Characteristic Research And Statistical Test Of Fractal Parameters Of Machine Joint Interfaces

Mechanical joint is widely existed in all kinds of mechanical structures.The study of mechanical joint is of great practical significance for the improvement of mechanical design theory and the design and manufacture of industrial equipment.In the research and development of the structure of NC machine tools with high precision,reliability and stability,contact characteristics of the joint are the key factors that affect the overall performance of the machine tool.The contact problem of the joint is a typical nonlinear problem,which still faces a very big challenge at present in the analysis method and the processing method.The difficulty of the research work lies in how to select the characterization parameters effectively that reflect the characteristics of the mechanical joint,and urgently need a joint model that can truly guide the engineering practice.In this paper,combining theory with application,fractal theory and statistical methods were used to deal with the nonlinear problem of joint contact.The contact characteristics of joint were studied from the internal mechanism.The fractal characterization parameters were extracted,and the fractal expression of surface contour of mechanical joint were studied as well.The fractal models of contact load and stiffness of the joint were established.The internal relation among the influencing factors were discussed as well.The friction and wear experiments were carried out to predict the state of friction by the characteristic parameters of the mechanical surface.The main work of this paper are as follows:The geometric parameters that effectively represent the characteristics of mechanical joints,including friction and wear characteristics,contact stiffness characteristics were proposed.Through theoretical analysis,statistical simulation and experimental testing,the essential characteristics and representational significance of fractal dimension have been discussed.From mechanical constraints for microscopic contact characteristics,fractal dimension is the most important parameter.Different from the general characterization parameters of surface roughness,the intrinsic significance and characterization function of fractal dimension were analyzed from multiple perspectives based on the statistical experiment of random simulation.Theoretically,fractal dimension is a measure parameter of similarity and an important parameter that affects the complexity of contour morphology.The fractal dimension had high sensitivity and identification degree in characterizing the fine roughness of contour revealed by experimental verification and statistical analysis of data.Based on theoretical analysis and simulation experiment,the contour curves corresponding to different fractal dimensions were compared,and it was concluded that the fractal dimension had significant influence on the height change,spatial frequency and fluctuation of contour.The contact load and stiffness models of the joints were established based on the fractal theory.Integrating theoretical analysis,experimental testing and machine learning,numerical simulation and experimental verification was carried out.Considering the transition deformation mechanism of mechanical joint surface,the premise and hypothesis in previous studies were weakened.The contact surface of the joint was extended from the equivalent sphere and the smooth rigid plane to the joint of two arbitrary quadric surfaces.By comparing the experimental mode with the fractal model,it has a good consistency.The natural frequency of the experiment is 2744.5Hz.The natural frequency of fractal model is 2789.1Hz.The errer is(2789.1-2744.5)/2744.5 =1.63%.The results of modal test are in good agreement with the simulation results of fractal model.Four experiments were designed and carried out on the basis of theoretical research.The significant advantage of surface fractal dimension of mechanical joint was verified by friction and wear experiment.It was pointed out that the extreme point of fractal dimension was an effective parameter to determine the wear state of mechanical surface.According to the characteristic parameter of fractal dimension,the advantages and disadvantages of Correlation function method,periodic diagram method,Bartlett method and Welch method were compared based on statistical simulation.The optimal method was obtained by point estimation and paired sample T test.To focus on the difficulty of that data of machine surface is limited,the prediction models of support vector machine were designed.The SVM prediction models not only overcame the difficulty of small data,but also improved the prediction accuracy.The intrinsic law of wear time and fractal dimension was discussed.Based on the principal component analysis and Wilcoxon symbolic rank test,the correlation between the fractal dimension of mechanical surface and wear time was obtained.Support vector machine regression model with fractal dimension of mechanical surface contour as input variable and wear time as output variable,the goodness of fit reached 91.07%.The prediction result is good.This paper is to provide statistical methods for parameter modeling of joint surface,propose a new idea for the parametric modeling of high-speed,high-precision and heavy-duty machine tools.It could give characterization parameter for mechanical wear time monitoring.It also could provide theoretical basis for performance prediction and optimization design of modern mechanical equipment such as linear rolling guide rail pair.