According to the suitable assumption, the deformation process of external spline cold rolling is analyzed. By the graphing method, the slip-line field of plastically deforming area in process of external spline cold r...According to the suitable assumption, the deformation process of external spline cold rolling is analyzed. By the graphing method, the slip-line field of plastically deforming area in process of external spline cold rolling is set up. Different friction-conditions are used in different contact areas in order to realistically reflect the actual situation. The unit average pressure on contact surface of the rolling process is solved according to the stress filed theory of slip-line. And the formulae of the rolling-force and rolling-moment are established. The theoretical result is well consistent with the finite element analysis. A theoretical basis is provided for the precise forming process of spline cold rolling and the production of external splined shafts.展开更多
The ratio of expectation crossings of dielectric elastomer balloon excited by random pressure is analytically evaluated in this letter. The Mooney-Rivlin model is adopted to describe the constitutive relation while th...The ratio of expectation crossings of dielectric elastomer balloon excited by random pressure is analytically evaluated in this letter. The Mooney-Rivlin model is adopted to describe the constitutive relation while the random pressure is described by Gaussian white noise. Through a specific transformation, the stochastic differential equations for the total energy and phase are derived. With the application of the stochastic averaging, the system total energy is then approximated by a one-dimensional diffusion pro-cess. Solving the associated Fokker-Planck-Kolmogorov （FPK） equation yields the stationary probability density of the system total energy. The ratio of expectation crossings is then derived based on the joint stationary probability density of stretch ratio and its ratio of change. The efficacy and accuracy of the proposed procedure are verified by comparing with the results from Monte Carlo simulation （MCS）.展开更多
基金This project is supported by National Natural Science Foundation of China (No. 50675145)Provincial Key Project of Science and Technology of Shanxi, China (No. 2006031147)+1 种基金Provincial Innovation Project for Graduate Students of Shanxi, China (No. 20061027)Provincial Key Project for Studied-abroad Returnee of Shanxi, China.
文摘According to the suitable assumption, the deformation process of external spline cold rolling is analyzed. By the graphing method, the slip-line field of plastically deforming area in process of external spline cold rolling is set up. Different friction-conditions are used in different contact areas in order to realistically reflect the actual situation. The unit average pressure on contact surface of the rolling process is solved according to the stress filed theory of slip-line. And the formulae of the rolling-force and rolling-moment are established. The theoretical result is well consistent with the finite element analysis. A theoretical basis is provided for the precise forming process of spline cold rolling and the production of external splined shafts.
基金supported by the National Natural Science Foundation of China(11672262,11472240,11532011,and 11621062)
文摘The ratio of expectation crossings of dielectric elastomer balloon excited by random pressure is analytically evaluated in this letter. The Mooney-Rivlin model is adopted to describe the constitutive relation while the random pressure is described by Gaussian white noise. Through a specific transformation, the stochastic differential equations for the total energy and phase are derived. With the application of the stochastic averaging, the system total energy is then approximated by a one-dimensional diffusion pro-cess. Solving the associated Fokker-Planck-Kolmogorov （FPK） equation yields the stationary probability density of the system total energy. The ratio of expectation crossings is then derived based on the joint stationary probability density of stretch ratio and its ratio of change. The efficacy and accuracy of the proposed procedure are verified by comparing with the results from Monte Carlo simulation （MCS）.
