Critical speeds of a flexible rotor with combined distributed parameter and lumped mass technique

1976 ◽  
Vol 45 (3) ◽  
pp. 441-459 ◽  
Author(s):  
B.B. Joshi ◽  
Y.K. Dange
Keyword(s):  
Distributed Parameter ◽  
Flexible Rotor ◽  
Lumped Mass ◽  
Critical Speeds

Determination of the Critical Operating Speeds of Planar Mechanisms by the Finite Element Method Using Planar Actual Line Elements and Lumped Mass Systems

1979 ◽  
Vol 101 (2) ◽  
pp. 210-223 ◽  
Author(s):  
S. Kalaycioglu ◽  
C. Bagci
Keyword(s):  
Dynamic Systems ◽  
Natural Frequencies ◽  
Dynamic Equilibrium ◽  
Large Error ◽  
Free Vibrations ◽  
Lumped Mass ◽  
Critical Speeds ◽  
Rotating Shafts ◽  
Line Elements ◽  
Kinematic Motion

It has been a well-established fact that dynamic systems in motion experience critical speeds, such as rotating shafts and geared systems whose undeformed reference geometry remain the same at all times. Their critical speeds are determined by their natural frequencies of considered type of free vibrations. Linkage mechanisms as dynamic systems in motion change their undeformed geometries as function of time during the cycle of kinematic motion. They do also experience critical operating speeds as rotating shafts and geared systems do, and their critical speeds are determined by the minima of their natural frequencies during a cycle of kinematic motion. Such a minimum occurs at the critical geometry of a mechanism, which is the position at which the maximum of the input power is required to maintain the instantaneous dynamic equilibrium of the mechanism. Actual finite line elements are used to form the global generalized coordinate flexibility matrix. The natural frequencies of the mechanism and the corresponding mode vectors (mode deflections) are determined as the eigen values and eigen vectors of the equations of instantaneous-position-free-motion of the mechanism. Method is formulated to include or exclude the link axial deformations, and apply to any number of loops having any type of planar pair. Critical speeds of planar four-bar, slider-crank, and Stephenson’s six-bar mechanisms are determined. Experimental results for the four-bar mechanism are given. Effect of axial deformations and link rotary inertias are investigated. Inclusion of link axial deformations in mechanisms having pairs with sliding freedoms is seen to predict critical speeds with large error.

Modeling and Analysis of an Optically-Actuated, Bistable MEMS Device

2010 ◽  
Author(s):  
Vijay Kumar ◽  
Jeffrey F. Rhoads
Keyword(s):  
Transient Behavior ◽  
Distributed Parameter ◽  
Mems Devices ◽  
Lumped Mass ◽  
Modeling And Analysis ◽  
Mems Switch ◽  
The Rich ◽  
Predictive Design ◽  
Commercial Applications ◽  
Excitation Parameters

Bistable microsystems have drawn considerable interest from the MEMS/NEMS research community not only due to their broad applicability in commercial applications, such as switching, but also because of the rich dynamic behavior they commonly exhibit. While a number of prior investigations have studied the dynamics of bistable microsystems, comparatively few works have sought to characterize their transient behavior. The present effort seeks to address this through the modeling and analysis of an optically-actuated, bistable MEMS switch. The work begins with the development of a distributed-parameter representation for the system, which is subsequently reduced to a lumped-mass analog and analyzed through the use of numerical simulation. The influence of various system and excitation parameters, including the applied axial load and optical actuation profile, on the system’s transient response is then investigated. Ultimately, the methodologies and results presented herein should provide for a refined predictive design capability for optically-actuated, bistable MEMS devices.

Modeling and Analysis of an Optically-Actuated, Bistable MEMS Device

2012 ◽  
Vol 7 (2) ◽  
Author(s):  
Vijay Kumar ◽  
Jeffrey F. Rhoads
Keyword(s):  
Transient Behavior ◽  
Distributed Parameter ◽  
Mems Devices ◽  
Lumped Mass ◽  
Modeling And Analysis ◽  
Mems Switch ◽  
The Rich ◽  
Predictive Design ◽  
Commercial Applications ◽  
Excitation Parameters

Bistable microsystems have drawn considerable interest from the MEMS/NEMS research community not only due to their broad applicability in commercial applications, such as switching, but also because of the rich dynamic behavior they commonly exhibit. While a number of prior investigations have studied the dynamics of bistable microsystems, comparatively few works have sought to characterize their transient behavior. The present effort seeks to address this through the modeling and analysis of an optically-actuated, bistable MEMS switch. This work begins with the development of a distributed-parameter representation for the system, which is subsequently reduced to a lumped-mass analog and analyzed through the use of numerical simulation. The influence of various system and excitation parameters, including the applied axial load and optical actuation profile, on the system’s transient response is then investigated. Ultimately, the methodologies and results presented herein should provide for a refined predictive design capability for optically-actuated, bistable MEMS devices.

On Adaptive-Passive Vibration Suppression Using Distributed-Parameter Absorbers

2000 ◽  
Author(s):  
Nader Jalili
Keyword(s):  
Vibration Suppression ◽  
Excitation Frequency ◽  
Wide Band ◽  
Distributed Parameter ◽  
Vibration Absorber ◽  
Frequency Bandwidth ◽  
Lumped Mass ◽  
Adaptive Capability ◽  
Active Vibration ◽  
Tuning Strategy

Abstract A semi-active vibration absorber with adaptive capability is presented to improve wide band vibration suppression characteristics of harmonically excited structures. The absorber subsection consists of a double-ended cantilever beam carrying an intermediate lumped mass. The adaptive capability is achieved through concurrent adjustment of the position of the moving mass, along the beam, to comply with the desired optimal performance. If such an absorber is attached to a vibrating body, it effectively absorbs vibrations at all frequencies that belong to the absorber frequency bandwidth. Numerical simulations are provided to verify the effectiveness of the proposed absorption scheme. It is shown that the tuning strategy tries to follow and match the absorber natural frequency with the excitation frequency. The optimally tuned absorber provides considerable vibration suppression improvement over the passive and de-tuned absorbers, for wide band excitation disturbances.

A Rotor-Fixed Modal Simulation Model for Flexible Rotating Equipment

1974 ◽  
Vol 96 (2) ◽  
pp. 659-669 ◽  
Author(s):  
D. W. Childs
Keyword(s):  
Theory Of Elasticity ◽  
Rigid Bodies ◽  
Distributed Parameter ◽  
Flexible Rotor ◽  
Fixed Frame ◽  
Small Deflection ◽  
Bending Mode ◽  
Engine System ◽  
Typical Model ◽  
Modal Coordinates

A transient, flexible rotor formulation is derived on the basis of a representation previously employed to simulate the motion of flexible spinning spacecraft. The distributed parameter characteristics of the rotor are approximated by modeling the rotor as an elastically connected group of n rigid bodies. The elastic rotor deflections of the component rigid bodies are defined in terms of a rotor-fixed frame of reference; hence, during constant synchronous whirling the elastic deflections appear to be constant. The model is initially simplified by the traditional small deflection assumptions of the theory of elasticity, and is additionally simplified by the use of modal coordinates. Modal coordinates dramatically reduce the dimensionality of the model, and significantly clarify the dynamic analysis of the problem. Required data input to the model, and typical model output are demonstrated for the Mark 15-F turbopump of the Rocketdyne J-2 engine system. The model is shown to correctly demonstrate the form of unstable rotor whirling associated with internal hysteresis damping when operating above the first bending-mode critical speed.

FEM Modeling Technology and Vibration Analysis of Flexible Rotor System

2012 ◽  
Vol 226-228 ◽  
pp. 257-261
Author(s):  
Zhi Chao Liang ◽  
Jie Hong ◽  
Yan Hong Ma ◽  
Tian Yuan He
Keyword(s):  
Finite Element ◽  
Structural Characteristics ◽  
Rotor System ◽  
Flexible Rotor ◽  
The Finite Element Method ◽  
Lumped Mass ◽  
Fem Modeling ◽  
Modeling Technology ◽  
Disk Method ◽  
Bypass Ratio

The low-pressure spool in a high-bypass ratio turbofan engine has its unique characteristics. The slightness rotor and the large lumped mass in blade and disk are the structural characteristics while the dynamic coupling between bladed-disk and shaft is the mechanical characteristic. This paper studies on the modeling technology of a flexible rotor system based on the finite element method (FEM). The equivalent-disk method, an equivalent principle of finite element modeling, is put forward. The blades are equivalent to a disk which can not only retain the structural and mechanical characteristics but also control the scale of the model and convert the periodic geometry into axisymmetric geometry. The results show that the equivalent-disk method is helpful to improve the modeling techniques of rotor system and can be used in engineering.

The Dynamics of Rotor-Bearing Systems Using Finite Elements

1976 ◽  
Vol 98 (2) ◽  
pp. 593-600 ◽  
Author(s):  
H. D. Nelson ◽  
J. M. McVaugh
Keyword(s):  
Element Model ◽  
Variable Cross Section ◽  
Distributed Parameter ◽  
Viscous Damping ◽  
Variable Cross ◽  
Mass Analysis ◽  
Lumped Mass ◽  
Rotatory Inertia ◽  
Rigid Disks ◽  
Rotor Bearing

A procedure is presented for dynamic modeling of rotor-bearing systems which consist of rigid disks, distributed parameter finite rotor elements, and discrete bearings. The formulation is presented in both a fixed and rotating frame of reference. A finite element model including the effects of rotatory inertia, gyroscopic moments, and axial load is developed using the consistent matrix approach. A reduction of coordinates procedure is utilized to model elements with variable cross-section properties. The bearings may be nonlinear, however, only the linear stiffness and viscous damping case is considered. The natural whirl speeds and unbalance response of a typical overhung system is presented for two sets of bearing parameters: (i) undamped isotropic, (ii) undamped orthotropic. A comparison of results is made with an independent lumped mass analysis.

Experiments on the Vibration Control of Flexible Rotor Using Shear Mode MR Elastomer Damper

2012 ◽  
Vol 215-216 ◽  
pp. 741-745 ◽  
Author(s):  
Jian Xiao Wang ◽  
Shi Wang Wang
Keyword(s):  
Magnetic Field ◽  
Vibration Control ◽  
Control Method ◽  
Silicone Oil ◽  
Active Vibration Control ◽  
Mr Damper ◽  
Rotor System ◽  
Shear Mode ◽  
Flexible Rotor ◽  
Critical Speeds

A shear mode magnetorheological (MR) elastomer damper is designed and manufactured, in which the MR elastomer is made by mixing RTV silicone, carbonyl iron particles and silicone oil, and solidifying under magnetic field. A flexible cantilever rotor system with single disk is constructed, and the controllability, effectiveness and stability of vibration control for the imbalance response of the rotor system using the MR damper are experimentally studied. From the test, it is found that as the strength of applied magnetic field increases, the damping and stiffness of the damper are increased; the critical speeds of the rotor system supported on the MR damper is increased distinctly, and the vibration at two critical speeds are restrained; the on-off control method may be used to control the rotor vibration while passing through the two critical speeds. The study shows that the shear mode MR elastomer damper is suitable for active vibration control of flexible rotor.

Harmonic Analysis of the High Speed Direct Coupled SCO2 Turbo-Generator

2021 ◽  
Author(s):  
Ashutosh Patel ◽  
Vijay Biradar ◽  
Pramod Kumar
Keyword(s):  
Finite Element ◽  
Harmonic Analysis ◽  
High Speed ◽  
Computation Time ◽  
Lumped Mass ◽  
Axisymmetric Model ◽  
Critical Speeds ◽  
Turbo Generator ◽  
Shaft Deflection ◽  
Rotor Assembly

Abstract The rotordynamics and harmonic characteristics of the rotor assembly designed for 40-kW high-speed sCO2 direct-coupled turbo-generator pair have been evaluated numerically using finite element solver “ANSYS Mechanical”. First, the shaft geometry and dimensions have been optimized using lumped mass-inertia-based AxSTREAM RotorDynamics module followed by the bearing selection analysis using SKF SimPro expert to ensure enough separation margin from the nearby critical speeds. Equivalent 2D geometry has been used with an FEA-based ANSYS general axisymmetric model to reduce the computation time. The effect of the damping on the forces transmitting to the bearings and shaft deflection at the critical speeds are analyzed by performing harmonic analysis under various damped and undamped conditions (ζ = 0, 0.005, 0.01, and 0.02).

Experimental Study on Vibration Properties and Control of Squeeze Mode MR Fluid Damper-Flexible Rotor System

2003 ◽  
Author(s):  
Jianxiao Wang ◽  
Guang Meng ◽  
Eric Hahn
Keyword(s):  
Vibration Control ◽  
Control Method ◽  
Rotor System ◽  
Flexible Rotor ◽  
Mr Fluid ◽  
Oil Film ◽  
Critical Speeds ◽  
Fluid Damper ◽  
Mr Fluid Damper ◽  
And Control

A squeeze mode MR fluid damper used for rotor vibration control is designed and manufactured, and the unbalance response properties and control method of a single-disk flexible rotor system supported by the damper are studied experimentally. It is found from the study that the magnetic pull force can decrease both the first critical speed and the critical amplitude; the oil film reaction force can decrease the amplitude at the undamped critical speeds, but increase the amplitude in a speed range between two undamped critical speeds. For the rotor system supported by a journal bearing and an MR fluid damper, it is possible to appear oil film instability as the increasing of the control current. The damper may have the best effect to make the vibration minimize within the range of all working speed by using on-off control method. The research show that the squeeze mode MR fluid damper has the advantages such as simple structure, clearly effectiveness, quick response, etc., and this kind of damper has a promising potential future in vibration control of flexible rotor systems.

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