Abstract
In this paper, for studying the influence of the randomness of structural parameters of high-speed elevator lifting system (HELS) caused by manufacturing error and installation error, a continuous time-varying model of HELS was constructed, considering the compensation rope mass and the tension of the tensioning system. The Galerkin weighted residual method is employed to transform the partial differential equation with infinite degrees of freedom (DOF) into the ordinary differential equation. The five-order polynomial is used to fit the actual operation state curve of elevator, and input as operation parameters. The precise integration method of time-varying model of HELS is proposed. The determination part and the random part response expression of the longitudinal dynamic response of HELS are derived by the random perturbation method. Using the precise integration method, the sensitivity of random parameters is determined by solving the random part response expression of time-varying model of HELS, and the digital characteristics of the acceleration response are analyzed. It is found that the line density of the hoisting wire rope has the maximum sensitivity on longitudinal vibration velocity response, displacement response and acceleration response, and the sensitivity of the elastic modulus of the wire rope is smallest.
Highlights
As a “vertically moving car”, the elevator has been widely used in high-rise buildings and super high-rise buildings
Manufacturing error and installation error in the highspeed elevator lifting system are objective. The random parameters such as wire rope density, and elastic modulus existing in the lifting system cause the vibration of the high-speed elevator lifting system (HELS) to be random vibration
Zhang et al [13] simplified the elevator hoisting rope to a variable length axial motion string with a certain mass attached to one end, the differential equations and energy equations for the vertical vibration of the HELS were established by the energy method and the Hamilton principle
Summary
As a “vertically moving car”, the elevator has been widely used in high-rise buildings and super high-rise buildings. Zhang et al [13] simplified the elevator hoisting rope to a variable length axial motion string with a certain mass attached to one end, the differential equations and energy equations for the vertical vibration of the HELS were established by the energy method and the Hamilton principle. For the time-varying dynamic model of the high-speed elevator traction hoisting system established above, because of its strong time-varying characteristics, the mass, damping and stiffness of the system are changing every moment. It is difficult for the general numerical method to achieve high accuracy for this kind of problem. According to equation (21), given initial condition z0, the steps are gradually performed to obtain z1, z2, . . . , zk, . . . , which is a typical “self-starting” algorithm
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