Machining fixture layout optimization using the genetic algorithm

Fixture design is a critical step in machining. An important aspect of fixture design is the optimization of the fixture, the primary objective being the minimization of workpiece deflection by suitably varying the layout of fixture elements and the clamping forces. Previous methods for fixture design optimization have treated fixture layout and clamping force optimization independently and/or used nonlinear programming methods that yield sub-optimal solutions. This paper deals with application of the genetic algorithm (GA) for fixture layout and clamping force optimization for a compliant workpiece. An iterative algorithm that minimizes the workpiece elastic deformation for the entire cutting process by alternatively varying the fixture layout and clamping force is proposed. It is shown via an example of milling fixture design that this algorithm yields a design that is superior to the result obtained from either fixture layout or clamping force optimization alone.

Optimisation of machining fixture layout under multi-constraints

Fixture layout for machining thin-walled structures plays an important role in fixture performance. This work focuses on the optimization design of machining fixture layout including clamp layout and the layout of support heads. A universal optimization methodology that can automatically generate the optimal machining fixture layout is proposed. The optimization of fixture layout is implemented based on the criteria of minimizing maximum deflection of the thin-walled workpiece while remain relatively small torque caused by the clamping tables. An evolutionary algorithm is employed to solve the fixture layout optimization for the optimal solution. The optimal position of the support heads and the layout of clamping tables obtained from this work vary along with the change of cutting force. To validate the proposed optimization methodology, a fixture layout design for a typical thin-walled structure is optimized as an example. The case study demonstrates the application of the proposed approach in the fixture layout design for thin-walled structures, which is beneficial to design an optimal fixture layout.

Fixture layout is an essential factor in intelligent manufacturing in the shipbuilding industry, affecting assembly quality and efficiency. Its optimization has become an urgent problem in the assembly process of compliant parts. Traditional fixture layout depends on workers’ experience, which leads to butt clearance along the assembly interface. Thus, this article proposes a butt clearance control-oriented fixture layout optimization (BCCFLO) methodology. First, a method for calculating the part dimensional variation under the influence of fixture layout and fixture locating error is developed. Then, a constrained multi-objective integer nonlinear programming (CMINP) model is innovatively formulated to optimize the fixture layout. Furthermore, the non-dominated sorting genetic algorithm-II based on Latin hypercube sampling is designed to address the CMINP model. The case study illustrates and validates that the fixture layout achieved by the proposed method could significantly control the butt clearance for large compliant part assembly in the shipbuilding industry.

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

For auto-body, fixture layout is very important to gravity deformation and dimensional variation of sheet metal assemblies. Conventionally, the satisfying fixture layouts can be generated by global optimization algorithms, such as genetic algorithm (GA), particle swarm optimization (PSO) and social radiation algorithm (SRA), etc. However, it is very difficult to generate the global optimalsolution because the combinations of fixture layouts are enormousand the gravity deformation must be calculated by finite element analysis for sheet metal parts. Therefore, this paper proposes a hybrid algorithm of GAOT (genetic algorithm in optimization toolbox in MATLAB) and RBF-NN(Radial basis function - neural network) to generate the global optimal fixture layouts. In this paper, the fixture locators are selected from a much smaller candidate pool based on filtering methods. The objective function is the gravity deformation of all measurement operations. A hybrid algorithm of GAOT and RBF-NN is used to optimize fixture locating scheme based on MATLAB macro commands of 3DCS, whose optimization process is fully automated. A case of bracketis applied to demonstrate the proposed method in this paper. The results show that the proposedhybridalgorithm can generate better optimal solutions thanthe current optimization methods.

Machining fixture locating and clamping position optimization using genetic algorithms

Optimisation of fixture layout is critical to reduce geometric and form error of the workpiece during the machining process. In this paper the optimal placement of fixture elements (locator and clamp locations) under dynamic conditions is investigated using evolutionary techniques. The application of the newly developed particle swarm optimisation (PSO) algorithm and widely used genetic algorithm (GA) is presented to minimise elastic deformation of the workpiece considering its dynamic response. To improve the performances of GA and PSO, an improved GA (IGA) obtained by basic GA (GA) with sharing and adaptive mutation and an improved PSO (IPSO) obtained by basic PSO (PSO) incorporated into adaptive mutation are developed. ANSYS parametric design language (APDL) of finite element analysis is employed to compute the objective function for a given fixture layout. Three layout optimisation cases derived from the high speed slot milling case are used to test the effectiveness of the GA, IGA, PSO and IPSO based approaches. The comparisons of computational results show that IPSO seems superior to GA, IGA and PSO approaches with respect to the trade-off between global optimisation capability and convergence speed for the presented type problems.

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.

Machining fixtures are used to locate and arrest the workpiece from deformation during machining operation. Fixture layout is the process of placing the locators and clamps in suitable position. The accuracy and quality of finished workpiece is depending on the number of fixturing elements and their positions. In this work, the fixture layout has been optimized by optimizing the number of fixture elements with optimal location. Initially 3-2-1 locating scheme has been followed to minimize the workpiece deformation, then the number of fixture elements are introduced to formthe new fixture plans such as 3-2-2, 3-3-1and 3-3-2. Finally, the optimum numbers of fixturing elements are confirmed. Moment equations has been developed for each fixture elements. Genetic algorithm-based optimization procedure is followed for obtaining optimum fixture layout. The moment equations are given to the GA as input objective function. Finite element solver ANSYS is used for predicting the workpiece deformation for various fixturing layouts.

Optimization of fixture layout by means of the genetic algorithm

This paper studies a fixture layout optimization problem for the ship assembly. Current studies focus on the positioning problem, i.e., optimizing the positions of a constant number of fixtures, while less considers the sizing problem, i.e., deciding the number of used fixtures. In most of the cases, it is difficult to assure that the adopted number of fixtures can lead to a layout that satisfies all the engineering requirements. The objective of this paper is to minimize the number of fixtures required while optimizing their positions, ensuring adherence to a set of engineering constraints. These include the maximum allowed nodal displacement and the assembly gap between two parts. We propose an efficient two-step metaheuristic approach. In the first step, fixtures are added iteratively to the parts until a feasible layout is achieved. In the second step, a large neighborhood search is employed to remove fixtures while maintaining the feasibility of the layout. To mitigate the computational cost required by finite element simulation, a Kriging model is proposed to evaluate the neighborhood solutions. Numerical experiments show that the proposed method can efficiently solve the fixture sizing and positioning problem in a case study of ship panel assembly. The efficacy of the Kriging model in accelerating layout optimization has been validated. Furthermore, the efficiency of the proposed method is demonstrated through comparisons with two existing approaches in the literature. Note to Practitioners—This paper was motivated by the problem of holding large compliant parts in the ship assembly process. Sheet metals with a low thickness-to-length ratio are susceptible to deformation during assembly when an inappropriate fixture layout is adopted. Existing approaches for layout design focus on optimizing the positions of the fixtures, while the number of fixtures needs to be determined based on engineering experience. This paper suggests a new approach to determine the minimum number of fixtures required, as well as their positions, to guarantee a set of quality requirements provided by the user. This approach employs the direct stiffness method to evaluate part deformation and an efficient metaheuristic to optimize the layout. During the optimization procedure, we use the Kriging technique to predict the layout’s performance, allowing us to obtain high-quality solutions with lower simulation efforts. We demonstrate that the proposed method can successfully generate a layout that satisfies the quality specifications in a case study of ship panel assembly. In comparison to two existing approaches, the proposed method yields a feasible layout with fewer fixtures, thereby reducing fixture setup time and building costs.

Improved workpiece location accuracy through fixture layout optimization

In assembly process control and design optimization, it is critical to establish a mathematical model that describes the relationship between the dimensional quality of the final product and the various process parameters (e.g., the fixture layout and locator position deviation). This article presents a surrogate modeling methodology for multistage assembly processes to characterize the relationship between fixture layout and product dimensional quality. The mathematical structure of the model is derived from a physical analysis based on first principles and then the parameters of the model are identified using data from computer experiments. The resulting surrogate model can enable fixture layout optimization in process planning. A comprehensive case study of a multistage assembly process is also presented to demonstrate the effectiveness and high fidelity of the developed method.

This article proposes a general fixture layout design framework that directly integrates the system equation with the convex relaxation method. Note that the optimal fixture design problem is a large-scale combinatorial optimization problem; we relax it to a convex Semi-Definite Programming (SDP) problem by adopting sparse learning and SDP relaxation techniques. It can be solved efficiently by existing convex optimization algorithms and thus generates a near-optimal fixture layout. A real case study in the half-to-half fuselage assembly process indicates the superiority of our proposed algorithm compared to the current industry practice and state-of-art methods.