Rolling Bearing Parametric Excitation of a Jeffcott Rotor System

2020 ◽  
Author(s):  
Ghasem Ghannad Tehrani ◽  
Chiara Gastaldi ◽  
Teresa Maria Berruti
Keyword(s):  
Parametric Excitation ◽  
Rotational Speed ◽  
Input Parameter ◽  
Equations Of Motion ◽  
Harmonic Balance Method ◽  
Rolling Bearing ◽  
Mean Value ◽  
Hertzian Contact ◽  
Rolling Bearings ◽  
Jeffcott Rotor

Abstract Rolling bearings are still widely used in aeroengines. Whenever rotors are modeled, rolling bearing components are typically modeled using springs. In simpler models, this spring is considered to have a constant mean value. However, the rolling bearing stiffness changes with time due to the positions of the balls with respect to the load on the bearing, thus giving rise to an internal excitation known as Parametric Excitation. Due to this parametric excitation, the rotor-bearings system may become unstable for specific combinations of boundary conditions (e.g. rotational speed) and system characteristics (rotor flexibility etc.). Being able to identify these instability regions at a glance is an important tool for the designer, as it allows to discard since the early design stages those configurations which may lead to catastrophic failures. In this paper, a Jeffcott rotor supported and excited by such rolling bearings is used as a demonstrator. In the first step, the expression for the time–varying stiffness of the bearings is analytically derived by applying the Hertzian Contact Theory. Then, the equations of motion of the complete system are provided. In this study, the Harmonic Balance Method (HBM) is used to as an approximate procedure to draw a stability map, thus dividing the input parameter space, i.e. rotational speed and rotor physical characteristics, into stable and unstable regions.

Hysteretic Resonances and Intermittency Chaos in Ball Bearings

2018 ◽  
Author(s):  
Zhiyong Zhang ◽  
Xiaoting Rui ◽  
Yushu Chen ◽  
Wenkai Dong ◽  
Lei Li
Keyword(s):  
Ball Bearing ◽  
Harmonic Balance Method ◽  
Rolling Bearing ◽  
Hertzian Contact ◽  
Ball Bearings ◽  
Rolling Bearings ◽  
Rotor Systems ◽  
Revolute Joints ◽  
Rolling Elements ◽  
Varying Compliance

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.

Rolling Bearing Parametric Excitation of a Jeffcott Rotor System

2021 ◽  
Author(s):  
GHASEM TEHRANI GHANNAD ◽  
CHIARA GASTALDI ◽  
Teresa Berruti
Keyword(s):  
Parametric Excitation ◽  
Rolling Bearing ◽  
Rotor System ◽  
Jeffcott Rotor

Information Entropy of Rolling Bearing Friction Torque as Data Series

2010 ◽  
Vol 44-47 ◽  
pp. 1115-1119 ◽  
Author(s):  
Xin Tao Xia ◽  
Long Chen ◽  
Fan Nian Meng
Keyword(s):  
Experimental Investigation ◽  
Information Entropy ◽  
Rotational Speed ◽  
Dynamic Performance ◽  
Rolling Bearing ◽  
Friction Torque ◽  
Data Series ◽  
Entropy Theory ◽  
Rolling Bearings ◽  
Bearing Friction

The information entropy theory is applied to evaluate the uncertainty of the rolling bearing friction torque. The data series are obtained via the experimental investigation on the friction torque of the rolling bearings under the condition of different rotational speeds. And the result shows that the information entropy of the friction torque increases with the rotational speed of the rolling bearing, revealing the new dynamic performance of the rolling bearing friction torque as a data series.

Trained Harmonic Balance Method for Parametrically Excited Jeffcott Rotor Analysis

2020 ◽  
Vol 16 (1) ◽  
Author(s):  
Ghasem Ghannad Tehrani ◽  
Chiara Gastaldi ◽  
Teresa M. Berruti
Keyword(s):  
Harmonic Balance ◽  
Harmonic Balance Method ◽  
Periodic Variation ◽  
Balance Method ◽  
Rolling Bearings ◽  
Parametrically Excited ◽  
Axial Forces ◽  
Catastrophic Failures ◽  
Jeffcott Rotor ◽  
The Stability

Abstract Being able to identify instability regions is an important task for the designers of rotating machines. It allows discarding, since the early design stages, those configurations which may lead to catastrophic failures. Instability can be induced by different occurrences such as an unbalanced disk, torsional, and axial forces on the shaft or periodic variation of system parameters known as “parametric excitation.” In this paper, the stability of a Jeffcott rotor, parametrically excited by the time-varying stiffness of the rolling bearings, is studied. The harmonic balance method (HBM) is here applied as an approximate procedure to obtain the well-known “transition curves (TCs)” which separate the stable from the unstable regions of the design parameter space. One major challenge in the HBM application is identifying an adequate harmonic support (i.e., number of harmonics in the Fourier formulation), necessary to produce trustworthy results. A procedure to overcome this issue is here proposed and termed “trained HBM” (THBM). The results obtained by THBM are compared to those computed by Floquet theory, here used as a reference. The THBM proves to be able to produce reliable TCs in a timely manner, compatible with the design process.

A Simplified Model for Structural Vibrations in Ball Bearings

1994 ◽  
Author(s):  
Kambiz Farhang ◽  
Kapil Mehra ◽  
Jayanta Datta
Keyword(s):  
Linear Model ◽  
Equations Of Motion ◽  
Linear Representation ◽  
Accurate Estimate ◽  
Rolling Element Bearing ◽  
Hertzian Contact ◽  
Outer Ring ◽  
Rolling Bearings ◽  
Geometrical Properties ◽  
Rolling Element

Abstract More often than not, in studies involving dynamics and vibration of rotor systems, the bearings within a rotor system are treated as linear components. However, it is well understood that bearing systems are nonlinear due to both their geometrical properties and Hertzian contact between their components. This paper develops a linear formulation to approximate the vibration behavior of rolling bearings. A study of the approximation in the linear representation for rolling bearings is presented in which the effects of preload, lubricant viscosity and outer ring mass on the accuracy of the linear representation are determined. The equations of motion governing the vibrations of rolling element bearing are found to be a set of second-order, nonlinear ordinary differential equations with position periodic coefficients. These equations are linearized about nominal values of the position vectors of the rolling element and the outer ring center. The linearized equations of motion are solved to obtain the small perturbations (displacements) from the nominal positions. The results show that the linear model representation is applicable for bearings with preload. Existence of damping and/or greater outer ring mass enhance the approximation provided by the linear model. Most importantly, the linear representation provides a conservative estimate of the rolling element motion and very accurate estimate of the outer ring motion.

Thermal interactions in rolling bearings

2019 ◽  
Vol 234 (8) ◽  
pp. 1233-1253 ◽  
Author(s):  
Pradeep K Gupta ◽  
Jared I Taketa ◽  
Craig M Price
Keyword(s):  
Shear Stress ◽  
Heat Generation ◽  
Equations Of Motion ◽  
Rolling Bearing ◽  
Temperature Fields ◽  
Time Step ◽  
Rolling Bearings ◽  
Bearing Materials ◽  
Very High ◽  
Good Agreement

Rolling bearing dynamics model, based on classical differential equations of motion of bearing elements coupled with thermal interactions, is presented. While churning and drag effects are based on classical laminar and turbulent flow theories, independently measured lubricant rheology, including shear dependence of viscosity, is used to model lubricant traction. The energy equation is integrated through the lubricant film to first compute Newtonian traction with thermal effects. Viscosity dependence on shear stress is then applied to model “shear-thinning” effects. At very high contact pressure and very low slide-to-roll ratios material creep effects, where the behavior of lubricated and dry contacts is similar, are implemented, while a shear stress limit is applied at very high slide-to-roll ratios. Traction predictions for a typical contact in a traction rig show good agreement with experimental traction data. Transient heat generations are time-averaged over thermal time step to compute time-varying temperature fields in the bearing, which alter properties of bearing materials, operating bearing geometry, and rheology of the lubricant. As the transient solutions converge to stable operating temperatures, bearing heat generation approaches the expected steady-state value. Heat generation predictions for both ball and rolling bearings are in good agreement with measured experimental data.

Efficiency of application of the phase-chronometric method and neurodiagnostics for monitoring the degradation of rolling bearings during operation

2020 ◽  
pp. 43-50
Author(s):  
A.S. Komshin ◽  
K.G. Potapov ◽  
V.I. Pronyakin ◽  
A.B. Syritskii
Keyword(s):  
Life Cycle ◽  
Wavelet Analysis ◽  
Metrological Support ◽  
Rolling Bearing ◽  
Technical Condition ◽  
Measurement Information ◽  
Rolling Bearings ◽  
Vibration Diagnostics ◽  
Bearing Life ◽  
Alternative Approach

The paper presents an alternative approach to metrological support and assessment of the technical condition of rolling bearings in operation. The analysis of existing approaches, including methods of vibration diagnostics, envelope analysis, wavelet analysis, etc. Considers the possibility of applying a phase-chronometric method for support on the basis of neurodiagnostics bearing life cycle on the basis of the unified format of measurement information. The possibility of diagnosing a rolling bearing when analyzing measurement information from the shaft and separator was evaluated.

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