Nonlinear Connections

2003 ◽  
pp. 97-108
Author(s):  
P. L. Antonelli
Keyword(s):  
Nonlinear Connections

Model Updating of a Wing-Engine Structure with Nonlinear Connections

2018 ◽  
pp. 373-374
Author(s):  
Mingming Song ◽  
Ludovic Renson ◽  
Jean-Philippe Noël ◽  
Babak Moaveni ◽  
Gaetan Kerschen
Keyword(s):  
Model Updating ◽  
Nonlinear Connections

Dry-Friction Whip and Whirl Predictions for a Rotor-Stator Model With Rubbing Contact at Two Locations

2011 ◽  
Author(s):  
Dara W. Childs ◽  
Dhruv Kumar
Keyword(s):  
Analytical Solutions ◽  
Dry Friction ◽  
Supported Housing ◽  
Precession Frequency ◽  
Rigid Rotor ◽  
Clearance Ratio ◽  
Running Speed ◽  
Nonlinear Simulation ◽  
Friction Forces ◽  
Nonlinear Connections

The present work investigates the phenomena of whip and whirl for a rigid rotor contacting at two bearing locations. The idea originated with a paper by Clark et al. in 2009 on an anemometer undergoing dry friction whip and whirl. The anemometer rotor was supported by two Teflon® bushings within an elastically supported housing. The dry-friction forces arose at the bushings. Prior models for dry friction whirl and whip have considered rub at one non-support location. The present analytical model consists of a rigid rotor connected to a rigid stator at two rubbing contact locations. Analytical solutions are developed for the following normal reaction forces at the contact locations: (1) In phase, and (2) 180 degrees out of phase. Analytical solutions are only possible for the same RCl (Radius to Clearance ratio) at the two rub locations and define regions where dry-friction whirl is possible plus indication possible boundaries between whirl and whip. These solutions are similar to Black’s in 1968. A flexible-rotor/flexible-stator model with nonlinear connections at the bearings was developed to more correctly establish the range of possible solutions. The nonlinear connections at the rub surface are modeled using Hunt and Crossley’s 1975 contact model with coulomb friction. Dry friction simulations are performed for the following rotor center of gravity (C.G.) configurations: (1) Centered, (2) 3/4 contact-span location and (3) Overhang location outside the contacts. Results from the in-phase analytical solutions and the nonlinear simulations agree to some extent with the rotor mass centered and at 3/4 location in that whirl-to-whip transitions occur near the pinned rotor-stator bounce frequency. For the overhung mass case, the nonlinear simulation predicts whip at different frequencies for the two contact locations. Neither analytical solution modes predicts this outcome. No out-of-phase solutions could be obtained via time-transient simulations. Dry-friction whirling is normally characterized as supersynchronous precession with a precession frequency equal to running speed times RCl. Simulation predictions for models with different RCl mimic whirling. Simulation predictions show increasing backward precessional (BP) frequency with increasing rotor speeds. However, individual contact velocities show slipping at all conditions. Slipping is greater at one location than the other, netting a “whirl-like” motion. For the overhung model with different RCl ratios, apart from whipping at different frequency the two contacts also whirl at different frequencies corresponding to the RCl at the respective contacts. Simulations predict a different running speed for the “jump up” in precession frequency associated with a transition from whirl-to-whip with increasing running speed than for the jump-down in precession frequency for whirl-to-whip in a speed-decreasing mode.

Dry-Friction Whip and Whirl Predictions for a Rotor-Stator Model With Rubbing Contact at Two Locations

2012 ◽  
Vol 134 (7) ◽  
Author(s):  
Dara W. Childs ◽  
Dhruv Kumar
Keyword(s):  
Analytical Solutions ◽  
Dry Friction ◽  
Supported Housing ◽  
Precession Frequency ◽  
Rigid Rotor ◽  
Clearance Ratio ◽  
Running Speed ◽  
Nonlinear Simulation ◽  
Friction Forces ◽  
Nonlinear Connections

The present work investigates dry-friction whip and whirl phenomena for a rigid rotor contacting at two bearing locations. The idea originated with a paper by Clark et al. (2009, “Investigation of the NRG #40 Anemometer Slowdown,” American Wind Energy Association, Windpower 2009, Chicago, IL, pp. 1-16) on an anemometer undergoing dry-friction whip and whirl. The anemometer rotor was supported by two Teflon® bushings within an elastically supported housing. The dry-friction forces arose at the bushings. Prior models for dry friction whirl and whip have considered rub at one nonsupport location. The present analytical model consists of a rigid rotor connected to a rigid stator at two rubbing-contact locations. Analytical solutions are developed for the following normal reaction forces at the contact locations: (1) In phase, and (2) 180° out of phase. Analytical solutions are only possible for the same radius-to-clearance ratio (RCl) at the two rub locations and define regions where dry-friction whirl is possible in addition to indicating possible boundaries between whirl and whip. These solutions are similar to Black’s (1968, “Interaction of a Whirling Rotor with a Vibrating Stator Across a Clearance Annulus,” J. Mech. Eng. Sci., 10(1), pp. 1-12) and Crandall’s (1990, “From Whirl to Whip in Rotordynamics,” IFToMM Third Intl. Conf. on Rotordynamics, Lyon, France, pp. 19-26). A flexible-rotor/flexible-stator model with nonlinear connections at the bearings was developed to more correctly establish the range of possible solutions. The nonlinear connections at the rub surface are modeled using Hunt and Crossley’s 1975 contact model with Coulomb friction (Hunt and Crossley, F., 1975, “Coefficient of Restitution Interpreted as Damping in Vibroimpact,” ASME J. Appl. Mech., 42, pp. 440). Dry friction simulations are performed for the following rotor center of gravity (C.G.) configurations with respect to the contact locations: (1) Centered, (2) [3/4]-span location, and (3) overhung, outside the contacts. Predictions from the in-phase analytical solutions and the nonlinear simulations agree to some extent when the rotor mass is centered and at the [3/4]-span location due to the fact that whirl-to-whip transitions occur near the pinned rotor-stator bounce frequency. For the overhung mass case, the nonlinear simulation predicts whip at different frequencies for the two contact locations. Neither analytical solution modes predicts this outcome. No 180 deg out-of-phase solutions could be obtained via time-transient simulations. Dry-friction whirling is normally characterized as supersynchronous precession with a precession frequency equal to the running speed ω times RCl. Simulation predictions for models with different RCl ratio mimic whirling. Specifically, with increasing rotor speed, the backward precessional (BP) frequency increases at each contact location. However, individual contact velocities show slipping at all conditions. Slipping is greater at one location than the other, netting a “whirl-like” motion. For the overhung model with different RCl ratios: in addition to whipping at different frequencies the two contacts also whirl at different frequencies corresponding to the separate RCl ratios at the respective contacts. Simulations predict a different running speed for the “jump up” in precession frequency associated with a transition from whirl-to-whip with increasing running speed than for the jump-down in precession frequency for whirl-to-whip in a speed-decreasing mode.

scholarly journals Nonlinear connections and spinor geometry

2004 ◽  
Vol 2004 (23) ◽  
pp. 1189-1237 ◽  
Author(s):  
Sergiu I. Vacaru ◽  
Nadejda A. Vicol
Keyword(s):  
Field Theory ◽  
Noncommutative Geometry ◽  
Finsler Geometry ◽  
Higher Order ◽  
Noncommutative Field Theory ◽  
Local Anisotropy ◽  
Nonlinear Connection ◽  
Nonlinear Connections ◽  
Spinor Geometry ◽  
Kaluza Klein

We present an introduction to the geometry of higher-order vector and covector bundles (including higher-order generalizations of the Finsler geometry and Kaluza-Klein gravity) and review the basic results on Clifford and spinor structures on spaces with generic local anisotropy modeled by anholonomic frames with associated nonlinear connection structures. We emphasize strong arguments for application of Finsler-like geometries in modern string and gravity theory, noncommutative geometry and noncommutative field theory, and gravity.

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