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.

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.

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.

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.

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

1976 ◽  
Vol 98 (2) ◽  
pp. 182-187 ◽  
Author(s):  
J. C. Nicholas ◽  
E. J. Gunter ◽  
P. E. Allaire
Keyword(s):  
Critical Speed ◽  
Direct Method ◽  
Influence Coefficient ◽  
Unbalance Response ◽  
Influence Coefficient Method ◽  
Single Mass ◽  
All Speeds ◽  
Optimum Balance ◽  
Coefficient Method ◽  
Speed Method

Three methods of balancing a rotor with a residual shaft bow were presented. Method I balanced the total shaft amplitude to zero at the balance speed. Method II balanced the elastic deflection to zero at the balance speed leaving the residual bow amplitude. Method III balanced the total shaft amplitude to zero at the critical speed without actually operating the rotor at the critical. After balancing by Method I, a large amplitude remained near the critical. Method II balanced the rotor to the residual bow amplitude at all speeds except near the critical where the amplitude is slightly larger than the residual amplitude. The optimum balance resulted from balancing by Method III. In this case, the amplitude was less than or equal to the residual bow amplitude for all speeds except at the critical where the amplitude was zero. Method III required that the critical speed be known prior to balancing. For all three balancing methods, the unbalance influence coefficient must be determined. Two procedures for determining this coefficient were discussed. One was the familiar trial weight influence coefficient method and the other was the direct method which does not require trial weights. Part I of this paper discussed the effect of shaft bow on unbalance response.

scholarly journals Fault Diagnosis of Brake Train Based on Multi-Sensor Data Fusion

Sensors ◽  
2021 ◽  
Vol 21 (13) ◽  
pp. 4370
Author(s):  
Yongze Jin ◽  
Guo Xie ◽  
Yankai Li ◽  
Xiaohui Zhang ◽  
Ning Han ◽  
...  
Keyword(s):  
Fault Diagnosis ◽  
Expectation Maximization ◽  
Monitoring Data ◽  
Sensor Data ◽  
Operating Environment ◽  
Mass Model ◽  
Multi Sensor Data Fusion ◽  
Diagnosis Method ◽  
Single Mass ◽  
Parameter Identifications

In this paper, a fault diagnosis method is proposed based on multi-sensor fusion information for a single fault and composite fault of train braking systems. Firstly, the single mass model of the train brake is established based on operating environment. Then, the pre-allocation and linear-weighted summation criterion are proposed to fuse the monitoring data. Finally, based on the improved expectation maximization, the braking modes and braking parameters are identified, and the braking faults are diagnosed in real time. The simulation results show that the braking parameters of systems can be effectively identified, and the braking faults can be diagnosed accurately based on the identification results. Even if the monitoring data are missing or abnormal, compared with the maximum fusion, the accuracies of parameter identifications and fault diagnoses can still meet the needs of the actual systems, and the effectiveness and robustness of the method can be verified.

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

scholarly journals Unbalance Response Prediction for Rotors on Ball Bearings Using Speed- and Load-Dependent Nonlinear Bearing Stiffness

2005 ◽  
Vol 2005 (1) ◽  
pp. 53-59 ◽  
Author(s):  
David P. Fleming ◽  
J. V. Poplawski
Keyword(s):  
Response Prediction ◽  
Rolling Element Bearing ◽  
Response Analysis ◽  
Ball Bearings ◽  
Moderate Amount ◽  
Constant Stiffness ◽  
Unbalance Response ◽  
Rolling Element ◽  
Bearing Stiffness ◽  
Element Bearing

Rolling-element bearing forces vary nonlinearly with bearing deflection. Thus, an accurate rotordynamic analysis requires that bearing forces corresponding to the actual bearing deflection be utilized. For this work, bearing forces were calculated by COBRA-AHS, a recently developed rolling-element bearing analysis code. Bearing stiffness was found to be a strong function of bearing deflection, with higher deflection producing markedly higher stiffness. Curves fitted to the bearing data for a range of speeds and loads were supplied to a flexible rotor unbalance response analysis. The rotordynamic analysis showed that vibration response varied nonlinearly with the amount of rotor imbalance. Moreover, the increase in stiffness as critical speeds were approached caused a large increase in rotor and bearing vibration amplitude over part of the speed range compared to the case of constant-stiffness bearings. Regions of bistable operation were possible, in which the amplitude at a given speed was much larger during rotor acceleration than during deceleration. A moderate amount of damping will eliminate the bistable region, but this damping is not inherent in ball bearings.

Analysis of Models for Torsional Vibration of Shaft System With Planetary Gearing

1997 ◽  
Author(s):  
Jinghui Sun ◽  
Lee Liu ◽  
William N. Patten
Keyword(s):  
Torsional Vibration ◽  
Planetary Gear ◽  
Gear Train ◽  
Mathematical Treatment ◽  
Dynamic Parameters ◽  
Mass Model ◽  
Planar Model ◽  
Shaft System ◽  
Effective Dynamic ◽  
Single Mass

Abstract The kinematics of planetary gearing are complex; thus, making it difficult to build an effective dynamic model. In this paper, a single-mass model of a planetary gear and shaft system is developed to study the torsional vibration of the mechanism. Two new models of the system are proposed: (a) a fictitious co-planar model and (b) an equivalent shaft model. The results from the calculations and analyses using these models indicate that: 1) the single-mass model and the general rotary model are both limited, either mathematically or geometrically; 2) the fictitious co-planar model includes all of the geometric and dynamic parameters of the general rotary model, and it can be connected with the shaft system easily; and 3) using a mathematical treatment, the equivalent shaft model is demonstrated to be the most useful and most effective model for the calculation of torsional vibration of a shaft and planetary gear train.

Estimating Critical Speeds of Stepped Shafts with Flexible Bearings

1971 ◽  
Vol 8 (03) ◽  
pp. 327-333
Author(s):  
R. H. Salzman
Keyword(s):  
High Speed ◽  
Critical Speed ◽  
Design Stage ◽  
Normal Range ◽  
Critical Speeds ◽  
Stepped Shaft ◽  
Bearing Stiffness ◽  
Variable Support ◽  
Method Show ◽  
Good Agreement

This paper presents a semi-graphical approach for finding the first critical speed of a stepped shaft with finite bearing stiffness. The method is particularly applicable to high-speed turbine rotors with journal bearings. Using Rayleigh's Method and the exact solution for whirling of a uniform shaft with variable support stiffness, estimates of the lowest critical speed are easily obtained which are useful in the design stage. First critical speeds determined by this method show good agreement with values computed by the Prohl Method for the normal range of bearing stiffness. A criterion is also established for determining if the criticals are "bearing critical speeds" or "bending critical speeds," which is of importance in design. Discusser E. G. Baker

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