Study On The Relationship Between The Actual Sizes,geometric Error Eigenvalue And Global Sizes Of Two Relative Parallel Surface Parts

The global sizes（the least squares size,the minimum circumscribed size,the maximum inscribed size and the minimax size）of two parallel opposite planes are defined in the new generation Geometrical Product Specifications（GPS）,but have not been seen at present research on the measurement and evaluation of the global sizes of two parallel opposite planes.In this thesis,a systematic study on the relationship between the actual sizes of two parallel opposite planes,geometric error eigenvalues and global sizes will be carried out.Based on the planar profiles extracted by the parallel line extraction strategy,the evaluation models of flatness error,parallelism error and global sizes were established.For the‘minimax’problem in the evaluation of the minimum zone flatness error,the minimum zone plane datum,the minimum circumscribed size,the maximum inscribed size and the minimax size of two parallel opposite planes,the Whale Optimization Algorithm（WOA）was improved,and the computer program of the Improved Whale Optimization Algorithm（IWOA）was developed.The adaptability of IWOA in the evaluation of the minimum zone of flatness error was studied.Based on BP neural network,four relationship models of input layer（actual size and geometric error eigenvalues）-hidden layer-output layer（global sizes）were established,namely,the input values of relationship model 1 are the mean value of feature sizes,the two least-squares flatness errors,the two parallelism errors（two planes are mutual datum and measured feature,least-squares datum planes）;the input values of relationship model 2 are the maximum value of feature sizes,the two least-squares flatness errors,the two parallelism errors（two planes are mutual datum and measured feature,least-squares datum planes）.the input values of relationship model 3 are the minimum value of feature sizes,the two least-squares flatness errors,the two parallelism errors（two planes are mutual datum and measured feature,least-squares datum planes）.The input values of the relationship model 4 are the mean value of the feature sizes,the two minimum zone flatness errors,and the two parallelism errors（two planes are mutual datum and measured feature,least-squares datum planes）.The output values of the relationship models 1,2,3 and 4 are the least squares size,the minimum circumscribed size,the maximum inscribed size and the minimax size,respectively,and IWOA was applied to the optimization of the relationship model parameters to reduce the mean square error（MSE）of the relationship model and improve the accuracy of the relationship model.The global sizes and geometric errors of the two parallel opposite planes were extracted from 65 shafts and 38 hole of two parallel opposite planes by using the measuring instrument of the global sizes and geometrical errors for two parallel opposite planes and their global sizes,flatness error（least squares method,minimum zone method）,parallel errors（least squares datum plane,minimum zone datum plane）were evaluated by the developed evaluation program.By optimizing the parameters related to the BP neural network（based on different training functions）with IWOA,four relationship models were trained,and the training results showed that:（1）the training function‘trainlm’is better than the training function‘trainbr’for the relationship model based on BP neural network;（2）the accuracy of the IWOA-based optimized relationship models is better than that of the relationship model optimized based on other algorithms;（3）the MSE of the four relationship models obtained based on IWOA-BP neural network training is less than 6.9×10^-7 mm²,and the accuracy of the above relationship models meet the measurement accuracy requirement of the global sizes of the two parallel opposite planes parts.Based on the above neural network relationship models,the limit deviations of global sizes of two parallel opposite planes with nominal dimensions of18mm～400mm,dimensional tolerances of IT5～IT8,geometric tolerances of Grade 5～8,and basic deviation codes such as h（H）for the global sizes were predicted,and the corresponding global dimensional limit deviation prediction values were given.The indirect measurement and limit deviation prediction method of global sizes based on neural network relationship model proposed in this thesis has certain theoretical support and practical value for the implementation of global size of two parallel opposite planes in manufacturing industry.