Fixture Layout Optimization Research Articles

A novel two-stage optimization approach to machining process selection using error equivalence method

The selection of a machining process involves the choice of machine tools, fixture elements, and fixture locator layout, as well as the allocation of tolerance in each operation. In practice, manufacturers frequently choose identical machine tools and fixture elements for each operation to reduce purchase cost. As such, fixture layout and tolerance allocation are critical in selecting or designing appropriate manufacturing processes. Conventional research deals with robust fixture layout design and simultaneous tolerance allocation for multiple types of error source separately. However, fixture layout design could also affect tolerance stackup caused by multiple error (not only the fixture error) sources. Therefore, considering the interaction between fixture layout and other types of error source is critical in the process selection to improve the process selection strategy. In this paper, a two-stage framework is proposed to optimize the process selection based on our previously developed error equivalence model, which transforms multiple errors into equivalent errors that occur on a fixture. In the first stage, a process is selected by determining the allowable tolerance for an aggregated base error given a fixture layout. In the second stage, a computer experiment model is established to search for the globally optimal fixture layout by exploring a large number of fixture layout alternatives. A real-world case study based on a two-operation machining process demonstrated the effectiveness of the proposed strategy in controlling manufacturing cost while ensuring product quality via proper fixture layout design.

Optimization of Fixture Layout Based on Error Amplification Factors

Fixture locators are used to precisely locate and stably support a workpiece so that the desired position and orientation (pose) of the workpiece relative to the cutting tool can be maintained during machining or inspection process. It is believed that manufacturing errors of locators and locating datum surfaces are key factors for the pose error between the workpiece and the cutting tool. Optimizing the layout of locators is helpful to reduce the pose error so as to improve machining accuracy of the workpiece. In order to minimize the pose error, we introduced, for the first time, a singular value decomposition (SVD) technique for the location matrix to derive error amplification factors (EAF) in six degrees-of-freedom of the workpiece. The EAF principle defines the maximal singular value, the condition number, the product of all singular values and the manipulability as the maximal error amplification factor, the relative error amplification factor, the error ellipsoid volume and the location stability, respectively. The four defined indices taken as objective functions are optimized, by a nondominated sort genetic algorithm (NSGA-II), so that an optimal layout of locators is obtained due to the minimization of the pose error. Also, the feasibility of the proposed method was comprehensively validated by simulation and machining experiments.

Erratum to “Fixture layout optimization for multi point respot welding of sheet metals”

There is one correction to make to the original article. The affiliation of the 3rd author, Muhammad Asad, was misprinted. The affiliation should be corrected as follows: 3 Mechanical Engineering Department, Prince Mohammad Bin Fahd University, AlKhobar 31952, Kingdom of Saudi Arabia

Fixture layout optimization for multi point respot welding of sheet metals

The high quality of welding in the automotive industry is achieved by proper positioning of the fixture elements. A new method, N-3-2-1 (N ≥ 1), is proposed for fixture layout optimization of sheet metals. The flexible nature of the sheet metals requires N+3 fixture elements to constrain it normal to the surface (primary plane), but 2-1 fixture elements for other two directions (secondary and tertiary). The objective function is to achieve high stiffness of the workpiece and is calculated in terms of strain energy. Finite element analysis (FEA) was combined with genetic algorithm. A method was also proposed to find the optimum fixturing position of the workpiece in multipoint respot welding operation. Two different kinds of case studies were solved and the performance of the proposed method was also tested in the industrial scenario by fixturing the workpiece and completing the respot welding operation with satisfactory results.

Optimization of flexible fixture layout using N-M principle

Fixture layout has a direct impact on the machining quality of thin-walled parts. However, there are few studies on the flexible fixture of automotive interior decoration, especially for car dashboards. With the development of individualized demand, the production trend of car dashboards is changing from large-quantity to multi-variety and small-batch, which makes the demand for flexible fixture of car dashboards. Therefore, a kind of flexible fixture for car dashboards based on a new N-M principle was proposed in this paper. With the scientific problem illustrated, this paper put forward a method by coupling genetic algorithm and finite element analysis to deal with the flexible fixture layout optimization. The optimization model of fixture layout based on the N-M principle was set up by taking the maximum deformation of car dashboards as the optimization objective and setting constraints. Finite element model was established to calculate the deformation by setting the boundary conditions, the equivalent cutting force. Genetic algorithm was used to search the optimal solution of the fixture layout. A case was studied to verify the method, and the result showed that the maximum deformation was reduced by 56.5% and the stiffness was increased by 0.77 times, which fully demonstrated the effectiveness of the method.

Fixture layout optimization in multi-station sheet metal assembly considering assembly sequence and datum scheme

One of the most influential causes of dimensional inaccuracy in automotive bodies is the inescapable fixture deviation, which is propagated in a Multi-Station Assembly (MSA) process. Therefore, a robust fixture design is necessary to increase product quality. The aim of this paper is to present a methodology for simultaneous optimization of fixture layout and assembly configuration, including assembly sequence and datum shift scheme, in MSA. To model the accumulated variation from one station to the downstream stations, a non-linear state-space representation is adopted. Feasible assembly sequences are automatically generated using a liaison graph and Breadth-First Search algorithm, and also all datum scheme options are provided based on a permutation method that is dependent on the number of parts and stations. Further, the sum of squared standard deviations for key product characteristics to be minimized is an optimization object. Part boundaries, design requirements, and assembly configuration feasibility are the constraints. This constrained problem is converted into an unconstrained one by two strategies: (i) Geometry boundaries and assembly configuration constraints are fulfilled through removing infeasible solutions from the design space and (ii) Design requirements are met by using a self-adaptive penalty function. Finally, the unconstrained problem is optimized using a genetic algorithm. The proposed methodology improved assembly process capability by 68 to 84% for an automotive body side in a case study.

Fixture Layout Design of Sheet Metal Parts Based on Global Optimization Algorithms

Fixture layout can affect deformation and dimensional variation of sheet metal assemblies. Conventionally, the assembly dimensions are simulated with a quantity of finite element (FE) analyses, and fixture layout optimization needs significant user intervention and unaffordable iterations of finite element analyses. This paper therefore proposes a fully automated and efficient method of fixture layout optimization based on the combination of 3dcs simulation (for dimensional analyses) and global optimization algorithms. In this paper, two global algorithms are proposed to optimize fixture locator points, which are social radiation algorithm (SRA) and GAOT, a genetic algorithm (GA) in optimization toolbox in matlab. The flowchart of fixture design includes the following steps: (1) The locating points, the key elements of a fixture layout, are selected from a much smaller candidate pool thanks to our proposed manufacturing constraints based filtering methods and thus the computational efficiency is greatly improved. (2) The two global optimization algorithms are edited to be used to optimize fixture schemes based on matlab. (3) Since matlab macrocommands of 3dcs have been developed to calculate assembly dimensions, the optimization process is fully automated. A case study of inner hood is applied to demonstrate the proposed method. The results show that the GAOT algorithm is more suitable than SRA for generating the optimal fixture layout with excellent efficiency for engineering applications.

Comparison of evolutionary techniques for the optimization of machining fixture layout under dynamic conditions

Modern manufacturing industries are striving to improve the machining accuracy and productivity to reduce the rejection rate and unit cost of the machined parts. The properly designed fixture layout enables the designer to minimize the vibration so that the requisite machining accuracy can be achieved. During machining, especially in end milling, the intermittent engagement of multitooth cutter induces vibration on the workpiece. When the excitation frequency of multitooth cutter coincides with any one of the natural frequencies of the fixtured workpiece, it leads to the condition of resonance. The vibration increases under these circumstances, which degrades the machining accuracy and surface finish of the machined workpiece. Hence, the issues related to the design of fixture layout are to be addressed by recognizing the dynamic behavior of the fixture–workpiece system. In this research paper, finite element method is utilized to simulate the end milling operation and to determine the natural frequency of the workpiece. The main focus is to maximize the difference between natural frequency of the fixtured workpiece and excitation frequency of the cutter to minimize the vibration on the workpiece. Two different evolutionary techniques genetic algorithm and particle swarm optimization are employed to maximize the difference between these frequencies by optimizing the machining fixture layout. The performance of genetic algorithm and particle swarm optimization on the fixture layout optimization is compared. The comparison of results concludes that particle swarm optimization is the most appropriate approach than the genetic algorithm in achieving the better results.

Optimum fixture locating layout for sheet metal part by integrating kriging with cuckoo search algorithm

Fixture locating layout has a direct and influential impact on the sheet metal mechanical behavior and dimensional quality during the manufacturing process. The N-2-1 locating principle is adopted to design the fixture locating layout for the sheet metal part to determine the spatial location and restrain the excessive deformation. However, efficient optimal design of fixture layout is not an easy-to-implement and trivial task. The state-of-the-art evolutionary optimization of fixture layout aiming for workpiece deformation control often involves hundreds or even thousands of calls of finite element analysis and therefore is faced with uncomfortable and challenging computation cost and burden. In order to reduce the computational cost and improve the optimization efficiency, a new approach for optimum sheet metal fixture locating layout based on the N-2-1 principle is proposed in this paper. The training and test data sets are generated by running only a few times of finite element analysis on the design sites standing for different fixture locating layouts selected through Latin hypercube sampling. The kriging surrogate model is built based on the training sample set to approximate the implicit function relationship between the fixture locating layout and the concerned sheet metal deformation and meanwhile is compared with back propagation neural network in terms of prediction accuracy by the test sample set. The cuckoo search algorithm is applied to the kriging model to find the optimal fixture locating layout. Flat and curved sheet metal cases based on the “4-2-1” locating scheme are conducted, and the results indicate that the proposed approach is effective and efficient in the design and optimization of the sheet metal fixture locating layout.

Intelligent design and optimization of machining fixtures

This work presents an integral system for machining fixture layout design and optimization. The optimization module of this system allows determination of optimal positions of locating and clamping elements, which provides required accuracy and surface quality, while at the same time guarantees design of collision-free fixtures. The design module performs selection of required fixture elements based on a set of predefined production rules. Adequate criteria for the selection of fixture elements are defined for locating, clamping, tool guiding, and tool adjustment elements, as well as for fixture body elements, connecting elements and add-on elements. The system uses geometry and feature workpiece characteristics, as well as the additional machining, and process planning information. It has been developed to accommodate machining processes of turning, drilling, milling, and grinding of rotational and prismatic workpieces. A segment of output results is also shown. Finally, conclusions are presented with directions for future investigation.

An integrated finite element method, response surface methodology, and evolutionary techniques for modeling and optimization of machining fixture layout for 3D hollow workpiece geometry

Machining fixtures play inevitable role in manufacturing to ensure the machining accuracy and workpiece quality. The layout of fixture elements, clamping forces, and machining forces significantly affect the workpiece elastic deformation during machining. The clamping and machining forces are necessary to immobilize and machine the workpiece, respectively. Finding the appropriate layout of fixture elements is the other possible way to reduce the workpiece deformation, which in turn improves the machining accuracy. The finite element method interfaced with evolutionary techniques is normally used for fixture layout optimization. In the finite element method, the workpiece is discretized into a number of small elements and fixture elements are placed only on the nodes. Hence, evolutionary techniques are capable of searching the optimal fixture layout from those discrete nodal points than from the entire area on the locating and clamping face. To overcome these limitations, in this research paper, response surface methodology is employed to establish a quadratic model between the position of fixture elements and maximum workpiece deformation. This enables the optimization techniques to search for the optimal solution in the continuous domain of the solution space. Then, the real-coded genetic algorithm based discrete optimization, continuous optimization based on binary-coded genetic algorithm and particle swarm optimization are employed to optimize the developed quadratic model and their performances are compared. The result clearly shows that the integration of finite element method, response surface methodology with particle swarm optimization is better than the integration with genetic algorithm to optimize the machining fixture layout and also reduces the computational complexity and time to a greater extent.

Optimal Fixture Design for Drilling of Elastomer using DOE and FEM

An elastomer is a polymer with the property of viscoelasticity generally having notably low Young's modulus and high yield strain compared with other materials. The elastomer which is used in our project is styrene-butadiene rubber. The drilling of elastomer work piece is not easy since it can easily deform. Hence the desired output cannot be obtained. By designing a proper fixture layout, the drilling of elastomer can be done accurately. The fixture design requires accurate positioning of locators and clamps to reduce the deformation of work piece during drilling. In this work six locators and three clamps are used. The primary design layout is done and then it is analyzed in ANSYS to find out the work piece deformation. The various possible design layouts are formed using L27 orthogonal array by MINITAB Software. Then all the 27 layouts are analyzed using ANSYS and the deformation values are found. The optimal layout is found using DOE – Taguchi method from MINITAB Software by giving the 27 layouts and the corresponding deformation values as inputs. From the obtained SN ratio graph, the optimal fixture layout is found for minimum deformation of the work piece.

Particle Swarm Optimization for Integrated Fixture Layout

Fixture is a work-holding or supporting device used in the manufacturing industry to hold the workpiece. Fixtures are used to securely locate (position in a specific location or orientation) and support the work, ensuring that all parts produced using the fixture will maintain conformity and interchangeability. The location of fixture elements is called as fixture layout. The fixture layout plays major role in the work piece deformation during the machining operation. Hence optimization of fixture layout to minimize the work piece deformation is one of the critical aspects in the fixture design process. Minimization the workpiece deformation which is the objective function in the present work is calculated using Finite Element Method (FEM) and the fixture layout is optimized using Discrete fixture layout optimization method (DFLOM), Continuous fixture layout optimization method (CFLOM) and Integrated fixture layout optimization method (IFLOM).The workpiece deformation is minimum in Particle Swarm Optimization (PSO) based IFLOM is reported for the selected fixture. In this paper the PSO is used as an optimization tool to optimize the workpiece deformation.

An integrated approach for optimal fixture layout design

Fixture layout optimization is a procedure to optimize position of locators and clamps in order to minimize specified objectives. Deformation of workpiece is a serious problem of concern while designing a fixture. Proper positioning of fixture elements is indispensable to achieve desired machining accuracy, better surface finish and high productivity. In this work, a novel methodology is proposed that incorporates full factorial design of experiments and statistical analysis. Furthermore, the stability of the workpiece is ensured prior to the prediction of objective function. The result of the proposed technique is compared with the results of the genetic algorithm–based optimization technique. A case study has been considered to evaluate the proposed methodology. The objective function determines maximum elastic deformation of the workpiece during the entire machining process. Finite element method is used to formulate the objective functions. The constraints are natural frequency of the workpiece–fixture system and reaction forces. Besides, artificial neural network–based model is developed to predict the elastic deformation of the workpiece–fixture system within the range of design parameters.

Optimization of machining fixture layout using integrated response surface methodology and evolutionary techniques

Fixtures are the work-holding devices, widely used in manufacturing, to completely immobilize the workpiece during machining. The position of fixture elements around the workpiece strongly influences the workpiece deformation which in-turn affects the machining accuracy. The workpiece deformation can be minimized by finding the appropriate position for the locators and clamps. Thus, it is necessary to model the complex behavioral relationship that exists in the fixture–workpiece system. In this research paper, response surface methodology is used to model the relationship between position of locators and clamps and maximum deformation of the workpiece during end-milling, and then the developed model has been optimized by genetic algorithm and particle swarm optimization. As the predictive model is being developed by response surface methodology, a huge reduction in computational complexity and time is achieved during the optimization of machining fixture layout. Also, it is evident that the approach which integrates response surface methodology and particle swam optimization produces better results.

Fixture layout optimisation based on a non-domination sorting social radiation algorithm for auto-body parts

Auto-body compliant parts are easily deformed during clamping and welding, and fixture layout is very important to the final product quality. However, it is very difficult to design fixture layout because it needs to synchronously satisfy the requirements of assembly tolerance and gravity deformation, which are calculated by finite element analysis. This paper proposes a new method to optimise fixture scheme by a non-domination sorting social radiation algorithm (NSSRA). Firstly, unfeasible nodes are eliminated by four rules according to manufacturing experiences. Afterwards, a few groups are divided based on positions of all feasible nodes. N groups are optimised using NSSRA. Finally, the best fixture layout is generated by selecting the feasible points among the optimal groups in last step. A case study of inner hood is used to illustrate the proposed method, and the results suggest that NSSRA has better efficiency and higher accuracy than NSGA-II.

Fixture Design Optimisation Considering Production Batch of Compliant Non-Ideal Sheet Metal Parts

Fixtures control the position and orientation of parts in an assembly process and thus significantly contribute to process capability that determines production yield and product quality. As a result, a number of approaches were developed to optimise a single- and multi-fixture assembly system with rigid (3-2-1 fixture layout) to deformable parts (N-2-1 fixture layout). These approaches aim at fixture layout optimisation of single ideal parts (as define by CAD model). However, as production yield and product quality are determined based on a production volume of real (non-ideal) parts. Thus, major challenges involving the design of a fixture layout for assembly of sheet metal parts can be enumerated into three categories: (1) non-ideal part consideration to emulate real part; (2) ‘N-2-1’ locating scheme due to compliant nature of sheet metal parts; and, (3) batch of non-ideal parts to consider the production process error at design stage.This paper presents a new approach to improve the probability of joining feasibility index by determining an N-2-1 fixture layout optimised for a production batch of non-ideal sheet metal parts. The proposed methodology is based on: (i) generation of composite parts to model shape variation within given production batch; (ii) selection of composite assembly representing production batch; (iii) parameterisation of fixture locators; and (iv) calculation of analytical surrogate model linking composite assembly model and fixture locators to probability of joining feasibility index. The analytical surrogate model is, then, utilised to maximise the probability of joining feasibility index starting from initial fixture locator layout. An industrial case study involving assembly process of remote laser welded door assembly illustrates and validates the proposed methodology.

A Memetic Algorithm for multi-objective fixture layout optimization

A proper scheme of fixture layout can reduce locating errors of a workpiece. However, a multi-objective fixture layout optimization, involving multiple conflicting objective functions, will lead to much more accurate solution and complex computation. This paper describes a new approach based on Memetic Algorithm (MA) to multi-objective fixture layout optimization, considering both location accuracy and stability. This approach uses an entropy method to obtain the weights of each objective functions, and establishes a fitness function. Then, a MA is developed to properly select the positions of locators to minimize the fitness function. An example illustrates that the new optimization method based on MA can improve the locating precision of a workpiece effectively and efficiently. This method is also suitable for solving a multi-objective fixture layout optimization problem with more objective functions.

Fixture layout optimization for deformable sheet metal workpiece

The purpose of the fixture layout design is to ensure the fixture positioning accuracy, which affects the resultant geometric variation of the positioned workpiece directly. The N–2–1 locating principle is widely applied in the fixture design for deformable sheet metal workpiece, not only for locating the workpiece, but also for restraining the excessive workpiece deformation. This paper proposes an approach to optimizing fixture layout for the sheet metal workpiece based on the 4–2–1 locating scheme. Firstly, three fixture locating points on the primary datum surface are optimized with genetic algorithm based on the rigid model considering the robustness and the geometry stability. Then based on finite element analysis, a back propagation neural network model is built to predict the deformation of the sheet metal workpiece under different fixture layouts and different fixture locator errors, and a genetic algorithm is used to find the optimal position of the fourth fixture locator based on the neural network prediction model. Finally, a case study is given to verify the proposed approach.

Fixture layout optimization in multi-station assembly processes using augmented ant colony algorithm

In recent years, ant colony algorithms (ACAs) are used to solve the fixture layout optimization problem for a single workpiece machined in a single manufacturing stage. Assembly processes, however, are normally multi-station manufacturing processes, whose fixture layout optimization problem is much more complex. The purpose of this research is to develop an augmented ACA based on continuous optimization methods to optimize fixture layouts for 2D rigid parts in multi-station assembly processes. The algorithm is augmented by changing the mutation step size in the global search, the limiting step size in the local search, the new pheromone value's expression of the ant, etc. The augmented ACA is used to properly select the coordinates of two locating pins to minimize the sensitivity index. A case about three-station automotive side aperture assembly processes is studied to verify the effectiveness of the augmented ACA. The results show that the augmented ACA can generate more accurate results with a faster rate of convergence and a better stability than the basic ACA. This work could also be applied to fixture layouts optimization problems for 3D rigid parts in multi-station manufacturing processes.