Design, Optimization, and Analysis of Machining Fixture Layout under Dynamic Conditions

Abstract

This paper presents a study on the optimization of fixture layout design in multi-operation machining processes to improve the dimensional accuracy, surface finish, and productivity of manufacturing industries. The study focuses on the role of fixture elements such as locators and clamps in holding, securing, and restraining the workpiece during machining operations. The improper fixture layout can increase the vibration of the fixture-workpiece system, leading to reduced accuracy and surface finish of the machined workpiece. The study employs Finite Element Method (FEM) and modal analysis to compute the natural frequencies of the fixture-workpiece system and proposes the use of a Genetic Algorithm (GA) and Particle Swarm Optimization (PSO) to optimize the fixture layout design. ANSYS 15.0 and MATLAB software are used to conduct the FEM analysis and develop the GA and PSO coding. The study also presents the validation of the proposed approach on both 2D and 3D fixture-workpiece systems. The results show that PSO-based optimization produces better results and is identified as the suitable method for fixture layout optimization problems. The proposed approach can aid designers in minimizing machining vibration and achieving the required machining accuracy in multi-operation machining processes.

Introduction

I. INTRODUCTION

This paper discusses the importance of fixtures in modern manufacturing industries to improve dimensional accuracy, surface finish, and productivity during the multi-operation machining process. Fixtures are work-holding devices used to reduce cycle time in automated manufacturing, inspection, and assembly operations. However, the design, fabrication, and testing of fixtures consume a major portion of new product development time. In a machining system, fixtures are designed to be flexible to reduce lead time, and fixture design and analysis software can assist in performing fixture planning, design, and verification functions in a short time. The paper explains the fundamentals of fixtures, including the different fixture elements such as locators, clamps, supports, and fixture body, which are used to hold, locate, and restrain the workpiece during the machining process. The stability of the workpiece during the machining process is achieved by placing the fixture elements appropriately in their location to constrain the workpiece. The paper also highlights the fixture requirements, which are necessary to fulfill several needs to retain the workpiece in a constant position during machining. The benefits of fixtures in manufacturing are explained, which include improved accuracy and uniform quality of components machined using fixtures, minimized labor cost, and reduced production cost by maximizing productivity and minimizing operating cost. The paper emphasizes the importance of fixture layout design, which is essential for machining the product and process designs while maintaining an optimal design for function and structural performance. A proper fixture layout design ensures the workpiece is positioned precisely in its position with respect to the cutting tool, improving machining accuracy and reducing the cost of quality control of the machined part. Finally, the paper discusses the need for Computer Aided Fixture Layout Design (CAFLD) to determine the optimal fixture layout for dynamic machining conditions. The CAFLD procedure can integrate the concepts in CAD and fixture layout design to find a feasible solution for complicated problems in fixture layout design. In conclusion, this paper provides a comprehensive overview of the fundamentals of fixtures and their importance in modern manufacturing industries.

II. LITERATURE REVIEW

This literature review focuses on the design and optimization of the machining fixture layout. The primary objective is to develop a frequency-based approach to minimize workpiece vibration during machining. The approach involves altering the natural frequency of the workpiece by placing fixture elements at various positions, making the difference between the natural frequency of the workpiece and the exciting frequency of the cutter to be maximum. This is achieved through modal analysis using FEM and integrating it with evolutionary techniques. The review highlights that most machining forces are dynamic, and the dynamic behavior of the fixture-workpiece system needs to be considered to design a fixture layout that can improve machining accuracy. The research aims to overcome the difficulties identified in the research gap, and the sub-objectives are framed to achieve the primary objective of the research. The first sub-objective is to create a finite element model of the 2D and 3D fixture-workpiece system using ANSYS 15.0 finite element analysis software. The second sub-objective is to conduct preliminary experiments of finite element simulations to study the dynamic behavior of the fixture-workpiece system. The third sub-objective is to determine and record the first three natural frequencies for all load steps and exciting frequencies. The fourth sub-objective is to calculate the value of the objective function, which is the difference between the natural frequencies of the fixture-workpiece system and the exciting frequency of the cutter. The fifth sub-objective is to apply GA and PSO-based optimization algorithms to find the near-optimal position of the locator and clamps to maximize the objective function. The sixth sub-objective is to analyze and justify the values of control parameters used in GA and PSO. Finally, the seventh sub-objective is to compare the performance of GA and PSO for identifying the suitable algorithm for the optimization of the machining fixture layout under dynamic conditions. The review highlights that some researchers have calculated the natural frequencies for their analysis, but the difference between natural and exciting frequencies has not been appropriately explored for analyzing the vibrations. Therefore, the frequency-based approach proposed in this research work could fill this research gap and improve the machining accuracy.

The research proposes using ANSYS 15.0 finite element analysis software to create a finite element model of the 2D and 3D fixture workpiece system. This is suitable software for simulating the dynamic behavior of the fixture-workpiece system, as it can analyze both linear and nonlinear static and dynamic behavior. Moreover, the proposed approach involves integrating FEM with evolutionary techniques, which could lead to more accurate and reliable results than using FEM alone. The review also highlights that GA and PSO are two optimization algorithms that can be used to find the near-optimal position of the locator and clamps. Both algorithms have their advantages and disadvantages, and the selection of the suitable algorithm depends on the specific problem and the required performance criteria. In conclusion, this literature review highlights the importance of considering the dynamic behavior of the fixture-workpiece system to design and optimize the machining fixture layout. The proposed frequency-based approach, which involves modal analysis using FEM and integrating it with evolutionary techniques, could improve the machining accuracy by minimizing workpiece vibration during machining. The sub-objectives proposed in this research work could achieve the primary objective of the research, and the performance of GA and PSO could be compared to identify the suitable algorithm for the optimization of machining fixture layout under dynamic conditions.

III. FINITE ELEMENT METHOD

Finite Element Method (FEM) is a numerical technique used to solve complex engineering problems, which are otherwise difficult to solve analytically. It is based on dividing the problem domain into smaller subdomains, called elements, which are easier to analyze. FEM involves solving a set of algebraic equations, based on a mathematical model that represents the physical behavior of the system. Dynamic analysis using FEM is used to study the response of structures to time-varying loads.

In dynamic analysis, when loads are variable with respect to time, mass and acceleration come into effect. The response of a structure to dynamic loads is studied by determining its natural frequencies and mode shapes. When a structure is elastically deformed and released suddenly, it vibrates about its equilibrium position. This is called free vibration, and the frequency corresponding to free vibration is the natural frequency of the structure.

The FEM is based on shape functions that represent the displacement of the structure at each node. For example, in a four-node quadrilateral element, the shape function for each node is defined as a constant value at that node and zero at all other nodes. The constant values are determined by the condition that the shape function is equal to 1 at the node it represents. The displacement of any point within the element is then determined using the shape functions and the nodal displacements.

The stiffness matrix of an element represents the resistance of the element to deformation. It is determined based on the strain energy of the element. The strain energy is the work done on the element to deform it, and it is calculated based on the strain-displacement relations of the element. The mass matrix of an element represents the mass distribution within the element, and it is determined based on the shape functions of the element.

In hexahedral or brick elements, the connectivity of nodes is defined by a consistent numbering scheme, and the shape functions are represented by Lagrange shape functions. The mass and stiffness matrices are then determined based on the shape functions and strain-displacement relations of the element.

Dynamic analysis using FEM involves solving the equations of motion for the system under the given time-varying loads. The kinetic and potential energy terms of the system are determined, and the Lagrangian equation is used to solve for the displacements of the system over time. The response of the system is then studied using frequency and time domain analysis techniques.

Conclusion

This research work focuses on minimizing machining errors and improving product quality by minimizing the vibration of the workpiece through an accurately designed fixture layout. The proposed frequency-based methodology optimizes the machining fixture layout to minimize workpiece vibration during the machining process. It combines FEM with evolutionary techniques of GA and PSO and has been implemented on a 2D fixture-workpiece system and a 3D fixture-workpiece system. The methodology has been validated using ANSYS 15.0 software, and MATLAB has been used to run the optimization algorithms. Modal analysis has been performed to determine the natural frequencies of the workpiece. The influence of fixture layout on the dynamic behavior of the workpiece during end milling operation is studied, and the effect of material removal is analyzed. The results show that PSO produces better optimal results than GA for both 2D and 3D fixture-workpiece systems. The difference between natural frequency of the fixture-workpiece system and exciting frequency of the cutter in end milling operation has been maximized, and the near optimal results obtained by GA and PSO are compared. The results suggest that PSO is more suitable for fixture layout optimization problems than GA. The major contributions of this research work are the development of a frequency-based approach to minimize workpiece vibration, the validation of the methodology on 2D and 3D fixture workpiece systems, and the comparison of GA and PSO for fixture layout optimization. This research work demonstrates the importance of accurate fixture design in reducing machining errors and improving product quality. The integration of FEM with the evolutionary techniques of GA and PSO provides a powerful tool for optimizing the fixture layout and reducing workpiece vibration. The results of this research work can be used to guide the design of machining fixtures and improve machining accuracy and quality.

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