CHAPTER 2 LITERATURE REVIEW

Transcription

1 7 CHAPTER 2 LITERATURE REVIEW 2.1 INTRODUCTION The current state of knowledge in the area of fixture design and optimization is reviewed in this chapter. However, the Literature on fixture configuration system requires the details in the following areas: Machining errors Fixture design Workpiece model - rigid body model, workpiece-fixture elastic contact model and workpiece elastic model Fixture stability analysis Finite Element Method (FEM) Fixture configuration / Layout design Friction at workpiece-locator contact point Fixture layout optimization methods Clamping force optimization

2 8 Number of fixture elements optimization Genetic Algorithm (GA) Artificial Neural Networks (ANN) Design of Experiments (DOE) 2.2 STUDIES RELATED TO MACHINING ERRORS To begin with, imperfections in manufacturing processes induce machining errors in components. Machining errors are introduced, transformed and accumulated when the workpiece is being machined. Djurdjanovic and Ni (2001) proposed an analytical engineering tool for machining error analysis and root cause identification. Static form errors in the peripheral milling of complex thin-walled workpieces have been predicted by Wan et al (2005) using the finite element formulation. Also they investigated cutter modelling, finite element discretization of cutting forces, tool-workpiece coupling and variation of the workpiece s rigidity in milling. An error compensation model by considering the geometric and cutting force induced errors in a 3-axis CNC milling machine has been proposed (Raksiri and Parnichkun 2004) and the combination of geometric and cutting force induced errors are modelled by the combined back propagation neural network. The influence of the wear of the cutting tool on machining errors has been demonstrated by an experimental study (Rahou et al 2010) and the circularity error has been evaluated from the measured profiles using computational geometric techniques (Venkaiah and Shunmugam 2007). Abdullah et al (2011) quantified geometric and dimensional error of an Autonomous Underwater Vehicle (AUV) propeller blade by comparing the profiles obtained from

3 9 optical method. They reported that the thickness error depends on deformation ratio of the blade. Wang et al (2005) addressed the special features of the deformation analysis between complex shaped components and fixture elements and reported that the deformation error of the fixture depends on the fixture layout. Cioata and Kiss (2009) presented analytic models of calculus of the errors due to contact deformation between locators and workpiece using the finite element method in order to determine the contact deformation. Literature related to machining errors concludes that the part errors are mainly because of machining errors and 20% to 60% of the overall machining errors are caused due to fixture errors (Cioata and Kiss 2009). 2.3 STUDIES RELATED TO FIXTURE DESIGN Fixture is an important element in most of the manufacturing processes and related to machining errors the role of fixture is very crucial. Studies pertaining to the design of machining fixture are generally of two categories i. e. fixture analysis and fixture synthesis. While fixture analysis deals with forces and deformations, the fixture synthesis is concerned with the design of fixture configuration to completely immobilize the work part when subjected to external forces. In the fixture analysis and synthesis, a concern on the conditions for constraining a workpiece is critical. The essential requirement of fixturing is the century-old concept and the same has been extensively studied by Mishra et al (1987) and Markenscoff et al (1990) in the field of robotics with efficient algorithms to synthesize positive grips for bounded polyhedral objects. Chou et al (1989) developed a mathematical theory for automatic configuration of machining fixtures for prismatic parts. The performance of fixture has been analyzed

4 10 based on the popular screw theory and engineering mechanics. The determination of locating and clamping points on workpiece surface and the determination of clamping forces have also been synthesized. Trappey and Liu (1990) carried out a literature survey of fixture design automation and emphasized computer aided fixture design. In the frictionless case, Lakshminarayana (1978) investigated the minimum requirements for the form closure of a rigid body and proved that at least four and seven contacts are necessary to achieve force closure for 2D and 3D parts respectively. For the same frictionless case, Salisbury and Roth (1982) demonstrated that a necessary and sufficient condition for force closure is that a strictly positive linear combination of the primitive wrenches at contacts is zero and the primitive wrenches span the whole wrench space. Mishra and Silver (1989) later proved that when friction is taken into account, three contacts are sufficient in the planar case while four are adequate in the spatial case. A Projective Spatial Occupancy Enumeration (PSOE) approach has been applied as a representational and manipulating scheme for developing algorithms in automatic fixture configuration by Trappey and Liu (1993). King and Lazaro (1994) optimized fixture for a particular datum specification and sequence of operations. Then the fixture system has been analyzed and presented via the CAD system. Deiab and Elbestawi (2005) stated that the tangential friction force plays an important role in fixture configuration design and presented the results of an experimental investigation of the workpiece-fixture contact characteristics. Roy and Liao (2002) reported that stability analysis plays a critical role in determining the applicability of a fixture design and developed a computational methodology for quantitatively analyzing the stability of the workpiece in the automated fixture design environment.

5 11 Liu et al (2004) proposed an algorithm for searching form-closure grasps of hard fingers on the surface of a three-dimensional object represented by discrete points with the consideration of both frictional and frictionless cases. This algorithm starts to search a form-closure grasp from a randomly selected grasp using an efficient local search procedure until encountering a local minimum. Workpiece location error is examined by considering the fixture geometric error and elastic deformation of the fixture and workpiece due to fixturing forces (Raghu and Melkote 2005). The deformations at the contact points are obtained by solving a constrained optimization model and the experimental validation is also provided for several fixtureworkpiece variable levels using a machining fixture. Kang and Peng (2009) reported designing and fabricating fixtures can take up to 10-20% of the total cost of a manufacturing system and reviewed various approaches used in Computer-Aided Fixture Planning (CAFP). Wang et al (2010) presented a literature survey of computer aided fixture design and automation, including their approaches, requirements and working principles. Related to computer aided fixture design approaches, an interactive Computer Aided Fixture Design (CAFD) system using the Gauss Elimination Method for the design of a fixture to hold prismatic components during machining on a CNC machining centre is described by Krishnamachary and Reddy (2005). Cecil (1995), Pehlivan et al (2009) and Nee et al (1987) have reported the other feature-based methodologies in CAFD. Boyle et al (2011) reviewed over seventy-five CAFD tools and approaches in terms of the fixture design phases and technology and reported two research issues that require further effort. The first is that current CAFD research is segmented in nature and there remains a need to provide more cohesive fixture design support. Secondly, a greater focus is

6 12 required on supporting the detailed design of a fixture s physical structure. The general situation of research on agile fixture design is summarized and pointed out the achievements and deficiencies in the field of case-based agile fixture design (Li et al 2002). The automation of fixture design and integration of setup and fixture planning is discussed by Stampfer (2009). Boonsuk and Frank (2009) presented a methodology for the automated design of a fixturing system for a rapid machining process. An adaptive fixture design system with an evolutionary search algorithm has been developed by Fathianathan et al (2007) to deal with the automatic design changes to meet the requirements of different domains. Armillotta et al (2010) described the procedure for kinematic and tolerance analysis and demonstrated its significance on a sample case of fixture design. Kinematic analysis verifies that any relative motion between the part and the worktable is constrained and the tolerance analysis tests the robustness of part orientation with respect to manufacturing errors on datum surfaces. Luo et al (2011) developed a novel model for workpiece positioning analysis by using surface-to-surface signed distance function and a two-sided quadratic model for fixture locating analysis. This model has potential applications in fixture design, tolerance analysis and fault diagnosis. Studies related to fixture design show that fixture design has received considerable attention in recent years. However, little attention has been focused on the optimum fixture layout and clamping forces.

7 AI and Expert System in Fixture Design In recent years, artificial intelligence (AI) techniques are widely used in many engineering optimization problems and the usage of AI in the field of fixture design is also notable. Latombe and Ingrand (1980) described an expert system for automatic fixture design and Nee et al (1987) set forth an artificial intelligence system for the development of fixture design where the basic fixture elements are clamping elements, positioning and guiding elements, supporting and base elements. A methodology for the automated design and robotic assembly of modular fixturing systems based on the integration of state-of-the-art methodologies is also proposed (Gandhi and Thompson 1987). Ferreira and Liu (1988) dealt with the automatic generation of workpiece orientations on a machine for machining operations and Boerma and Kals (1988) described the automatic selection of the faces for the positioning, clamping and support of workpieces. An automated fixture-design system using a rule/objectbased approach to group the machining features into appropriate fixture setups, and to recommend suitable clamping, locating and supporting points has been developed by Senthilkumar et al (1992). Darvishi and Gill (1988) presented an exploratory approach to the design of fixtures using an expert system. An automatic fixture design using a development method together with a knowledge model is also proposed by Hunter et al (2010) and a semi-automated methodology to aid the generation of the fixture design for a given part design is developed by Peng et al (2011). Studies related to AI in fixture design reveal that the scope of AI is more intense in the field machining fixture layout design.

8 Modular Fixtures To improve flexibility in the manufacturing field, the dedicated fixtures are replaced by modular fixturing systems and these are most widely used in industry for job and batch production. Liu (1994) provided a systematic design method to help dedicated fixture users to convert into modular fixturing system users. Rong and Bai (1997) designed a modular fixture element assembly Relationship Graph (MFEARG) to represent combination relationships between fixture elements and developed algorithms to search all suitable fixturing unit candidates and mount them into appropriate positions on a baseplate with interference checking. A modular fixture design method based on case based reasoning (CBR) algorithm is proposed by Sun and Chen (2007). Zheng and Qian (2007) introduced a systematic study of 3-D modular fixtures, particularly for complex objects. For fixturing the object, seven fixels on the base plates are used to contact the object in various directions to achieve form closure. The importance of fixture design automation is emphasized and a general structure of the automated design system for modular fixture design system is presented (Vukelic et al 2009) and also a system for computer-aided fixture design has been verified by Vukelic et al (2011) which comprise of methods and techniques for fixture design and it allowed fixtures to be designed based on geometric features of workpiece, process planning and machining information.

9 STUDIES RELATED TO FIXTURE CONFIGURATION / LOCATING SCHEME The fixture configuration mainly consists of locators and clamps. The function of each locator is to provide a deterministic location of the workpiece whereas the function of each clamp is to exert suitable force on the surface of the workpiece to prevent it from losing contact with the locators. Based on the classical screw theory several formal methods for the fixture analysis have been developed. Most of the dedicated fixtures for prismatic parts are designed using the locating principle. Here, refers to 3 locators on the primary locating surface, 2 locators on the secondary locating surface and 1 locator on the tertiary locating surface of the workpiece. The twelve degrees of freedom of a free body in space are shown in Figure 2.1 and out of twelve, nine degrees of freedom are restricted by using locating principle as shown in Figures 2.2, 2.3 and 2.4. Source : Figure 2.1 Twelve degrees of freedom of a free body

10 16 Source : Figure 2.2 Three supports on the primary locating surface restrict five degrees of freedom Source : Figure 2.3 Addition of two locators on a side restricts eight degrees of freedom

11 17 Source : Figure 2.4 Addition of final locator to another side restricts nine degrees of freedom, completing the location Due to its less complexity and effectiveness, the locating scheme has been used by most of the researchers. Kang and Peng (2009) illustrated the locating method for a prismatic workpiece called valve body which is shown in Figure 2.5. The valve body is located by three perpendicular locating planes where the bottom surface of the valve body forms the primary locating plane, the secondary locating plane is the side surface contacting two locators and the tertiary locating plane is the side surface against one locator. Four vertical clamps have been applied on the top surface. For fixture clamping force optimization, the workpiece-fixture configuration used by Li and Melkote (2001a) is shown in Figure 2.6 where, L 1 -L 6 are the workpiece-fixture locator contacts and Xg, Yg, Zg, are the global coordinate frames. They (Li and Melkote 2001) also used locating scheme for optimizing fixture design based on workpiece

12 18 dynamics which is shown in Figure 2.7, where C 1 -C 4 are clamps. Figure 2.8 shows the N-2-1 fixturing scheme presented by S anchez et al (2006) in the Fixture analysis methods for calculating the contact load distribution and the valid clamping regions in the machining processes. Source: Kang and Peng (2009) Figure locating method for a valve body Source: Li and Melkote (2001) Figure 2.6 Fixture configuration with locating scheme

13 19 Source: Li and Melkote (2001) Figure fixturing scheme : L 1 -L 6, locators; C 1 -C 4, clamps Source: S anchez et al (2006) Figure 2.8 N-2-1 fixturing system The fixture-workpiece system considered to predict workpiece deformation using the finite element method reported by Siebenaler and Melkote (2005) is shown in Figure 2.9. In this study, a hollow block of rectangular section and uniform wall thickness has been restrained by a fixture layout. A fixture layout with two clamps for a rectangular hollow workpiece shown in Figure 2.10 has been used by

14 20 Raghu and Melkote (2005) for modelling of workpiece location error because of fixture geometric error and fixture-workpiece compliance. Literature related to locating scheme shows that most of the researchers have used locating scheme to constrain prismatic workpieces and literature for optimization of number of fixture elements is rarely found. Source: Siebenaler and Melkote (2005) Figure fixture layout for a hollow workpiece Source: Raghu and Melkote (2005) Figure 2.10 Schematic of fixture layout with 2 clamps

15 21 Studies related to locating schemes show that most researchers concentrated with layout and indicate that more attention can be given for optimization of number of locators. 2.5 STUDIES RELATED TO OPTIMUM FIXTURE LAYOUT DESIGN Fixture layout is the positioning of fixturing elements such as locators and clamps on the workpiece. The optimum fixture layout shows minimum elastic deformation of the workpiece under machining condition. Menassa and DeVries (1991) proposed a nonlinear optimization algorithm to determine the optimal positions of the three supports on the primary locating plane. Here, the support positions are design variables and the deflection of the workpiece is the objective function. Finite element analysis (FEA) is used for calculating deflection at selected points as the design criteria. Trappey et al (1995) used the finite element analysis (FEA) approach to estimate the dynamic stress-strain behavior of a work-piece when machining and clamping forces are applied and a mathematical optimization model has been formulated to minimize the deformation of a workpiece under the corresponding force effects for a feasible configuration. De Meter (1995) disclosed an algorithm using min-max loading criteria for optimal locations of locators and clamps. Kashyap and DeVries (1999) scheduled a nonlinear programming method of analysing and optimizing a fixture design for minimal workpiece deflection during machining. Finite Element Analysis (FEA) is used for calculating deflection at selected points. Li and Melkote (1999) used a nonlinear programming method to solve the layout optimization problem. The method minimizes workpiece location errors due to localized elastic deformation of the workpiece at the fixturing points

16 22 by optimally placing the locators and clamps around the workpiece. The problem of fixture synthesis for fixture elements placement (Wang 2000) and the problem of characterizing the accuracy of deterministic localization of fixtures (Wang 2002) have been addressed. The fixturing tolerance and stability verification have been explored by Kang et al (2003) with the framework of computer-aided fixture design verification based on geometric and kinematic models. Kim and Ding (2004) investigated the various aspects of optimal fixture layout design in multistation panel assembly processes which are variation modelling, design criteria and optimization methods. Different optimization methods have been explored and compared. Wang et al (2006) established the optimal fixture layout in a global range and it is especially suitable for the workpiece with complex surfaces. Zhu and Ding (2007) proposed an efficient algorithm for grasp synthesis and fixture layout design in discrete domain and it is implemented by solving a single linear program. Loose et al (2007) have developed a linear model to describe the dimensional variation propagation of machining processes through kinematic analysis of the relationships among fixture, datum, machine geometric errors, and the dimensional quality of the product. Zhu and Ding (2009) has carried out a comparative study on several widely used optimality criteria for fixture layout design and Vishnupriyan et al (2010) optimized machining fixture layout for tolerance requirements under the influence of locating errors. Qin et al (2006) have elucidated a general analysis methodology that is able to characterize the effects of localization source errors based on the position and orientation of the workpiece. Also they have presented locating correctness based on Venn diagram and a general algorithm to determine the locator number and layout (Qin et al 2010). Qin et al (2008)

17 23 developed a machining-dimension-based locating scheme design approach. In that approach, first the relationship is established between the machining dimensions and the Degrees of Freedoms (DOFs) to be constrained. Then, the fixture locating scheme is established to characterize the practical constrained DOFs of a workpiece in terms of the known locator number and positions. Genetic Algorithm (GA) has been proven to be a useful technique in solving optimization problems in engineering. Fixture design has a large solution space and requires a search tool to find the better design. GAs has been used by few researchers for fixture design and fixture layout problems. Vallapuzha et al (2002) reviewed the various optimization methods for optimizing the layout of fixture elements and reported 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. The application of genetic algorithms to the fixture configuration optimization problem is presented by Wu and Chan (1996) while Kulankara et al (2002) expounded GA-based iterative fixture layout and clamping force design optimization procedure for a compliant workpiece. The algorithm minimizes the workpiece elastic deformation for the entire cutting process by alternatively varying the fixture layout and clamping force. Kaya (2006) has used GA integrated with a commercial finite element solver to find the optimal locator and clamp positions in 2D workpiece. Initially, GA is tested by using two test cases and it can be seen that the GA successfully converges to global minimum. Yildiz and Ozturk (2006) used hybrid enhanced genetic algorithm to select optimal machining parameters in turning operation. Then GA is used to optimize the 2D fixture layout. Prabhakaran et al (2007) posited a fixture layout

18 24 optimization method that uses genetic algorithm (GA) and Ant Colony Algorithm (ACA) separately. In this connection, three different number of node systems are defined on the same workpiece geometry to find the consistency in the performance of GA and ACA. For all three different number of node systems, the optimal solution, which is the most minimum deformation value among the entire possible layout is determined separately. The solution obtained using GA and ACA for each node system is compared with their respective optimal solution separately and ACA reports faster and accurate solutions. ACA is also used by Padmanaban et al (2009) for machining fixture layout design. Chen et al (2008) highlighted a fixture layout design and clamping force optimization procedure based on the GA and Finite Element Method (FEM). The objectives are minimizing the maximum deformation of the machined surfaces and maximizing the uniformity of the deformation. Padmanaban and Prabhakaran (2008) have exemplified an ACA and GA based fixture layout optimization with the objective of minimizing the dynamic response of the workpiece. A non-linear multivariable optimization model formulated by Ramesh and Jerald (2009) is tested for various stack-up conditions on a simple mechanical assembly using GA to get optimal tolerance value. Amaral et al (2005) developed a method for modelling workpiece boundary conditions and applied loads during a machining process using FEA. The workpiece boundary conditions are defined by locators and clamps and the locators are placed in a fixture configuration and clamps are modelled as point loads. The workpiece is loaded to model cutting forces during drilling and milling machining operations. The literature relevant to fixture layout optimization specifies that most of the researchers used FEM along with GA to optimize fixture

19 25 layouts and indicates that more attention can be focussed on workpiece elastic deformation to reduce part errors. 2.6 STUDIES RELATED TO FIXTURE LAYOUT AND CLAMPING FORCE OPTIMIZATION Along with fixture layout optimization only a few researchers have considered clamping force optimization to minimize machining errors. Few works are also carried out in determining the minimum clamping forces, required in the fixture system, because these are critical and decide the stick/slip conditions during machining. Since FEM is a better tool for determining the deformation of the workpiece, many researchers have used FEM with suitable optimization tools for fixture layout and clamping forces optimization problems. The influence of clamping preload and machining force on the surface quality of the machined workpiece is investigated by Liao and Hu (2001). They developed an integrated finite element analysis model of the entire fixture-workpiece system and found that the magnitude of surface error is linearly proportionally affected by the magnitudes of the external loads (clamping and machining forces). Also the analysis concluded that based on the material, structure and fixturing scheme of a workpiece, the clamping preloads and machining forces have different influences on the machined surface error. De Meter et al (2001) invented a linear, clamp pre-load (LCPL) model that computes the minimum required pre-loads necessary to prevent workpiece slip at the fixture-workpiece joints throughout the machining process. Li and Melkote (2001) offered a fixture layout and clamping force optimal synthesis approach that accounts for workpiece dynamics

20 26 during machining with the objective of minimizing the maximum positional error at the machining point. Also they (Li and Melkote 2001) pioneered a new method for determining the optimum clamping forces for a multiple clamp fixture work-piece system subjected to quasi-static machining loads and developed an algorithm for clamping force optimization based on contact mechanics. Xiong et al (2002) presented a qualitative analysis to minimize the sum of all normal contact forces and the maximum normal contact force. The problem of synthesizing robust optimal clamping schemes on three-dimensional parts with and without friction is addressed by Marin and Ferreira (2002). They proposed a method to compute optimum clamping forces and positions on cylindrical faces. Kang and Rong (2003) introduced a first comprehensive CAFDV framework which uses both geometric and kinetic models (Kang and Rong 2003c) to verify locating completeness, locating accuracy (Kang and Rong 2003a), and fixturing stability (Kang and Rong 2003b). The models have also been used for locating tolerance assignment and the determination of minimum clamping force required in machining operations. Raghu and Melkote (2004) modelled analytically the effect of clamping sequence on the workpiece location error for a fixture-workpiece system. An algorithmic procedure is designed to understand the change in forces and deformations as clamps are applied, whereas Deng and Melkote (2006) endorsed a model-based framework for determining the minimum required clamping forces that ensure the dynamic stability of fixtured workpiece during machining. It consists of a dynamic model for simulating the vibratory behavior during machining, a geometric model for capturing continuously changing geometry during machining, a static model for determining the contact deformation due to clamping, a model for checking dynamic stability and a

21 27 model determining the optimal set of clamping forces that satisfies the stability criteria. Hamedi (2005) has used Artificial Neural Network (ANN) for clamping force optimization to predict the deformation and it has been proved that ANN predicts the required output. Aoyama et al (2006) developed a clamping condition optimization system to determine the optimum clamping positions and clamping force by analyzing the deformation of the workpiece model using FEM. The genetic algorithm is applied to the optimization of clamping positions and the effectiveness is confirmed. S anchez et al (2006a) proposed two analysis methods for fixturing systems in machining to determine the most suitable clamping regions. Chen et al (2007) established a dual optimization model of fixture layout and dynamic clamping force for machining the thin-walled workpieces. Based on the optimal fixture layout dynamic clamping forces are optimized. The workpiece deformation has been analysed by using finite element method and a genetic algorithm has been developed to solve the optimization model. Weifang Chen et al (2008) proffered a fixture layout design and clamping force optimization procedure based on the GA and FEM, in which multi objective optimization procedure is used. The objectives are minimizing the maximum deformation of the machined surfaces and maximizing the uniformity of the deformation. The ANSYS software package has been used for FEM calculation of fitness values. Jiang and Meng (2010) have analyzed the workpiece elastic deformation caused by clamping force, its location and support location using the case of Aluminum alloy 6061 part. Sun et al (2011) have analyzed the clamping process using FEM to optimize fixture layout and clamping force for minimizing the workpiece deformation via GA.

22 28 Fixture layout and clamping forces optimization studies express the fact that FEM and GA are the most common techniques used and so due importance can be given on the influence of fixture layout and clamping forces on the overall workpice elastic deformation. 2.7 STUDIES RELATED TO MODELLING AND ANALYSIS OF WORKPIECE-FIXTURE SYSTEM Numerous research efforts have been reported in the past decades for modelling and analysis of machining fixture-workpiece systems. The majority of prior work treats the fixture-workpiece system as quasi-static and ignores the system dynamics. In reality, machining processes such as milling are characterized by periodic forces. Li and Melkote (1999) modelled the workpiece as elastic in the contact region and rigid elsewhere. The fixture is assumed to be completely rigid. The locators are modelled as displacement constraints that prevent workpiece translation in the normal direction. They modelled the clamping force as uniformly distributed force acting over the workpiece-clamp contact area and workpiece is considered as 3D. Static analysis is conducted to predict the elastic deformation by ignoring machining force. Li et al (2000) proposed a model for analysing the reaction forces and moments for machining fixtures with large contact areas and it has been developed using a contact mechanics approach where the workpiece is assumed to be elastic in the contact region and the fixture element is treated as rigid. The model has also been used to determine the minimum clamping force necessary to keep the workpiece in static equilibrium during machining. Kishnakumar et al (2002) considered the workpiece as elastic and the fixturing elements are rigid. Static analysis is considered to determine the workpiece deformation. Tan et al (2004) described the

23 29 modelling and analysis of optimal fixturing configurations by the methods of force closure, optimization, and FEM. Force closure has been employed to find optimal clamping positions and optimization is used for determining the minimum clamping forces required to balance the cutting forces. FEM is used to determine the deformation in the workpiece and fixtures. Satyanarayana and Melkote (2004) analysed the effects of different finite element boundary conditions on the deformation and reaction force predictions for a single fixture-workpiece contact. They developed specific guidelines for finite element modelling of locatorworkpiece/clamp-workpiece contacts. Song and Rong (2005) proposed a methodology to characterize fixture system s geometry constraint status with focus on under-constraint. Kaya (2006) used dynamic analysis to find out the deformation of the workpiece under machining. The entire tool path is discrtized into 13 load steps. The workpiece-fixture model is analysed with respect to tool movement. The workpiece is assumed to be elastic. The fixture is assumed to be completely rigid. Prabhakaran et al (2006) modelled the workpiece-fixture system by considering the workpiece as an elastic body and fixture as a rigid body. The locators are modelled as displacement constraints that prevent workpiece translation in the normal direction. The clamping force is modelled as point force. The workpiece is considered as 2D by assuming that the workpiece is subjected to plane stress. Static analysis is used to find out the elastic deformation of the workpiece under machining. Chen et al (2007) modelled the workpiecefixture system as semi-elastic contact model considering friction effect, where the materials are assumed linearly elastic. Each locator or support is represented by three orthogonal springs that provide restraints in the X, Y and Z directions and each clamp is similar to a locator but clamping force

24 30 in normal direction. The spring in normal direction is called normal spring and the other two springs are called tangential springs. The literature pertaining to modelling and analysis of workpiece-fixture system depicts most of the studies using either workpiece rigid-body model or workpiece-elastic contact model and the workpiece elastic deformation caused during machining is rarely considered. 2.8 STUDIES RELATED TO MODELLING OF MACHINING FORCES AND MATERIAL REMOVAL EFFECT The removal of the material during machining alters the geometry and the structural stiffness of the workpiece, in turn, leads to higher deformation. Thus, there is a need to consider material removal effects for achieving realistic results in the dynamic analysis. Kulankara et al (2002) used FEM to simulate the machining operation. The machining and clamping forces are considered as point forces acting over the tool path. Static analysis is performed to simulate the machining operation in which the material removal effect is not considered. Kaya and Ozturk (2003) simulated the machining operations by using a finite-element model. The machining forces are considered as area force applied over the tool workpiece contact area. The model is analysed with respect to tool movement and material removal using element death technique. Three dimensional nonlinear finite element analysis is carried out. Deng (2006) developed a model-based framework for analysis and synthesis of the dynamic performance, emphasizing fixturing dynamic stability, of a machining fixture-workpiece system accounting for the material removal effect.

25 31 Kaya (2006) used time-dependent forces to define the machining operation. The material removal effect is taken into account in the analysis. The entire tool path is divided into 13 load steps. The workpiece-fixture model is analysed with respect to tool movement. The workpiece is assumed to be elastic. The fixture is assumed to be completely rigid. These studies represent, in most cases, the workpiece is assumed as elastic; fixture is assumed as completely rigid; machining and clamping forces are considered as point forces and material removal effect is considered by using element death technique. 2.9 STUDIES RELATED TO NUMBER OF FIXTURE ELEMENTS OPTIMIZATION Hurtado and Melkote (2002) presented a model for the synthesis of the fixturing configuration in pin-array type flexible machining fixtures to keep the workpiece rigid body motion due to fixture elastic deformation at or below a user-specified value. The minimum clamping loads and the optimal number, position and dimensions of the pins necessary to achieve the conformability have also been found. Wang and Pelinescu (2003) described an approach to optimal design of a fixture layout with the minimum required number of elements. This approach has been applied to parts with arbitrary 3-D geometry and is restricted to be within a discrete domain of locations for placing the fixture elements of nonfrictional contacts. Liu et al (2007) proposed an optimization method to optimize the number and positions of the locators in the peripheral milling of a lowrigidity workpiece simultaneously. First the initial layout of the locators is determined and based on the initial layout, the number and positions of the locators are optimized. Qin et al (2010) presented locating correctness

26 32 based on Venn diagram and a general algorithm to determine the locator number and layout. On the whole, studies related to number of fixture elements optimization display very little attention has been shown towards the number of fixturing elements optimization and most of the researchers have used locating principle CONCLUDING REMARKS Review of the literature in the above areas reveals the following: Most of the studies use either the rigid-body model or workpiece-elastic contact model and these studies do not consider the workpiece elastic deformation caused during machining Only little attention has been focused on the fixture layout and clamping forces optimization with an objective of minimizing the dimensional and form errors caused due to workpiece elastic deformation In most of the researches finite element method (FEM) has been mainly used for determining the elastic deformation only at workpiece-fixture contact points Most of the studies use linear or nonlinear programming methods, which often do not give the global optimum solution. Most of the fixture layout optimization procedures start with an initial feasible layout. Solutions from these methods depend on the initial fixture layout. They do not consider the fixture layout optimization on overall workpiece deformation

27 33 Though it is more suitable tool in the field of fixture layout optimization, the application of ANN for the optimization of machining fixture layout to minimize the deformation of the workpiece is rarely found in the literature Most of the studies do not consider the dynamic machining forces in the fixture layout optimization design to minimize the dynamic response of the workpiece Most researchers considered 2D workpiece-fixture system by ignoring the normal force acting on the workpiece during machining. Most researchers did not consider the material removal effects in their analysis. In most cases GA has been interfaced with FEM for the fixture layout optimization problems Most of the researchers have used locating principle and the optimization of the number of fixturing elements towards minimum workpiece elastic deformation is rarely considered The above listed findings motivated the author to carry out the research work in the field of fixture layout optimization to minimize the workpiece elastic deformation caused during machining. The following sections present the research problem and objectives considered in this research work RESEARCH PROBLEM During machining operation, fixtures are used to locate and constrain a workpiece. The most important criteria for fixturing are workpiece position accuracy and workpiece deformation. In any

28 34 manufacturing operation, a certain amount of deformation will occur in the workpiece due to the clamping and machining forces. Deformation in the workpiece will lead to dimensional and form errors in the workpiece. To achieve the specified workpiece dimensions and tolerances, it should be properly located and clamped. A good fixture design minimizes workpiece geometric and machining errors by limiting the workpiece elastic deformation. An ideal fixture design consists of optimal fixture layout, optimum clamping forces and optimum number of fixturing elements such as locators and clamps. So, Optimization has three main aspects in fixture design which are the positions of locators and clamps, number of locators and clamps and the magnitude of clamping forces. These should be properly selected and calculated so that the workpiece deformation due to clamping and cutting forces is minimized and uniformed. Either the rigid-body model or work piece-elastic contact model has been used in most of the fixture layout optimization literatures where the workpiece elastic deformation caused during machining is rarely considered. Most researchers have used locating principle where the number of fixturing elements optimization is rarely considered and the usage of artificial neural networks is very limited for the optimization of fixture layout to minimize the overall deformation of the workpiece. Hence, in this research work, the machining fixture layout, number of fixturing elements and clamping forces optimization problems are considered with an objective of minimizing the workpiece elastic deformation caused during machining.

29 OBJECTIVES OF THE RESEARCH WORK The dimensional and form errors induced in the workpiece during machining are the major influencing factors of the component quality. To minimize the dimensional and form errors and to enhance the quality of components fixture design has to be optimized. Based on the conclusions from literature review, the following research objectives are framed: (i) (ii) (iii) The main aim is to minimize the overall workpiece elastic deformation during machining in order to minimize the dimensional and form errors in the workpiece. Optimization of number and position of fixture elements with optimal clamping forces to minimize the overall workpiece elastic deformation during machining. Developing a suitable methodology to optimize the machining fixture layout design with an objective of minimizing the workpiece elastic deformation. In this research work, the fixture layout, clamping forces and number of fixturing elements are optimized using nontraditional algorithms and mathematical approach in order to meet the research objectives.