Theoretical and Experimental Investigation of Elevator Cable Dynamics and Control

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

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.

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).

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.

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

Schematic of the experimental setup

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

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

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

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

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)

Schematic of the prototype elevator

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

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).

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.  5, 6.

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