On the Dynamic Behavior of Hybrid Journal Bearings

1976 ◽  
Vol 98 (1) ◽  
pp. 90-94 ◽  
Author(s):  
S. M. Rohde ◽  
H. A. Ezzat
Keyword(s):  
Dynamic Behavior ◽  
High Frequency ◽  
Journal Bearings ◽  
Damping Coefficients ◽  
Stiffness Coefficients ◽  
Bearing Stiffness ◽  
Coupling Stiffness ◽  
High Frequency Excitation ◽  
Frequency Excitation ◽  
Stiffness And Damping

An analysis of the dynamic behavior of hybrid journal bearings is presented. The analysis accounts for the compressibility of the lubricant in the bearing recesses and supply line. Results show that when the journal is subjected to high frequency excitation the bearing stiffness and damping can change drastically. The behavior is characterized by a “break frequency” beyond which the bearing stiffness increases sharply. This is accompanied by a rapid decrease in bearing damping. It is also shown that the cross-coupling stiffness coefficients are reduced at high excitation frequencies. The asymptotic behavior of the stiffness and damping coefficients is examined at both ends of the frequency spectrum.

scholarly journals Bifurcation analysis of rotor/bearing system using third-order journal bearing stiffness and damping coefficients

2021 ◽  
Author(s):  
T. A. El-Sayed ◽  
Hussein Sayed
Keyword(s):  
Equations Of Motion ◽  
Journal Bearings ◽  
Third Order ◽  
Damping Coefficients ◽  
The Third ◽  
Rotor Bearing ◽  
Bearing Stiffness ◽  
Rotor Stiffness ◽  
Stiffness And Damping ◽  
Bearing System

AbstractHydrodynamic journal bearings are used in many applications which involve high speeds and loads. However, they are susceptible to oil whirl instability, which may cause bearing failure. In this work, a flexible Jeffcott rotor supported by two identical journal bearings is used to investigate the stability and bifurcations of rotor bearing system. Since a closed form for the finite bearing forces is not exist, nonlinear bearing stiffness and damping coefficients are used to represent the bearing forces. The bearing forces are approximated to the third order using Taylor expansion, and infinitesimal perturbation method is used to evaluate the nonlinear bearing coefficients. The mesh sensitivity on the bearing coefficients is investigated. Then, the equations of motion based on bearing coefficients are used to investigate the dynamics and stability of the rotor-bearing system. The effect of rotor stiffness ratio and applied load on the Hopf bifurcation stability and limit cycle continuation of the system are investigated. The results of this work show that evaluating the bearing forces using Taylor’s expansion up to the third-order bearing coefficients can be used to profoundly investigate the rich dynamics of rotor-bearing systems.

Nonlinear Dynamics and Control of a Pneumatic Vibration Isolator

2005 ◽  
Vol 128 (4) ◽  
pp. 439-448 ◽  
Author(s):  
Marcel Heertjes ◽  
Nathan van de Wouw
Keyword(s):  
Nonlinear Dynamics ◽  
Nonlinear Control ◽  
Dynamic Behavior ◽  
High Frequency ◽  
High Energy ◽  
Special Focus ◽  
Vibration Isolator ◽  
Generalized Force ◽  
High Frequency Excitation ◽  
Frequency Excitation

The nonlinear dynamics of a single-degree-of-freedom pneumatic vibration isolator are studied. Based on a physical model, a nonsymmetric stiffness nonlinearity is derived to describe the stiffness property of the isolator. For a full nonlinear pneumatic isolator model, the response to two different types of disturbances is studied: forces applied to the isolated payload and base vibrations. The dynamic behavior of the isolator in case of a disturbance applied to the payload is studied using the generalized force-mobility function and features coexisting steady-state responses and a superharmonic resonance. Base vibrations transmitted via the isolator are studied on the basis of the generalized transmissibility function again showing rich nonlinear dynamic behavior. The presence of a nonsymmetric nonlinearity also induces high-energy low-frequency response to multiple high-frequency excitation. For both types of excitation, the nonlinear behavior is seriously compromising the performance of the isolator. To avoid any expression of nonlinearity whatsoever and, at the same time, to enhance the performance of the passive isolator, an overall nonlinear control design is proposed. It consists of a linear PID-based controller together with a nonlinear computed torque controller (CTC). For either linear or nonlinear control, the isolator performance is quantified in terms of generalized force mobility and transmissibility. The latter with a special focus on multiple high-frequency excitation.

Numerical Analysis on Dynamic Coefficients of Self-Acting Gas-Lubricated Tilting-Pad Journal Bearings

2007 ◽  
Vol 130 (1) ◽  
Author(s):  
Yang Lihua ◽  
Qi Shemiao ◽  
Yu Lie
Keyword(s):  
Dynamic Stiffness ◽  
Cross Coupling ◽  
Damping Coefficients ◽  
Dynamic Coefficients ◽  
Stiffness Coefficients ◽  
Tilting Pad ◽  
Coupling Stiffness ◽  
Perturbation Frequency ◽  
Stiffness And Damping ◽  
Gas Bearing

Although gas-lubricated tilting-pad bearings are widely used in high-speed turbomachinery, the theoretical prediction of the dynamic characteristics of tilting-pad gas bearings is also a very difficult problem because of its structural complexity. Several approaches have been proposed to solve this problem such as the pad assembly method and the small perturbation method. A numerical method by combining the partial derivative method with the equivalent coefficient method is presented in this paper to evaluate the dynamic stiffness and damping coefficients of self-acting tilting-pad gas bearing. The dynamic coefficients with the pads fixed and with the pads perturbation are, respectively, obtained for a typical self-acting tilting-pad gas bearing by using the proposed method to mainly explain the dependency of the bearing dynamic coefficients on the perturbation frequency. For bearings with the pads perturbation, the cross-coupling stiffness and damping coefficients are almost negligible compared with the direct ones. At lower perturbation frequency, the stiffness coefficients increase, while the damping coefficients decrease with an increasing frequency. The higher perturbation frequencies have very little effects on the bearing dynamic coefficients. Dynamic stiffness coefficients approach to the constant and damping coefficients to zero. However, with the pads fixed, in a low range of frequency, the absolute values of cross-coupling stiffness coefficients decrease with frequency. Furthermore, the cross-coupling coefficients are not negligible compared with the direct ones. In addition, the effects of pad inertia on dynamic coefficients are studied and compared with the results of pad inertia neglected.

Ball bearing turbocharger vibration management: application on high speed balancer

2020 ◽  
Vol 21 (6) ◽  
pp. 619
Author(s):  
Kostandin Gjika ◽  
Antoine Costeux ◽  
Gerry LaRue ◽  
John Wilson
Keyword(s):  
Dynamic Behavior ◽  
High Speed ◽  
Internal Combustion Engines ◽  
Ball Bearing ◽  
Squeeze Film ◽  
Design And Technology ◽  
Squeeze Film Damper ◽  
Damping Coefficients ◽  
Bearing Loads ◽  
Stiffness And Damping

Today's modern internal combustion engines are increasingly focused on downsizing, high fuel efficiency and low emissions, which requires appropriate design and technology of turbocharger bearing systems. Automotive turbochargers operate faster and with strong engine excitation; vibration management is becoming a challenge and manufacturers are increasingly focusing on the design of low vibration and high-performance balancing technology. This paper discusses the synchronous vibration management of the ball bearing cartridge turbocharger on high-speed balancer and it is a continuation of papers [1–3]. In a first step, the synchronous rotordynamics behavior is identified. A prediction code is developed to calculate the static and dynamic performance of “ball bearing cartridge-squeeze film damper”. The dynamic behavior of balls is modeled by a spring with stiffness calculated from Tedric Harris formulas and the damping is considered null. The squeeze film damper model is derived from the Osborne Reynolds equation for incompressible and synchronous fluid loading; the stiffness and damping coefficients are calculated assuming that the bearing is infinitely short, and the oil film pressure is modeled as a cavitated π film model. The stiffness and damping coefficients are integrated on a rotordynamics code and the bearing loads are calculated by converging with the bearing eccentricity ratio. In a second step, a finite element structural dynamics model is built for the system “turbocharger housing-high speed balancer fixture” and validated by experimental frequency response functions. In the last step, the rotating dynamic bearing loads on the squeeze film damper are coupled with transfer functions and the vibration on the housings is predicted. The vibration response under single and multi-plane unbalances correlates very well with test data from turbocharger unbalance masters. The prediction model allows a thorough understanding of ball bearing turbocharger vibration on a high speed balancer, thus optimizing the dynamic behavior of the “turbocharger-high speed balancer” structural system for better rotordynamics performance identification and selection of the appropriate balancing process at the development stage of the turbocharger.

scholarly journals Empirical Expression for AC Magnetization Harmonics of Magnetic Nanoparticles under High-Frequency Excitation Field for Thermometry

Nanomaterials ◽  
2020 ◽  
Vol 10 (12) ◽  
pp. 2506
Author(s):  
Zhongzhou Du ◽  
Dandan Wang ◽  
Yi Sun ◽  
Yuki Noguchi ◽  
Shi Bai ◽  
...  
Keyword(s):  
Magnetic Nanoparticles ◽  
High Frequency ◽  
Planck Equation ◽  
Magnetization Dynamics ◽  
Excitation Field ◽  
Fokker Planck Equation ◽  
High Frequency Excitation ◽  
Frequency Excitation ◽  
Ac Magnetization ◽  
Fokker Planck

The Fokker–Planck equation accurately describes AC magnetization dynamics of magnetic nanoparticles (MNPs). However, the model for describing AC magnetization dynamics of MNPs based on Fokker-Planck equation is very complicated and the numerical calculation of Fokker-Planck function is time consuming. In the stable stage of AC magnetization response, there are differences in the harmonic phase and amplitude between the stable magnetization response of MNPs described by Langevin and Fokker–Planck equation. Therefore, we proposed an empirical model for AC magnetization harmonics to compensate the attenuation of harmonics amplitude induced by a high frequency excitation field. Simulation and experimental results show that the proposed model accurately describes the AC M–H curve. Moreover, we propose a harmonic amplitude–temperature model of a magnetic nanoparticle thermometer (MNPT) in a high-frequency excitation field. The simulation results show that the temperature error is less than 0.008 K in the temperature range 310–320 K. The proposed empirical model is expected to help improve MNPT performance.

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