Secondary critical speed of flexible rotors with inertia slots

1983 ◽  
Vol 87 (1) ◽  
pp. 61-70 ◽  
Author(s):  
M. Sakata ◽  
M. Endo ◽  
K. Kishimoto ◽  
N. Hayashi
Keyword(s):  
Critical Speed ◽  
Flexible Rotors

Steady-State Performance of Squeeze Film Damper Supported Flexible Rotors

1977 ◽  
Vol 99 (4) ◽  
pp. 552-558 ◽  
Author(s):  
M. D. Rabinowitz ◽  
E. J. Hahn
Keyword(s):  
Steady State ◽  
Critical Speed ◽  
Rolling Element Bearing ◽  
Squeeze Film ◽  
Response Curves ◽  
Flexible Rotors ◽  
Steady State Operation ◽  
Bearing Life ◽  
Rolling Element ◽  
Single Mass

The synchronous steady-state operation of a centrally preloaded single mass flexible rotor supported in squeeze film bearing dampers is examined theoretically. Assuming the short bearing approximation and symmetric motions, frequency response curves are presented exhibiting the effect of relevant system parameters on rotor excursion amplitudes and unbalance transmissibilities for both pressurized and unpressurized lubricant supply. Hence, the influence of rotor flexibility, rotor mass distribution, rotor speed, bearing dimensions, lubricant viscosity, support flexibility can be readily determined, allowing for optimal rotor bearing system design. It is shown that with pressurized bearing mounts, the possibility of undesirable operation modes is eliminated and a smooth passage through the first pin-pin critical speed of the rotor is feasible, while absence of pressurization significantly limits the maximum safe unbalance in the vicinity of this critical speed. Significant decrease in transmissibility and rotor excursion amplitudes over those obtainable with rigid mounts are shown to be a practical possibility, with consequent decrease in the vibration level of the rotor mounts and prolongation of rolling element bearing life, while maintaining acceptable rotor vibration amplitudes. A design example is included to illustrate the use of the data.

A Minimum Strain Energy Approach for Obtaining Optimal Unbalance Distribution in Flexible Rotors

1982 ◽  
Vol 104 (4) ◽  
pp. 875-880 ◽  
Author(s):  
T. F. Conry ◽  
P. R. Goglia ◽  
C. Cusano
Keyword(s):  
Strain Energy ◽  
Critical Speed ◽  
Optimization Problem ◽  
Equations Of Motion ◽  
Rotor System ◽  
Quadratic Program ◽  
Unique Minimum ◽  
Flexible Rotors ◽  
Minimum Strain Energy ◽  
Selection Of

A method is developed to design for optimal unbalance distribution in a rotor system which has elements that are assembled on the shaft and operates above the first critical speed. This method can also be used for computing the optimal selection of balance weights in specified planes for a rotor with a known distribution of unbalance—the classic balancing problem. The method is an optimization problem where the strain energy of the rotor and its supports are minimized subject to the constraints of the equations of motion of the rotor system at a particular balancing speed. The problem is a quadratic program that has a unique minimum.

Balancing of Flexible Rotors by the Complex Modal Method

1983 ◽  
Vol 105 (1) ◽  
pp. 94-100 ◽  
Author(s):  
S. Saito ◽  
T. Azuma
Keyword(s):  
Physical Meaning ◽  
Critical Speed ◽  
Damping Ratio ◽  
Exciting Force ◽  
Force Vector ◽  
Fluid Film Bearings ◽  
Flexible Rotors ◽  
The Right ◽  
Modal Method ◽  
Complex Modal

A new calculation method of the modal unbalance response for general flexible rotors in fluid film bearings has been developed by introducing the concept of modal exciting force vector into the usual complex modal method, and the physical meaning of the damping ratio at a critical speed is discussed. Next, application of this method, that correction weights can be determined in only one trial operation, is reported, and positions to measure vibration and to correct unbalance weight are discussed on the basis of the right eigenvector and the exciting factor mode, respectively. Lastly, it is shown by experiments that the proposed balancing method is of use for actual rotors.

Optimum Bearing and Support Damping for Unbalance Response and Stability of Rotating Machinery

1978 ◽  
Vol 100 (1) ◽  
pp. 89-94 ◽  
Author(s):  
L. E. Barrett ◽  
E. J. Gunter ◽  
P. E. Allaire
Keyword(s):  
Approximate Method ◽  
Critical Speed ◽  
Exact Methods ◽  
Mass Model ◽  
Unbalance Response ◽  
Flexible Rotors ◽  
Bearing Stiffness ◽  
Single Mass ◽  
Internal Rotor ◽  
Stability Limits

This paper presents a rapid approximate method for calculating the optimum bearing or support damping for multimass flexible rotors to minimize unbalance response and to maximize stability in the vicinity of the rotor first critical speed. A multimass rotor is represented by an equivalent single-mass model for purposes of the analysis. The optimum bearing damping is expressed as a function of the bearing stiffness and rotor modal stiffness at the rigid bearing critical speed. Stability limits for aerodynamic cross coupling and viscous internal rotor friction damping are also presented. Comparison of the optimum damping obtained by this approximate method with that obtained by full scale linearized transfer matrix methods for several rotor-bearing configurations shows good agreement. The method has the advantage of being quickly and easily applied and can reduce analysis time by eliminating a time consuming search for the approximate optimum damping using more exact methods.

A General Method for Calculating Critical Speeds of Flexible Rotors

1945 ◽  
Vol 12 (3) ◽  
pp. A142-A148 ◽  
Author(s):  
M. A. Prohl
Keyword(s):  
Cross Section ◽  
Critical Speed ◽  
The Other ◽  
Circular Symmetry ◽  
Critical Speeds ◽  
Flexible Rotors ◽  
The Moment ◽  
The One ◽  
Elastically Supported ◽  
General Method

Abstract The existing methods for determining critical speeds are subject to the following limitations: On the one hand the methods that are general, i.e., that permit the calculation of higher critical speeds as well as the fundamental, involve computations so complicated as to be impractical for any but the simplest of rotors. On the other hand, the methods for which the computations are comparatively simple, such as the familiar methods of Rayleigh and Stodola, lack generality in that critical speeds other than the fundamental cannot be definitely determined (1). The calculation method presented in this paper combines generality with comparative simplicity. Any critical speed—first, second, or higher—may be calculated with equal ease. The rotor may have any number of spans and its cross section may vary in any prescribed manner provided circular symmetry is maintained. Any number of disks or symmetrical masses may be attached. The shaft journals may be considered to be elastically supported in the bearing with respect to both deflection and tilting of the journals; the elastic constants must, however, be symmetrical. The so-called “gyroscopic effect” associated with the moment of inertia of the disks on the rotor may be readily taken into account.

Synchronous Unbalance Response of an Overhung Rotor With Disk Skew

1979 ◽  
Author(s):  
O. J. Salamone ◽  
E. J. Gunter
Keyword(s):  
Phase Angle ◽  
Critical Speed ◽  
Rapid Phase ◽  
Single Plane ◽  
Unbalance Response ◽  
Flexible Rotors ◽  
All Speeds

This paper deals with the influence of disk skew on the synchronous unbalance of flexible rotors in damped bearings. A simple overhung rotor 1E treated to illustrate the effects of various combinations of unbalance and disk skew on the amplitude and phase angle response at the disk and bearings. The paper shows that it is impossible to balance the rotor at all speeds by single plane balancing even if three correction planes are employed. The presence of disk skew may be best detected by monitoring the far bearing for a rapid phase angle decrease after passing through the first critical speed.

Magnetic Bearing Sizing for Flexible Rotors

1992 ◽  
Vol 114 (2) ◽  
pp. 223-229 ◽  
Author(s):  
E. H. Maslen ◽  
P. E. Allaire
Keyword(s):  
Critical Speed ◽  
Load Capacity ◽  
Magnetic Bearing ◽  
Flexible Rotor ◽  
Rotor Systems ◽  
Motion Constraints ◽  
Mass Unbalance ◽  
Flexible Rotors ◽  
Bearing Load ◽  
External Loads

Magnetic bearing load capacity in flexible rotor systems must be adequate to accommodate external loads acting on the rotor. The first part of this paper develops the theoretical basis for computing the bearing load capacity requirements of flexible rotors subject to bounded external harmonic loads and strict motion constraints. The second part of this work illustrates the application of the theory to a specific example: a fairly simple three disk flexible rotor subject to mass unbalance loads. Load capacity requirements are computed for the example shaft at its first three free-free forward whirl critical speeds. Based on the bounds obtained, two bearing design cases are examined: one with 45 N load capacity and the other with 223 N load capacity. The performance of the rotor is not improved with the higher capacity bearing and neither is capable of adequately constraining the rotor at its second critical speed. It is concluded that this shaft cannot be operated above its second free-free critical speed without a midspan bearing.

Should a Flexible Rotor Be Balanced in N or (N + 2) Planes?

1972 ◽  
Vol 94 (2) ◽  
pp. 548-558 ◽  
Author(s):  
W. Kellenberger
Keyword(s):  
Critical Speed ◽  
System Of Equations ◽  
Flexible Rotor ◽  
Orthogonal Functions ◽  
Linear System Of Equations ◽  
Flexible Rotors ◽  
Speed Range ◽  
Set Up ◽  
Limiting Case ◽  
Analytical Expressions

The problem of balancing flexible rotors consists mainly of eliminating rotating bearing forces. Analytical expressions are derived for the deformation and the rotating bearing forces of a rotor, using orthogonal functions. With this kind of representation it is possible to set up simple conditions for the vanishing rotating bearing forces. They lead to a linear system of equations giving the compensating unbalances in each of a set number of balancing planes. Two methods used in practice are theoretically explained and compared. The “N” method employs N planes for balancing a speed range up to, and including, the Nth critical speed and can be characterized by the condition A = 0, see equation (13). The “(N + 2)” method requires two more planes for the same speed range and is characterized by A = 0 and B = 0. It is proved that limlimN→∞B=0, so that in the limiting case of an infinite number of balancing planes (speed range from zero to infinity) both methods are of equal value. The two methods differ for finite N in their accuracy and the amount of calculation. Considering simple examples with known unbalance distribution it will be shown that the main error of the N method is the result of treating B as equal to 0, which it is not, thus accounting for the greater accuracy of the N + 2 method. The additional effort needed for the latter method is justified in those cases where greater accuracy is demanded.

Synchronous Unbalance Response of an Overhung Rotor with Disk Skew

1980 ◽  
Vol 102 (4) ◽  
pp. 749-755 ◽  
Author(s):  
D. J. Salamone ◽  
E. J. Gunter
Keyword(s):  
Phase Angle ◽  
Critical Speed ◽  
Rapid Phase ◽  
Single Plane ◽  
Unbalance Response ◽  
Flexible Rotors ◽  
All Speeds

This paper deals with the influence of disk skew on the synchronous unbalance response of flexible rotors in damped bearings. A simple overhung rotor is treated to illustrate the effects of various combinations of unbalance and disk skew on the amplitude and phase angle response at the disk and bearings. The paper shows that it is impossible to balance the rotor at all speeds by single plane balancing even if three correction planes are employed. The presence of disk skew may be best detected by monitoring the far bearing for a rapid phase angle decrease after passing through the first critical speed.

Modal Balancing of Flexible Rotors during Operation: Design and Manual Operation of Balancing Head

1987 ◽  
Vol 201 (5) ◽  
pp. 349-355 ◽  
Author(s):  
C-W Lee ◽  
Y-D Kim
Keyword(s):  
Critical Speed ◽  
Manual Operation ◽  
Flexible Rotors ◽  
Rotor Bearing ◽  
Bearing System

Modal balancing experiments are performed with a rotor bearing system by using a single wireless, manually controlled precision balancing head. The balancing head designed is proven to be accurately functioning, effective in modal balancing and reliable well over the first critical speed.

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