Research On The Prediction Of Machining Errors For Free-form Surfaces Based On Grey Theory

With the rapid development of industrial manufacturing in China,the demand for precision parts is increasing,and the free-form surfaces are more widely used,being used in aerospace,automotive and other high-end manufacturing industries.At the same time,the 14 th Five-Year Plan has also put forward intelligent and efficient manufacturing requirements.In order to meet the needs of social development,product testing,as an important part of manufacturing,is also facing a major transformation.Based on this background,this paper presents an in-depth study of the application of grey prediction models to the prediction of free-form machining errors.The main content includes the following areas.(1)Based on the characteristics of the distribution of free-form surface machining errors,the shortcomings of the traditional grey prediction model were analysed,and the model was optimised in conjunction with the new information priority theory.The improved prediction model was investigated by example to verify the feasibility of the grey prediction model for the application of free-form surface machining error prediction.And the improved grey prediction model has improved the prediction accuracy compared with the traditional model,but the prediction range was smaller,and the model’s prediction accuracy was not high when the processing error data fluctuates a lot.(2)In response to the problem that the traditional univariate grey prediction model does not fit the data simulation well and cannot analyse the data trend in the case of strong data fluctuation during the forecasting process,a multivariate grey prediction model was proposed to predict the free-form surface machining errors.The problem of inaccurate construction of background value expressions in traditional grey prediction models has an impact on the prediction results of the models.A method was given to optimise the background value expressions of the models and to improve the structural compatibility of the models so as to improve their prediction accuracy and generalisation.(3)The advantages and disadvantages of a single prediction model were analysed,by combining grey and neural network models in an effective way.Three different structures of combined prediction models were proposed,namely series grey neural network,parallel grey neural network and embedded grey neural network.The improved sparrow search algorithm was also used to optimise the neural network and improve the problem of too slow convergence of the neural network in the prediction process.Finally,the prediction accuracy of the three models was analysed through examples,verifying that the combined prediction models were feasible for predicting free-form machining errors and providing technical support for error compensation.(4)By analysing the fact that combined forecasting models do not have the same forecasting accuracy at each stage in forecasting,a dynamic analysis of the weights of combined forecasting models was proposed and the mean absolute error was used to determine the weights of a single forecasting model.A BP neural network model,a Markov prediction model and a modified multivariate grey prediction model were selected to model the combined prediction of free-form surface machining errors.Finally,the prediction accuracy of the combined prediction model was compared with that of a single model,proving the advantages of the combined prediction method and that the combination of variable weights was more effective.