Nonlinear Dynamic Analysis and Experimental Verification of an Unbalanced Rotor Supported by Ball Bearings

2011 ◽  
Author(s):  
S. H. Upadhyay ◽  
Satish C. Sharma ◽  
S. P. Harsha
Keyword(s):  
Dynamic Properties ◽  
Nonlinear Dynamic Analysis ◽  
Peak Frequency ◽  
Nonlinear Damping ◽  
Rotor System ◽  
System Stability ◽  
System Response ◽  
Ball Bearings ◽  
Unbalanced Rotor ◽  
Radial Forces

In this paper, a dynamic model is presented for studying the dynamic properties of unbalanced rotor system supported by ball bearings under the effects of radial internal clearance and unbalanced rotor effect. The Newmark-β method is used to solve the nonlinear equations. The dynamics behaviors of a rigid rotor system are studied through frequency responses of the system. Clearances, nonlinear stiffness & nonlinear damping, radial forces and unbalanced forces—all these bring a significant influence to bear on the system stability. The validity of the proposed model verified by comparison of frequency components of the system response with those obtained from experiments. The peak-to-peak frequency response of the system for each speed is obtained.

CALCULATION OF ADDITIONAL AXIAL FORCE OF ANGULAR-CONTACT BALL BEARINGS IN ROTOR SYSTEM

2016 ◽  
Vol 40 (4) ◽  
pp. 585-596
Author(s):  
Zhenhuan Ye ◽  
Zhansheng Liu ◽  
Liqin Wang
Keyword(s):  
Axial Force ◽  
Dynamic Properties ◽  
Descent Method ◽  
Rotor System ◽  
Ball Bearings ◽  
Rolling Bearings ◽  
System A ◽  
Calculation Results ◽  
Relationship Of ◽  
Raphson Method

Based on a loading-deformation relationship of bearing elements and the coordination of displacement between bearings in the rotor system, a model for calculating the additional axial force of angular-contact ball bearings in a single-rotor system is established. Nonlinear equations of this model are solved through the Rapid Descent method and Newton-Raphson method. The simulation results which are based on Gupta’s example verify that both the model and solving methods in this paper are reliable. A pair of 276927NK1W1(H) angular-contact ball bearings in symmetry in the single-rotor system is used as the example, calculation results of the additional axial force of bearings from the model in this paper and from the ISO method are compared and the influence of bearing geometry parameters and working conditions on the additional axial force is further studied. This model and its conclusions could provide the basic data and reference for analyzing the carrying ability and dynamic properties of rolling bearings.

Dynamic Analysis of Ball Bearings Due to Clearance Effect

2009 ◽  
Author(s):  
S. H. Upadhyay ◽  
S. C. Jain ◽  
S. P. Harsha
Keyword(s):  
Chaotic Behavior ◽  
Equations Of Motion ◽  
Peak Frequency ◽  
System Response ◽  
Ball Bearings ◽  
Outer Race ◽  
Lagrange’S Equation ◽  
Rolling Elements ◽  
Machine Systems ◽  
The Individual

In this paper, the nonlinear dynamic behavior of ball bearings due to radial internal clearance and rotor speed has been analyzed. The approach presented in this paper accounts for the contact between rolling elements and inner/outer races. The equations of motion of a ball bearing are formulated in generalized coordinates, using Lagrange’s equation considering the vibration characteristics of the individual constitute such as inner race, outer race, rolling elements. The effects of speed of rotor in which rolling element bearings shows periodic, quasi-periodic and chaotic behavior are analyzed. The results also show the intermittent chaotic behavior in the dynamic response is seen to be strongly dependent on the speed of the rotor. The results are obtained in the form of frequency responses. The validity of the proposed model verified by comparison of frequency components of the system response with those obtained from experiments. The peak-to-peak frequency response of the system for each speed is obtained. The current study provides a powerful tool design and health monitoring of machine systems.

scholarly journals Design and Experimental Implementation of a Beam-Type Twin Dynamic Vibration Absorber for a Cantilevered Flexible Structure Carrying an Unbalanced Rotor: Numerical and Experimental Observations

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Abdullah Özer ◽  
Mojtaba Ghodsi ◽  
Akio Sekiguchi ◽  
Ashraf Saleem ◽  
Mohammed Nasser Al-Sabari
Keyword(s):  
Rotor System ◽  
Operating Conditions ◽  
System Response ◽  
Flexible Structure ◽  
Vibration Absorber ◽  
Dynamic Vibration Absorber ◽  
Element Analysis ◽  
Dynamic Vibration ◽  
Unbalanced Rotor ◽  
Beam Type

This paper presents experimental and numerical results about the effectiveness of a beam-type twin dynamic vibration absorber for a cantilevered flexible structure carrying an unbalanced rotor. An experimental laboratory prototype setup has been built and implemented in our laboratory and numerical investigations have been performed through finite element analysis. The proposed system design consists of a primary cantilevered flexible structure with an attached dual-mass cantilevered secondary dynamic vibration absorber arrangement. In addition, an unbalanced rotor system is attached to the tip of the flexible cantilevered structure to inspect the system response under harmonic excitations. Numerical findings and experimental observations have revealed that significant vibration reductions are possible with the proposed dual-mass, cantilevered dynamic vibration absorber on a flexible cantilevered platform carrying an unbalanced rotor system at its tip. The proposed system is efficient and it can be practically tuned for variety of design and operating conditions. The designed setup and the results in this paper can serve for practicing engineers, researchers and can be used for educational purposes.

Nonlinear Dynamic Analysis of a Rotor System With Aerodynamic Journal Bearings

2007 ◽  
Author(s):  
T. N. Shiau ◽  
W. C. Hsu ◽  
B. W. Deng
Keyword(s):  
Nonlinear Dynamic ◽  
Nonlinear Dynamic Analysis ◽  
Journal Bearings ◽  
Rotor System ◽  
Least Square ◽  
Filter Method ◽  
System Response ◽  
Recursive Least Square ◽  
Bearing Force ◽  
Rotor Mass

This paper investigates nonlinear dynamic characteristics of a rotor system with aerodynamic journal bearings. The Finite Difference Method (FDM) is employed to solve the Reynolds equation, which is used to determine the nonlinear compressible gas force of the aerodynamic bearing. By applying the gas bearing force to system equations of motion, the system response can be determined by the numerical integration method. Results show that the aerodynamic bearing will provide higher loading capacity to support the rotor when the eccentricity ratio is increased. The aerodynamic bearing force increases when the rotor is speeding up or the squeeze frequency is raised. The rotor trajectory presents aperiodic behavior, and it becomes significant as the rotor mass increases. When the squeeze frequency decreases or the rotor mass increases, the radius of the rotor trajectory will increase. Recursive Least Square Method and Kalman Filter Method are used to identify the aerodynamic bearing parameters from the system response. The parameters include the damping and stiffness coefficients of the aerodynamic bearing. According to the results of identification, both identified parameters by these two methods are in good accordance. The results show that the aerodynamic bearing force can be precisely identified and the system response can be quickly solved by the identified system with less computer time. But the identified system lost its accuracy as the rotor speed or the squeeze frequency increase because these will enhance the nonlinearity of the aerodynamic bearing force.

scholarly journals Vibration characteristics of triple-gear-rotor system in compressed air energy storage under variable torque load

2021 ◽  
Vol 104 (1) ◽  
pp. 003685042098705
Author(s):  
Xinran Wang ◽  
Yangli Zhu ◽  
Wen Li ◽  
Dongxu Hu ◽  
Xuehui Zhang ◽  
...  
Keyword(s):  
Large Scale ◽  
Three Dimensional ◽  
Element Model ◽  
Rotor System ◽  
Dynamic Responses ◽  
System Response ◽  
Rotating Speed ◽  
Torque Load ◽  
Set Up ◽  
Two Stages

This paper focuses on the effects of the off-design operation of CAES on the dynamic characteristics of the triple-gear-rotor system. A finite element model of the system is set up with unbalanced excitations, torque load excitations, and backlash which lead to variations of tooth contact status. An experiment is carried out to verify the accuracy of the mathematical model. The results show that when the system is subjected to large-scale torque load lifting at a high rotating speed, it has two stages of relatively strong periodicity when the torque load is light, and of chaotic when the torque load is heavy, with the transition between the two states being relatively quick and violent. The analysis of the three-dimensional acceleration spectrum and the meshing force shows that the variation in the meshing state and the fluctuation of the meshing force is the basic reasons for the variation in the system response with the torque load. In addition, the three rotors in the triple-gear-rotor system studied show a strong similarity in the meshing states and meshing force fluctuations, which result in the similarity in the dynamic responses of the three rotors.

Stability of Ring-Type MEMS Gyroscopes Subjected to Stochastic Angular Speed Fluctuation

2017 ◽  
Vol 139 (4) ◽  
Author(s):  
Samuel F. Asokanthan ◽  
Soroush Arghavan ◽  
Mohamed Bognash
Keyword(s):  
Angular Velocity ◽  
Degrees Of Freedom ◽  
Microelectromechanical Systems ◽  
Damping Ratio ◽  
Operating Conditions ◽  
System Stability ◽  
System Response ◽  
Ring Type ◽  
Mems Gyroscopes ◽  
The Stability

Effect of stochastic fluctuations in angular velocity on the stability of two degrees-of-freedom ring-type microelectromechanical systems (MEMS) gyroscopes is investigated. The governing stochastic differential equations (SDEs) are discretized using the higher-order Milstein scheme in order to numerically predict the system response assuming the fluctuations to be white noise. Simulations via Euler scheme as well as a measure of largest Lyapunov exponents (LLEs) are employed for validation purposes due to lack of similar analytical or experimental data. The response of the gyroscope under different noise fluctuation magnitudes has been computed to ascertain the stability behavior of the system. External noise that affect the gyroscope dynamic behavior typically results from environment factors and the nature of the system operation can be exerted on the system at any frequency range depending on the source. Hence, a parametric study is performed to assess the noise intensity stability threshold for a number of damping ratio values. The stability investigation predicts the form of threshold fluctuation intensity dependence on damping ratio. Under typical gyroscope operating conditions, nominal input angular velocity magnitude and mass mismatch appear to have minimal influence on system stability.

scholarly journals Dynamics and Protein–Solvent Interactions of Hemoglobin in T and R Quaternary Conformation

2002 ◽  
Vol 16 (3-4) ◽  
pp. 227-233 ◽  
Author(s):  
Chiara Caronna ◽  
Antonio Cupane
Keyword(s):  
Quaternary Structure ◽  
Dynamic Properties ◽  
Low Frequency ◽  
Helical Structure ◽  
Blue Shift ◽  
Peak Frequency ◽  
The Other ◽  
Solvent Interactions ◽  
Reported Data ◽  
Increasing Temperature

In this work we report the thermal behaviour of the amide I′ band of carbonmonoxy and deoxy hemoglobin in 65% v/v glycerolD8/D2O solutions and in the temperature interval 10–295 K. Following recent suggestions in the literature, we analyze the amide I′ band in terms of two components, one at about 1630 cm−1and the other at about 1650 cm−1, that are assigned to solvent‒exposed and buried α‒helical regions, respectively.For deoxy hemoglobin (in T quaternary structure) both components are narrower with respect to carbonmonoxy hemoglobin (in R quaternary structure), while the peak frequency blue shift observed, upon increasing temperature, for the component at about 1630 cm−1is smaller. The reported data provide evidence of the dependence of hemoglobin dynamic properties upon the protein quaternary structure and suggest a more compact α‒helical structure of hemoglobin in T conformation, with reduced population of low‒frequency modes involving the solvent and protein.

scholarly journals Dynamic control of maximal ventricular elastance via the baroreflex and force-frequency relation in awake dogs before and after pacing-induced heart failure

2010 ◽  
Vol 299 (1) ◽  
pp. H62-H69 ◽  
Author(s):  
Xiaoxiao Chen ◽  
Javier A. Sala-Mercado ◽  
Robert L. Hammond ◽  
Masashi Ichinose ◽  
Soroor Soltani ◽  
...  
Keyword(s):  
Heart Failure ◽  
Transfer Function ◽  
Transfer Functions ◽  
Dynamic Properties ◽  
System Response ◽  
Force Frequency ◽  
Arterial Baroreflex ◽  
Ventricular Elastance ◽  
Arterial Blood ◽  
Frequency Relation

We investigated to what extent maximal ventricular elastance ( Emax) is dynamically controlled by the arterial baroreflex and force-frequency relation in conscious dogs and to what extent these mechanisms are attenuated after the induction of heart failure (HF). We mathematically analyzed spontaneous beat-to-beat hemodynamic variability. First, we estimated Emax for each beat during a baseline period using the ventricular unstressed volume determined with the traditional multiple beat method during vena cava occlusion. We then jointly identified the transfer functions (system gain value and time delay per frequency) relating beat-to-beat fluctuations in arterial blood pressure (ABP) to Emax (ABP→ Emax) and beat-to-beat fluctuations in heart rate (HR) to Emax (HR→ Emax) to characterize the dynamic properties of the arterial baroreflex and force-frequency relation, respectively. During the control condition, the ABP→ Emax transfer function revealed that ABP perturbations caused opposite direction Emax changes with a gain value of −0.023 ± 0.012 ml−1, whereas the HR→ Emax transfer function indicated that HR alterations caused same direction Emax changes with a gain value of 0.013 ± 0.005 mmHg·ml−1·(beats/min)−1. Both transfer functions behaved as low-pass filters. However, the ABP→ Emax transfer function was more sluggish than the HR→ Emax transfer function with overall time constants (indicator of full system response time to a sudden input change) of 11.2 ± 2.8 and 1.7 ± 0.5 s ( P < 0.05), respectively. During the HF condition, the ABP→ Emax and HR→ Emax transfer functions were markedly depressed with gain values reduced to −0.0002 ± 0.007 ml−1 and −0.001 ± 0.004 mmHg·ml−1·(beats/min)−1 ( P < 0.1). Emax is rapidly and significantly controlled at rest, but this modulation is virtually abolished in HF.

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