Forced Response of Translating Media With Variable Length and Tension: Application to High-Speed Elevators

2004 ◽  
Author(s):  
W. D. Zhu ◽  
Y. Chen
Keyword(s):  
High Speed ◽  
Initial Conditions ◽  
Control Volume ◽  
String Model ◽  
Forced Response ◽  
Rate Of Change ◽  
Variable Length ◽  
Lateral Response ◽  
Discretization Schemes ◽  
Fixed Boundaries

The lateral response of vertically translating media with variable length and tension, subjected to general initial conditions and external excitation, are determined. The translating media are modeled as a taut string and tensioned beams with pinned and fixed boundaries. In each model a rigid body is attached to the lower end of the medium and has a prescribed displacement along the horizontal direction. The rate of change of the energy of the translating medium is analyzed from the control volume and system viewpoints. The models are used to predict the forced response of a moving cable in a high-speed elevator. Three spatial discretization schemes are used to calculate the response and shown to yield the same results. The convergence of the solution for each model is investigated. The approximate solution for the string model with constant tension is compared with its exact solution from the wave method.

Forced response of translating media with variable length and tension: Application to high-speed elevators

2005 ◽  
Vol 219 (1) ◽  
pp. 35-53 ◽  
Author(s):  
W D Zhu ◽  
Y Chen
Keyword(s):  
High Speed ◽  
Initial Conditions ◽  
Control Volume ◽  
String Model ◽  
Forced Response ◽  
Rate Of Change ◽  
Variable Length ◽  
Lateral Response ◽  
Discretization Schemes ◽  
Fixed Boundaries

The lateral response of vertically translating media with variable length and tension, subjected to general initial conditions and external excitation, are determined. The translating media are modelled as a taut string and tensioned beams with pinned and fixed boundaries. In each model a rigid body is attached to the lower end of the medium and has a prescribed displacement along the horizontal direction. The rate of change in the energy of the translating medium is analysed from the control volume and system viewpoints. The models are used to predict the forced response of a moving cable in a high-speed elevator. Three spatial discretization schemes are used to calculate the response and shown to yield the same results. The convergence of the solution for each model is investigated. The approximate solution for the string model with constant tension is compared with its exact solution from the wave method.

Forced Response of Translating Media With Variable Length and Tension and a Mass-Spring Termination

2005 ◽  
Author(s):  
Yan Chen ◽  
W. D. Zhu
Keyword(s):  
High Speed ◽  
Initial Conditions ◽  
Resonance Condition ◽  
Control Volume ◽  
Forced Response ◽  
Variable Length ◽  
Lateral Response ◽  
Suspension Stiffness ◽  
Rail Irregularity ◽  
Mass Spring

The lateral response of vertically translating media with variable length and tension and a mass-spring termination is determined for general initial conditions and external excitation. The translating media are modeled as a taut string and tensioned beams with pinned and fixed boundary at the upper end. In each case a spring-mass sub-system is attached at the lower end of the translating medium. The rates of change of the energies in each case are analyzed and interpreted from the control volume and system viewpoints. The models are used to predict the forced response of cable-car systems in high-speed elevators due to building sway, pulley eccentricity, and guide-rail irregularity. The optimal design of the suspension stiffness of the car is investigated. A resonance condition y(x,t) that leads to dramatically increasing vibratory energy of the cable-car system is identified.

Exact Response of a Translating String With Arbitrarily Varying Length Under General Excitation

2008 ◽  
Vol 75 (3) ◽  
Author(s):  
W. D. Zhu ◽  
N. A. Zheng
Keyword(s):  
Boundary Conditions ◽  
Initial Conditions ◽  
Control Volume ◽  
Parametric Instability ◽  
Transformation Method ◽  
Forced Response ◽  
Rate Of Change ◽  
Solution Methods ◽  
Vibrating String ◽  
Varying Length

The exact response of a translating string with constant tension and arbitrarily varying length is determined under general initial conditions and external excitation. The governing equation is transformed to a standard hyperbolic equation using characteristic transformation. The domain of interest for the transformed equation is divided into groups of subdomains according to the properties of wave propagation. d’Alembert’s solution for any point in the zeroth subdomain group is obtained by using the initial conditions. The solution is extended to the whole domain of interest by using the boundary conditions, and a recursive mapping is found for the solution in the second and higher groups of subdomains. The least upper bound of the displacement of the freely vibrating string is obtained for an arbitrary movement profile. The forced response of the string with nonhomogeneous boundary conditions is obtained using a transformation method and the direct wave method. A new method is used to derive the rate of change of the vibratory energy of the translating string from the system viewpoint. Three different approaches are used to derive and interpret the rate of change of the vibratory energy of the string within a control volume, and the energy growth mechanism of the string during retraction is elucidated. The solution methods are applied to a moving elevator cable with variable length. An interesting parametric instability phenomenon in a translating string with sinusoidally varying length is discovered.

Exact Response of a Translating String With Arbitrarily Varying Length Under General Excitation

2007 ◽  
Author(s):  
W. D. Zhu ◽  
N. A. Zheng
Keyword(s):  
Boundary Conditions ◽  
Initial Conditions ◽  
Control Volume ◽  
Parametric Instability ◽  
Transformation Method ◽  
Forced Response ◽  
Rate Of Change ◽  
Solution Methods ◽  
Vibrating String ◽  
Varying Length

The exact response of a translating string with constant tension and arbitrarily varying length is determined under general initial conditions and external excitation. The governing equation is transformed to a standard hyperbolic equation using characteristic transformation. The domain of interest for the transformed equation is divided into groups of sub-domains according to the properties of wave propagation. The d’Alembert’s solution for any point in the zeroth sub-domain group is obtained by using the initial conditions. The solution is extended to the whole domain of interest by using the boundary conditions, and a recursive mapping is found for the solution in the second and higher groups of sub-domains. The least upper bound of the displacement of the freely vibrating string is obtained for an arbitrary movement profile. The forced response of the string with non-homogeneous boundary conditions is obtained using a transformation method and the direct wave method. A new method is used to derive the rate of change of the vibratory energy of the translating string from the system viewpoint. Three different approaches are used to derive and interpret the rate of change of the vibratory energy of the string within the control volume, and the energy growth mechanism of the string during retraction is elucidated. The solution methods are applied to a moving elevator cable with variable length. An interesting parametric instability phenomenon in a translating string with sinusoidally varying length is discovered.

High-Speed Imaging to Study an Auto-Oscillating Vocal Fold Replica for Different Initial Conditions

2017 ◽  
Vol 09 (05) ◽  
pp. 1750064 ◽  
Author(s):  
A. Van Hirtum ◽  
X. Pelorson
Keyword(s):  
Vocal Fold ◽  
High Speed ◽  
Initial Conditions ◽  
Vocal Folds ◽  
High Speed Imaging ◽  
Human Voice ◽  
Manual Intervention ◽  
Geometrical Features ◽  
Upstream Pressure

Experiments on mechanical deformable vocal folds replicas are important in physical studies of human voice production to understand the underlying fluid–structure interaction. At current date, most experiments are performed for constant initial conditions with respect to structural as well as geometrical features. Varying those conditions requires manual intervention, which might affect reproducibility and hence the quality of experimental results. In this work, a setup is described which allows setting elastic and geometrical initial conditions in an automated way for a deformable vocal fold replica. High-speed imaging is integrated in the setup in order to decorrelate elastic and geometrical features. This way, reproducible, accurate and systematic measurements can be performed for prescribed initial conditions of glottal area, mean upstream pressure and vocal fold elasticity. Moreover, quantification of geometrical features during auto-oscillation is shown to contribute to the experimental characterization and understanding.

scholarly journals Nonlinear Behavior of a Magnetic Bearing System

1995 ◽  
Vol 117 (3) ◽  
pp. 582-588 ◽  
Author(s):  
L. N. Virgin ◽  
T. F. Walsh ◽  
J. D. Knight
Keyword(s):  
Degrees Of Freedom ◽  
Initial Conditions ◽  
Nonlinear Behavior ◽  
Analytical Techniques ◽  
Magnetic Bearing ◽  
Forced Response ◽  
The Mathematical Model ◽  
Two Degree Of Freedom ◽  
Sensitivity To Initial Conditions ◽  
Bearing System

This paper describes the results of a study into the dynamic behavior of a magnetic bearing system. The research focuses attention on the influence of nonlinearities on the forced response of a two-degree-of-freedom rotating mass suspended by magnetic bearings and subject to rotating unbalance and feedback control. Geometric coupling between the degrees of freedom leads to a pair of nonlinear ordinary differential equations, which are then solved using both numerical simulation and approximate analytical techniques. The system exhibits a variety of interesting and somewhat unexpected phenomena including various amplitude driven bifurcational events, sensitivity to initial conditions, and the complete loss of stability associated with the escape from the potential well in which the system can be thought to be oscillating. An approximate criterion to avoid this last possibility is developed based on concepts of limiting the response of the system. The present paper may be considered as an extension to an earlier study by the same authors, which described the practical context of the work, free vibration, control aspects, and derivation of the mathematical model.

High-Performance Motion Control With Slosh: A Constrained Sliding Mode Approach

2008 ◽  
Author(s):  
Hanz Richter ◽  
Kedar B. Karnik
Keyword(s):  
High Speed ◽  
High Performance ◽  
Design Methodology ◽  
Closed Loop ◽  
Sliding Mode ◽  
Initial Conditions ◽  
Rectilinear Motion ◽  
Industrial Setting ◽  
Open Container ◽  
Nominal Performance

The problem of controlling the rectilinear motion of an open container without exceeding a prescribed liquid level and other constraints is considered using a recently-developed constrained sliding mode control design methodology based on invariant cylinders. A conventional sliding mode regulator is designed first to address nominal performance in the sliding mode. Then an robustly-invariant cylinder is constructed and used to describe the set of safe initial conditions from which the closed-loop controller can be operated without constraint violation. Simulations of a typical transfer illustrate the usefulness of the method in an industrial setting. Experimental results corresponding to a high-speed transfer validate the theory.

Experimental Investigation of Turbine Stage Flow Field and Performance at Varying Cavity Purge Rates and Operating Speeds

2016 ◽  
Author(s):  
Johan Dahlqvist ◽  
Jens Fridh
Keyword(s):  
Mach Number ◽  
Flow Field ◽  
High Speed ◽  
Control Volume ◽  
Spatial Average ◽  
Turbine Stage ◽  
Wide Range ◽  
Annulus Flow ◽  
Purge Flow ◽  
Secondary Air

The aspect of hub cavity purge has been investigated in a high-pressure axial low-reaction turbine stage. The cavity purge is an important part of the secondary air system, used to isolate the hot main annulus flow from cavities below the hub level. A full-scale cold-flow experimental rig featuring a rotating stage was used in the investigation, quantifying main annulus flow field impact with respect to purge flow rate as it was injected upstream of the rotor. Five operating speeds were investigated of which three with respect to purge flow, namely a high loading case, the peak efficiency, and a high speed case. At each of these operating speeds, the amount of purge flow was varied across a very wide range of ejection rates. Observing the effect of the purge rate on measurement plane averaged parameters, a minor outlet swirl decrease is seen with increasing purge flow for each of the operating speeds while the Mach number is constant. The prominent effect due to purge is seen in the efficiency, showing a similar linear sensitivity to purge for the investigated speeds. An attempt is made to predict the efficiency loss with control volume analysis and entropy production. While spatial average values of swirl and Mach number are essentially unaffected by purge injection, important spanwise variations are observed and highlighted. The secondary flow structure is strengthened in the hub region, leading to a generally increased over-turning and lowered flow velocity. Meanwhile, the added volume flow through the rotor leads to higher outlet flow velocities visible in the tip region, and an associated decreased turning. A radial efficiency distribution is utilized, showing increased impact with increasing rotor speed.

Rotordynamics Performance of Hybrid Foil Bearing Under Forced Vibration Input

2017 ◽  
Author(s):  
Daejong Kim ◽  
Brian Nicholson ◽  
Lewis Rosado ◽  
Garry Givan
Keyword(s):  
Impulse Response ◽  
High Speed ◽  
Load Capacity ◽  
Supply System ◽  
Forced Response ◽  
Experimental Results ◽  
Lateral Acceleration ◽  
Foil Bearings ◽  
Foil Bearing ◽  
Gas Supply

Foil bearings are one type of hydrodynamic air/gas bearings but with a compliant bearing surface supported by structural material that provides stiffness and damping to the bearing. The hybrid foil bearing (HFB) in this paper is a combination of a traditional hydrodynamic foil bearing with externally-pressurized air/gas supply system to enhance load capacity during the start and to improve thermal stability of the bearing. The HFB is more suitable for relatively large and heavy rotors where rotor weight is comparable to the load capacity of the bearing at full speed and extra air/gas supply system is not a major added cost. With 4,448N∼22,240N thrust class turbine aircraft engines in mind, the test rotor is supported by HFB in one end and duplex rolling element bearings in the other end. This paper presents experimental work on HFB with diameter of 102mm performed at the US Air force Research Laboratory. Experimental works include: measurement of impulse response of the bearing to the external load corresponding to rotor’s lateral acceleration of 5.55g, forced response to external subsynchronous excitation, and high speed imbalance response. A non-linear rotordynamic simulation model was also applied to predict the impulse response and forced subsynchronous response. The simulation results agree well with experimental results. Based on the experimental results and subsequent simulations, an improved HFB design is also suggested for higher impulse load capability up to 10g and rotordynamics stability up to 30,000rpm under subsynchronous excitation.

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