Investigation into the Damped Critical Speeds of Rotating Shafts : 1st Report, Influences of the Damping and the Bearing/Shaft Stiffness Ratio on the Critical Damping Ratio

1977 ◽  
Vol 43 (376) ◽  
pp. 4474-4484 ◽  
Author(s):  
Shinobu SAITO ◽  
Tsuneo SOMEYA
Keyword(s):  
Damping Ratio ◽  
Stiffness Ratio ◽  
Critical Speeds ◽  
Rotating Shafts ◽  
Critical Damping

Determination of the Critical Operating Speeds of Planar Mechanisms by the Finite Element Method Using Planar Actual Line Elements and Lumped Mass Systems

1979 ◽  
Vol 101 (2) ◽  
pp. 210-223 ◽  
Author(s):  
S. Kalaycioglu ◽  
C. Bagci
Keyword(s):  
Dynamic Systems ◽  
Natural Frequencies ◽  
Dynamic Equilibrium ◽  
Large Error ◽  
Free Vibrations ◽  
Lumped Mass ◽  
Critical Speeds ◽  
Rotating Shafts ◽  
Line Elements ◽  
Kinematic Motion

It has been a well-established fact that dynamic systems in motion experience critical speeds, such as rotating shafts and geared systems whose undeformed reference geometry remain the same at all times. Their critical speeds are determined by their natural frequencies of considered type of free vibrations. Linkage mechanisms as dynamic systems in motion change their undeformed geometries as function of time during the cycle of kinematic motion. They do also experience critical operating speeds as rotating shafts and geared systems do, and their critical speeds are determined by the minima of their natural frequencies during a cycle of kinematic motion. Such a minimum occurs at the critical geometry of a mechanism, which is the position at which the maximum of the input power is required to maintain the instantaneous dynamic equilibrium of the mechanism. Actual finite line elements are used to form the global generalized coordinate flexibility matrix. The natural frequencies of the mechanism and the corresponding mode vectors (mode deflections) are determined as the eigen values and eigen vectors of the equations of instantaneous-position-free-motion of the mechanism. Method is formulated to include or exclude the link axial deformations, and apply to any number of loops having any type of planar pair. Critical speeds of planar four-bar, slider-crank, and Stephenson’s six-bar mechanisms are determined. Experimental results for the four-bar mechanism are given. Effect of axial deformations and link rotary inertias are investigated. Inclusion of link axial deformations in mechanisms having pairs with sliding freedoms is seen to predict critical speeds with large error.

Seismic Performance of T-Shaped CFT Column to Steel Frame Beam Connection – Experimental Study

2014 ◽  
Vol 919-921 ◽  
pp. 951-959 ◽  
Author(s):  
Yan Tao Li ◽  
Cheng Xiang Xu ◽  
Guo Feng Du
Keyword(s):  
Failure Mechanism ◽  
Damping Ratio ◽  
Local Buckling ◽  
Steel Tube ◽  
Steel Frame ◽  
Hysteretic Behavior ◽  
Stiffness Ratio ◽  
Joint Models ◽  
Panel Zone ◽  
Axial Forces

The focus of this research program is T-shaped CFT central column to steel frame beam connection. 3 joints with strong columns-weak beams and 1 joint with strong beams-weak columns 1:2 scale specimens were tested under constant axial loads and cyclic horizontal loads. Overall impact of axial force ratio and beam to column linear stiffness ratio on joint failure mechanism, hysteretic behavior, deformation ductility, and energy dissipation capability was investigated. Results showed that the failure mechanism for specimens with strong columns-weak beams was local buckling of the steel beam flanges and formation of the plastic hinges. There was minimum damage on the concrete column and joint panel zone. For a specimen with strong beams-weak columns, there was local buckling fracture on steel tube above and below the joint panel zone. Crushing of the core concrete was also observed with formation of the column hinges. It was found that both axial forces and beam to column linear stiffness ratio had impacts on joint capacity and ductility behavior of the specimens. Experiment results showed that the joint models had deformation ductility factor between 3.39 and 3.91 and viscous damping ratio between 0.46 and 0.51.

Using Guided Balls to Auto-Balance Rotors

2002 ◽  
Vol 124 (4) ◽  
pp. 971-975 ◽  
Author(s):  
H. L. Wettergren
Keyword(s):  
Natural Frequency ◽  
Damping Ratio ◽  
Rotating Machinery ◽  
Instability Region ◽  
Instability Threshold ◽  
Asymptotically Stable ◽  
Circular Groove ◽  
Stable Position ◽  
Critical Damping

By using balancing balls constrained to move in a circular groove filled with oil, the vibration of rotating machinery can, under certain circumstances, be reduced. This paper shows that the damping from the oil reduces the instability region, i.e., the conditions when the balancing balls don’t find their equilibrium positions. However, the instability region seems to increase with increasing number of balancing balls. The critical ball damping ratio is highest just above the natural frequency and then rapidly decreases. Consequently, since the region between instability and critical damping is quite small, the ball damping should be made as small as possible without getting too close to the instability threshold. Bearing damping has a large effect on the instability region. High bearing damping will suppress the instability. The time it takes to reach the asymptotically stable position seems to increase with increasing number of balls. Keeping this time low is one of the most important things when designing a balancing ring.

Experimental Study on the Performance of the Laminated Steel Isolators

2013 ◽  
Vol 423-426 ◽  
pp. 1603-1607
Author(s):  
Yao Guo Xie ◽  
Ping He ◽  
Xian Qiang Qu ◽  
Hong Bin Cui
Keyword(s):  
Experimental Study ◽  
Vibration Isolation ◽  
Dynamic Stiffness ◽  
Damping Ratio ◽  
Dynamic Performance ◽  
Performance Testing ◽  
Stiffness Ratio ◽  
Static Stiffness ◽  
Comparison Of The Results

Through the analysis and comparison of the results of static and dynamic performance testing of a series of laminated steel pieces isolators used in the vibration isolation of warships, in the number and thickness of laminated steel pieces of the same circumstances, laminated steel arc and preload of test samples had a certain impact on the values ​​of static stiffness, dynamic stiffness, damping ratio as well as dynamic and static stiffness ratio.

Analysis on Stability of POGO and Parameters of Propulsion System in Liquid Rocket

2014 ◽  
Vol 664 ◽  
pp. 158-162
Author(s):  
Hou Wang Li ◽  
Cong Wang ◽  
Xiao Shi Zhang
Keyword(s):  
Natural Frequency ◽  
Damping Ratio ◽  
Coupled System ◽  
Propulsion System ◽  
Suction Line ◽  
Liquid Rocket ◽  
The Stability ◽  
Critical Damping

To explore effective methods of avoiding POGO instability, this paper starts with a thorough study on influence of parameters on natural frequency of propulsion system in liquid rocket. By adopting the method of critical damping ratio, stability of coupled structure-propulsion system is analyzed. The results show that installing an accumulator in suction line can effectively decrease natural frequency of propulsion system, which can improve the stability of coupled system. When cavitation and inertance of accumulator increases or installation position gets closer to top of pump, the influence of accumulator on the natural frequency becomes more significant.

On the Dynamical Behavior of Rotating Shafts Driven by Universal (Hooke) Couplings

1958 ◽  
Vol 25 (1) ◽  
pp. 47-51
Author(s):  
R. M. Rosenberg
Keyword(s):  
Critical Speed ◽  
Dynamical Behavior ◽  
Rotating Shaft ◽  
Critical Speeds ◽  
Elastic Shaft ◽  
Rotating Shafts

Abstract The system considered here is a massless, uniform elastic shaft carrying at its mid-point a disk (having mass) and supported at the ends by universal (Hooke) joints. The purpose of this investigation is to examine the effect of Hooke-joint angularity (as obtained by design, or from faulty alignment) on the bending stability of the rotating shaft. It is found that separate investigations are required for shafts not transmitting axial torques and for those required to transmit torques. Each gives rise to instabilities which are absent when the Hooke joint is straight. In the absence of axial torques, the shaft develops unsuspected mild critical speeds at odd integer submultiples of the “familiar” critical speed found with a straight Hooke joint. When the shaft is required to transmit moderate axial torques, the joint angularity produces true instabilities near all integer submultiples of the familiar critical speed. Surprisingly, these instabilities vanish for sufficiently large axial torques.

Parameters optimization of dynamic vibration absorber based on grounded stiffness, inerter, and amplifying mechanism

2021 ◽  
pp. 107754632110382
Author(s):  
Peng Sui ◽  
Yongjun Shen ◽  
Shaopu Yang ◽  
Junfeng Wang
Keyword(s):  
Analytical Solution ◽  
Vibration Isolation ◽  
Damping Ratio ◽  
Vibration Absorber ◽  
Primary System ◽  
Vibration Absorbers ◽  
Stiffness Ratio ◽  
Dynamic Vibration Absorber ◽  
Dynamic Vibration ◽  
Dynamic Vibration Absorbers

In the field of dynamics and control, some typical vibration devices, including grounded stiffness, inerter and amplifying mechanism, have good vibration isolation and reduction effects, especially in dynamic vibration absorber (DVA). However, most of the current research studies only focus on the performance of a single device on the system, and those DVAs are gradually becoming difficult to meet the growth of performance demand for vibration control. On the basis of Voigt dynamic vibration absorber, a novel dynamic vibration absorber model based on the combined structure of grounded stiffness, inerter, and amplifying mechanism is presented, and the analytical solution of the optimal design formula is derived. First, the motion differential equation of the system is established, and the normalized amplitude amplification factor of the displacement is calculated. It is found that the system has three fixed points unrelated to the damping ratio. The optimal frequency ratio is obtained based on the fixed-point theory. In order to ensure the stability of the system, it is found that inappropriate inerter coefficient will cause the system instable when screening optimal grounded stiffness ratio. Accordingly, the best working range of inerter is determined. Finally, optimal grounded stiffness ratio and approximate optimal damping ratio are also obtained. The influence of inerter coefficient and magnification ratio on the response of the primary system is analyzed. The correctness of the derived analytical solution is verified by numerical simulation. Compared with other dynamic vibration absorbers, it is verified that presented model has superior vibration absorption performance and provides a theoretical basis for the design of a new type of dynamic vibration absorbers.

Using Guided Balls to Auto-Balance Rotors

2001 ◽  
Author(s):  
Håkan L. Wettergren
Keyword(s):  
Natural Frequency ◽  
Damping Ratio ◽  
Rotating Machinery ◽  
Instability Region ◽  
Instability Threshold ◽  
Asymptotically Stable ◽  
Circular Groove ◽  
Stable Position ◽  
Critical Damping

By using balancing balls constrained to move in a circular groove filled with oil, the vibration of rotating machinery can, under certain circumstances, be reduced. This paper shows that the damping from the oil reduces the instability region, i.e. the conditions when the balancing balls don’t find their equilibrium positions. However, the instability region seems to increase with increasing number of balancing balls. The critical ball damping ratio is highest just above the natural frequency and then rapidly decreases. Consequently, since the region between instability and critical damping is quite small, the ball damping should be made as small as possible without getting too close to the instability threshold. Bearing damping has a large effect on the instability region. High bearing damping will suppress the instability. The time it takes to reach the asymptotically stable position seems to increase with increasing number of balls. Keeping this time low is one of the most important things when designing a balancing ring.

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