Critical Speeds, Divergence, and Flutter Instability in High-Speed Planetary Gears

2012 ◽  
Author(s):  
Christopher G. Cooley ◽  
Robert G. Parker
Keyword(s):  
High Speed ◽  
Critical Speed ◽  
Numerical Results ◽  
Planetary Gears ◽  
Critical Speeds ◽  
Flutter Instability ◽  
Divergence Instability ◽  
Translational Mode

The structured properties of the critical speeds and associated critical speed eigenvectors of high-speed planetary gears are given. Planetary gears have only planet, rotational, and translational mode critical speeds. Divergence instability is possible at speeds adjacent to critical speeds. Numerical results verify the critical speed locations. Divergence and flutter instabilities are investigated numerically for each mode type.

Formation of Standing Waves in Radial Tires

1984 ◽  
Vol 12 (1) ◽  
pp. 44-63 ◽  
Author(s):  
Y. D. Kwon ◽  
D. C. Prevorsek
Keyword(s):  
High Speed ◽  
Critical Speed ◽  
Unit Length ◽  
Standing Waves ◽  
Rolling Resistance ◽  
Damping Coefficient ◽  
Circular Membrane ◽  
Critical Speeds ◽  
Steel Cord ◽  
The Individual

Abstract Radial tires for automobiles were subjected to high speed rolling under load on a testing wheel to determine the critical speeds at which standing waves started to form. Tires of different makes had significantly different critical speeds. The damping coefficient and mass per unit length of the tire wall were measured and a correlation between these properties and the observed critical speed of standing wave formation was sought through use of a circular membrane model. As expected from the model, desirably high critical speed calls for a high damping coefficient and a low mass per unit length of the tire wall. The damping coefficient is particularly important. Surprisingly, those tire walls that were reinforced with steel cord had higher damping coefficients than did those reinforced with polymeric cord. Although the individual steel filaments are elastic, the interfilament friction is higher in the steel cords than in the polymeric cords. A steel-reinforced tire wall also has a higher density per unit length. The damping coefficient is directly related to the mechanical loss in cyclic deformation and, hence, to the rolling resistance of a tire. The study shows that, in principle, it is more difficult to design a tire that is both fuel-efficient and free from standing waves when steel cord is used than when polymeric cords are used.

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

The Dynamic Analysis of SFD-Sliding Bearing Flexible Rotor System Based on Optimization Design

2012 ◽  
Vol 159 ◽  
pp. 355-360
Author(s):  
Ji Yan Wang ◽  
Rong Chun Guo ◽  
Xu Fei Si
Keyword(s):  
High Speed ◽  
Optimization Design ◽  
Critical Speed ◽  
Structural Parameters ◽  
Rotor System ◽  
Flexible Rotor ◽  
Optimization Analysis ◽  
Sliding Bearing ◽  
Critical Speeds ◽  
Design Variables

The paper establishes the mechanical model of SFD-sliding bearing flexible rotor system, adopting Runge-Kutta method to solve nonlinear differential equation, thus acquiring the unbalanced response curve and then gaining the first two critical speeds of the system. Meanwhile, the paper analyzes the sensitivity of the system on the first two critical speeds towards structural parameters, offering design variables to optimization analysis. Based on sensitivity analysis, genetic algorithm is employed to give an optimization analysis on critical speed, which aims to remove critical speed from working speed as much as possible. The critical speed ameliorates after the optimization which supplies theoretical basis as well as theoretical analysis towards the dynamic stability of high-speed rotor system and provides reference for the design of such rotor system.

Whirling with Spring Bearings and Rough Snubbers

1963 ◽  
Vol 67 (625) ◽  
pp. 66-67
Author(s):  
B. Irons
Keyword(s):  
Gas Turbine ◽  
High Speed ◽  
Critical Speed ◽  
Peak Amplitude ◽  
Amplitude Response ◽  
Critical Speeds ◽  
Bearing Load

To an increasing extent, aero gas turbine manufacturers are supporting high speed rotors on spring bearings, in order to escape the consequences of lightly damped and inconveniently placed critical speeds. While experience has been generally good, engineering doubts periodically arise.(a) By introducing the flexible bearings, the critical speed is reduced, say, from 9,000 r.p.m. to 3,000 r.p.m. At 3,000 r.p.m. a peak amplitude response is experienced, although the bearing load is comparatively low. (Some spring bearing designs incorporate damping as an accidental feature, many do not, and very few have damping designed into them.) The peak amplitude at 3,000 r.p.m. can rub the seals or overstress the spring, and to prevent this the bearing amplitude is restricted by a circular stop known here as the “snubber.”

scholarly journals A CFD Study of the Resistance Behavior of a Planing hull in Restricted Waterways

2021 ◽  
Vol 3 (1) ◽  
Author(s):  
Ahmed O. Elaghbash
Keyword(s):  
Shallow Water ◽  
High Speed ◽  
Lift Force ◽  
Critical Speed ◽  
Wave Pattern ◽  
Numerical Results ◽  
Experimental Results ◽  
Total Resistance ◽  
Computational Fluid Dynamics Analysis ◽  
Speed Range

The demand for high-speed boats that operating near to shoreline is increasing nowadays. Understanding the behavior and attitude of high-speed boats when moving in different waterways are very important for boat designer. Usually, they using experimental model testing for resistance prediction and dynamic force but this method is high consuming time, and cost. When planing boats are moving at high speed, two forces participate in their support, they are the hydrodynamic lift created by the shape of the planing hull, and the lift force resulting from displacing part of the liquid (buoyancy force).This research uses a CFD (Computational Fluid Dynamics) analysis to investigate the shallow water effects on prismatic planing hull. The turbulence flow around the hull was described by Reynolds Navier Stokes equations RANSE using the k-ɛ turbulence model. The free surface was modelled by the volume of fluid (VOF) method. The analysis is steady for all the ranges of speeds except those close to the critical speed range Fh =0.84 to 1.27 due to the propagation of the planing hull solitary waves at this range. For this fluctuation in the results, the average numerical value of the results was taken to compare it with the experiment.In this study, the planing hull lift force, total resistance, and wave pattern for the range of subcritical speeds, critical speeds, and supercritical speeds have been calculated using CFD. The numerical results have been compared with experimental results. The dynamic pressure distribution on the planing hull and its wave pattern at critical speed in shallow water were compared with those in deep water.The numerical results give a good agreement with the experimental results whereas total average error equals 7% for numerical lift force, and 8% for numerical total resistance. The worst effect on the planing hull in shallow channels occurs at the critical speed range, where solitary wave formulates.

Taylor-vortex instability and annulus-length effects

1976 ◽  
Vol 75 (1) ◽  
pp. 1-15 ◽  
Author(s):  
J. A. Cole
Keyword(s):  
Critical Speed ◽  
Taylor Vortex ◽  
Vortex Instability ◽  
Critical Speeds ◽  
Taylor Vortices ◽  
Torque Measurements ◽  
Concentric Cylinders ◽  
Theoretical Predictions ◽  
Range Of Values ◽  
Visual Observations

Critical speeds for the onset of Taylor vortices and for the later development of wavy vortices have been determined from torque measurements and visual observations on concentric cylinders of radius ratios R1/R2 = 0·894–0·954 for a range of values of the clearance c and length L: c/R1 = 0·0478–0·119 and L/c = 1–107. Effectively zero variation of the Taylor critical speed with annulus length was observed. The speed at the onset of wavy vortices was found to increase considerably as the annulus length was reduced and theoretical predictions are realistic only for L/c values exceeding say 40. The results were similar for all four clearance ratios examined. Preliminary measurements on eccentrically positioned cylinders with c/R1 = 0·119 showed corresponding effects.

Rotordynamic Performance of a Rotor Supported on Bump Type Foil Gas Bearings: Experiments and Predictions

2006 ◽  
Vol 129 (3) ◽  
pp. 850-857 ◽  
Author(s):  
Luis San Andrés ◽  
Dario Rubio ◽  
Tae Ho Kim
Keyword(s):  
High Speed ◽  
Critical Speed ◽  
Load Capacity ◽  
Test System ◽  
Foil Bearings ◽  
Rotor Imbalance ◽  
Synchronous Motion ◽  
Damping Characteristics ◽  
Rotor Surface ◽  
Stiffness And Damping

Gas foil bearings (GFBs) satisfy the requirements for oil-free turbomachinery, i.e., simple construction and ensuring low drag friction and reliable high speed operation. However, GFBs have a limited load capacity and minimal damping, as well as frequency and amplitude dependent stiffness and damping characteristics. This paper provides experimental results of the rotordynamic performance of a small rotor supported on two bump-type GFBs of length and diameter equal to 38.10mm. Coast down rotor responses from 25krpm to rest are recorded for various imbalance conditions and increasing air feed pressures. The peak amplitudes of rotor synchronous motion at the system critical speed are not proportional to the imbalance introduced. Furthermore, for the largest imbalance, the test system shows subsynchronous motions from 20.5krpm to 15krpm with a whirl frequency at ∼50% of shaft speed. Rotor imbalance exacerbates the severity of subsynchronous motions, thus denoting a forced nonlinearity in the GFBs. The rotor dynamic analysis with calculated GFB force coefficients predicts a critical speed at 8.5krpm, as in the experiments; and importantly enough, unstable operation in the same speed range as the test results for the largest imbalance. Predicted imbalance responses do not agree with the rotor measurements while crossing the critical speed, except for the lowest imbalance case. Gas pressurization through the bearings’ side ameliorates rotor subsynchronous motions and reduces the peak amplitudes at the critical speed. Posttest inspection reveal wear spots on the top foils and rotor surface.

Propulsion shafting whirling vibration: case studies and perspective

2015 ◽  
Author(s):  
Yuriy Batrak ◽  
Roman Batrak ◽  
Dmytro Berin ◽  
Andriy Mikhno
Keyword(s):  
Case Studies ◽  
Fatigue Failure ◽  
High Speed ◽  
Rotating Machinery ◽  
Lateral Vibration ◽  
Critical Speeds ◽  
Universal Joints

Since 1869 the main goal of whirling vibration calculations of rotating machinery was to determine critical speeds. Currently, all Classification Societies require a propulsion shafting whirling vibration calculation (also named bending or lateral vibration calculation) in the scope of the critical speeds i.e. free whirling vibration calculation. However, fatigue failure of the bracket and aft stern tube bearings, destruction of high-speed shafts with universal joints, noise and hull vibrations, generated by shafting, indicate the importance and inevitability of forced whirling vibration calculations. This paper presents some latest results of free and forced whirling vibration calculations obtained using the software intended for shaft design.

Frictionally Excited Thermoelastic Instability in Automotive Drum Brakes

1999 ◽  
Vol 122 (4) ◽  
pp. 849-855 ◽  
Author(s):  
Kwangjin Lee
Keyword(s):  
Coefficient Of Friction ◽  
Material Properties ◽  
Critical Speed ◽  
Hot Spot ◽  
Frictional Heating ◽  
Friction Material ◽  
Thermoelastic Instability ◽  
Critical Speeds ◽  
Drum Brake ◽  
The Coefficient Of Friction

Thermoelastic instability in automotive drum brake systems is investigated using a finite layer model with one-sided frictional heating. With realistic material properties of automotive brakes, the stability behavior of the one-sided heating mode is similar to that of the antisymmetric mode of two-sided heating but the critical speed of the former is higher than that of the latter. The effects of the friction coefficient and brake material properties on the critical speeds are examined and the most influential properties are found to be the coefficient of friction and the thermal expansion coefficient of drum materials. Vehicle tests were performed to observe the critical speeds of the drum brake systems with aluminum drum materials. Direct comparisons are made between the calculation and measurement for the critical speed and hot spot spacing. Good agreement is achieved when the critical speeds are calculated using the temperature-dependent friction material properties and the reduced coefficient of friction to account for the effect of intermittent contact. [S0742-4787(00)01503-4]

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