Identification of Bearing Force Coefficients in Flexible Rotors: Extensions to a Field Method

2005 ◽  
Author(s):  
Luis San Andre´s ◽  
Oscar De Santiago
Keyword(s):  
Field Method ◽  
Mode Shapes ◽  
Flexible Rotor ◽  
Identification Procedure ◽  
Force Coefficients ◽  
Flexible Rotors ◽  
Rotor Bearing ◽  
Support Force ◽  
Order Of Magnitude ◽  
Bearing Force

Rotor-bearing system characteristics, such as mode shapes and their associated natural frequencies and damping ratios are essential to diagnose and correct vibration problems during system operation. Of the above characteristics, reliable identification of fluid film bearing force parameters, i.e. stiffness and damping coefficients, is one of the most difficult to achieve, in particular during field operation. Results of an enhanced method to estimate support force coefficients in flexible rotor-bearing systems based on imbalance response measurements obtained near the bearing locations are presented herein. The procedure can be conducted on site with minimal instrumentation. A test flexible rotor mounted on two-lobe hydrodynamic bearings is used to validate the identification procedure. Imbalance response measurements for various imbalance magnitudes are obtained near the bearing locations and also at rotor mid-span. At shaft speeds around the bending critical speed, the displacements at rotor mid span are an order of magnitude larger than the shaft displacements at the bearings. The identification procedure renders reliable bearing force coefficients for shaft speeds between 1 krpm and 4 krpm. The sensitivity of the method and derived parameters to noise in the measurements is also quantified.

Nonlinear Dynamics of Flexible Rotors Supported on Journal Bearings—Part I: Analytical Bearing Model

2017 ◽  
Vol 140 (2) ◽  
Author(s):  
Mohammad Miraskari ◽  
Farzad Hemmati ◽  
Mohamed S. Gadala
Keyword(s):  
Journal Bearing ◽  
Nonlinear Coefficient ◽  
Journal Bearings ◽  
Flexible Rotor ◽  
Dynamic Coefficients ◽  
Flexible Rotors ◽  
Rotor Bearing ◽  
Bearing Force ◽  
Derivatives Of ◽  
Bearing System

To determine the bifurcation types in a rotor-bearing system, it is required to find higher order derivatives of the bearing forces with respect to journal velocity and position. As closed-form expressions for journal bearing force are not generally available, Hopf bifurcation studies of rotor-bearing systems have been limited to simple geometries and cavitation models. To solve this problem, an alternative nonlinear coefficient-based method for representing the bearing force is presented in this study. A flexible rotor-bearing system is presented for which bearing force is modeled with linear and nonlinear dynamic coefficients. The proposed nonlinear coefficient-based model was found to be successful in predicting the bifurcation types of the system as well as predicting the system dynamics and trajectories at spin speeds below and above the threshold speed of instability.

Identification of Bearing Force Coefficients From Measurements of Imbalance Response of a Flexible Rotor

2004 ◽  
Author(s):  
Luis San Andre´s ◽  
Oscar C. De Santiago
Keyword(s):  
High Performance ◽  
Fluid Film ◽  
Flexible Rotor ◽  
Simple Method ◽  
Force Coefficients ◽  
Fluid Film Bearings ◽  
Support Force ◽  
Bearing Force ◽  
Rotor Structure ◽  
Motion Amplitude

Field identification of fluid film bearing parameters is critical for adequate interpretation of rotating machinery performance and necessary to validate or calibrate predictions from restrictive computational fluid film bearing models. This paper presents a simple method for estimating bearing support force coefficients in flexible rotor-bearing systems. The method requires two independent tests with known mass imbalance distributions and the measurement of the rotor motion (amplitude and phase) at locations close to the supports. The procedure relies on the modeling of the rotor structure and finds the bearing transmitted forces as a function of observable quantities (rotor vibrations at bearing locations). Imbalance response measurements conducted with a two-disk flexible rotor supported on two-lobe fluid film bearings allow validation of the identification method estimations. Predicted (linearized) bearing force coefficients agree reasonably well with the parameters derived from the test data. The method advanced neither adds mathematical complexity nor requires additional instrumentation beyond that already available in most high performance turbomachinery.

Theoretical and Experimental Studies on Squeeze Film Stabilizers for Flexible Rotor-Bearing Systems Using Newtonian and Viscoelastic Lubricants

1990 ◽  
Vol 112 (4) ◽  
pp. 473-482 ◽  
Author(s):  
B. Halder ◽  
A. Mukherjee ◽  
R. Karmakar
Keyword(s):  
High Speed ◽  
Experimental Studies ◽  
Squeeze Film ◽  
Experimental Investigations ◽  
Flexible Rotor ◽  
Stability Range ◽  
High Speeds ◽  
Flexible Rotors ◽  
Rotor Bearing

A combination of a squeeze film damper and a plane journal bearing is studied as a stabilizing scheme. The damper is made to play the role of a stabilizer to postpone the instability threshold speeds of flexible rotors. Both Newtonian and viscoelastic fluids are used in the rotor-bearing system. Dynamics of the system is theoretically analyzed using bond graphs. Analysis reveals that the use of a Newtonian fluid in the stabilizer largely improves the high speed stability range. However, viscoelastic stabilizing fluid has a detrimental effect on highly flexible rotors. Experimental investigations, conducted on a flexible rotor (natural frequency, 30 Hz), confirm the theoretical findings. In addition, experiments indicate that though the use of viscoelastic stabilizing fluids leads to instability in flexible rotors, the growth of large amplitude whirl is postponed to very high speeds.

Modally Tuned Influence Coefficients for Low-Speed Balancing of Flexible Rotors

2013 ◽  
Vol 136 (2) ◽  
Author(s):  
Y. A. Khulief ◽  
Wasiu Oke ◽  
M. A. Mohiuddin
Keyword(s):  
Experimental Test ◽  
High Speed ◽  
Mode Shapes ◽  
Flexible Rotor ◽  
Test Rig ◽  
Low Speed ◽  
Modal Characteristics ◽  
Flexible Rotors ◽  
Influence Coefficients ◽  
Experimental Test Rig

The need to devise a low-speed balancing method for balancing high-speed rotors was recognized and addressed. In this paper, a scheme that combines both the influence coefficients and modal balancing techniques is presented. The scheme is developed for low-speed balancing of high-speed rotors, and relies on knowledge of the modal characteristics of the rotor. The conditions for applicability of the method were stated in the light of the experientially estimated rotor deflection mode shapes. An experimental test rig of a flexible rotor was constructed to verify the applicability and reliability of the low-speed balancing scheme.

Flexible rotor balancing without trial runs using experimentally tuned FE based rotor model

2021 ◽  
Vol 21 (1) ◽  
pp. 20-26
Author(s):  
Yahya Muhammed Ameen ◽  
Jaafar Khalaf Ali
Keyword(s):  
Mode Shapes ◽  
Influence Coefficient ◽  
Flexible Rotor ◽  
Rotating Disks ◽  
Finite Elements Analysis ◽  
Response Data ◽  
Flexible Rotors ◽  
Low Efficiency ◽  
Rotor Balancing ◽  
Rotor Model

A method based on experimentally calibrated rotor model is proposed in this work for unbalance identification of flexible rotors without trial runs. Influence coefficient balancing method especially when applied to flexible rotors is disadvantaged by its low efficiency and lengthy procedure, whilst the proposed method has the advantage of being efficient, applicable to multi-operating spin speeds and do not need trial runs. An accurate model for the rotor and its supports based on rotordynamics and finite elements analysis combined with experimental modal analysis, is produced to identify the unbalance distribution on the rotor. To create digital model of the rotor, frequency response functions (FRFs) are determined from excitation and response data, and then modal parameters (natural frequencies and mode shapes) are extracted and compared with experimental analogies. Unbalance response is measured traditionally on rotor supports, in this work the response measured from rotating disks instead. The obtained results show that the proposed approach provides an effective alternative in rotor balancing. Increasing the number of balancing disks on balancing quality is investigated as well.

Variation of Fluid Flow Forces in Seals With Rotor Bending

1995 ◽  
Author(s):  
K. Kwanka
Keyword(s):  
Stability Limit ◽  
Mode Shapes ◽  
Flexible Rotor ◽  
Labyrinth Seals ◽  
Identification Procedure ◽  
Dynamic Coefficients ◽  
Exciting Forces ◽  
Direct Stiffness ◽  
The Stability ◽  
Turbomachine Rotor

Abstract Fluid-induced forces in labyrinth seals can cause unstable self-excited vibrations of the turbomachine rotor. Generally, a linear approach employing dynamic coefficients is used to describe these forces. A new procedure for the identification of the coefficients which uses two excitation sources placed on a flexible rotor is presented. The change in the stability limit and vibrational frequency caused by the investigated labyrinth gas seal contains the dynamic coefficients. It is important that problems which may also occur in the real turbomachine are considered by the identification procedure. The conservative dynamic coefficients, such as the direct stiffness, influence the bending of the mode shapes and thus affect indirectly the stability limit. The magnitude of the exciting forces depends on the axial positioning of the excitation source and also on the mode shape bending. These two dependencies are investigated by experiment and considered in the identification procedure.

Stability and Unbalance Analysis of Rigid Rotors Supported by Spiral Groove Bearings: Comparison of Different Approaches

2021 ◽  
Author(s):  
Elia Iseli ◽  
Jurg Schiffmann
Keyword(s):  
Load Capacity ◽  
Critical Mass ◽  
Mode Shapes ◽  
Response Analysis ◽  
Full Time ◽  
Number Range ◽  
Force Coefficients ◽  
Unbalance Response ◽  
Bearing Force ◽  
Gas Bearing

Abstract The dynamic behavior of spiral-grooved gas bearing supported 4DoF rotors is investigated by means of linearized bearing force coefficients and full time-integrated transient analysis. The two methods are compared for a variation of test rotors and bearing geometries in a given compressibility number interval of Lambda = [0,40]. The limitations and weaknesses of the linearized model are presented. It is shown that shafts with two symmetric herringbone-groove journal bearings have their maximum stability and load capacity if the center of gravity lays in the middle of the two bearings. For symmetric rotors (la/lb = 1) the two rigid modes, cylindrical and conical, are present and are influenced by the mass and transverse moment of inertia independently. For asymmetric rotors (la/lb < 1) the stability region decreases and the modes have a mixed shape. It is no longer possible to clearly distinguish between pure cylindrical and pure conical mode shapes. The two methods predict the critical mass and critical transverse moment of inertias within a difference of < 7%. A quasi-linear unbalance module for rigid gas bearing supported rotors is presented, which considers eccentricity dependent bearing force coefficients, allowing to speed up the unbalance response analysis by four orders of magnitude. The unbalance module is compared with the full transient orbital analysis, suggesting that the quasi-linear module predicts the non-linear unbalance response with <6% deviation for amplitudes up to e < 0.5 within the complete compressibility number range.

Nonlinear Vibration Analysis of a Flexible Rotor Supported by a Journal Bearing Considering Journal Angular Motion

2019 ◽  
Author(s):  
Nuntaphong Koondilogpiboon ◽  
Tsuyoshi Inoue
Keyword(s):  
Nonlinear Vibration ◽  
Ball Bearing ◽  
Journal Bearing ◽  
Angular Motion ◽  
Experimental Result ◽  
Flexible Rotor ◽  
Large Disk ◽  
Rotor Bearing ◽  
Bearing Force ◽  
Bearing System

Abstract The effect of bearing length to diameter (L/D) ratio and large disk position on nonlinear vibration (limit cycle and bifurcation type) of a flexible rotor-bearing system is investigated. The rotor consists of a shaft modeled by 1-D finite elements (FE), two small disks and a large disk. It is supported by a self-aligning ball bearing and an axial-groove journal bearing with L/D ratio of 0.4 and 0.6. Two large disk positions: 340 and 575 mm measured from the ball bearing are investigated. The journal angular motion, which is essential for the highly flexible rotor but typically not considered in the previous nonlinear vibration literature; is considered in nonlinear bearing force calculation. The degrees of freedom (DOF) of the rotor-bearing system are reduced to those of the node that the nonlinear journal bearing force and moment act on by real mode component mode synthesis (CMS) that retains only the 1st forward and backward modes. Shooting method and Floquet multiplier analysis are applied to the reduced rotor-bearing system to obtain limit cycles and their stability of each bearing L/D ratio and large disk position case. Numerical results indicate that supercritical Hopf bifurcation only occurs in the case of L/D = 0.4 and large disk position 575 mm, otherwise subcritical occurs. However, if the typical bearing model that does not consider journal angular motion is used, the bifurcation type for the case of L/D = 0.6 with large disk position 575 mm will change to supercritical. Lastly, the experiments with the same L/D ratio and large disk position investigated in the calculation are performed as a validation. The experimental result of each case shows the same bifurcation type as the calculation result using the bearing model that considers the journal angular motion.

The Excitability of Flexible Rotors in Short Sleeve Bearings

1975 ◽  
Vol 97 (1) ◽  
pp. 105-115 ◽  
Author(s):  
E. J. Hahn
Keyword(s):  
Flexible Rotor ◽  
External Disturbances ◽  
Stability Threshold ◽  
Flexible Rotors ◽  
Rotor Bearing ◽  
Operating Regions ◽  
The Stability ◽  
Linearized Model ◽  
Lubricant Viscosity ◽  
Bearing System

Assuming the short bearing approximation and constant lubricant properties, the root loci of the pertinent characteristic function were obtained for the linearized model of a simple symmetric flexible rotor bearing system. Using these loci, design maps consisting of lines of constant damping and vibration frequency pertaining to the dominant roots are presented as a function of the equilibrium eccentricity ratio and a frequency parameter for relevant degrees of flexibility. These maps display undesirable operating regions where external disturbances such as shock or unbalance loading are likely to excite undesirable vibrations, as well as regions of instability. The maps may conveniently be used to determine the effect of changing journal speed, lubricant viscosity and/or bearing clearance. Increased flexibility is seen to reduce the stability threshold in a predictable manner and to reduce damping at the pin-pin critical speed. The approach is applicable to more complex rotor bearing systems. It is felt that the use of such maps will enhance the understanding of rotor bearing system behavior, particularly at operating regions close to the stability threshold.

Modally-Tuned Influence Coefficients for Low-Speed Balancing of Flexible Rotors

2011 ◽  
Author(s):  
Y. A. Khulief ◽  
M. A. Mohiuddin
Keyword(s):  
Experimental Test ◽  
High Speed ◽  
Mode Shapes ◽  
Flexible Rotor ◽  
Test Rig ◽  
Low Speed ◽  
Modal Characteristics ◽  
Flexible Rotors ◽  
Influence Coefficients ◽  
Experimental Test Rig

The need to devise a low-speed balancing method for balancing high-speed rotors was recognized and addressed. In this paper, a scheme that combines both the influence coefficients and modal balancing techniques is presented. The scheme is developed for low-speed balancing of high-speed rotors, and relies on knowledge of modal characteristics of the rotor. The conditions for applicability of the method were stated in the light of the experientially estimated rotor deflection mode shapes. An experimental test rig of a flexible rotor was constructed to verify the applicability and reliability of the low-speed balancing scheme.

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