A Study on Stability and Response Analysis of a Nonlinear Rotor System With Mass Unbalance and Side Load

1993 ◽  
Vol 115 (2) ◽  
pp. 218-226 ◽  
Author(s):  
T. N. Shiau ◽  
J. L. Hwang ◽  
Y. B. Chang
Keyword(s):  
Steady State ◽  
Nonlinear Differential Equations ◽  
Rotor System ◽  
Collocation Methods ◽  
Squeeze Film ◽  
System Response ◽  
Response Analysis ◽  
Mass Unbalance ◽  
The Stability ◽  
Nonlinear Rotor System

The stability of steady-state synchronous and nonsynchronous response of a nonlinear rotor system supported by squeeze-film dampers is investigated. The nonlinear differential equations that govern the motion of rotor bearing systems are obtained by using the Generalized Polynomial Expansion Method. The steady-state response of the system is obtained by using the hybrid numerical method, which combines the merits of the harmonic balance and collocation methods. The stability of system response is examined using the Floquet-Liapunov theory. Using the theory, the performance may be evaluated with the calculation of derivatives of nonlinear hydrodynamic forces of the squeeze-film damper with respect to displacement and velocity of the journal center. In some cases, these derivatives can be expressed in closed form and the prediction of the dynamic characteristic of the nonlinear rotor system will be more effective. The stability results are compared to those using a direct numerical integration method and both are in good agreement.

scholarly journals A Study on Stability and Response Analysis of a Nonlinear Rotor System With Mass Unbalance and Side Load

1992 ◽  
Author(s):  
Ting Nung Shiau ◽  
Jon Li Hwang ◽  
Yuan Bin Chang
Keyword(s):  
Steady State ◽  
Nonlinear Differential Equations ◽  
Rotor System ◽  
Collocation Methods ◽  
Squeeze Film ◽  
System Response ◽  
Response Analysis ◽  
Mass Unbalance ◽  
The Stability ◽  
Nonlinear Rotor System

The stability of steady state synchronous and nonsynchronous response of a nonlinear rotor system supported by squeeze-film dampers is investigated. The nonlinear differential equations which govern the motion of rotor bearing system are obtained by using the Generalized Polynomial Expansion Method. The steady state response of system is obtained by using the hybrid numerical method which combines the merits of the harmonic balance and collocation methods. The stability of system response is examined using Floquet-Liapunov theory. Using the theory, the performance may be evaluated with the calculation of derivatives of nonlinear hydrodynamic forces of the squeeze-film damper with respect to displacement and velocity of the journal center. In some cases, these derivatives can be expressed in closed form and the prediction of the dynamic characteristic of the nonlinear rotor system will be more effective. The stability results are compared to those using a direct numerical integration method and both are in good agreement.

Analytical and Experimental Investigation of the Stability of Intershaft Squeeze Film Dampers—Part 1: Demonstration of Instability

1977 ◽  
Vol 99 (1) ◽  
pp. 47-52 ◽  
Author(s):  
D. H. Hibner ◽  
R. G. Kirk ◽  
D. F. Buono
Keyword(s):  
Analytical Model ◽  
High Speed ◽  
Rotor System ◽  
Dynamics Simulation ◽  
Squeeze Film ◽  
Response Analysis ◽  
Turbine Engine ◽  
Engine Vibration ◽  
Bearing Loads ◽  
The Stability

Modern high-speed multishaft gas tubine engines incorporate viscous damped bearings to decrease overall system vibration and bearing loads. As viscous damper technology is applied to advanced engine design, more sophisticated analytical and experimental techniques are required to prove new concepts. This analysis will present the results of an investigation of the feasibility of damping engine vibration with a viscous damped intershaft bearing on a two-shaft gas turbine engine. Experimental results from a rotor dynamics simulation rig indicate an instability of the rotor system at speeds above a fundamental critical speed. An analytical model of the two-rotor system is presented and the results of both a classical stability analysis and a time transient response analysis verify the experimental data. The analytical model may be used to predict the stability of two-shaft engines which incorporate an intershaft damped bearing.

Stability Analysis and Complex Dynamics of a Gear-Pair System Supported by a Squeeze Film Damper

1997 ◽  
Vol 119 (1) ◽  
pp. 85-88 ◽  
Author(s):  
Chin-Shong Chen ◽  
S. Natsiavas ◽  
H. D. Nelson
Keyword(s):  
Steady State ◽  
Periodic Solutions ◽  
Squeeze Film ◽  
Time Behavior ◽  
Steady State Response ◽  
Squeeze Film Damper ◽  
State Response ◽  
Mass Unbalance ◽  
Periodic Steady State ◽  
The Stability

The stability properties of periodic steady state response of a nonlinear geared rotordynamic system are investigated. The nonlinearity arises because one support of the system includes a cavitated squeeze film damper, while the excitation is caused by mass unbalance. The dynamical model and the procedure which leads to periodic steady state response of the system examined have been developed in an earlier paper. Here, the emphasis is placed on analyzing the stability characteristics of located periodic solutions. Also, within ranges of the excitation frequency where no stable periodic solutions are detected, the long time behavior of the system is investigated by direct integration of the equations of motion. It is shown that large order subharmonic, quasiperiodic and chaotic motions may coexist with unstable periodic response in these frequency ranges. Finally, attention is focused on practical consequences of these motions.

Dynamic Analysis of a Coupled Dual-Rotor With Squeeze Film Damper Considering Sudden Unbalance

2021 ◽  
Author(s):  
Ying Cui ◽  
Yuxi Huang ◽  
Guogang Yang ◽  
Yongliang Wang ◽  
Han Zhang
Keyword(s):  
Steady State ◽  
Transient Response ◽  
Rotor System ◽  
Lubricating Oil ◽  
Squeeze Film ◽  
Radial Clearance ◽  
Oil Viscosity ◽  
Squeeze Film Damper ◽  
Damping Effect ◽  
Bistable State

Abstract A nonlinear multi-degree-of-freedom dynamic model of a coupled dual-rotor system with an intershaft bearing and uncentralized squeeze film damper is established by using finite element method. Based on the model, the critical speed characteristic diagram and vibration modes of the system were calculated. The steady-state unbalance response is obtained by using Newmark-β algorithm. The numerical results show the effect of SFD position in the dual-rotor system on response amplitude. It is found that with the decrease of radial clearance and the increase of length-diameter ratio and lubricating oil viscosity, the damping effect of SFD is enhanced and the bistable state phenomenon can be suppressed. The transient response of the system in case of sudden unbalance occurring at the fan was simulated by applying a step function. It is demonstrated that the SFD can effectively reduce the duration and maximum amplitude of the transient process, but at certain speeds, the SFD will increase the amplitude after the system returns to steady state, the damping effect on the transient response is also enhanced with the increase of length-diameter and the decrease of radial clearance, and with the increase of the sudden unbalance value, the response is more likely to stabilized at the high amplitude state of the bistable state.

Effect of flight/structural parameters and operating conditions on dynamic behavior of a squeeze-film damped rotor system during diving–climbing maneuver

2020 ◽  
pp. 095441002094261
Author(s):  
Xi Chen ◽  
Xiaohua Gan ◽  
Guangming Ren
Keyword(s):  
Dynamic Characteristics ◽  
Rotor System ◽  
Elastic Support ◽  
Outer Ring ◽  
Squeeze Film ◽  
Inertial Forces ◽  
Oil Film ◽  
Maneuvering Flight ◽  
Mass Unbalance ◽  
Static Eccentricity

During aircraft maneuvering flights, engine's rotor-bearing systems are subjected to parametric excitations and additional inertial forces, which may cause severe vibration and abnormal operation. Based on Lagrange's principle combined with finite element modeling, the differential equations of motion for a squeeze film damped rotor-bearing system mounted on an aircraft in maneuvering flight are derived. Using Newmark–Hilber–Hughes–Taylor integration method, dynamic characteristics of the nonlinear rotor system under maneuvering flight are investigated. The factors are considered, involving mass unbalance, oil–film force, gravity, parametric excitations and additional inertial forces, and instantaneous static eccentricity of journal induced by maneuvering loads. The effects of forward velocity, radius of curvature, rotating speed, mass unbalance, oil–film clearance, and elastic support stiffness on transient responses of rotor system are discussed during diving–climbing maneuver. The results indicate that when the aircraft performs a diving–climbing maneuver in the vertical plane, the journal deviates from the center of oil–film outer ring, and the excursion direction of whirl orbit is determined by centrifugal acceleration and additional gyroscopic moment. The journal whirls asynchronously around the instantaneous static eccentricity and its magnitude is related to the maneuvering loads and the supporting stiffness. Increasing forward velocity or decreasing pitching radius, the rotor vibration will enter earlier into or withdraw later from the relatively large eccentricity. Rotating near critical speeds or excessive mass unbalances should be prevented during maneuvering flights. For large maneuver, the oil–film radial clearance needs to be enlarged properly to avoid hard contact between journal and outer ring. In addition, the stiffness of elastic support needs to be appropriately determined for damping performance. Overall, it provides a flexible approach with good expandability to predict dynamic characteristics of on-board squeeze-film damped rotor system during maneuvering flights in the design process.

Steady-State Characteristics of a Dual-Rotor System With Intershaft Bearing Subjected to Mass Unbalance and Base Motions

2018 ◽  
Author(s):  
Xi Chen ◽  
Mingfu Liao
Keyword(s):  
Steady State ◽  
High Efficiency ◽  
Equations Of Motion ◽  
Axial Rotation ◽  
Rotor System ◽  
Mode Shapes ◽  
Mass Unbalance ◽  
Moving Base ◽  
Lateral Rotation ◽  
Force Vectors

A dual-rotor system with an intershaft bearing subjected to mass unbalance and base motions is established. Using Lagrange’s principle, equations of motion for dual-rotor system relative to moving base are derived. Rotary inertia, gyroscopic inertia, transverse shear deformation, mass unbalance, and six components of deterministic base motions are taken into account. Using state-space vector, steady-state characteristics of dual-rotor system are analyzed through dual-rotor critical speed map, mode shapes, unbalance responses considering base rotations, frequency responses due to base motions, and shaft orbits. The results show that base translations just add external force vectors, while base rotations bring on parametric system matrices and additional force vectors. Base rotations not only change natural frequencies of dual-rotor system, but also break the symmetry of dynamic characteristics in the case of base lateral rotation. Excited by base harmonic translation, resonant frequencies correspond to whirl frequencies. The orbit remains circular under base axial rotation, while it becomes elliptical with a static offset under lateral rotation and then a complicated curve due to harmonic translation. When harmonic frequency of base translation gets close to dual-rotor excitation frequencies, obvious beat vibration appears. Overrall, this flexible approach can ensure calculation accuracy with high efficiency and good expandability.

On an Independent Period-1 Motion in a Flexible Rotor System

2019 ◽  
Author(s):  
Yeyin Xu ◽  
Albert C. J. Luo
Keyword(s):  
Numerical Simulations ◽  
Internal Resonance ◽  
Mapping Method ◽  
Rotor System ◽  
Flexible Rotor ◽  
Periodic Motions ◽  
Phase Trajectories ◽  
Stability And Bifurcation ◽  
The Stability ◽  
Nonlinear Rotor System

Abstract This paper investigates stable and unstable period-1 motions in a rotor system through the discrete mapping method. The discrete mapping of a nonlinear rotor system is for stable and unstable period-1 motions. The stability and bifurcation of periodic motions are determined. Numerical simulations of periodic motions are completed and phase trajectories, displacement orbits and velocity plane are illustrated. The period-1 motion near the internal resonance is determined with large vibration in the nonlinear rotor system.

Nonlinear Oscillation of a Rotor-AMB System With Time Varying Stiffness and Multi-External Excitations

2009 ◽  
Vol 131 (3) ◽  
Author(s):  
M. Kamel ◽  
H. S. Bauomy
Keyword(s):  
Steady State ◽  
Order Approximation ◽  
Nonlinear Differential Equations ◽  
Steady State Solution ◽  
Magnetic Bearing ◽  
Active Magnetic Bearing ◽  
Multiple Time ◽  
Time Varying ◽  
The Stability ◽  
Amb System

The rotor-active magnetic bearing system subjected to a periodically time-varying stiffness having quadratic and cubic nonlinearities is studied and solved. The multiple time scale technique is applied to solve the nonlinear differential equations governing the system up to the second order approximation. All possible resonance cases are deduced at this approximation and some of them are confirmed by applying the Rung–Kutta method. The main attention is focused on the stability of the steady-state solution near the simultaneous principal resonance and the effects of different parameters on the steady-state response. A comparison is made with the available published work.

Rotordynamic Evaluation of an Advanced Multi-Squeeze Film Damper: Imbalance Response and Bladeloss Simulation

1991 ◽  
Author(s):  
J. F. Walton ◽  
H. Heshmat
Keyword(s):  
Steady State ◽  
Rotor System ◽  
Squeeze Film ◽  
Turbine Engines ◽  
Gas Turbine Engines ◽  
Flexible Rotor ◽  
High Eccentricity ◽  
Squeeze Film Damper ◽  
Wide Range ◽  
Damper Design

In this paper results of rotordynamic response and transient tests of a novel, high load squeeze film damper design, are presented. The spiral foil multi-squeeze film damper has been previously shown to provide two to four fold or larger increases in damping levels without resorting to significantly decreased damper clearances or increased lengths. By operating with a total clearance of approximately twice conventional designs, the non-linearities associated with high eccentricity operation are avoided. Rotordynamic tests with a dual squeeze film configuration were completed. As a part of the overall testing program, a flexible rotor system was subjected to high steady state imbalance levels and transient simulated bladeloss events for up to 0.254 mm (0.01 in) mass c.g offset or 180 gm-cm (2.5 oz-in) imbalance. The spiral foil multi-squeeze film damper demonstrated that the steady state imbalance and simulated bladeloss transient response of a flexible rotor operating above its first bending critical speed could be readily controlled. Rotor system imbalance sensitivity and logarithmic decrement are presented showing the characteristics of the system with the damper installed. The ability to accommodate high steady state and transient imbalance conditions make this damper well suited to a wide range of rotating machinery, including aircraft gas turbine engines.

scholarly journals Vibration Control of an Unbalanced Single-Side Cantilevered Rotor System with a Novel Integral Squeeze Film Bearing Damper

2019 ◽  
Vol 9 (20) ◽  
pp. 4371 ◽  
Author(s):  
Yipeng Zhang ◽  
Lidong He ◽  
Jianjiang Yang ◽  
Fangteng Wan ◽  
Jinji Gao
Keyword(s):  
Finite Element ◽  
Energy Distribution ◽  
Finite Element Model ◽  
Vibration Control ◽  
Element Model ◽  
Rotor System ◽  
Squeeze Film ◽  
Single Side ◽  
The Stability ◽  
Stability Energy

In this paper, vibration control of an unbalanced single-side cantilevered rotor system using a novel integral squeeze film bearing damper in terms of stability, energy distribution, and vibration control is analyzed. A finite element model of such a system with an integral squeeze film bearing damper (ISFBD) is developed. The stability, energy distribution, and vibration control of the unbalanced single-side cantilevered rotor system are calculated and analyzed based on the finite element model. The stiffness of the integral squeeze film bearing damper is designed using theoretical calculation and finite element model (FEM) simulation. The influence of installation position and quantity of integral squeeze film bearing dampers on the vibration control of the unbalanced cantilevered rotor system is discussed. An experimental platform is developed to validate the vibration control effect. The results show that the installation position and quantity of the integral squeeze film bearing dampers have different effects on the stability, energy distribution, and vibration control of the unbalanced cantilevered rotor system. When ISFBDs are installed at both bearing housings, the vibration control is best, and the vibration components of the time and frequency domains have good vibration control effects in four working conditions.

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