Modeling and analysis of nonlinear rotordynamics due to higher order deformations in bending

A mathematical model incorporating the higher order deformations in bending is devel- oped and analyzed to investigate the nonlinear dynamics of rotors. The rotor system con- sidered for the present work consists of a flexible shaft and a rigid disk. The shaft is modeled as a beam with a circular cross section and the Euler Bernoulli beam theory is applied with added effects such as rotary inertia, gyroscopic effect, higher order large deformations, rotor mass unbalance and dynamic axial force. The kinetic and strain (defor- mation) energies of the rotor system are derived and the Rayleigh–Ritz method is used to discretize these energy expressions. Hamilton’s principle is then applied to obtain the mathematical model consisting of second order coupled nonlinear differential equations of motion. In order to solve these equations and hence obtain the nonlinear dynamic response of the rotor system, the method of multiple scales is applied. Furthermore, this response is examined for different possible resonant conditions and resonant curves are plotted and discussed. It is concluded that nonlinearity due to higher order deformations significantly affects the dynamic behavior of the rotor system leading to resonant hard spring type curves. It is also observed that variations in the values of different parameters like mass unbalance and shaft diameter greatly influence dynamic response. These influences are also presented graphically and discussed

Rotor-to-stator Partial Rubbing and Its Effects on Rotor Dynamic Response

Results from experimental and analytical studies on rotor to stationary element partial rubbings at several locations and their effects on rotor dynamic responses are presented. The mathematical model of a rubbing rotor is given. The computer program provides numerical results which agree with experimentally obtained rotor responses

Numerical study on the coupled vibration characteristics of dual-rotors system with little rotation speed difference

In view of statically indeterminate structures of the decanter centrifuge, an iteration calculation model of nonlinear bearing stiffness is built innovatively. Based on gear meshing stiffness, material and lubricant film damping, coupled dual-rotors vibration model of screw-differential mechanism-bowl is constructed using solid elements. Applying ANSYS modal analysis, critical speeds along with vibration modes of dual-rotors and single-rotor are simulated, and the impacts of the differential mechanism and single-rotor modal on dual-rotors modal are obtained. Built on the harmonic response analysis, the results indicate that the system responses differently for the different rotors by manipulating the dynamic responses of the centrifuge under single rotor unbalance excitation. On the basis of transient structural analysis, beat vibration characteristics of dual-rotors system with little rotation speed difference are obtained, and a conclusion of the system responses separately for the unbalance mass of different rotors at a low rotating speed is acquired. The models and methods adopted in simulation are proved to be reasonable and feasible by experiment. The results have certain significance for the design and the dynamic balancing technique of the decanter centrifuge

Model Order Reduction for Rotating Electrical Machines

The simulation of electric rotating machines is both computationally expensive and memory intensive. To overcome these costs, model order reduction techniques can be applied. The focus of this contribution is especially on machines that contain non-symmetric components. These are usually introduced during the mass production process and are modeled by small perturbations in the geometry (e.g., eccentricity) or the material parameters. While model order reduction for symmetric machines is clear and does not need special treatment, the non-symmetric setting adds additional challenges. An adaptive strategy based on proper orthogonal decomposition is developed to overcome these difficulties. Equipped with an a posteriori error estimator the obtained solution is certified. Numerical examples are presented to demonstrate the effectiveness of the proposed method

Vibration transmission through rolling element bearings in geared rotor system, part 1

A mathematical model is proposed to examine the vibration transmission through rolling element bearings in geared rotor systems. Current bearing models, based on either ideal boundary conditions for the shaft or purely translational stiffness element description, cannot explain how the vibratory motion may be transmitted from the rotating shaft to the casing. This study clarifies this issue qualitatively and quantitatively by developing a comprehensive bearing stiffness matrix of dimension 6 model for the precision rolling element bearings from basic principles. The proposed bearing formulation is extended to analyze the overall geared rotor system dynamics including casing and mounts. The bearing stiffness matrix is included in discrete system models using lumped parameter and/or dynamic finite element techniques. Eigensolution and forced harmonic response due to rotating mass unbalance or kinematic transmission error excitation for a number of examples are computed

Dynamic characteristic of spur gear with flexible support of gearbox

In this study, a nonlinear translation-torsion model of spur gear pair with flexible support of gearbox is proposed. The time-varying meshing stiffness, transmission error and backlash are considered in this model. Lagrange’s equations are used for establishing the mathematic model. The numerical method is presented for solutions of nonlinear differential equations. The effect of rotating speed and support stiffness of gearbox is analyzed. The numerical results show that the flexibility of the support of gearbox has a significant effect on the amplitude-frequency characteristic of the spur gear pair at low rotating speeds. The response shows flexibility while the support stiffness is smaller than the bearings and rigidity while the support stiffness is larger than the bearings. The maximum deformation of the driving gear bearings under the flexible support is generally greater than the one under rigid support

SIRM 2017

This volume contains selected papers presented at the 12th International Conference on vibrations in rotating machines, SIRM, which took place February 15-17, 2017 at the campus of the Graz University of Technology. By all meaningful measures, SIRM was a great success, attracting about 120 participants (ranging from senior colleagues to graduate students) from 14 countries. Latest trends in theoretical research, development, design and machine maintenance have been discussed between machine manufacturers, machine operators and scientific representatives in the field of rotor dynamics. SIRM 2017 included thematic sessions on the following topics: Rotordynamics, Stability, Friction, Monitoring, Electrical Machines, Torsional Vibrations, Blade Vibrations, Balancing, Parametric Excitation, and Bearings. The papers struck an admirable balance between theory, analysis, computation and experiment, thus contributing a richly diverse set of perspectives and methods to the audience of the conference