Duffing’s Vibration of a Rotor Supported on Gas Foil Bearings With Base Excitation: Measurements and Model Predictions

2016 ◽  
Author(s):  
Tae Ho Kim ◽  
Young Min Kim ◽  
Jongsung Lee ◽  
Moon Sung Park ◽  
Kyoung-Ku Ha ◽  
...  
Keyword(s):  
Nonlinear Equation ◽  
Eddy Current ◽  
Dynamic Load ◽  
Excitation Frequency ◽  
Dynamic Loads ◽  
Base Excitation ◽  
Test Rig ◽  
Foil Bearings ◽  
Model Predictions ◽  
Excitation Frequencies

The widespread application of gas foil bearings (GFBs) to high-performance microturbomachinery requires accurate predictions for their physical models based on experimental test data. This paper presents the experimental measurements and model predictions of Duffing’s vibration in a rotor supported on GFBs with base excitation, implemented for small oil-free turbomachinery. The rotor consisted of an impeller at one end and a thrust collar at the other end. Two gas foil journal bearings (GFJBs) located between the impeller and thrust collar supported the rotor, and one pair of gas foil thrust bearings (GFTBs) supported the thrust collar. A series of dynamic excitation tests on the rotor-GFBs system was conducted with increasing dynamic load and excitation frequency, with the rotor operating at 20,000 rpm. An electromagnetic shaker provided dynamic sine sweep loads at excitation frequencies of 10–200 Hz to the test rig base in the axial and horizontal directions. An accelerometer installed on the test rig measured the acceleration due to the dynamic loads and provided it to the shaker controller for use as a reference signal. The acceleration level was controlled to ensure a constant value, while the excitation frequency increased. During the excitation tests, two sets of orthogonally positioned eddy current sensors and one axially positioned eddy current sensor recorded the rotor’s horizontal, vertical, and axial vibrations. The test measurements demonstrated that the rotor’s vibrational motions synchronous to the shaker excitation were the most dominant. At a constant dynamic load, as the excitation frequency increased, the amplitude of the rotor motion gradually increased until it reached a certain frequency, after which it jumped down at the higher frequencies. This amplitude jump-down phenomenon became more pronounced as the dynamic load increased. In general, both the peak amplitude and jump-down frequency increased nonlinearly with the increasing dynamic loads, thus revealing the typical Duffing’s vibration. For benchmarking against the test measurements, a previously developed numerical integration of a nonlinear equation of motion (EOM) was modified to predict the rotor’s vibrational motions with base excitations to an acceleration of 9 G (gravity). This nonlinear equation uses a third-order polynomial equation that best fits the measured structural foil bearing deflection versus static load. Comparisons of the predicted synchronous amplitude and acceleration of the rotor for the increasing excitation frequencies and the predicted waterfall plot of the amplitude of the rotor motion with the test measurements showed excellent agreements, thus validating the predictive model of the rotor-GFB system with base excitation.

Identification of Dynamic Characteristics of Gas Foil Thrust Bearings Using Base Excitation

2016 ◽  
Author(s):  
Tae Ho Kim ◽  
Moon Sung Park ◽  
Jongsung Lee ◽  
Young Min Kim ◽  
Kyoung-Ku Ha ◽  
...  
Keyword(s):  
Dynamic Characteristics ◽  
Dynamic Load ◽  
Loss Factor ◽  
Load Capacity ◽  
Excitation Frequency ◽  
Vibrational Amplitude ◽  
Test Rig ◽  
Thrust Bearings ◽  
Bearing Plate ◽  
Bearing Stiffness

Gas foil bearings (GFBs) have clear advantages over oil-lubricated and rolling element bearings, by virtue of low power loss, oil-free operation in compact units, and rotordynamic stability at high speeds. However, because of the inherent low gas viscosity, GFBs have lower load capacity than the other bearings. In particular, accurate measurement of load capacity and dynamic characteristics of gas foil thrust bearings (GFTBs) is utmost important to widening their applications to high performance turbomachinery. In this study, a series of excitation tests were performed on a small oil-free turbomachinery with base excitations in the rotor axial direction to measure the dynamic load characteristics of a pair of six-pad, bump-type GFTBs, which support the thrust collar. An electromagnetic shaker provided dynamic sine sweep loads to the test bench (shaking table), which held rigidly the turbomachinery test rig for increasing excitation frequency from 10 Hz to 200 Hz. The magnitude of the shaker dynamic load, represented as an acceleration measured on the test rig, was increased up to 9 G (gravity). An eddy current sensor installed on the test rig housing measured the axial displacement (or vibrational amplitude) of the rotor thrust collar during the excitation tests. The axial acceleration of the rotor relative to the test rig was calculated using the measured displacement. A single degree-of-freedom base excitation model identified the frequency-dependent dynamic load capacity, stiffness, damping, and loss factor of the test GFTB for increasing shaker dynamic loads and increasing bearing clearances. The test results show that, for a constant shaker force and the test GFTB with a clearance of 155 μm, an increasing excitation frequency increases the dynamic load carried by the test GFTB, i.e., bearing reaction force, until a certain value of the frequency where it jumps down suddenly because of the influence from Duffing’s vibrations of the rotor. The bearing stiffness increases and the damping decreases dramatically as the excitation frequency increases. Generally, the bearing loss factor ranges from 0.5 to 1.5 independent of the frequency. As the shaker force increases, the bearing dynamic load, stiffness, damping, and loss factor increase depending on the excitation frequency. Interestingly, the agreements between the measured GFTB dynamic load versus the thrust runner displacement, the measured GFTB static load versus the structural deflection, and the predicted static load versus the thrust runner displacement are remarkable. Further tests with increasing GFTB clearances of 155, 180, 205, and 225 μm revealed that the vibrational amplitude increases and the jump-down frequency decreases with increasing clearances. The bearing load increases, but the bearing stiffness, damping, and loss factor decrease slightly as the clearance increases. The test results after a modification of the GFTB by rotating one side bearing plate by 30° relative to the other side bearing plate revealed insignificant changes in the dynamic characteristics. The present dynamic performance measurements provide a useful database of GFTBs for use in microturbomachinery.

EXPERIMENTAL INVESTIGATION OF A FOIL BEARING STRUCTURE WITH A POLYMER COATING UNDER DYNAMIC LOADS

Tribologia ◽  
2018 ◽  
Vol 281 (5) ◽  
pp. 5-12 ◽  
Author(s):  
Paweł BAGIŃSKI ◽  
Grzegorz ŻYWICA
Keyword(s):  
Excitation Frequency ◽  
Dynamic Loads ◽  
Test Rig ◽  
Static Tests ◽  
Structural Part ◽  
Foil Bearing ◽  
Wide Range ◽  
Load Tests ◽  
Excitation Force ◽  
Stiffness And Damping

This paper presents the results of research on the structural elements of a prototypical foil bearing in terms of its dynamic loads. In the framework of dynamic tests, several dozens of measurement series were carried out on a test rig specially prepared for this purpose. Dynamic excitations were applied using an electromagnetic exciter that enables changing the amplitude and frequency of the excitation force. Owing to this, it was possible to determine characteristics of the tested system in a wide range of loads and frequencies. A value of 400 Hz was assumed as the upper limit of the excitation frequency. The test rig enabled considering the direction of dynamic loads, which, as it turned out, had a significant impact on the obtained results. The research findings show that both the amplitude and frequency of an excitation force have a major impact on the stiffness and damping of the structural part of the foil bearing. The results of dynamic load tests complement the results of static tests performed earlier.

Characterization of Foil Bearing Structure for Increasing Shaft Temperatures: Part II—Dynamic Force Performance

2008 ◽  
Author(s):  
Tae Ho Kim ◽  
Luis San Andre´s ◽  
Anthony W. Breedlove
Keyword(s):  
Friction Coefficient ◽  
Dry Friction ◽  
Excitation Frequency ◽  
Forced Response ◽  
Dynamic Loads ◽  
Dynamic Force ◽  
Viscous Damping ◽  
Structural Stiffness ◽  
Foil Bearing ◽  
Excitation Frequencies

The forced response of a gas foil bearing (GFB), a typical rotor support in oil-free microturbomachinery, relies heavily on its resilient bump-strip layers structure, which also offers dry-friction type damping to ameliorate rotor vibrations. Operation at high temperature not only changes the FB elastic support material properties, but also produces thermal growth of the rotor and bearing components which ultimately affect the bearing structural stiffness and energy dissipation characteristics. The paper presents dynamic shaker load versus foil bearing structural deflection measurements for increasing shaft temperatures, from ambient to 188°C. In the tests, a FB supported on a non-rotating shaft is excited with a shaker at three load amplitudes (13 N, 22 N, and 31 N) and frequencies ranging from 40 to 200 Hz. A mechanical impedance model identifies the frequency dependent FB structural stiffness and equivalent viscous damping coefficient or dry-friction coefficient. Surface plots show trends in test results across increasing dynamic loads, shaft temperatures, and excitation frequencies. The FB stiffness increases by as much as 50% with dynamic loads amplitudes increasing from 13 N to 31 N. The stiffness nearly doubles from low to high frequencies; and most importantly, it decreases by a third as the shaft temperature rises to 188°C. In general, the FB dynamic structural stiffness is lower than its static stiffness, reported in a companion paper, at low excitation frequencies, while it becomes larger with increasing excitation frequency due apparently to a bump slip-stick phenomenon. The bearing viscous damping is inversely proportional to the amplitude of dynamic load, excitation frequency, and shaft temperature. The FB structure dry-friction coefficient decreases with increasing amplitude of applied load and shaft temperature, and increases with increasing excitation frequency. The experimental results demonstrate the paramount effect of operating temperature on the structural parameters of a foil bearing.

Identification of Structural Stiffness and Energy Dissipation Parameters in a Second Generation Foil Bearing: Effect of Shaft Temperature

2010 ◽  
Vol 133 (3) ◽  
Author(s):  
Luis San Andrés ◽  
Keun Ryu ◽  
Tae Ho Kim
Keyword(s):  
Energy Dissipation ◽  
Dynamic Load ◽  
Loss Factor ◽  
Static Load ◽  
Mechanical Energy ◽  
Excitation Frequency ◽  
Structural Stiffness ◽  
Foil Bearings ◽  
Foil Bearing ◽  
Mechanical Energy Dissipation

Established high temperature operation of gas foil bearings (GFB) is of great interest for gas turbine applications. The effects of (high) shaft temperature on the structural stiffness and mechanical energy dissipation parameters of a foil bearing (FB) must be assessed experimentally. Presently, a hollow shaft warmed by an electric heater holds a floating second generation FB that is loaded dynamically by an electromagnetic shaker. In tests with the shaft temperature up to 184°C, the measurements of dynamic load and ensuing FB deflection render the bearing structural parameters, stiffness and damping, as a function of excitation frequency and amplitude of motion. The identified FB stiffness and viscous damping coefficients increase with shaft temperature due to an increase in the FB assembly interference or preload. The bearing material structural loss factor best representing mechanical energy dissipation decreases slightly with shaft temperature while increasing with excitation frequency. Separate static load measurements on the bearing also make evident the preload of the test bearing-shaft system at room temperature. The loss factor obtained from the area inside the hysteresis loop of the static load versus the deflection curve agrees remarkably with the loss factor obtained from the dynamic load measurements. The static procedure offers substantial savings in cost and time to determine the energy dissipation characteristics of foil bearings. Post-test inspection of the FB reveals sustained wear at the locations, where the bumps contact the top foil and the bearing sleeve inner surface, thus, evidences the bearing energy dissipation by dry friction.

Comparing Shock, Random and Sine Vibration Loads of the Electronic Equipment

2005 ◽  
Author(s):  
Frank Fan Wang
Keyword(s):  
Dynamic Load ◽  
Random Vibration ◽  
Sine Wave ◽  
Electronic Equipment ◽  
Dynamic Loads ◽  
Peak Acceleration ◽  
Maximum Acceleration ◽  
Dynamic Excitations ◽  
Dynamic Damage ◽  
Resonant Point

It is a challenge to correlate different dynamic loads. Often, attempts are made to compare the peak acceleration of sine wave to the root mean square (RMS) acceleration of random vibration and shock. However, peak sine acceleration is the maximum acceleration at one frequency. Random RMS is the square root of the area under a spectral density curve. These are not equivalent. This paper is to discuss a mathematical method to compare different kinds of dynamic damage at the resonant point of the related electronic equipment. The electronic equipment will vibrate at its resonance point when there are dynamic excitations. The alternative excitation at the resonant frequency causes the most damage. This paper uses this theory to develop a method to correlate different dynamic load conditions for electronic equipment. The theory is that if one kind of dynamic load causes the same levels of damaging effects as the other, the levels of vibration can then be related.

Modeling and Experimental Validations of a Piezoelectric Energy Harvester Under Combined Galloping and Base Excitations

2014 ◽  
Author(s):  
Amin Bibo ◽  
Abdessattar Abdelkefi ◽  
Mohammed F. Daqaq
Keyword(s):  
Bluff Body ◽  
Energy Harvester ◽  
Constitutive Relations ◽  
Excitation Frequency ◽  
Primary Resonance ◽  
Beam Theory ◽  
Excitation Amplitude ◽  
The Body ◽  
Base Excitation ◽  
Piezoelectric Energy

This paper develops an experimentally validated model of a piezoelectric energy harvester under combined aeroelastic-galloping and base excitations. To that end, an energy harvester consisting of a thin piezoelectric cantilever beam subjected to vibratory base excitation is considered. To permit galloping excitation, a bluff body is rigidly attached at the free end such that a net aerodynamic lift is generated as the incoming airflow separates on both sides of the body giving rise to limit cycle oscillations when the flow velocity exceeds a critical value. A nonlinear electromechanical distributed-parameter model of the harvester under the combined excitation is derived using the energy approach and by adopting the nonlinear Euler-Bernoulli beam theory, linear constitutive relations for the piezoelectric transduction, and the quasi-steady assumption for the aerodynamic loading. The partial differential equations of the system are discretized and a reduced-order-model is obtained. The mathematical model is validated by conducting a series of experiments with different loading conditions represented by wind speed, base excitation amplitude, and excitation frequency around the primary resonance.

Design and structural performance measurements of a novel multi-cantilever foil bearing

2014 ◽  
Vol 229 (10) ◽  
pp. 1830-1838 ◽  
Author(s):  
Kai Feng ◽  
Xueyuan Zhao ◽  
Zhiyang Guo
Keyword(s):  
Dynamic Characteristics ◽  
Dynamic Load ◽  
Dynamic Stiffness ◽  
Excitation Frequency ◽  
Viscous Damping ◽  
Equivalent Viscous Damping ◽  
Foil Bearing ◽  
Load Tests ◽  
Stiffness And Damping ◽  
Motion Amplitude

With increasing need for high-speed, high-temperature, and oil-free turbomachinery, gas foil bearings (GFBs) have been considered to be the best substitutes for traditional oil-lubricated bearings. A multi-cantilever foil bearing (MCFB), a novel GFB with multi-cantilever foil strips serving as the compliant underlying structure, was designed, fabricated, and tested. A series of static and dynamic load tests were conducted to measure the structural stiffness and equivalent viscous damping of the prototype MCFB. Experiments of static load versus deflection showed that the proposed bearing has a large mechanical energy dissipation capability and a pronounced nonlinear static stiffness that can prevents overly large motion amplitude of journal. Dynamic load tests evaluated the influence of motion amplitude, loading orientation and misalignment on the dynamic stiffness and equivalent viscous damping with respect to excitation frequency. The test results demonstrated that the dynamic stiffness and damping are strongly dependent on the excitation frequency. Three motion amplitudes were applied to the bearing housing to investigate the effects of motion amplitude on the dynamic characteristics. It is noted that the bearing dynamic stiffness and damping decreases with incrementally increasing motion amplitudes. A high level of misalignment can lead to larger static and dynamic bearing stiffness as well as to larger equivalent viscous damping. With dynamic loads applied to two orientations in the bearing midplane separately, the dynamic stiffness increases rapidly and the equivalent viscous damping declines slightly. These results indicate that the loading orientation is a non-negligible factor on the dynamic characteristics of MCFBs.

The Specific Characteristics of Shock and Blast Impacts on Construction Sites

2021 ◽  
pp. 81-88
Author(s):  
A.A. Komarov ◽  
Keyword(s):  
Dynamic Load ◽  
Static Load ◽  
Dynamic Loads ◽  
Potential Hazard ◽  
Construction Sites ◽  
Static Loads ◽  
Equivalent Static Loads ◽  
Plane Crash ◽  
Nuclear Plants ◽  
The Impact

The practices of hazardous and unique facilities’ construction imply that specific attention is paid to the issues of safety. Threats associated with crash impacts caused by moving cars or planes are considered. To ensure safety of these construction sites it is required to know the potential dynamic loads and their destructive capacity. This article considers the methodology of reducing dynamic loads associated with impacts caused by moving collapsing solids and blast loads to equivalent static loads. It is demonstrated that practically used methods of reduction of dynamic loads to static loads are based in schematization only of the positive phase of a dynamic load in a triangle forms are not always correct and true. The historical roots of this approach which is not correct nowadays are shown; such approach considered a detonation explosion as a source of dynamic load, including TNT and even a nuclear weapon. Application of the existing practices of reduction of dynamic load to static load for accidental explosions in the atmosphere that occur in deflagration mode with a significant vacuumization phase may cause crucial distortion of predicted loads for the construction sites. This circumstance may become a matter of specific importance at calculations of potential hazard of impacts and explosions in unique units — for instance, in the nuclear plants. The article considers a situation with a plane crash, the building structure load parameters generated at the impact caused by a plane impact and the following deflagration explosion of fuel vapors are determined.

An experimental investigation of a microturbine simulated rotor supported on multileaf gas foil bearings with backing bump foils

2017 ◽  
Vol 232 (9) ◽  
pp. 1169-1180 ◽  
Author(s):  
Bo Zhang ◽  
Shemiao Qi ◽  
Sheng Feng ◽  
Haipeng Geng ◽  
Yanhua Sun ◽  
...  
Keyword(s):  
High Speed ◽  
Preliminary Test ◽  
Journal Bearings ◽  
Rotating Machinery ◽  
System Stability ◽  
Test Rig ◽  
Thrust Bearings ◽  
Foil Bearings ◽  
Simulated System ◽  
First Time

Two multileaf gas foil journal bearings with backing bump foils and one set of gas foil thrust bearings were designed, fabricated, and used in a 100 kW class microturbine simulated rotor system to ensure stability of the system. Meanwhile, a preliminary test rig had been built to verify the simulated system stability. The rotor synchronous and subsynchronous responses were well controlled by using of the gas foil bearings. It is on the multileaf gas foil bearings with backing bump foils that the test was conducted and verified for the first time in open literatures. The success in the experiments shows that the design and fabrication of the rotor and the gas foil bearings can provide a useful guide to the development of the advanced high speed rotating machinery.

Experimental Investigations Into Nonlinear Vibro-Acoustics for Detection of Delaminations in a Composite Laminate

2018 ◽  
Vol 2 (1) ◽  
Author(s):  
Ashish Kumar Singh ◽  
Vincent B. C. Tan ◽  
Tong Earn Tay ◽  
Heow Pueh Lee
Keyword(s):  
Frequency Dependence ◽  
Composite Laminate ◽  
Excitation Frequency ◽  
Excitation Amplitude ◽  
Experimental Investigations ◽  
Frequency Sweep ◽  
Ultrasonic Methods ◽  
Acoustic Methods ◽  
Different Depths ◽  
Excitation Frequencies

In recent years, nonlinear vibro-acoustic methods have shown potential to identify defects which are difficult to detect using linear ultrasonic methods. However, these methods come with their own challenges such as frequency dependence, requirement for a high excitation amplitude, and difficulties in distinguishing nonlinearity from defect with nonlinearity from other sources to name a few. This paper aims to study the dependence of nonlinear vibro-acoustic methods for detection of delaminations inside a composite laminate, on the excitation methods and excitation frequencies. It is shown that nonlinear vibro-acoustic methods are highly frequency dependent and commonly used excitation signals which utilize particular values of excitation frequencies might not always lead to a clear distinction between intact and delaminated regions of the specimen. To overcome the frequency dependence, signals based on frequency sweep are used. Interpretation of output response to sweep signals to identify damage is demonstrated using an earlier available approach, and a simpler approach is proposed. It is demonstrated that the damage detection with sweep signal excitations is relatively less dependent on excitation frequency than the conventional excitation methods. The proposed interpretation technique is then applied to specimens with delamination of varying sizes and with delaminations at different depths inside the laminate to demonstrate its effectiveness.

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