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.

A Simulation Model for Flexible Rotating Equipment

1972 ◽  
Vol 94 (1) ◽  
pp. 201-209 ◽  
Author(s):  
D. W. Childs
Keyword(s):  
Simulation Model ◽  
Coordinate System ◽  
Simulation Models ◽  
Theory Of Elasticity ◽  
Numerical Results ◽  
Lumped Parameter ◽  
Small Deflection ◽  
Engine System ◽  
Rotating Equipment ◽  
Vector Mechanics

The objective of the analysis which follows is the derivation of simulation models for flexible rotating equipment such as turbine rotors. The analysis employed is based on relatively simple concepts of vector mechanics and results in a “lumped-parameter” simulation model. The basic simulation model is simplified by invoking the small-deflection assumptions of the theory of elasticity. It is then restated in terms of a non-body-fixed (nonspinning) coordinate system. Methods for modeling bearing constraints and the applicability of eigenanalaysis are discussed. Representative numerical results are provided for a simulation of the Mark 15-F turbopump of the J-2 engine system.

scholarly journals Prediction of Vertical Tail Buffet Using CFD/CSD Coupling Method

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Bing Han ◽  
Min Xu
Keyword(s):  
Vortex Breakdown ◽  
Peak Frequency ◽  
Basis Functions ◽  
Resonance Phenomenon ◽  
Structural Dynamic ◽  
Flexible Tail ◽  
Bending Mode ◽  
Tail Structure ◽  
Tail Buffet ◽  
Modal Coordinates

The vertical tail buffet induced by the vortex breakdown flow is numerically investigated. The unsteady flow is calculated by solving the RANS equations. The structural dynamic equations are decoupled in the modal coordinates. The radial basis functions (RBFs) are employed to generate the deformation mesh. The buffet response of the flexible tail is predicted by coupling the three sets of equations. The results show that the presence of asymmetry flow on the inner and outer surface of the tail forced the structural deflection offsetting the outboard. The frequency of the 2nd bending mode of the tail structure meets the peak frequency of the pressure fluctuation upon the tail surface, and the resonance phenomenon was observed. Therefore, the 2nd bending responses govern the flow field surrounding the vertical tail. Finally, the displacement of the vertical tail is small, while the acceleration with a large quantitation forces the vertical tail undergoing severe addition inertial loads.

Simulation models for flexible spinning bodies

SIMULATION ◽  
1969 ◽  
Vol 12 (6) ◽  
pp. 291-296 ◽  
Author(s):  
Dara Childs
Keyword(s):  
Simulation Model ◽  
Final Section ◽  
Simulation Models ◽  
Theory Of Elasticity ◽  
Small Deflection ◽  
Spinning Bodies ◽  
Turbine Rotors ◽  
Vector Mechanics

The objective of the analysis which follows is the deriva tion of simulation models for flexible spinning bodies. The analysis employed is based on relatively simple con cepts of vector mechanics and results in a lumped-param eter simulation model. The simulation models which are first derived are subsequently simplified by invoking the small deflection assumptions of the theory of elasticity. A final section deals with some analysis steps used in adapting the basic simulation model for the description of turbine rotors.

Two Jeffcott-Based Modal Simulation Models for Flexible Rotating Equipment

1975 ◽  
Vol 97 (3) ◽  
pp. 1000-1014 ◽  
Author(s):  
Dara W. Childs
Keyword(s):  
Arbitrary Number ◽  
Space Shuttle ◽  
Simulation Models ◽  
Computer Time ◽  
Rigid Bodies ◽  
Simulation Approach ◽  
Flexible Rotor ◽  
Computationally Efficient ◽  
Efficient Simulation ◽  
Main Engine

Two transient modal simulation models are presented based on the Jeffcott-Green flexible-rotor formulation. One of the models is based on the conventional “non-spinning” formulation, while the second employs a rotor fixed formulation. Numerical results are presented for these two basic models for the SSME (Space Shuttle Main Engine) turbopumps. The results presented demonstrate that either of the basic formulations is a computationally efficient simulation approach for a flexible rotor, which is to be modeled by a large number of rigid bodies. They also demonstrate that the models can readily account for an arbitrary number of bearings having nonlinear or speed-dependent characteristics, and for the motion of the bearing support structure. The results presented demonstrate that the rotor-fixed formulation generally requires less computer time than does the conventional formulation. Moreover, the modal cordinate solutions in the rotor-fixed formulation provide a significantly clearer picture of potential flexible-rotor-instability problems.

Operation of Foil Bearings Beyond the Bending Critical Mode

1999 ◽  
Vol 122 (1) ◽  
pp. 192-198 ◽  
Author(s):  
Hooshang Heshmat
Keyword(s):  
High Speed ◽  
Modern Technology ◽  
Flexible Rotor ◽  
Critical Mode ◽  
Foil Bearings ◽  
Optimum Position ◽  
Bending Mode ◽  
Series Of Experiments ◽  
Bearing Design

A series of experiments were conducted to determine a foil bearings ability to operate in the region of the bending mode of a flexible rotor. Three different bearings, spaced at three different positions along the shaft, were tested in order to make super-bending-critical operation possible. This was achieved with a proper bearing design located at an optimum position with respect to the bending nodes. After proper trim balancing the bearings passed the 34,100 rpm first bending critical and went on to operate up to 85,000 rpm, 2.5 times the bending critical. Throughout, the amplitudes of vibration remained small. The documented ability of these bearings to operate in the domain of a flexible rotor’s bending mode makes these bearings a prime candidate for the high-speed machinery of modern technology. [S0742-4787(00)02401-2]

Active Vibration Control of the Flexible Rotor in High Energy Density Magnetically Suspended Motor With Mode Separation Method

2015 ◽  
Vol 137 (8) ◽  
Author(s):  
Enqiong Tang ◽  
Jiancheng Fang ◽  
Bangcheng Han
Keyword(s):  
Energy Density ◽  
Critical Speed ◽  
Active Vibration Control ◽  
High Energy ◽  
Separation Method ◽  
High Energy Density ◽  
Flexible Rotor ◽  
Mode Separation ◽  
Displacement Signal ◽  
Bending Mode

Since the mass of the rotor in high energy density magnetically suspended motor (HEDMSM) is always large and there are only three balancing planes on the flexible rotor restricted by the structure of the motor, which means that the second bending mode cannot be balanced using N + 1 planes method which is always applied to balance the flexible rotor. Then, the rotor displacements maybe large and this situation will make the system consume large amplifier currents when the rotor passes the first bending critical speed. Therefore, the mode separation method is proposed to separate the first and the second bending modes in rotor displacement and reconstruct the displacement signal nearby the first bending mode. Then, the original rotor displacement signal used by the digital controller is substituted by the reconstructed displacement signal and the amplifier current is reduced a lot when the rotor passes the first bending critical speed. Finally, the experiment of mode separation is carried out in 100 kW magnetically suspended motor and the experiment results show the effectiveness and superiority of the mode separation method in reducing the amplifier current when the rotor passes the first bending critical speed.

scholarly journals Analytical Modeling and Experimental Validation of an Energy Harvesting System for the Smart Plate with an Integrated Piezo-Harvester

Sensors ◽  
2019 ◽  
Vol 19 (4) ◽  
pp. 812 ◽  
Author(s):  
Andrzej Koszewnik
Keyword(s):  
Energy Harvesting ◽  
Analytical Modeling ◽  
Plate Theory ◽  
Distributed Parameter ◽  
Simply Supported ◽  
Case Research ◽  
Piezoelectric Energy ◽  
Energy Harvesting System ◽  
Experimental Validations ◽  
Modal Coordinates

The literature on piezoelectric energy harvesting (PEH) is strongly focused on structures, like cantilever beams with piezoceramic layers, due to the fact that they are easily modelled and implemented. As compared to the number of studies dealing with the aforementioned case, research on 2D structures with an attached piezoceramic patch harvester is very limited. Thus, an analytical modeling and experimental validations of a piezo harvester structurally integrated on a thin plate with SFSF (Simply supported-Free-Simply supported-Free) boundary conditions is presented in this paper. The distributed parameter electroelastic model of a harvester bonded to an aluminum plate with both piezo-patch actuators is developed on the basis of the Kirchhoff plate theory and the modal analysis for physical and modal coordinates. This allows to estimate the steady-state value output voltage for each odd mode in the frequency range of 10–300 Hz. Finally, the obtained results for the electroelastic analytical model is experimentally verified on a laboratory stand.

Dynamic Simulation of Reeving Systems With the Extension of the Modal Approach in the Axial Direction

2021 ◽  
Author(s):  
Narges Mohammadi ◽  
José Luis Escalona
Keyword(s):  
Axial Strain ◽  
Equations Of Motion ◽  
Axial Direction ◽  
Rigid Bodies ◽  
Arbitrary Lagrangian Eulerian ◽  
Absolute Nodal Coordinates ◽  
Lagrange’S Equation ◽  
Axial Forces ◽  
Nodal Coordinates ◽  
Modal Coordinates

Abstract In this work, the simulation of reeving systems has been studied by including axial modes using the Arbitrary Lagrangian-Eulerian (ALE) description. The reeving system is considered as a deformable multibody system in which the rigid bodies are connected by the elastic wire ropes through sheaves and reels. A set of absolute nodal coordinates and modal coordinates is employed to describe the motion and deformation in the axial direction. This new method allows the analysis of elements with non-constant axial strain along its length. In addition, modal coordinates are employed to describe the dynamic motion in the transverse direction. The non-constant axial displacement within the wire rope is computed in terms of the absolute position coordinates, longitudinal material coordinates, and modal deformation coordinates. To derive the governing equations of motion, Lagrange’s equation is employed. The formulation is validated for a simple pendulumlike motion actuated by an initial velocity. The simulation results are provided to trace the movements of the payload. It can be seen that by adding modal coordinates, the axial force within the element changes. Moreover, the effects of modal coordinates in the axial direction are presented for a different number of nodes, and the resulting axial forces are compared with reference solution.

Calculations and Experiments on the Unbalance Response of a Flexible Rotor

1967 ◽  
Vol 89 (4) ◽  
pp. 785-796 ◽  
Author(s):  
J. W. Lund ◽  
F. K. Orcutt
Keyword(s):  
Critical Speed ◽  
Distributed Parameter ◽  
Distributed Parameter System ◽  
Flexible Rotor ◽  
Parameter System ◽  
Damping Coefficients ◽  
The Third ◽  
Tilting Pad ◽  
Speed Range ◽  
Bearing System

The results of a combined analytical and experimental investigation of the unbalance vibrations of a rotor are presented. The analysis applies to a general rotor-bearing system in which the dynamic bearing forces are represented by four spring coefficients and four damping coefficients. The rotor can be represented as either a lumped or a distributed parameter system, and gyroscopic moments are included. In general, the unbalance whirl motion of the rotor will be elliptical. The analysis has been programmed for a digital computer to obtain results for comparison with the experimental data. The test rotor is a uniform, flexible shaft with heavy wheels mounted at the ends and in the middle. The rotor is supported in two silicone fluid-lubricated, tilting-pad bearings. The rotor amplitude caused by an induced unbalance has been measured over a speed range of 3000 to 24,000 rpm for three different rotor configurations, obtained by removing one or both end wheels. This speed range extends to or through the third critical speed for each of the rotor configurations. The results are compared with the theoretical values and, in general, the agreement is found to be good.

Sign in / Sign up

Export Citation Format

Share Document