to represent each fixture–workpiece contact. Reduction in workpiece locating error due to rigid body displacements is achieved through optimal placement of locators and clamps around the workpiece. The layout optimization model is also shown to improve the overall workpiece deflection and reaction force characteristics.     

Analysis of the effects of fixture clamping sequence on part location errors

Several fixture-related error sources are known to contribute to part location error, which can lead to poor part quality. In addition to typical error sources, such as fixture geometric error and elastic deformation of the fixture and part due to clamping forces, the clamping sequence used can also influence part position and orientation. In this paper, the effect of clamping sequence on workpiece location error is modeled analytically for a fixture–workpiece system where all major compliance sources and fixture geometric error are considered. Part location error is quantified by the displacement of a response point on the part surface. An algorithmic procedure designed to understand how forces and deformations change as clamps are applied sequentially is presented. The effect of clamping sequence on part location error and locator reaction force is examined through model simulations and experiments via an example involving a 3-2-1 machining fixture.     

Finite element method based machining simulation environment for analyzing part errors induced during milling of thin-walled components

The rigid body motion of the workpieces and their elastic–plastic deformations induced during high speed milling of thin-walled parts are the main root causes of part geometrical and dimensional variabilities; these are governed mainly from the choice of process plan parameters such as fixture layout design, operation sequence, selected tool path strategies and the values of cutting variables. Therefore, it becomes necessary to judge the validity of a given process plan before going into actual machining. This paper presents an overview of a comprehensive finite element method (FEM) based milling process plan verification model and associated tools, which by considering the effects of fixturing, operation sequence, tool path and cutting parameters simulates the milling process in a transient 3D virtual environment and predicts the part thin wall deflections and elastic–plastic deformations during machining. The advantages of the proposed model over previous works are: (i) Performs a computationally efficient transient thermo-mechanical coupled field milling simulation of complex prismatic parts comprising any combination of machining features like steps, slots, pockets, nested features, etc., using a feature based milling simulation approach; (ii) Predicts the workpiece non-linear behavior during machining due to its changing geometry, inelastic material properties and fixture–workpiece flexible contacts; (iii) Allows the modelling of the effects of initial residual stresses (residing inside the raw stock) on part deformations; (iv) Incorporates an integrated analytical machining load (cutting force components and average shear plane temperature) model; and (v) Provides a seamless interface to import an automatic programming tool file (APT file) generated by CAM packages like CATIA V5. The prediction accuracy of the model was validated experimentally and the obtained numerical and experimental results were found in good agreement.     

Determination of minimum clamping forces for dynamically stable fixturing

This paper presents a model-based framework for determining the minimum required clamping forces that ensure the dynamic stability of a fixtured workpiece during machining. The framework consists of a dynamic model for simulating the vibratory behavior of the fixtured workpiece subjected to time- and space-varying machining loads, a geometric model for capturing the continuously changing geometry and inertia of the fixture–workpiece system during machining, a static model for determining the localized fixture–workpiece contact deformations due to clamping, a model for checking the dynamic stability of the fixtured workpiece, and a model for determining the optimal set of clamping forces that satisfies the stability criteria for a given machining operation. The clamping force optimization problem is formulated as a bilevel nonlinear programming problem and solved using the Particle Swarm Optimization (PSO) technique featuring computational intelligence. A simulation example solved using the developed approach reveals that the minimum required clamping forces for dynamically stable fixturing are significantly affected by the fixture–workpiece system dynamics and its continuous change during machining due to the material removal effect.     

An experimental evaluation of coefficients of static friction of common workpiece–fixture element pairs

Most machining fixtures utilize clamping forces and friction at fixture–workpiece joints to help prevent the workpiece from slipping out of the fixture during machining. The magnitudes of the clamping forces required are a direct function of the coefficients of static friction at the joints. Recently, analytical methods have been developed to predict minimum clamping forces. However, these methods require accurate estimates of the friction coefficients.One source of friction data are handbooks. However, these data are typically listed relative to the materials of the contacting elements and are otherwise completely generalized. This paper will illustrate that the coefficient of static friction for typical fixture–workpiece joints is not a simple function of the workpiece materials. Instead it is also a function of factors such as fixture element geometry, workpiece surface topography, clamping forces, the presence or absence of cutting fluids, and normal joint rigidity.     

A model for synthesis of the fixturing configuration in pin-array type flexible machining fixtures

This paper presents a model for the synthesis of the fixturing configuration in pin-array type flexible machining fixtures. These fixtures possess an array of pins that hold parts by conforming to their shape. The proposed algorithm aims to achieve a specified level of fixture–workpiece conformability and stable equilibrium while keeping the workpiece rigid body motion due to fixture elastic deformation at or below a user-specified value. Specifically, the model finds the minimum clamping loads and the optimal number, position and dimensions of the pins necessary to achieve the conformability and stiffness goals for a workpiece having an arbitrary geometry and subjected to quasi-static machining/assembly forces. Experimental data for the X-clamp^® flexible pin-array vise is used to validate the proposed synthesis model.     

Flexible multibody dynamics based fixture-workpiece analysis model for fixturing stability

The machining force and torque exerted on a workpiece vary as the cutter moves along the tool path, therefore a dynamic approach is essential for fixturing stability analysis. This paper presents a technique to dynamically model and analyze the fixture-workpiece system subjected to time-varying machining loads. Combining the advantages of FEA (Finite Element Analysis) and nonlinear rigid body dynamics, a flexible multibody dynamic model is formulated to incorporate the overall interaction (clamping forces, machining loads, and contact friction) between flexible workpiece and compliant fixture elements. Three major parameters affecting the fixturing stability, namely the magnitude, application sequence, and placement of fixturing clamps, are analyzed. Additionally, the time dependent deformation of a flexible workpiece under clamping and machining loads is estimated. A scaled engine block with the 3–2–1 fixturing scheme subjected to face milling operation is given as an example. Comparison between the simulation result and experimental data shows a reasonable agreement.     

航空薄壁件铣削加工铣削力预测方法研究

铣削加工中铣削力是导致加工变形的直接原因,而航空薄壁件加工中,加工变形是加工误差产生的主要因素.本文以航空薄壁件铣削加工过程的铣削力为研究对象,通过确定铣削力模型和切削系数参数,建立了刚性和考虑刀具工件变形耦合的柔性预测两种模型.在柔性模型中,采用预扭Timoshenko梁单元的刀具/工件独立建模的方法建立有限元模型,利用Python语言在通用有限元软件Abaqus下迭代求解.实验验证表明预测模型具有很高的准确性和有效性.     

An investigation of the effectiveness of fixture layout optimization methods

Deriving the optimal layout of fixture elements is critical to minimizing the impact of fixture–workpiece deformation on machined feature error. Various optimization methods for solving this problem have been reported. Unfortunately no investigation has been executed to compare their relative performance. This paper presents the methodology and results of an extensive investigation into the relative effectiveness of the main elements of these competing methods. All methods were tested over a broad range of conditions. Performance measures that were tracked included solution quality, solution repeatability, and computation time. The results of this investigation show that the best overall performance is provided by optimization methods that use both the genetic algorithm and continuous interpolation for the distribution of boundary conditions.     

一种高精密液胀定位夹具的优化设计

考虑到薄壁套筒的薄壁长度、厚度,薄壁套筒环状凹槽的深度以及薄壁所受液压力的大小对工件的变形量、定位精度和夹紧力会造成影响,应用ANSYS平台对液胀定位夹具进行有限元建模,分析得出了薄壁套筒薄壁长度、厚度等参数对工件夹紧变形的影响规律,并且通过对目标进行结构优化设计,获得了优化的结构参数,优化后的结构使得液压油密封性能更好,工件和薄壁套筒变形更小,同时能够得到良好的夹紧力矩。结果表明:工件的变形量从1.5μm减小到0.9μm,薄壁套筒最大应力由292.88 MPa减小到282.34 MPa,薄壁套筒两端结合面径向变形由11.8μm减小到8.6μm,夹紧力矩由124.36 N·m减小到67.33 N·m。     

Deformation analysis for cold rolling of Al-Cu double layered sheet by physical modeling and finite element method

The deformation characteristics of Al-Cu double layered sheet during rolling with various process parameters were studied by both a physical modeling technique and the finite element method. Physical modeling and the finite element method are complementary, due to their different advantages and limitations. Physical modeling simulates metal forming operations by using a model workpiece under conditions similar to those in actual production. The deformation characteristics of double layered sheet during rolling were also simulated using a commercial finite element code, FORGE?. The effects of process parameters, such as total reduction ratio, initial thickness ratio and differential speed ratio on the rolling characteristics were the primary focus of the investigation. In addition, an analytical model for double layered sheet rolling is also proposed with the use of a force-thickness diagram. From the results, the effect of the process parameters on the rolling of the Al-Cu double layered sheet has been determined.     

Experimental determination of the friction coefficient on the workpiece-fixture contact surface in workholding applications

Surface flatness, geometric integrity and micro-surface finish characteristics are crucial for automotive industry to properly seal joints, reduce leakage and consequently increasing engines efficiency and reducing emissions. Optimum fixture layout is a key element in achieving this goal. Machining of flexible parts impose further challenges to the selection of a proper fixture scenario.Workpiece motion arising from localized elastic deformation at the workpiece/fixture contacts due to machining and clamping forces significantly affect the workpiece location accuracy and hence the machined part quality. The tangential friction force plays an important role in fixture configuration design as it can be utilized to reduce the number of fixture components, thereby the workpiece features accessibility to machining operations and providing a damping mechanism to dissipate input energy from machining forces out of the workpiece/fixture system.Although the literature is full of research on friction and its application, it lacks research that relates to the contact found in workpiece/fixture systems. This paper presents the results of an experimental investigation of the workpiece/fixture contact characteristics.     

多腔缸体零件端面铣削加工的高精密夹具设计及其优化

针对发动机多腔体缸体的结构复杂和刚度小的问题,对该缸体铣削端面加工工序确定高精密夹具的定位和夹紧方案.在初步分析夹具方案之后,运用有限元法对夹具的主要零件进行了变形分析和计算,并在此基础上对夹具结构进行了优化,最终确定了高精密夹具设计新方案.结果表明优化得到的设计方案优于经验设计方案,提高了夹具的定位和夹紧精度,从而保证了加工质量,在实际生产中效果良好.     

纵向旋转切削加工对环形零件畸变的影响

通过旋转试验和有限元分析介绍了工件在切削加工过程中产生的畸变情况，分析了工件的装夹方式、切削速度、切削深度和进刀量对100Cr6钢环圆度的影响。通过去应力退火释放冷加工诱发的残余应力后工件的圆度与切削参数有关。另外测试了被试验环的表面残余应力，其表面残余应力与装夹方式有关。将测量的装夹力作为计算参数输入，通过有限元分析方法测试了装夹方式对工件变形的影响。协同测量结果示出了装夹方式影响工件变形的一个主要因素，表面残余应力与工件的径向变形有关，最大的拉伸应力位于夹口位置。旋转切削试验结果表明，提高切削速度圆度会稍有增加；随着切削深度的加大，圆度呈下降趋势，尽管切削力增加了；进给量的增加会导致更高的切削力，因此圆度值也增加；常规的去应力退火可使被加工环的圆度值增加。     

Analysis–synthesis of dimensional deviation of the machining feature for discrete-part manufacturing processes

Dimensional deviation analysis has been an active and important research topic in mechanical design, manufacturing processes, and manufacturing systems. This paper proposes a comprehensive dimensional deviation evaluation framework for discrete-part manufacturing processes (DMP). A generic, explicit, and transmission model is developed to describe the dimensional deviation accumulation of machining processes by means of kinematic analysis of relationships between fixture error, datum error, machine tool geometric error, fixturing force inducing error and the dimensional quality of the product. The developed modeling technology can deal with general fixture configurations. In addition, the local contact deformations of the workpiece–fixture system are determined by solving a nonlinear programming problem of minimizing the total complementary energy of the frictional workpiece–fixture subsystem in machining system. Moreover, the deviation of an arbitrary point on machining feature can be also evaluated based on a point deviation model with prediction dimension deviation from the transmission model. The dimensional error transmission within the machining process is quantitatively described in this model. A systematic procedure to construct the model is presented and validated. This model can be also applied to process design evaluation for complicated machining processes.     

基于BP神经网络的磨床力误差补偿方法

为建立磨削加工参数与磨削力导致的力变形误差之间的关系模型,提出基于神经网络的力误差建模和实时补偿方法.建立经遗传算法优化的BP神经网络以表征磨削参数与磨削力的关系;运用有限元方法对零件进行力学分析,建立磨削力与力变形量的关系模型;建立加工参数与切削力误差映射模型,预测误差补偿量,进行实时补偿.实验结果表明:该切削力误差...     

基于遗传算法的接头类薄壁件装夹布局优化设计

以接头类薄壁件为研究对象,针对其在铣削加工中装夹位置的优化设计进行研究。利用UG对四刃立铣刀和零件进行了三维建模。通过有限元分析软件ABAQUS,对不同装夹位置对接头结构件变形的影响进行了模拟。以平均变形量最小为目的,基于MATLAB遗传算法对装夹位置进行了优化计算,确定了最优装夹位置。为航空接头结构件铣削加工中装夹位置对变形的控制提供了有效的方法。     

Analysis of the machining accuracy when dry turning via experiments and finite element simulations

Workpiece and tool are subjected to severe mechanical and thermal loads when turning. These loads cause thermal expansions and mechanically induced deflections of the tool and the workpiece. Such deformations induce deviations from the nominal workpiece geometry. In order to decrease these deviations, the cutting condition needs to be optimized prior to actual machining. In this paper, the accuracy of machining when dry turning aluminum is analyzed via experiments and finite element simulations. For this purpose, seven characteristic values were used: the forces, the deflection of the workpiece, the quantity of heat in the workpiece, the temperature distribution in the workpiece, the temperature of the tool, the temperature of the tool holder, and the actual dimension of the workpiece after turning. These experimentally determined results serve in addition as boundary conditions for a 3D finite element model of the workpiece, which calculates the deformations of the workpiece. The continuous removal of material affecting the temperature distribution in the workpiece is considered. The actual dimensions of the workpiece after turning revealed a remarkable influence of the cutting condition used on the accuracy of machining. Differences of up to 116 μm regarding the deviation from the nominal workpiece diameter of 30 mm were observed. The analysis of the machining accuracy reveals that particularly the use of both high cutting speeds and feeds enhances the accuracy of machining when dry turning aluminum.