Intelligent Fixture Design through a Hybrid System of Artificial Neural Network and Genetic Algorithm

In designing fixtures for machining operations, clamping scheme is a complex and highly nonlinear problem that entails the frictional contact between the workpiece and the clamps. Such parameters as contact area, state of contact, clamping force, wear and damage in the contact area and deformation of the component are of special interest. A viable fixture plan must include the optimum values of clamping forces. Along research efforts carried out in this area, this comprehensive problem in fixture design needs further investigation. In this study, a hybrid learning system that uses nonlinear finite element analysis (FEA) with a supportive combination of artificial neural network (ANN) and genetic algorithm (GA) is discussed. A frictional model of workpart–fixture system under cutting and clamping forces is solved through FEA. Training and querying an ANN takes advantage of the results of FEA. The ANN is required to recognize a pattern between the clamping forces and state of contact in the workpiece–fixture system and the workpiece maximum elastic deformation. Using the identified pattern, a GA-based program determines the optimum values for clamping forces that do not cause excessive deformation/stress in the component. The advantage of this work against similar studies is manifestation of exact state of contact between clamp elements and workpart. The results contribute to automation of fixture design task and computer aided process planning (CAPP).     

基于有限元逆算法的压边力优化

依据理想形变理论，研究开发了冲压成形过程模拟的有限元逆算法，实现了计算机程序，并利用有限元逆算法，以变形后工件中厚度分布误差为目标函数，对冲压过程中的压边力进行优化。通过实例证明了逆算法及基于逆算法的冲压工艺参数优化方法的有效性。     

Multi-Objective Approach to Automated Fixture Synthesis Incorporating Deep Neural Network for Deformation Evaluation

In machining, the synthesis of a fixturing schema significantly impacts the accuracy of the final product. Moreover, A robust and automatic configuration of fixture elements can reduce production costs and eliminate the need for expert labor to perform the task. Given the multi-modal problem of fixture synthesis, this article presents a multi-objective approach to fixture synthesis in the discrete domain. The performance criteria are localization accuracy, detachment of locators, workpiece deformation, severity and dispersion of reaction loads, and the spacing between contact points. Optimization is performed via an improved Declining Neighborhood Simulated Annealing algorithm (DNSA). To achieve consistent performance over different inputs, the number of iterations follows a Shanon entropy index reflecting the recurrence of folds/corners. Except for deformation, all other objectives are derived from the kinematic analysis of the workpiece-fixtures system. In contrast, deformation is estimated via a Constitutive Deep Neural Network (CDNN). Both models incorporate the machining loads as quasi-static intervals. A new strategy is adopted for the trade-off based on the Z-score quantification of objectives through a pre-calibration run of DNSA. Numerical examples demonstrate the implementation flow of our generalized CAD-based tool developed for the purpose. The approach is verified and proved efficient in automating the robust selection of a fixture layout for a prismatic workpiece.     

Non-jamming conditions in multi-contact rigid-body dynamics

This paper addresses an issue related to a multi-rigid-body frictional contact application, the non-jamming condition for the applying force such that the workpiece can move while maintaining existing contacts. The issue arises from the study of fixture loading planning. While rigid-body frictional contacts could restrict workpiece motion in both normal and tangential directions, it is found that the reason for jamming is from the tangential constraints by frictional forces. We first enumerate all the possible contact states for multiple contacts, and the contact constraints are classified into two categories, the configuration constraints and kinematic constraints. We then find an interesting result related with a non-jamming condition. That is, in a general situation, the applying force that can induce all-sliding contacts will never result in jamming. Moreover, a method to find the applied force on the workpiece that results in sliding on all contact points is presented, based on the sufficient condition for non-jamming. Numerical examples are presented and the results of the method are compared with the results of a quasi-static method.     

Dynamic modeling of the fixture-workpiece system

This paper presents a methodology for dynamic modeling and simulation of a fixture-workpiece system. A simulation approach is required since standards typically do not exist for dynamic situations like machining operations. In addition, an accurate model is developed for the contact interface at each locating and clamping region on the workpiece's surface. An end milling operation is simulated to analyze the effects of various factors on workpiece accuracy and demonstrate the advantage of the simulation approach. The clamping forces required to keep the workpiece in contact with its locators are obtained, and the influences of locator placement, clamp placement, clamping forces, and clamping sequence on linear and angular errors are reported. Elastic effects of the locator-workpiece and clamp-workpiece contacts, yielding nonlinear dynamic equations of motion, are included in the model. Since system dynamics are considered, results are obtained as a function of time. The study compares well with previous experimental work by other investigators, and the method shows promise as a fixture design tool.     

Finite element analysis and optimization in fixture design

Fixturing locating point synthesis considers the workpiece and the fixturing elements to be rigid, but however they are elastic and deformable. To ensure sustained quality of manufacture to meet the design tolerances, fixture design must be predictably repeatable. This paper is concerned with minimizing deformation of the workpiece due to machining loads about fixturing support positions, especially in thin castings. Finite element analysis is used in simulating the deformation of the workpiece at selected points. An optimization algorithm is developed to minimize deflections at these selected nodal points by considering the support and tool localtions as design variables. The resulting support locations and tool point designs ensure part support, kinematic closure and minimal workpiece deflections during machining.     

STEP-NC compliant approach for setup planning problem on multiple fixture pallets

Manufacturing system configuration is a broad problem that involves various topics concerning workpiece, cutters, fixture and machine. This paper presents an approach to solve the setup planning problem on machining centres based on a STEP-NC compliant data structure. The aim of this approach is to shorten the time required for the process planning activity by automating some time-consuming steps without compromising the solution accuracy. In the proposed approach, a CAM software tool is employed to associate the geometric and technological data regarding the product. Using the proposed data structure, a method is proposed for solving the setup planning problem based on mathematical programming. The developed approach has been tested on a real case.     

The stencil buffer sweep plane algorithm for 5-axis CNC tool path verification

A new algorithm based on the sweep plane approach to determine the machined part geometry in 5-axis machining with general APT tools is presented. Undercut and overcut can be determined. Collision detection between the toolholder, workpiece and workpiece fixture can also be detected. The subtraction of the removed material is obtained for each sweep plane by using a stencil buffer. A flat plane is swept through the blank part, fixture and tool swept volume geometry. The intersections of sweep planes and the swept tool volume are computed based on the canonical representation of a cone, torus and sphere. The necessary data to compute all the intersections is stored in a text file, here called the M-Plane file (Memory Plane). The equations of the intersections are approximated by a polygon with variable accuracy. The resulting APT tool intersection in each sweep plane is then clipped against the blank workpiece intersection with the current sweep plane. The stencil buffer provides automatically the union of all tool intersections and the subtraction from the blank workpiece. This algorithm provides a 3D geometric model of the tool swept volume. The display algorithm is based on the Painter's algorithm, but there is no time consuming sorting from back to front required, as the sweep proceeds from back to front. The accuracy of the algorithm can be varied as a function of the requirements by changing the polygon approximation and the distance between the sweep planes.     

基于GA和FEM的夹具布局和变夹紧力优化设计

通过夹具布局和夹紧力大小的优化可以提高薄壁件加工精度．建立了夹具布局和变夹紧力分层优化模型．首先,以工件加工变形最小化和变形最均匀化为目标函数,对夹具布局进行优化设计;其次,基于优化的夹具布局对变夹紧力进行设计．采用有限元法计算工件的加工变形,加工变形求解时综合考虑了接触力、摩擦力、切削力、夹紧力和切屑的影响．采用遗传算法求解优化模型,获得优化的夹具布局和变夹紧力．通过实例分析,验证了分层优化设计方法可以进一步减小工件加工变形,提高加工变形均匀度．     

Top-Rem grinding tool modification considering loaded edge contact for spiral bevel gears

Focusing on the collaborative manufacturing requiring meshing interface physical performances, an innovative Top-Rem grinding tool modification considering loaded edge contact is proposed for spiral bevel gears. Accurate Top-Rem grinding tool parameters can instead of machine-tool settings and their impact in the sophisticated flank topography correction technique. At first, the whole Top-Rem tool modification includes: i) arc-shaped blade part; ii) Top-Rem part; iii) top fillet part. Then, grinding tool modification model considering both loaded contact and geometric accuracy is established. Where, three important constraint conditions were taken into accounts: i) geometric boundary considering loaded edge contact, ii) root overcutting, and iii) flank geometric accuracy. Moreover, two kinds of optimization strategies are proposed to improve the accuracy and efficiency of the whole modification: i) two types of modification by the different tool modification parameters; ii) sensitivity analysis with respect to ease-off for optimization operation of the unknown variables. Finally, the given instances can verify that it can get accurate and effective loaded contact performance optimization in early stage of full life cycle product development.     

Data-driven bending fatigue life forecasting and optimization via grinding Top-Rem tool parameters for spiral bevel gears

To establish a bridge between grinding tool parameters and loaded tooth fatigue life, an innovative data-driven root flank bending fatigue life forecasting and optimization via Top-Rem tool parameters was proposed for grinding spiral bevel gears. The recent machine settings modification is extended into grinding Top-Rem tool parameters modification in case that geometric accuracy and root bending fatigue life are integrated into a collaborative optimization. The proposed Top-Rem modification includes three key steps: (I) arc-shaped blade, (II) top part, and (III) top fillet part. Then, while root bending stress is determined by using finite element method (FEM)-based simulated loaded tooth contact analysis (SLTCA), data-driven fatigue life forecasting is developed by correlating with the multiaxial fatigue damage model based assessment. Moreover, data-driven bending fatigue life optimization model is established by using Top-Rem tool parameters modification, where the important constraints in target flank determination includes: (i) root overcutting, (ii) geometric accuracy, and, (iii) fatigue life. For high accuracy and efficiency, two different strategies are proposed: (i) the different parameters modification types; and, (ii) sensitivity analysis of grinding Top-Rem tool parameters. Finally, proposed method can verify that bending fatigue life can be significantly improved by modifying the key Top-Rem tool parameters in early stage of the whole life product development for spiral bevel gears.     

Surface Smoothing Procedures in Computational Contact Mechanics

This work addresses the problems arising in the finite element simulation of contact problems undergoing large deformation. The frictional contact problem is formulated in the continuum framework, introducing the interface laws for the normal and tangential stress components in the contact area. The variational formulation is presented, considering different methods to enforce the contact constraints. The spatial discretization within the finite element method is applied, as well as the temporal discretization required to solve the three sources of nonlinearities: geometric, material and frictional contact. The discretization of contact surfaces is discussed in detail, including different surface smoothing procedures. This numerical strategy allows to solve the difficulties associated with the discontinuities in the contact surface geometry introduced by finite element discretization, which leads to nonphysical oscillations of the contact force for large sliding problems. The geometrical accuracy of different interpolation methods is evaluated, paying particular attention to the Nagata patch interpolation recently proposed. In this framework, the Node-to-Nagata contact elements are developed using the augmented Lagrangian method to regularize the variational frictional contact problem. The techniques used to search for contact in case of large deformations are discussed, including self-contact phenomena. Several numerical examples are presented, comprising both the contact between deformable and rigid obstacles and the contact between deformable bodies. The results show that the accuracy and robustness of the numerical simulations is improved when the contact surface is smoothed with Nagata patches.     

应用Two-Stage方法的薄板零件定位策略优化设计

针对当前柔性薄板夹具定位策略优化需要大量的有限元分析,限制了夹具设计的效率和质量的问题,为了减少有限元分析的次数,提出一种基于Two-Stage方法的夹具定位方案设计方法.该方法以刚体模型为基础,应用粒子群算法进行三定位点优化,再建立基于径向基函数的响应面模型优化其他定位点.通过尾灯支架板实例对文中方法进行优化的结果表明,其具有良好的模拟效果和较高的预测精度.     

Study of variational inequality and equality formulations for elastostatic frictional contact problems

Summary An overview ofvariational inequality andvariational equality formulations for frictionless contact and frictional contact problems is provided. The aim is to discuss the state-of-the-art in these two formulations and clearly point out their advantages and disadvantages in terms of mathematical completeness and practicality. Various terms required to describe the contact configuration are defined.Unilateral contact law and classical Coulomb’s friction law are given.Elastostatic frictional contact boundary value problem is defined. General two-dimensional frictionless and frictional contact formulations for elastostatic problems are investigated. An example problem of a two bar truss-rigid wall frictionless contact system is formulated as an optimization problem based on the variational inequality approach. The problem is solved in a closed form using the Karush-Kuhn-Tucker (KKT) optimality conditions. The example problem is also formulated as a frictional contact system. It is solved in the closed form using a new two-phase analytical procedure. The procedure avoids use of the incremental/iterative techniques and user defined parameters required in a typical implementation based on the variational equality formulation. Numerical solutions for the frictionless and frictional contact problems are compared with the results obtained by using a general-purpose finite element program ANSYS (that uses variational equality formulation). ANSYS results match reasonably well with the solutions of KKT optimality conditions for the frictionless contact problem and the two-phase procedure for the frictional contact problem. The validity of the analytical formulation for frictional contact problems (with one contacting node) is verified. Thevariational equality formulation for frictionless and frictional, contact problems is also studied in detail. The incremental/iterative Newton-Raphson scheme incorporating the penalty approach is utilized. Studies are conducted to provide insights for the numerical solution techniques. Based on the present study it is concluded that alternate formulations and computational procedures need to be developed for analysis of frictional contact problems.     

Model testing of fixture–workpiece interface compliance in dynamic conditions

This paper is focused on the problem of compliance of interface between clamping/locating fixture elements and workpiece, under dynamic loads during machining. In contrast to previous investigations, the authors have developed a special device dedicated to testing of physical models which represent clamping/locating elements and workpiece. This device allows optimization of a large number of input parameters which are critical to interface compliance. It was used in experimental investigations to establish the impact that the radius of the spherical tip of a clamping/locating element has on the interface compliance and load capacity. The results of experimental investigation show that, under certain conditions, the clamping/locating elements with larger-radius spherical tips provide significantly lower interface compliance. Future investigations should be aimed at finding optimum macro- and micro-geometries of contact interface, as well as the selection of materials for clamping/locating elements.     

Automated modular fixture planning: Geometric analysis

Attendant Processes such as fixture and die design are often a necessary but time-consuming and expensive component of a production cycle. Coupling such attendant processes to product design via feature-based CAD will lead to more responsive and affordable product design and redesign. In the context of on-going research in automating fixture configuration design, this paper presents a fundamental study of automated fixture planning with a focus on geometric analysis. The initial conditions for modular fixture assembly are established together with geometric relationships between fixture components and the workpiece to be analyzed. Of particular focus is the design of alternative locating points and components, together with examples of 3-D fixture designs.     

Automated modular fixture planning: Accuracy, clamping, and accessibility analyses

Attendant Processes such as fixture and die design are often a necessary but time-consuming and expensive component of a production cycle. Coupling such attendant processes to product design via feature-based CAD will lead to more responsive and affordable product design and redesign. In the context of on-going research in automating fixture configuration design, this paper presents a fundamental study of automated fixture planning with a focus on geometric analysis. The initial conditions for modular fixture assembly are established together with geometric relationships between fixture components and the workpiece to be analyzed. Of particular focus is the design of alternative locating points and components, together with examples of 3-D fixture designs.     

Modeling of cutting geometry and forces for 5-axis sculptured surface machining

5-Axis sculptured surface machining is simulated using discrete geometric models of the tool and workpiece to determine the tool contact area, and a discrete mechanistic model to estimate the cutting forces. An extended Z-buffer model represents the workpiece, while a discrete axial slice model represents the cutting tool. Determination of the contact area for a given tool move requires a swept envelope (SWE) of the tool path. The SWE is used to find the intersections of the tool envelope with Z-buffer elements (ZDVs) representing the workpiece. A 3-axis approximation of the 5-axis tool movement is used to simplify the calculations while maintaining a desired level of accuracy. The intersection of the SWE with each ZDV yields segments which are used to find the contact area between the cutter and the workpiece for a given tool path. The contact area is subsequently used with the discrete force model to calculate the vector cutting force acting on the tool.     

基于工艺特征约束的改进遗传算法

为提高飞机装配的精度,减小定位的误差,优化具有复杂工艺特征的机身框件的支撑序列.针对优化中工艺特征约束处理问题,建立了工艺特征约束的广义数学模型,从理论角度提出了一种针对此类约束的不可行解修补算法,并基于此算法设计一种改进的遗传算法.使用改进的遗传算法优化某型飞机机身框在可重构柔性工装上的支撑序列,优化过程稳定,最优序列下框的柔性定位误差减小93.08%,保证了飞机装配的精度.理论基础分析和仿真结果分析表明,改进的遗传算法通用性强,适用于各种约束优化问题;收敛速度快且稳定,具备可行性.     

Parametric shape optimization techniques based on Meshless methods: A review

In the product development process, structural optimization plays vital role because it deals with size, shape and topology of the structures. However, structural performance greatly depends on its geometric shape and hence structural shape optimization has remained one of the most active research areas since early 1970s. Conventional parametric shape optimization technique employs grid-based numerical tools like FEM and BEM for structural analysis, which experiences some innate limitations like mesh distortion and frequent remeshing, element locking and poor approximation while dealing with large shape changes during the optimization process. Meshless Methods (MMs) can alleviate these issues when used as a structural analysis tool in shape optimization. In last two decades, MMs have been explored for structural shape optimization along with various deterministic and stochastic optimization algorithms. The objective of present work is twofold, first is to review advanced parametric shape optimization techniques which are based on MMs like Element Free Galerkin (EFG) method and Reproducing Kernel Particle Method (RKPM) for linear elastic, thermoelastic, hyperelastic, frictional contact and structure dynamics optimization problems and second is to emphasize benefits of meshless techniques in shape optimization. Based on the review, the article presents some critical observations including Design Sensitivity Analysis (DSA) in meshless environment, numerical integration techniques in MMs and benefits of coupled FEM-MM approach in shape optimization. At the end, promising future research directions in shape optimization field based on MMs are presented along with concluding remarks.