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TECHNICAL PAPERS

Theoretical and Experimental Investigation of Elevator Cable Dynamics and Control

[+] Author and Article Information
W. D. Zhu

Department of Mechanical Engineering,  University of Maryland, Baltimore County, Baltimore, MD 21250wzhu@umbc.edu

Y. Chen

Department of Mechanical Engineering,  University of Maryland, Baltimore County, Baltimore, MD 21250yanchen1@umbc.edu

J. Vib. Acoust 128(1), 66-78 (Apr 05, 2005) (13 pages) doi:10.1115/1.2128640 History: Received December 09, 2003; Revised April 05, 2005

The vibratory energy of a moving cable in an elevator increases in general during upward movement. A control method is presented to dissipate the energy associated with the lateral vibration of the cable. A novel experimental method is developed to validate the theoretical predictions for the uncontrolled and controlled lateral responses of a moving cable in a high-rise elevator. This includes the design and fabrication of a scaled elevator, experimental setup, and development of measurement and parameter estimation techniques. Experimental results show good agreement with the theoretical predictions.

Copyright © 2006 by American Society of Mechanical Engineers
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Figures

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Figure 1

Schematic of the prototype elevator

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Figure 2

Schematic of the model elevator. The motor can be placed at the top or bottom left position.

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Figure 3

Movement profile of the prototype elevator: (a) position, (b) velocity, (c) acceleration, and (d) jerk

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Figure 4

The prototype tension at the top of the car under the movement profile in Fig. 3 is shown in (a). The tensions at the top of the car for the full and half models under the movement profiles corresponding to that for the prototype in Fig. 3 are shown in (b) and (c), respectively, with the motor at the top left (solid), bottom left (dashed), top right (dashed-dotted), and bottom right (dotted) positions.

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Figure 5

The displacement and velocity of the prototype cable (solid) at xp=12m and those predicted by the half model (dashed) with the motor at the top left position are shown in (a) and (b), respectively. The vibratory energy of the prototype cable (solid) and those predicted by the half models with the motor at the top (dashed) and bottom (dotted) left positions are shown in (c).

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Figure 6

The displacement and velocity of the prototype cable (solid) at xp=12m and those predicted by the full model (dashed) with the motor at the top left position are shown in (a) and (b), respectively. The vibratory energy of the prototype cable (solid) and those predicted by the full models with the motor at the top (dashed) and bottom (dotted) left positions are shown in (c).

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Figure 7

The dependence of the damping effect of the prototype cable during upward movement on the damping coefficient, where the initial displacement corresponds to each of its first 12 mode shapes, and the initial velocity is zero, and ldp=2.5m. The curves from top to bottom have increasing mode numbers as labeled.

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Figure 8

Uncontrolled (solid) and controlled displacements (a) and vibratory energies (b) of the prototype cable with natural damping with Kvp=2050Ns∕m (dashed) and Kvp=375Ns∕m (dotted); ldp=2.5m. The initial conditions are the same as those used in Figs.  56.

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Figure 9

Contour plot of the average energy ratio for the sixth mode response of the prototype cable with its isoline values in percentage labeled

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Figure 10

(a) Instrumented scaled elevator. (b) Certain components in the scaled elevator.

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Figure 11

Schematic of the experimental setup

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Figure 12

Measured tension difference of the band between upward and downward movements with constant velocity as a function of the position of the car: dotted, original signal; dashed, filtered signal; solid, linearly curve-fitted, filtered signal

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Figure 13

Natural damping ratio of the stationary band with varying length, where (◻) are experimental data and the line is from the linear curve-fit of the data

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Figure 14

Measured (solid) and calculated (dashed) responses of the uncontrolled (a) and controlled (b), stationary bands with natural damping

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Figure 15

Measured (solid) and prescribed (dashed) movement profiles: (a) position, (b) velocity, and (c) acceleration; and calculated tensions (d) using measured (solid) and prescribed (dashed) movement profiles

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Figure 16

Measured (solid) and calculated (dashed) responses of the uncontrolled (a) and controlled (b) bands and calculated vibratory energies (c) of the uncontrolled band with (solid) and without (dotted) natural damping and the controlled band with natural damping (dashed)

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