Accurate Simulation of the Dynamics of Elevator Systems
Creators: name: Ren, Hui
Publisher: name: Maryland Shared Open Access Repository
Year: 2011
Subjects: Elevator Systems
Multibody Dynamics
Slack Cables
Spatially Discretization
Substructural Method

description: Accurate simulation of dynamics of elevator systems is important in addressing challenges in the design of elevators. This dissertation is dedicated to the methodologies and applications of the numerical simulation of the dynamics of elevator cable-car systems, pulley-cable systems, and traveling and compensation cables.  A new spatial discretization and substructure method is developed to calculate the dynamic responses of one-dimensional systems, which consist of length-variant distributed-parameter components such as strings, rods, and beams, and lumped-parameter components such as point masses and rigid bodies. This methodology is used to study the longitudinal, transverse, and their coupled dynamics of moving elevator cable-car systems. There are complicated matching conditions between the cable and the car, which cannot be satisfied in traditional methods, but can be satisfied in the current method. Hence not only the displacements, but also the internal forces/moment, such as the axial force, the bending moment, and the shear force, which are related to the spatial derivatives of the longitudinal or transverse displacement, are accurately calculated. The longitudinal-transverse coupled vibrations of a moving cable-car  system are also studied using this method, and the results are compared with those from the linear models. While the result from the linear model for the transverse vibration agrees well with that from the nonlinear coupled model, the axial force calculated from the linear model can significantly differ from that from the nonlinear model when the car approaches the top of the hoist way. It is found that a large slope in the transverse vibration can significantly increase the vibratory tension in the cable, and attenuate the safety of the system. These results can be explained by theoretical analysis and verified by the absolute nodal coordinate formulation.  The methodology is also used in conjunction with a simple belt creep model to study the dynamics of pulley-cable systems.  A nonlinear, planar model of a slack cable with bending stiffness and arbitrarily moving ends is developed, using the slope angle of the  centroid line of the cable to describe the motion of the cable,  and is applied to elevator traveling and compensation cables.  It is found that a vertical motion of the car can introduce a horizontal vibration of a traveling or compensation cable. This model is more efficient than the finite element models as it uses a much smaller number of elements to reach the same accuracy. Moreover, based on the asymptotic analysis of this model, a computationally efficient, linear model is developed for calculating the natural frequencies, mode shapes, and dynamic responses of stationary elevator traveling and compensation cables. The linear cable model consists of two vertical cable segments connected by a half circular loop at the bottom.  There is a good agreement between the predictions from the linear and nonlinear models and between the measured natural frequencies from a full-scale experiment and the corresponding calculated ones.