scholarly journals Torsional vibrations in reciprocating engine shafts

1925 ◽  
Vol 109 (749) ◽  
pp. 99-119 ◽  
Keyword(s):  
Large Amplitude ◽  
Critical Speed ◽  
Practical Calculation ◽  
Torsional Vibrations ◽  
Connecting Rod ◽  
Elastic Vibrations ◽  
Critical Speeds ◽  
Reciprocating Engine ◽  
Complicated System ◽  
Equivalent Mass

It is well known that, in the case of reciprocating engines, there are certain critical speeds of running at which the torsional vibrations in the shaft become large in amplitude and introduce an element of danger into the system. Fairly simple methods have been devised for the practical calculation, from the constants of the machinery, of the location of these critical speeds. In these methods, the reciprocating parts of the engine are replaced by an “equivalent mass” which is assumed to contribute to the elastic vibrations of the shaft in exactly the same way as do the actual, rather complicated, system of crank, connecting-rod, piston and piston-rod. It is the main purpose of this paper to examine the correctness of this equivalence. In two particular cases examined by the author, the automatic records of the shaft vibrations at about a critical speed showed a large amplitude at the expected point, but the period of the vibration was twice that anticipated. This anomaly is examined on p.116 and the conditions of its existence exhibited.

Non-Linear Torsional Vibration of a Two-Degree-of-Freedom System Having Variable Inertia

1965 ◽  
Vol 7 (1) ◽  
pp. 101-113 ◽  
Author(s):  
B. Porter
Keyword(s):  
Normal Mode ◽  
Torsional Vibration ◽  
Large Amplitude ◽  
Critical Speed ◽  
Degree Of Freedom ◽  
Reciprocating Engine ◽  
Non Linear ◽  
Two Degree Of Freedom

A variant of Kryloff and Bogoliuboff's method is used to analyse the periodic vibrations of a non-linear two-degree-of-freedom system which is an idealization of the crankshaft of a two-cylinder in-line reciprocating engine. It is shown that there are two critical speed ranges associated with each normal mode of the system within which periodic harmonic or subharmonic vibrations of large amplitude can occur as a result of variable-inertia excitation. Extensions of the results to homogeneous in-line engines having any number of cylinders are indicated.

Predicting critical speeds in various rotordynamics problems

2016 ◽  
Vol 231 (21) ◽  
pp. 3913-3922
Author(s):  
Raymond H Plaut ◽  
Lawrence N Virgin ◽  
Josiah D Knight
Keyword(s):  
Large Amplitude ◽  
Critical Speed ◽  
Experimental Results ◽  
Nondestructive Technique ◽  
New Approach ◽  
Practical Utility ◽  
Critical Speeds ◽  
Model Free ◽  
Measured Information ◽  
Rotating Shafts

Rotating shafts often experience undesirable large-amplitude whirling oscillations associated with resonance at critical speeds. This paper further develops a nondestructive technique in which measured information about the growing nature of the response is used to predict an incipient critical speed. A number of models of varying degrees of sophistication are developed and tested using the new approach, but the main advantage of the method is that it is model-free and thus possesses considerable practical utility. In addition, further experimental results are presented for the case of two disks mounted on a shaft, and the technique is successfully demonstrated in predicting a critical speed associated with a higher mode.

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.

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.

Non-linear torsional oscillation of a two-degree-of-freedom system incorporating a Hooke joint

1964 ◽  
Vol 277 (1368) ◽  
pp. 92-106 ◽  
Keyword(s):  
Large Amplitude ◽  
Critical Speed ◽  
Torsional Oscillation ◽  
Degree Of Freedom ◽  
Non Linear ◽  
Two Degree Of Freedom

The non-linear torsional oscillation of the system is analyzed by means of a variant of Kryloff and Bogoliuboff’s method. It is shown that each mode of the system can perform oscillations of large amplitude in a number of critical speed ranges, and that hysteresis effects and discontinuous jumps in amplitude are to be expected in these speed ranges if the damping is light.

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

Comprehensive design methodology for an engine journal bearing

2000 ◽  
Vol 214 (4) ◽  
pp. 401-412 ◽  
Author(s):  
H Hirani ◽  
K Athre ◽  
S Biswas
Keyword(s):  
Film Thickness ◽  
High Speed ◽  
Design Methodology ◽  
Design Procedure ◽  
Maximum Pressure ◽  
Connecting Rod ◽  
Automotive Engine ◽  
Reciprocating Engine ◽  
High Power Output ◽  
Minimum Film Thickness

The trend towards high power output, high speed and low power loss in engines requires a better understanding of bearing behaviour. Research in this area is directed more towards different aspects involved in bearing analyses, rather than providing a comprehensive guideline on design of bearing. This effort compiles the design methodology for selection of diametral clearance and bearing length by limiting the minimum film thickness, maximum pressure and temperature. The design procedure is summarized on the basis of the existing rapid bearing analyses for evaluation of the journal trajectory, minimum film thickness and maximum pressure and simplified thermal analysis. A flow chart is provided for step-by-step bearing design. Finally, two case studies of engine bearings are described: one investigates the VEB bigend connecting-rod bearing for a large industrial reciprocating engine and the other a main crankshaft bearing for an automotive engine. The methodology translates into easy-to-use expressions and the overall procedure is outlined, using practical data to demonstrate how this can be employed effectively by users.

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]

scholarly journals Dynamical analysis of hollow-shaft dual-rotor system with circular cracks

2020 ◽  
pp. 146134842094828
Author(s):  
Yang Yongfeng ◽  
Wang Jianjun ◽  
Wang Yanlin ◽  
Fu Chao ◽  
Zheng Qingyang ◽  
...  
Keyword(s):  
Critical Speed ◽  
Equations Of Motion ◽  
Harmonic Balance Method ◽  
Circular Crack ◽  
Rotor System ◽  
Resonance Phenomenon ◽  
Dynamical Analysis ◽  
Dynamical Response ◽  
Critical Speeds ◽  
Hollow Shaft

In this paper, we considered a dual-rotor system with crack in shaft. The influence of circular crack in hollow shaft on dynamical response was studied. The equations of motion of 12 elements dual-rotor system model were derived. Harmonic balance method was employed to solve the equations. The critical speed and sub-critical speed responses were investigated. It was found that the circular crack in hollow shaft had greater influence on the first-backward critical speed than the first-forward critical speed. Owing to the influence of crack, the vibration peaks occurred at the 1/2, 1/3 and 1/4 critical speeds of the rotor system, along with a reduction in sub-critical speeds and critical speeds. The deeper crack away from the bearing affected the rotor more significantly. The whirling orbits, the time-domain responses and the spectra were obtained to show the super-harmonic resonance phenomenon in hollow-shaft cracked rotor system.

scholarly journals Study on Thermal Unstable Vibration of Rotor under Journal Whirl with Large Amplitude in Journal Bearing

2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Qilong Hu ◽  
Min Zhu ◽  
Jiangang Yang
Keyword(s):  
Surface Temperature ◽  
Temperature Difference ◽  
Large Amplitude ◽  
Critical Speed ◽  
Journal Bearing ◽  
Lubricant Film ◽  
Analysis Model ◽  
Rotor Vibration ◽  
Thermal Bending ◽  
Unstable Vibration

To investigate the thermal unstable vibration caused by journal whirls with large amplitude in journal bearing, an analysis model of lubricant film thickness is established. The journal surface temperature distribution is solved, and the reason for journal surface temperature difference appearance and its influence on rotor vibration are analyzed. Taking a turbogenerator as an example, the journal surface temperature difference and the induced rotor thermal bending under synchronous whirl in the bearing are calculated. Meanwhile, an engineering vibration fault with its treatment is presented. Results show that, the journal surface circumferential temperature difference is caused by viscous shearing within lubricant film under journal whirls with large amplitude in journal bearing. The direction of temperature difference is related to the direction of unbalanced force acting on journal. The temperature difference causes rotor thermal bending, which can be converted to a thermal unbalance on the rotor. The rotor vibration is caused by both thermal and initial unbalance. When the rotor is running below or at the critical speed, the vibration is on the increase until it leads to instability of the rotor eventually. When the rotor is running above the critical speed, the rotor vibration fluctuates periodically. Reducing the initial (mechanical) unbalances decreases the rotor vibration and the journal surface circumferential temperature difference.

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