Abstract
In a high-rise elevator system lateral vibrations of the suspension and compensating ropes, coupled with vertical motions of the car and counterweight are induced by the building structure motions. When the frequency of the building coincides with the fundamental natural frequency of the ropes, large resonance whirling motions of the ropes result. This phenomenon leads to impacts of the ropes on the elevator walls, large displacements of the car and counterweight making the building and elevator system unsafe. This paper presents a comprehensive mathematical model of a high-rise elevator system taking into account the combined lateral stiffness of the roller guides and guide rails. The results and analysis presented in the paper demonstrate frequency curve veering phenomena and a wide range of resonances that occur in the system. A case study is presented when the car is parked at a landing level where the fundamental natural frequencies of the car, suspension and compensating rope system coincide with one of the natural frequencies of the high-rise building. The results show a range of nonlinear dynamic interactions between the components of the elevator system that play a significant role in the operation of the entire installation.
Highlights
Lateral vibrations of the suspension and compensating ropes in a high-rise elevator system are induced by the building motions caused by high winds
In lifting applications the multibody dynamic behaviour of ropes has been studied when heavy cargo is suspended by ropes in a floating crane system [4], and the kinematic and dynamic analysis of rope winding process has been the subject of a study presented in [5]
This paper extends the analysis presented in the previous research to develop a comprehensive mathematical model of a high-rise elevator system in order, to understand and to predict the interaction between the lateral vibrations of the suspension and compensating ropes coupled with the longitudinal vibrations of the elevator car, compensating sheave, and counterweight taking into account the combined lateral stiffness characteristics of the elevator car guiding system
Summary
Lateral vibrations of the suspension and compensating ropes in a high-rise elevator system are induced by the building motions caused by high winds. In lifting applications the multibody dynamic behaviour of ropes has been studied when heavy cargo is suspended by ropes in a floating crane system [4], and the kinematic and dynamic analysis of rope winding (unwinding) process has been the subject of a study presented in [5] Another example of engineering applications of ropes is in building elevators and mine hoists [6,7,8,9]. RV1/W1irnjp, RV2/W2irnjp coefficients corresponding to the cubic nonlinear coupling of the system for the ith rope for the lateral in plane and out of plane direction Ru1/u2, Ru1/u2/u3/u4, Ru1/u2/u3/u4 coefficients that account for the lateral in plane and out of plane quadratic nonlinear terms acting in the longitudinal direction of the elevator car, compensating sheave, and counterweight. T i UCR, UCS, UCW tension of the ith rope dynamic displacements in the longitudinal direction of the elevator car, compensating sheave and counterweight
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