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

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.

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.”

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.

The development characteristics of the discontinuous leader under the positive switching impulse with low rate of voltage rising

2018 ◽  
Vol 83 (2) ◽  
pp. 20802 ◽  
Author(s):  
Yaoheng Xie ◽  
Yue Yishi ◽  
Huisheng Ye ◽  
Liu Yun ◽  
Yongheng Zhong ◽  
...  
Keyword(s):  
High Speed ◽  
Large Scale ◽  
Unit Length ◽  
Leader Development ◽  
Air Gap ◽  
Discharge Process ◽  
Temperature Changes ◽  
Channel Temperature ◽  
Impulse Voltage ◽  
Low Rate

Discontinuous leader development is the most important discharge process under the application of the switching impulse voltage with the low rate of voltage rising, which is of great significance to study the external insulation characteristics of ultra-high voltage (UHV) large scale air gap. Based on the CMOS high-speed camera, a discharge test with different operating impulse voltage is carried out by constructing a comprehensive observation platform of rod-plate air gap discharge, and a clear discontinuous leader development process picture is captured. Moreover, the leader current, injection charge and leader channel unit length charge, and their characteristics of the change trend are also obtained. Further analysis based on the experimental results shows that the discontinuous leader development under the action of the impulse voltage with low rate of voltage rising has two different laws. Finally, this paper uses the thermodynamic equation, combined with the test results, the channel temperature changes in the discontinuous leader development stagnation stage were calculated. The results show that the leader channel temperature is still greater than 1500 K in the hundreds of microsecond time scales in the leader stagnation stage, and the subsequent leader can continue to develop on the original leader channel.

The biological basis of aptitude: the endurance runner

1981 ◽  
Vol 13 (S7) ◽  
pp. 103-112 ◽  
Author(s):  
Clyde Williams
Keyword(s):  
Oxygen Transport ◽  
High Speed ◽  
Endurance Athlete ◽  
Endurance Athletes ◽  
High Rate ◽  
Type I ◽  
Carbon Dioxide Elimination ◽  
Endurance Runner ◽  
Genetic Endowment ◽  
The Individual

SummaryAptitude for a particular sport is governed by many factors, not least of which are obvious environmental influences. There are, however, individuals who, through genetic endowment, have the necessary biological characteristics which identify them as potentially elite athletes. These characteristics have been described more fully for endurance athletes because prolonged, almost steady-state running, lends itself more readily to investigation by biologists, than do the more complex sports.These studies show that the potentially elite endurance athlete is an individual endowed with an above average cardio-respiratory system, capable of a high rate of oxygen transport and carbon dioxide elimination. Not only does the elite endurance athlete have a greater rate of oxygen transport than the average sportsman or sportswoman, but the muscles receiving the oxygen are composed mainly of type I, i.e. low-twitch oxidative fibres, which are designed for endurance exercise. Furthermore, the elite endurance athlete also appears to be pre-programmed genetically to lay down less fat, in the form of sub-cutaneous adipose tissue, than the average sportsman or sportswoman of the same age and sex.Although genetic endowment dictates the potential ability of an individual for sustained high speed running, only appropriate training will allow the realization of this potential and so enable the individual to join the fraternity of the world's elite endurance athletes.

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