Fixture Locating Layout Planning For Sheet Metal Part Using CSA-OK Model

Sheet metal part is widely used in aviation,aerospace and automobile industries because of its light weight and high strength,etc.What's more,there are plenty of sheet metal parts extensively employed by the airframe mainly made up of pieces of panels,and the car body.Owing to the thin wall,large size,low rigidity,etc.of sheet metal,the fixture for sheet metal part is often designed based on the"N-2-1"locating principle,that is placing N?N>3?locators on the main datum plane of the workpiece so as to constrain its excessive deformation along the normal direction and ensure its manufacturing precision.The"N-2-1"sheet metal fixture locating layout design about how to determine the specific number and location of the N locating points on the main datum plane naturally becomes a must-to-be-solved problem in the manufacturing process and fixture design.The traditional method based on experience or trial and error often leads to low efficiency of fixture design,high manufacturing cost,moreover the deformation of the product out of tolerance in the machining and assembly process,which ultimately affects the manufacturing precision and quality of the aircraft and other products.With the manufacturing precision and lightweight requirements for the product to be increased further in aviation,aerospace,automotive and other industries,the research on the"N-2-1"sheet metal fixture locating layout design methods for controlling the deformation of the workpiece becomes very urgent.In recent years,the development and application of the computer-aided fixture design?CAFD?technology has greatly improved the quality and efficiency of fixture design.However,the effective and efficient"N-2-1"sheet metal fixture locating layout design optimization is still a technically difficult problem to be solved.Seen from the perspective of the inverse problem theory,the"N-2-1"sheet metal fixture locating layout design belongs to the typical kind of boundary condition control inverse problem and therefore solving it has to depend on the numerical method.The state-of-the-art method based on the evolutionary algorithm coupled with finite element analysis often involves hundreds of thousands of times of calling the time-consuming finite element solver and leads to such huge computation cost while the emerging and potential method based on the evolutionary algorithm combined with the surrogate model makes it difficult to ensure the quality of the solution.To this end,based on finite element simulation modeling and by introducing Latin hypercube sampling?LHS?,cuckoo search algorithm?CSA?and ordinary Kriging?OK?surrogate model,this paper conducts the research on the design methods of the"N-2-1"sheet metal fixture locating layout for the workpiece deformation control in order to provide the theoretical guidance for the"N-2-1"sheet metal fixture locating layout design.The main work of the paper is as follows:1.The CSA based method for building the CSA-OK surrogate model is presented.CSA is introduced to the estimation of the hyper-parameters in order to build the OK surrogate model by searching the optimal values of the correlation parameter vector of the maximum likelihood function.The two standard test functions of Branin and Six hump camel back are used as numerical cases to verify the effectiveness of the presented method,and the results show that there is no need to fine-tune the control parameters in building the CSA-OK surrogate model,and the CSA-OK surrogate model is robust and more accurate than PS-OK based on the same training and test data set,which lays the foundation of the subsequent research work.2.The sequential approximate approach for modeling the"N₀-2-1"sheet metal fixture locating layout is proposed based on the mean squared error infilling sampling criterion.Given that the number of the locating points on the primary datum plane of the workpiece is set as N₀,the initial CSA-OK surrogate model is established based on the initial training data set,which is acquired through LHS and limited times of parametric finite element analysis,to approximate the implicit mapping relationship between the fixture locating layout and the concerned sheet metal deformation response.A new sample is generated via optimizing the auxiliary function of the mean squared error infilling sampling criterion by CSA and finite element analysis.The current training data set is updated by adding the newly generated sample and does not stop being employed to iteratively update the current CSA-OK surrogate model until the predictive accuracy requirements of the current CSA-OK surrogate model for the sheet metal fixture locating layout are met to complete the dynamic adjustment and improvement of the prediction capability of the"N₀-2-1"sheet metal fixture locating layout model.3.The sequential approximate approach for the feasible design of the"N₀-2-1"sheet metal fixture locating layout is proposed based on the goal seeking infilling sampling criterion given the tolerable deformation of the workpiece.The initial CSA-OK surrogate model is established to approximate the implicit mapping relationship between the fixture locating layout and the tolerable sheet metal deformation response.Based on the conditional maximum likelihood estimation theory,a new sample is generated via optimizing the auxiliary function of the goal seeking infilling sampling criterion by CSA and finite element analysis.The current training data set is updated by adding the newly generated sample and does not stop being employed to iteratively update the current CSA-OK surrogate model for the sheet metal fixture locating layout until a feasible fixture locating layout is found to complete the sequential inverse design of the feasible"N₀-2-1"sheet metal fixture locating layout.4.The sequential approximate approach for the optimal design of the"N₀-2-1"sheet metal fixture locating layout to minimize the concerned deformation of the workpiece is proposed based on the expected improvement infilling sampling criterion.The initial CSA-OK surrogate model is established to approximate the implicit mapping relationship between the fixture locating layout and the concerned sheet metal deformation response.A new sample is generated via optimizing the auxiliary function of the expected improvement infilling sampling criterion by CSA and finite element analysis.The current training data set is updated by adding the newly generated sample and does not stop being employed to iteratively update the current CSA-OK surrogate model for the sheet metal fixture locating layout until the stopping condition is met to complete the sequential optimization design of the"N₀-2-1"sheet metal fixture locating layout.5.The three stage method for designing the integral fixture locating layout for sheet metal part based on the"N-2-1"locating principle is proposed.The integral"N-2-1"sheet metal fixture locating layout design process is decomposed into three stages given the tolerable deformation of the workpiece.At the first stage,CSA is adopted to accomplish the robust design of the determinant"3-2-1"fixture locating layout of the workpiece;At the second stage,the minimum number of the locating points on the primary datum plane satisfying the tolerable deformation of the workpiece,that is N_min,is obtained by self-increasing N_min one by one from 4 and applying the sequential approximate approach for the inverse design of the feasible sheet metal"N₀-2-1"fixture locating layout;At the final stage,the optimum location of the remaining"N_min-3"locating points on the primary datum plane of the workpiece is achieved by applying the sequential approximate approach for the optimal design of the sheet metal"N₀-2-1"fixture locating layout to complete the integral"N_min-2-1"sheet metal fixture locating layout design.The aluminum flat and curved sheet metal parts are adopted as the cases throughout the paper to complete the sheet metal"N₀-2-1"fixture locating layout modeling,the inverse design of the feasible"N₀-2-1"sheet metal fixture locating layout,the sheet metal"N₀-2-1"fixture locating layout optimization design and the integral"N-2-1"sheet metal fixture locating layout design.The case study results verify the effectiveness of the proposed methods.