Dynamic force transmissibility of flywheel rotor systems supported by angular contact ball bearings considering clearance fit

Ball bearings are essential parts of mechanical systems to support the rotors or constitute the revolute joints. The time-varying compliance (VC), bearing clearance and the Hertzian contact between the rolling elements and raceways are three fundamental nonlinear factors in a ball bearing, hence the ball bearing can be considered as a nonlinear system. The hysteresis and jumps induced by the nonlinearities of rolling bearings are typical phenomena of nonlinear vibrations in the rolling bearing-rotor systems. And the corresponding hysteretic impacts have direct effects on the cleavage derivative and fatigue life of the system components. Therefore, the behaviors of hysteresis and jumps are given full attentions and continued studies in the theoretical and engineering fields. Besides, many researchers have done a lot of calculations to depict the various characteristics of bifurcations and chaos in the rolling bearings and their rotor systems, but few researches have been addressed on the inherent mechanism of the typical intermittency vibrations in rolling bearings. With the aid of the HB-AFT (the harmonic balance method and the alternating frequency/time domain technique) method and Floquet theory, this paper will investigate deeply the resonant hysteresis and intermittency chaos in ball bearings.

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Force Transmissibility of Heavy Truck Tires

Tire Science and Technology ◽

10.2346/1.2139535 ◽

1994 ◽

Vol 22 (1) ◽

pp. 60-74 ◽

Cited By ~ 3

Author(s):

J. T. Tielking

Keyword(s):

Amplitude Ratio ◽

Single Frequency ◽

Dynamic Force ◽

Force Transmission ◽

Truck Tires ◽

Tire Dynamics ◽

Heavy Truck ◽

Cyclic Displacement ◽

Force Transmissibility ◽

Force Displacement

Abstract A laboratory study of force transmission in radial truck tires is described. The experiments are conducted with the tire-wheel assembly attached to a fixed, nonrotating axle. Contact with the tire is provided by a flat surface. Single frequency displacement cycles are applied to the loaded tire footprint, and the dynamic force transmitted through the tire is measured at the fixed axle. Fourier transform signal analysis is used to extract the cyclic displacement and force amplitudes. The amplitude ratio force/displacement is defined as the force transmissibility. The experiments show inflation pressure and tire load to have little effect on force transmissibility. A single degree of freedom tire model for force transmissibility is described. The model uses easily measured tire parameters and is intended for use in vehicle models to include the effect of tire dynamics.

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Dynamic force transmissibility in helical gear pairs

Mechanism and Machine Theory ◽

10.1016/0094-114x(94)00048-p ◽

1995 ◽

Vol 30 (3) ◽

pp. 323-339 ◽

Cited By ~ 30

Author(s):

G. Wesley Blankenship ◽

Rajendra Singh

Keyword(s):

Helical Gear ◽

Dynamic Force ◽

Force Transmissibility

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A New Dynamic Model of Ball-Bearing Rotor Systems Based on Rigid Body Element

Journal of Manufacturing Science and Engineering ◽

10.1115/1.4032582 ◽

2016 ◽

Vol 138 (7) ◽

Cited By ~ 18

Author(s):

Hongrui Cao ◽

Yamin Li ◽

Xuefeng Chen

Keyword(s):

Rigid Body ◽

Dynamic Model ◽

Ball Bearing ◽

Rotor System ◽

Radial Clearance ◽

Fe Model ◽

Ball Bearings ◽

Rolling Ball ◽

Rotor Systems ◽

Body Element

Ball-bearing rotor systems are key components of rotating machinery. In this work, a new dynamic modeling method for ball-bearing rotor systems is proposed based on rigid body element (RBE). First, the concept of RBE is given, and then the rotor is divided into several discrete RBEs. Every two adjacent RBEs are connected by imaginary springs, whose stiffness is calculated according to properties of the RBEs. Second, all the parts of rolling ball bearings (i.e., outer ring, inner ring, ball, and cage) are considered as RBEs, and Gupta's model is employed to model bearings which include radial clearance, waviness, pedestal effect, etc. Finally, the rotor and all the rolling ball bearings are coupled to develop a dynamic model of the ball-bearing rotor system. The vibration responses of the ball-bearing rotor system can be calculated by solving dynamic equations of each RBE. The proposed method is verified with both simulation and experiment. The RBE model of the rotor is compared with its finite element (FE) model first, and numerical simulation shows the validity of the RBE model. Then, experiments are conducted on a rotor test rig which is supported with two rolling ball bearings as well. Good agreements between measurement and simulation show the ability of the model to predict the dynamic behavior of ball-bearing rotor systems.

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Dynamic Analysis of a Pneumatic Mounting System for Marine Propulsion Engines

Volume 1: 21st Biennial Conference on Mechanical Vibration and Noise, Parts A, B, and C ◽

10.1115/detc2007-34192 ◽

2007 ◽

Cited By ~ 2

Author(s):

Wei Xu ◽

Lin He ◽

Zhi-Qiang Lv

Keyword(s):

Pressure Distribution ◽

Natural Frequencies ◽

Air Pressure ◽

Dynamic Force ◽

Air Spring ◽

Engine Model ◽

Marine Propulsion ◽

Force Transmissibility ◽

Stiffness Characteristics ◽

System Characteristics

To reduce the vibration and noise level in ships, marine propulsion engines are conventionally supported by rubber mounts. But the design of a rubber mounting system for medium- and low-speed propulsion engines could be very complicated due to the large stiffness and rubber creep of rubber mounts. Air spring, which is superior in many respects to rubber mount, can be used as the propulsion engine mounting system. The superiority and potential of pneumatic mounting system is discussed in this paper. The pneumatic system’s loading and stiffness characteristics, which are distinct from rubber system, are analyzed. And an optimized air pressure distribution among air springs is given. The system natural frequencies and force transmissibility are calculated based on a fictitious propulsion engine model. The results show that the pneumatic mounting system can effectively attenuate the dynamic force transmitted to the ship floor, and the system characteristics are not apparently affected by the air pressure distribution.

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Nonlinear Dynamic Analysis of an Asymmetric Ball Bearing Rotor System

Volume 4: Dynamics, Vibration, and Control ◽

10.1115/imece2019-12218 ◽

2019 ◽

Author(s):

Doğancan Bahan ◽

Ender Ciğeroğlu

Keyword(s):

Ball Bearing ◽

Nonlinear Dynamic Analysis ◽

Harmonic Balance Method ◽

Beam Theory ◽

Hertzian Contact ◽

Radial Clearance ◽

Ball Bearings ◽

Algebraic Equations ◽

Rotor Systems ◽

Nonlinear Algebraic Equations

Abstract Performance of ball bearing–rotor systems are highly dependent on and often limited by characteristics of ball bearings. Several studies are available in the literature, investigating varying compliance and subharmonic resonances of ball bearings. Most of the studies are carried out with rigid rotors to focus on modelling of the bearings. There exist few studies which take flexibility of rotors into account. Furthermore, even if the rotor flexibility is modelled, most of the time symmetrical rotors are considered. However, rotors are rarely symmetric in realistic applications due to different locations of bearings and different weights of rotor components (compressors, turbines etc.). In this study, an asymmetric, balanced, flexible rotor supported by ball bearings considering Hertzian contact and radial clearance is investigated. Rotor shaft is modelled with Nelson finite rotor elements using Timoshenko beam theory and disks are considered as rigid masses. Harmonic Balance Method (HBM) is used to obtain nonlinear algebraic equations in the frequency domain and Alternating Frequency Time (AFT) method is utilized to find Fourier coefficients of nonlinear bearing forces. In order to decrease the number of nonlinear equations to be solved, Receptance Method (RM) is applied. Resulting set of nonlinear algebraic equations is solved by using Newton’s method with arclength continuation. Several case studies are performed and effects of asymmetry on nonlinear periodic vibration response of rotors are studied.

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Ball Bearings

Scientific American ◽

10.1038/scientificamerican12021893-14938bsupp ◽

1893 ◽

Vol 36 (935supp) ◽

pp. 14938-14940

Keyword(s):

Ball Bearings

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Reduction of structural vibrations with the piezoelectric stacks ring

International Journal of Applied Electromagnetics and Mechanics ◽

10.3233/jae-209384 ◽

2020 ◽

Vol 64 (1-4) ◽

pp. 729-736

Author(s):

Jincheng He ◽

Xing Tan ◽

Wang Tao ◽

Xinhai Wu ◽

Huan He ◽

...

Keyword(s):

Vibration Control ◽

Mechanical Energy ◽

Electrical Energy ◽

Structural Vibrations ◽

Rotor Systems ◽

Fea Model ◽

Piezoelectric Stacks ◽

Shunt Damping ◽

Reduction Effect ◽

Euler Bernoulli Beam

It is known that piezoelectric material shunted with external circuits can convert mechanical energy to electrical energy, which is so called piezoelectric shunt damping technology. In this paper, a piezoelectric stacks ring (PSR) is designed for vibration control of beams and rotor systems. A relative simple electromechanical model of an Euler Bernoulli beam supported by two piezoelectric stacks shunted with resonant RL circuits is established. The equation of motion of such simplified system has been derived using Hamilton’s principle. A more realistic FEA model is developed. The numerical analysis is carried out using COMSOL® and the simulation results show a significant reduction of vibration amplitude at the specific natural frequencies. Using finite element method, the influence of circuit parameters on lateral vibration control is discussed. A preliminary experiment of a prototype PSR verifies the PSR’s vibration reduction effect.

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