Longitudinal Time-varying Characteristics Of Lifting System For High-speed Traction Elevators

As the "vertical sports car",elevators have become the indispensable means of transportation in our daily lives,and their safety and comfort have become the basic requirements for elevators.Elevator hoisting wire rope has a certain time-varying characteristic,and its quality,rigidity and damping are constantly changing with the up and down operation of the elevator.The rising of high-rise and super high-rise buildings promotes the development of elevators in the direction of long stroke and high speed.The speed increase will make the time-variant characteristic of elevator hoisting ropes even more obvious,which seriously affect the dynamic performance of elevators,especially the longitudinal dynamic performance indicators.In addition,the time-variation of the hoisting rope will also cause dynamic changes in the tension of the hoisting rope and affect the safety of the elevator.Therefore,it is necessary to study the longitudinal time-varying characteristic of the highspeed elevator hoisting system,grasp the mechanism of its action and guide the vibration damping design of the high-speed elevator to improve the safety and comfort of the elevator.In this paper,theoretical analysis and numerical simulation are used to systematically study the longitudinal time-varying effect of high-speed elevator hoisting system.Firstly,considering the effect of high-speed elevator compensation rope weight and the pre-tightening force provided by the tensioning system,the high-speed elevator hoisting rope is simplified as a string moving up and down and subjected to an axial preload,the car is reducible to a rigid weight block with a mass of m without considering its specific structure.And then a partial differential equation for the longitudinal time-varying dynamics of highspeed elevator hoisting system is constructed based on the energy method and generalized Hamilton principle.To solve the problem that partial parameters in partial differential equation are difficult to determine,the fifth-order polynomial is used to fit the actual operating state parameters of the elevator,and the value of the elastic modulus of the steel wire rope is analyzed.Secondly,aiming at the problem of the infinite degrees of freedom and the difficulty in solving of the partial differential control equations,the Galerkin method in the weighted residual method is used to transform the partial differential equations with the infinite degrees of freedom of the equations to the ordinary differential equations with finite freedoms.Then a precise integration method for the longitudinal time-varying model of high-speed elevators is proposed by considering the time-varying characteristic of the model and the accuracy of the numerical algorithm,and the transformed differential dynamics equations are solved.In view of the random parameters caused by the manufacturing and installation errors of high-speed elevator hoisting system,the stochastic perturbation theory is used to derive the expressions of the deterministic and stochastic parts of the longitudinal acceleration response of the high-speed elevator hoisting system.The sensitivity expressions for displacement,velocity and acceleration of random parameters are derived by solving the stochastic response expressions,and then the influence of random parameters on longitudinal vibration displacement,speed and acceleration response of elevator hoisting system is analyzed.The results show that the sensitivity of lifting wire rope density is the biggest,followed by lifting quality,and the sensitivity of lifting wire rope's elastic modulus is the smallest.What's more,the three random parameters of improving the quality-the quality of lifting,the elastic modulus of wire rope and the density of wire rope-are the most sensitive to the response of the vibration acceleration,the second is the response of the vibration velocity,and the sensitivity of the response of the vibration displacement is the least.Then,the dynamic characteristics of the elevator up and down and the influence of different structural parameters on the dynamic characteristics are analyzed based on the vertical time-varying model of the high-speed elevator hoisting system.It is found that the shorter the elevator hoisting rope is,the greater the longitudinal vibration frequency of the elevator will be.In addition,the peak value of the longitudinal vibration acceleration response of the elevator is negatively related to the length,hoisting quality,model and the elastic modulus of the wire rope,and has a positive correlation with the pretension provided by the tensioning system.Finally,the time-varying tension model of the high-speed elevator hoisting rope is constructed by considering the effects of the compensation rope and the preload.The elevator operation parameters fitted by the five order polynomial are used as the input,and then the time variant tension is simulated by the fine integral method,the influence of some structural parameters on the time-varying tension is analyzed.It is found that the time-varying tension peak and the range of change of the hoisting wire rope have a negative correlation with the size of the hoisting wire rope,and the influence degree is relatively small;it has a positive correlation with the elevator's rated quality and the elevator pretightening force,and the influence is more prominent.