Based on the loading conditions of engine, applying difference method to solve the hydrodynamic lubrication equation of piston skirt movement, the force acting on piston skirt and the moment on wrist pin were obtained...Based on the loading conditions of engine, applying difference method to solve the hydrodynamic lubrication equation of piston skirt movement, the force acting on piston skirt and the moment on wrist pin were obtained. A computer program for simulating the piston second order motion was conducted to calculate the lateral motion of the upper part and the bottom part of piston skirts of the engine of automotive model CA1091. From the simulated result, the maximal impacting phase and the maximal impacting region of the piston were obtained. The result can be used for designing engine, diagnosing the noise of piston knocking cylinder wall and explaining many practical fault phenomena in theory.展开更多
The m-th order detrended Brownian motion is defined as the orthogonal component of projection of the standard Brownian motion onto the subspace spanned by polynomials of degree up to m. We obtain the Karhunen-Loeve ex...The m-th order detrended Brownian motion is defined as the orthogonal component of projection of the standard Brownian motion onto the subspace spanned by polynomials of degree up to m. We obtain the Karhunen-Loeve expansion for the process and establish a connection with the generalized (m-th order) Brownian bridge developed by MacNeill (1978) in the study of distributions of polynomial regression. The resulting distribution identity is also verified by a stochastic Fubini approach. As applications, large and small deviation asymptotic behaviors for the L2 norm are given.展开更多
文摘Based on the loading conditions of engine, applying difference method to solve the hydrodynamic lubrication equation of piston skirt movement, the force acting on piston skirt and the moment on wrist pin were obtained. A computer program for simulating the piston second order motion was conducted to calculate the lateral motion of the upper part and the bottom part of piston skirts of the engine of automotive model CA1091. From the simulated result, the maximal impacting phase and the maximal impacting region of the piston were obtained. The result can be used for designing engine, diagnosing the noise of piston knocking cylinder wall and explaining many practical fault phenomena in theory.
基金supported by the Fundamental Research Funds for the Central Universities(Grant No.DL13BBX10)
文摘The m-th order detrended Brownian motion is defined as the orthogonal component of projection of the standard Brownian motion onto the subspace spanned by polynomials of degree up to m. We obtain the Karhunen-Loeve expansion for the process and establish a connection with the generalized (m-th order) Brownian bridge developed by MacNeill (1978) in the study of distributions of polynomial regression. The resulting distribution identity is also verified by a stochastic Fubini approach. As applications, large and small deviation asymptotic behaviors for the L2 norm are given.