Nonlinear Effects of Surface Texturing on the Performance of Journal Bearings in Flexible Rotordynamic Systems

2017 ◽  
Vol 139 (5) ◽  
Author(s):  
Jocelyn Rebufa ◽  
Fabrice Thouverez ◽  
Erick Le Guyadec ◽  
Denis Mazuyer
Keyword(s):  
Harmonic Balance ◽  
Vibration Amplitude ◽  
Surface Texturing ◽  
Harmonic Balance Method ◽  
Nonlinear Effects ◽  
Coupled System ◽  
Journal Bearings ◽  
Internal Damping ◽  
Rotating Shaft ◽  
Mean Pressure

A dynamic model of a rotating shaft on two textured hydrodynamic journal bearings is presented. The hydrodynamic mean pressure is computed using multiscale periodic homogenization and is projected on a flexible shaft with internal damping. Harmonic balance method (HBM) is used to study the limit cycles of unbalance response of the coupled system discretized by finite element method (FEM). Stability is analyzed with Floquet multipliers computation. An example of an isotropic texturing pattern representing laser dimples on a lightweight rotor is analyzed. Vibration amplitude and stability zone are compared with plain bearing lubrication. It is shown in an example that full surface texturing leads to relatively higher vibration amplitude compared to plain bearings.

Finding Periodic Solutions of Forced Systems With Local Nonlinearities: A Mixed Shooting Harmonic Balance Method

2015 ◽  
Author(s):  
Frederic Schreyer ◽  
Remco Leine
Keyword(s):  
Dynamical Systems ◽  
Periodic Solutions ◽  
Harmonic Balance ◽  
Shooting Method ◽  
Mechanical Systems ◽  
Harmonic Balance Method ◽  
Nonlinear Effects ◽  
Balance Method ◽  
Pros And Cons ◽  
Numerical Approaches

Several numerical approaches have been developed to capture nonlinear effects of dynamical systems. In this paper we present a mixed shooting-harmonic balance method to solve large mechanical systems with local nonlinearities efficiently. The Harmonic Balance Method as well as the shooting method have both their pros and cons. The proposed mixed shooting-HBM approach combines the efficiency of HBM and the accuracy of the shooting method and has therefore advantages of both.

Efficient Damping Prediction of Bolted Structures Using Harmonic Balance Method

2012 ◽  
Author(s):  
Pascal Reuss ◽  
Jens Becker ◽  
Lothar Gaul
Keyword(s):  
Harmonic Balance ◽  
Normal Force ◽  
Contact Stiffness ◽  
Harmonic Balance Method ◽  
Computation Time ◽  
Nonlinear Effects ◽  
Element Model ◽  
Balance Method ◽  
Friction Damper ◽  
Step Size

In this paper damping induced by extensive friction occurring in the interface between bolted structures is considered by simulations and experiments. A friction damper is attached to a beam-like flexible structure by screws such that the normal force in the interface can be varied by the clamping force of the screws. Contact and friction force parameters are identified by the comparison of simulated and experimentally determined FRFs for a particular normal force. Afterward a prediction of damping for different configurations is established. For simulations a finite element model is used where suitable contact and friction models are implemented. A time simulation of the system is expensive due to the large number of DoFs of the discretized substructures and the required small step size due to the high contact stiffness. Therefore model reduction methods are used. A further reduction of the computation time can be achieved by using the Harmonic Balance Method (HBM) for a direct frequency domain computation of FRFs. This enables an efficient procedure to approximate the reachable damping as well as to search the optimal damper position and the optimal normal force. The dependency of the friction to the vibration amplitude is therefore taken into account. A more detailed investigation of the nonlinear effects, e.g. higher harmonic response, is then accomplished by transient simulations for the optimal configured system in the time domain and the results are compared to experimental results.

Analytical Solution for the Nonlinear Dynamics of Planetary Gears

2010 ◽  
Vol 6 (2) ◽  
Author(s):  
Cheon-Jae Bahk ◽  
Robert G. Parker
Keyword(s):  
Nonlinear Dynamics ◽  
Dynamic Response ◽  
Harmonic Balance ◽  
Gear Tooth ◽  
Harmonic Balance Method ◽  
Nonlinear Effects ◽  
Mesh Stiffness ◽  
Planetary Gears ◽  
Parallel Finite Element ◽  
The Impact

Planetary gears are parametrically excited by the time-varying mesh stiffness that fluctuates as the number of gear tooth pairs in contact changes during gear rotation. At resonance, the resulting vibration causes tooth separation leading to nonlinear effects such as jump phenomena and subharmonic resonance. This work examines the nonlinear dynamics of planetary gears by numerical and analytical methods over the meaningful mesh frequency ranges. Concise, closed-form approximations for the dynamic response are obtained by perturbation analysis. The analytical solutions give insight into the nonlinear dynamics and the impact of system parameters on dynamic response. Correlation between the amplitude of response and external torque demonstrates that tooth separation occurs even under large torque. The harmonic balance method with arclength continuation confirms the perturbation solutions. The accuracy of the analytical and harmonic balance solutions is evaluated by parallel finite element and numerical integration simulations.

Investigation on the Steady-State Responses of Asymmetric Rotors

1992 ◽  
Vol 114 (2) ◽  
pp. 194-208 ◽  
Author(s):  
Yuan Kang ◽  
Yuan-Pin Shih ◽  
An-Chen Lee
Keyword(s):  
Harmonic Balance ◽  
Mathematical Formulation ◽  
Harmonic Balance Method ◽  
Element Formulation ◽  
Internal Damping ◽  
Gyroscopic Moment ◽  
Steady State Responses ◽  
Angular Displacements ◽  
Stiffness And Damping ◽  
State Responses

This paper is to generalize the previous work by utilizing finite element formulation to accommodate the effects of both deviatoric inertia and stiffness due to asymmetry of flexible shaft and disk. A Timoshenko beam element is employed to simulate rotor-bearing systems by taking the gyroscopic moment, rotary inertia, shear deformation of shaft and, asymmetry of disk and shaft into account. Internal damping is not included but the extension is straightforward. Eulerian angles are used to describe the orientations of shaft element and disk, by which, in opposite to the vectorial approach, the mathematical formulation will be symmetric for angular displacements in two directions. The effects of the angle between the major axes of shaft and disk, deviatoric inertia of the asymmetric shaft, and characteristics of bearing on synchronous critical and subcritical speeds are estimated in conjunction with the harmonic balance method. Numerical examples show that the resonant speeds, at which peak responses occur, change due to various angles between major axes, asymmetry of shaft, stiffness, and damping of bearing.

scholarly journals The Characteristics and Locking Process of Nonlinear MEMS Gyroscopes

Micromachines ◽  
2020 ◽  
Vol 11 (2) ◽  
pp. 233
Author(s):  
Yan Su ◽  
Pengfei Xu ◽  
Guowei Han ◽  
Chaowei Si ◽  
Jin Ning ◽  
...  
Keyword(s):  
Harmonic Balance ◽  
Vibration Amplitude ◽  
Harmonic Balance Method ◽  
Micro Electro Mechanical System ◽  
Drive Mode ◽  
Iterative Calculation ◽  
Start Up ◽  
Mems Gyroscopes ◽  
Order Of Magnitude ◽  
Frequency Curves

With the miniaturization of micro-electro-mechanical system (MEMS) gyroscopes, it is necessary to study their nonlinearity. The phase-frequency characteristics, which affect the start-up time, are crucial for guaranteeing the gyroscopes’ applicability. Nevertheless, although the amplitude-frequency (A-f) effect, one of the most obvious problems in nonlinearity, has been well studied, the phase response of nonlinear gyroscopes is rarely mentioned. In this work, an elaborate study on the characteristics and locking process of nonlinear MEMS gyroscopes is reported. We solved the dynamic equation using the harmonic balance method and simulated the phase-locked loop (PLL) actuation process with an iterative calculation method. It was shown that there existed an apparent overhanging and multi-valued phenomenon in both the amplitude–frequency and phase–frequency curves of nonlinear gyroscopes. Meanwhile, it was ascertained by our simulations that the locking time of PLL was retarded by the nonlinearity under certain conditions. Moreover, experiments demonstrating the effect of nonlinearity were aggravated by the high quality factor of the drive mode due to the instability of the vibration amplitude. A nonlinear PLL (NPLL) containing an integrator was designed to accelerate the locking process. The results show that the start-up time was reduced by an order of magnitude when the appropriate integral coefficient was used.

Nonlinear Dynamics of Planetary Gears With Equal Planet Spacing

2007 ◽  
Author(s):  
Cheon-Jae Bahk ◽  
Robert G. Parker
Keyword(s):  
Nonlinear Dynamics ◽  
Dynamic Response ◽  
Harmonic Balance ◽  
Gear Tooth ◽  
Harmonic Balance Method ◽  
Planetary Gear ◽  
Nonlinear Effects ◽  
Planetary Gears ◽  
Parallel Finite Element ◽  
The Impact

Planetary gears are parametrically excited by the time-varying mesh stiffness that fluctuates as the number of gear tooth pairs in contact changes during gear rotation. The resulting vibration causes tooth separation leading to nonlinear effects such as classical jump phenomena and sub- and superharmonic resonance. The nonlinear dynamics of the planetary gear is examined by both numerical and analytical methods over the meaningful mesh frequency ranges. Concise, closed-form approximations for the dynamic response are obtained by perturbation analysis. The analytical solutions give insight into the nonlinear dynamics and the impact of system parameters on dynamic response. The harmonic balance method with arclength continuation confirms the perturbation solutions. The accuracy of the analytical and harmonic balance solutions is validated by parallel finite element and numerical integration simulations.

scholarly journals Prediction of Transient Pressure Fluctuations within a Low-Pressure Turbine Cascade Using a Lanczos-Filtered Harmonic Balance Method

2021 ◽  
Vol 6 (3) ◽  
pp. 25
Author(s):  
Jan Philipp Heners ◽  
Stephan Stotz ◽  
Annette Krosse ◽  
Detlef Korte ◽  
Maximilian Beck ◽  
...  
Keyword(s):  
Turbulence Model ◽  
Harmonic Balance ◽  
Separation Bubble ◽  
Pressure Fluctuations ◽  
Harmonic Balance Method ◽  
Low Pressure ◽  
Filter Method ◽  
Turbine Cascade ◽  
Transient Pressure ◽  
Low Pressure Turbine

Unsteady pressure fluctuations measured by fast-response pressure transducers mounted in a low-pressure turbine cascade are compared to unsteady simulation results. Three differing simulation approaches are considered, one time-integration method and two harmonic balance methods either resolving or averaging the time-dependent components within the turbulence model. The observations are used to evaluate the capability of the harmonic balance solver to predict the transient pressure fluctuations acting on the investigated stator surface. Wakes of an upstream rotor are generated by moving cylindrical bars at a prescribed rotational speed that refers to a frequency of f∼500 Hz. The excitation at the rear part of the suction side is essentially driven by the presence of a separation bubble and is therefore highly dependent on the unsteady behavior of turbulence. In order to increase the stability of the investigated harmonic balance solver, a developed Lanczos-type filter method is applied if the turbulence model is considered in an unsteady fashion.

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