Nonlinear Dynamic Analysis of an Asymmetric Ball Bearing Rotor System

Bahan, Doğancan
Ciğeroğlu, Ender
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.


Nonlinear vibration analysis of rotors supported by ball bearings
Bahan, Doğancan; Ciğeroğlu, Ender; Department of Mechanical Engineering (2019)
Performance of ball bearing-rotor systems is highly dependent on and often limited by characteristics of ball bearings. Ball bearings are nonlinear by their nature and this nonlinearity must be investigated rigorously to correctly predict vibration response of the system. The steady-state periodic response of rotor systems with nonlinear ball bearings is investigated. The rotor is modeled with the Finite Element Method. Nonlinear model for the bearings considers finite number of balls, bearing clearance and...
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In this study, a nonlinear 3-D mathematical model for horizontal drum type washing machines is developed considering rotating unbalance type excitation. Nonlinear differential equations of motion are converted into a set of nonlinear algebraic equations by using Harmonic Balance Method (HBM). The resulting nonlinear algebraic equations are solved by using Newton’s method with arc-length continuation. Several case studies are performed in order to observe the effects of orientation angles of springs and damp...
Development of load distribution model and micro-geometry optimization of four-point contact ball bearings
Yılmaz, Sinan; Akkök, Metin; Department of Mechanical Engineering (2018)
The unique kinematic characteristics and load-carrying capabilities of four-point contact ball bearings make these bearings being widely used in demanding applications. Particularly, four-point contact ball bearings are preferred due to their reverse axial load carrying capability and high level of stability. In this study, micro and macro geometrical aspects of these bearings are investigated and compared with the conventional ball bearings. Once the geometry and internal kinematics of four-point contact b...
A new jacobian matrix calculation method to decrease computational time in periodic force response analysis of nonlinear structures
Kızılay, Hazım Sef; Ciğeroğlu, Ender; Department of Mechanical Engineering (2019)
The contact interfaces between the components used in high speed systems such as the turbo machinery cause nonlinear vibrations. In order to understand the dynamic characteristic of nonlinear systems, it is important to perform nonlinear vibration analysis. In nonlinear vibration analysis, due to the properties of nonlinear elements used, it is not possible to calculate the Jacobian matrix analytically or it becomes very complicated and difficult, therefore, Jacobian matrix is calculated as numerically. In ...
IDER, YZ; Gençer, Nevzat Güneri; ATALAR, E; TOSUN, H (1990-03-01)
An algorithm is developed for electrical impedance tomography (EIT) of finite cylinders with general cross-sectional boundaries and translationally uniform conductivity distributions. The electrodes for data collection are assumed to be placed around a crosssectional plane; therefore the axial variation of the boundary conditions and also the potential field are expanded in Fourier series. For each Fourier component a two-dimensional (2-D) partial differential equation is derived. Thus the 3-D forward probl...
Citation Formats
D. Bahan and E. Ciğeroğlu, “Nonlinear Dynamic Analysis of an Asymmetric Ball Bearing Rotor System,” 2019, Accessed: 00, 2020. [Online]. Available: