Closure to “Discussions of ‘Effect of Residual Shaft Bow on Unbalance Response and Balancing of a Single Mass Flexible Rotor—Parts I and II’” (1976, ASME J. Eng. Power, 98, pp. 187–188)

1976 ◽  
Vol 98 (2) ◽  
pp. 188-189
Author(s):  
J. C. Nicholas ◽  
E. J. Gunter ◽  
P. E. Allaire
Keyword(s):  
Flexible Rotor ◽  
Unbalance Response ◽  
Single Mass

Effect of Residual Shaft Bow on Unbalance Response and Balancing of a Single Mass Flexible Rotor—Part I: Unbalance Response

1976 ◽  
Vol 98 (2) ◽  
pp. 171-181 ◽  
Author(s):  
J. C. Nicholas ◽  
E. J. Gunter ◽  
P. E. Allaire
Keyword(s):  
Phase Angle ◽  
Response Speed ◽  
Rotor Speed ◽  
Flexible Rotor ◽  
Simple Method ◽  
Unbalance Response ◽  
Single Mass ◽  
Reverse Situation ◽  
Rigid Supports ◽  
Timing Mark

The effect of residual shaft bow on the unbalance response of a single mass rotor on rigid supports has been examined with a theoretical analysis. The analysis determined the amplitude, phase angle, and peak rotor response speed for various combinations of residual bow and unbalance. For most combinations the phase angle corresponding to the peak rotor response speed was significantly different from the 90 degrees observed in the conventional unbowed rotor. If the residual bow and unbalance were exactly out of phase, the rotor amplitude was zero for a rotor speed equal to the square root of the ratio of residual bow amplitude to unbalance eccentricity. The results of the study suggested a simple method for determining the relative amplitudes of residual bow and unbalance eccentricity based upon the motion of a timing mark on an oscilliscope screen. If the residual bow was less than the unbalance eccentricity, the timing mark moved first in the direction of rotor rotation as the speed is increased and then moved in the opposite direction at a speed less than the critical speed. In the reverse situation, the timing mark moved opposite to the direction of rotation as the speed is increased. At some speed above the critical, it reversed direction. Part II of this paper presents theoretical and experimental results for balancing of a single mass rotor with a residual bow.

Iterative Determination of Squeeze Film Damper Eccentricity for Flexible Rotor Systems

1982 ◽  
Vol 104 (2) ◽  
pp. 334-338 ◽  
Author(s):  
L. M. Greenhill ◽  
H. D. Nelson
Keyword(s):  
System Analysis ◽  
Squeeze Film ◽  
Flexible Rotor ◽  
Rotor Systems ◽  
Root Finding ◽  
Unbalance Response ◽  
Rotor Bearing ◽  
Single Mass ◽  
Stiffness And Damping ◽  
Film Stiffness

A method is presented to determine the eccentricity of multiple squeeze film dampers used in multishaft rotor bearing unbalance response analyses. The procedure is iterative and is based upon the secant root finding algorithm. Unbalance response is calculated using the iteratively determined eccentricity in closed form expressions of squeeze film stiffness and damping coefficients, for either long or short bearing theory. Circular centered synchronous operation is assumed. The method is demonstrated by determining the response of a single mass centrally preloaded rotor, a multimass flexible rotor supported by two squeeze films, and a multishaft flexible rotor system employing three squeeze film supports. The results obtained in the flexible rotor analysis are compared to test data, with the correlation found to be good. Due to rapid convergence and multiple squeeze film capability, the procedure is particularly suited to large multishaft flexible rotor-bearing system analysis.

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.

The Effect of Support Flexibility and Damping on the Synchronous Response of a Single-Mass Flexible Rotor

1972 ◽  
Vol 94 (1) ◽  
pp. 221-232 ◽  
Author(s):  
R. G. Kirk ◽  
E. J. Gunter
Keyword(s):  
Steady State ◽  
Equations Of Motion ◽  
Optimization Procedure ◽  
Dynamic Vibration Absorber ◽  
Steady State Analysis ◽  
Transient Motion ◽  
Unbalance Response ◽  
Single Mass ◽  
Effect Of Support ◽  
State Analysis

This paper deals with the dynamic unbalance response and transient motion of the single-mass Jeffcott rotor in elastic bearings mounted on damped, flexible supports. A steady-state analysis of the shaft and the bearing housing motion was made by assuming synchronous precession of the system. The conditions under which the support system would act as a dynamic vibration absorber at the rotor critical speed were studied and plots of the rotor and support amplitudes, phase angles, and forces transmitted were evaluated by the computer and the performance curves were plotted by an automatic plotter unit. Curves are presented on the optimization of the support housing characteristics to attenuate the rotor synchronous unbalance response. The complete transient motion including rotor unbalance was examined by integrating the equations of motion numerically using a modified 4th-order Runge–Kutta procedure and the resulting whirl orbits were plotted by an automatic plotter unit. The results of the transient analysis are discussed with regard to the design optimization procedure derived from the steady-state analysis.

scholarly journals Steady-State Unbalance Response of a Three-Disk Flexible Rotor on Flexible, Damped Supports

1978 ◽  
Vol 100 (3) ◽  
pp. 563-573 ◽  
Author(s):  
R. E. Cunningham
Keyword(s):  
Ball Bearing ◽  
Squeeze Film ◽  
Flexible Rotor ◽  
Frequency Range ◽  
Lateral Bending ◽  
Damping Coefficients ◽  
The Third ◽  
Unbalance Response ◽  
Squeeze Film Damping ◽  
Squeeze Film Dampers

Experimental data are presented for the unbalance response of a flexible, ball bearing supported rotor to speeds above the third lateral bending critical. Values of squeeze film damping coefficients obtained from measured data are compared to theoretical values obtained from short bearing approximation over a frequency range from 5000 to 31,000 cycles/min. Experimental response for an undamped rotor is compared to that of one having oil squeeze film dampers at the bearings. Unbalances applied varied from 0.62 to 15.1 gm-cm.

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