Method of estimating the lateral vibration of an elevator rope from the vertical vibration of a compensating sheave

Observing the vibration of the elevator ropes in an elevator shaft is a difficult task. Although several methods of observing the displacement using image processing or laser displacement meters and then estimating the vibration through an observer or a Kalman filter have been developed, it is difficult to install sensors because of the movement of the elevator car and the thinness of the rope as an observation target. Therefore, in this study, we focus on a pulley called a compensating sheave that does not change its lateral position as the car and ropes move. The horizontal vibration of the ropes causes the compensating sheave to vibrate in the vertical direction. A method of estimating the horizontal vibration from this vertical vibration using arc length calculations and a short-time fast Fourier transform is proposed. First, the vertical vibration of the compensating sheave is distributed to the various mode responses based on the predominant frequency of the vertical vibration. The mode-decomposed vertical vibration is then converted into a horizontal mode response using an arc length relational expression. Analysis of seismic response data confirms that the proposed method can estimate the 1st, 2nd, and 3rd horizontal mode responses from the vertical vibration.