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.

scholarly journals Dynamic Characteristics of Air Cycle Machine Rotor System

2018 ◽  
Vol 2018 ◽  
pp. 1-16 ◽  
Author(s):  
Dongjiang Han ◽  
Long Hao ◽  
Jinfu Yang
Keyword(s):  
Critical Speed ◽  
Dynamic Balance ◽  
Exciting Force ◽  
Rotor System ◽  
Parameters Optimization ◽  
Response Analysis ◽  
Response Characteristics ◽  
Bearing Stiffness ◽  
Harmonic Response Analysis ◽  
Modal Method

Parameters optimization in the critical speed region has the important influence on operational stability of an air cycle machine. Effects of bearing stiffness and unbalanced exciting force on critical speed and response characteristics are investigated by the modal method and harmonic response analysis. Resonance separation phenomenon in the critical speed region is analyzed in detail. When difference exists in the phase of unbalanced exciting force, resonance separation appears in the conical whirling speed region. The characteristics after resonance separation are closely related to the phase difference value and amplitude of unbalanced exciting force. The paper provides theoretical and experimental foundations for resonance separation analysis and also provides data support for dynamic balance and dynamic design of the rotor system.

Study of Damped Critical Speeds and Damping Ratios of Flexible Rotors

1984 ◽  
Vol 106 (1) ◽  
pp. 62-71 ◽  
Author(s):  
Shinobu Saito ◽  
Tsuneo Someya
Keyword(s):  
Vibration Amplitude ◽  
Critical Speed ◽  
Damping Ratio ◽  
Ball Bearings ◽  
Test Results ◽  
Oil Film ◽  
Critical Speeds ◽  
Flexible Rotors ◽  
The Relationship

Influences of bearing damping on critical speeds of flexible rotors are investigated. First, the damped critical speed and the damping ratio of a uniform shaft supported at both ends are examined. It is shown that there exists an optimum bearing damping that gives the maximum damping ratio for each order of critical speed, and that with increasing support stiffness the optimum damping increases but the maximum damping ratio decreases. The meaning of critical speed map is discussed on the basis of the attainable maximum damping ratio. Next, the critical speed characteristics of a uniform shaft supported by three or four bearings are examined. Especially, for the case of 3-bearing-support, the relationship between the maximum damping ratio or the optimum bearing damping and the support stiffness is discussed. Finally, experiments to verify the existence of the optimum bearing damping are carried out for two cases of support stiffness using a test rotor supported by ball bearings and oil film damper bearings. The test results reveal that for each support stiffness there exists an optimum bearing damping, under which the vibration amplitude at the critical speed becomes minimum.

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.

Dynamic Vibration Absorber Design to Suppress Boring Chatter: Absorber Parameters Identification Based on Modal Correlation

2013 ◽  
Vol 753-755 ◽  
pp. 1816-1820 ◽  
Author(s):  
Zhen Kun Hu ◽  
Ming Wang ◽  
Tao Zan
Keyword(s):  
Damping Ratio ◽  
Correlation Method ◽  
Vibration Absorber ◽  
Dynamic Vibration Absorber ◽  
Element Analysis ◽  
Simple Method ◽  
Dynamic Vibration ◽  
The Finite Element Analysis ◽  
Chatter Control ◽  
Modal Method

The dynamic vibration absorber (DVA) is generally used to suppress the machining vibration in boring processes. The DVA consists of an additional massspringdamper sub-system, and needs accurately tuning of its natural frequency and damping ratio to match the main structure for vibration control. For obtaining the optimal performance of the DVA, the parameters of the DVA used in a boring bar is identified using modal correlation method, which combines the finite element analysis method with test modal method to validate the FEMs results. The analysis results show that the modal correlation method is an effective and simple method to accurately identify the dynamic parameters of DVA and guarantee the optimal design of the DVA for boring chatter control.

A Complex Modal Analysis Method for Damped Vibration Systems (The Representation in the Second Order Differential Form of a Modal Equation and its Use for Practical Application)

1985 ◽  
Vol 107 (1) ◽  
pp. 13-18
Author(s):  
Y. Inoue ◽  
T. Fujikawa
Keyword(s):  
Modal Analysis ◽  
Damping Ratio ◽  
Second Order ◽  
Response Analysis ◽  
Modal Damping Ratio ◽  
Vibration Problems ◽  
Modal Mass ◽  
Modal Equation ◽  
Damped Vibration Systems ◽  
Complex Modal

Second order uncoupled differential equations for the general damped vibration systems are derived theoretically. The equations are written in a form similar to the classical real modal equations by using the natural frequency, the modal damping ratio, and the newly defined complex modal mass. Introducing supplementary variables, the response analysis is carried out in a similar manner to the real modal analysis. By comparing these equations to the classical ones, physical meanings of the derived equations are clarified. For the vibration problems near the resonant point, approximate complex modal equations are derived which have almost the same form as the classical one. Some applications of the proposed method to vibration problems are discussed.

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.

Jørgen W. Lund: Theories Versus Tests, Part 1: Balancing and Response of Flexible Rotors

2003 ◽  
Vol 125 (4) ◽  
pp. 482-488 ◽  
Author(s):  
Jørgen Tonnesen
Keyword(s):  
Experimental Work ◽  
Journal Bearing ◽  
Rotor Dynamics ◽  
Flexible Rotor ◽  
Late Professor ◽  
Fluid Film Bearings ◽  
Condensed Form ◽  
Flexible Rotors ◽  
The Subject ◽  
Rotor Balancing

The contribution of the late Professor Jørgen W. Lund in the field of rotor dynamics and fluid film bearings is presented in a condensed form with the emphasis on the experimental work and results that confirm and support many of Dr. Lund’s theories and analyses. Part 1(A) covers the subject of rotor balancing by the influence method and Part 1(B) the unbalance response of a flexible rotor. In Part 2(A), experiments on instability and the influence of unbalance on whirl frequency are discussed for two rotors supported in cylindrical bearings. In Part 2(B), experiments using a cylindrical, two-axial groove journal bearing over a range of loads and speeds are reviewed.

Complex modal balancing of flexible rotors including residual bow

1988 ◽  
Vol 4 (3) ◽  
pp. 245-251 ◽  
Author(s):  
W. L. Meacham ◽  
P. B. Talbert ◽  
H. D. Nelson ◽  
N. K. Cooperrider
Keyword(s):  
Flexible Rotors ◽  
Complex Modal
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