Effects of Frequency on Structural Stiffness and Damping in a Self-Acting Compliant Foil Journal Bearing

Author(s):  
C.-P. Roger Ku ◽  
Hooshang Heshmat

This paper presents the results of an investigation into the dynamic structural properties of self-acting compliant foil journal bearings. A test facility with a journal supported by a compliant foil journal bearing was built. The nonrotating journal was driven by two shakers which were used to simulate the dynamic forces acting on the bump foil strips. The structural stiffness and equivalent viscous damping coefficients are calculated based on the experimental measurements for a wide range of operating conditions. The results are compared to the analytical predictions obtained by a theoretical model developed earlier, and the effects of frequency are investigated. Both theoretical and experimental results show that an increase in the excitation frequency decreases the direct damping term. The effect of frequency on the cross-coupling terms is much less than on the direct terms.

1994 ◽  
Vol 116 (1) ◽  
pp. 76-82 ◽  
Author(s):  
Hooshang Heshmat ◽  
C.-P. Roger Ku

This paper describes an experimental investigation into the dynamic characteristics of corrugated foil (bump foil) strips used in compliant surface foil journal bearings and dampers. In the experimental method described herein, a test facility with a journal supported by a compliant foil journal bearing was built. The nonrotating journal was driven by two shakers which were used to simulate dynamic forces acting on bump foil strips. The dynamic structural stiffness and equivalent viscous damping coefficients are calculated based on the experimental measurements for a wide range of operating conditions. The results are compared to the analytical predictions obtained by a theoretical model developed earlier.


2004 ◽  
Vol 129 (1) ◽  
pp. 154-161 ◽  
Author(s):  
Mohsen Salehi ◽  
Hooshang Heshmat ◽  
James F. Walton

This paper presents the results of an experimental investigation into the dynamic structural stiffness and damping characteristics of a 21.6‐cm(8.5in.)-diameter compliant surface foil journal bearing. The goal of this development was to achieve high levels of damping without the use of oil, as is used in squeeze film dampers, while maintaining a nearly constant dynamic stiffness over a range of frequencies and amplitudes of motion. In the experimental work described herein, a full compliant foil bearing was designed, fabricated, and tested. The test facility included a non-rotating journal located inside the bearing. The journal was connected to an electrodynamic shaker so that dynamic forces simulating expected operating conditions could be applied to the structurally compliant bump foil elements. Excitation test frequencies to a maximum of 400Hz at amplitudes of motion between 25.4 and 102μm were applied to the damper assembly. During testing, both compressive preload and unidirectional static loads of up to 1335 and 445N, respectively, were applied to the damper assembly. The experimental data from these tests were analyzed using both a single degree of freedom model and an energy method. These methods of data analysis are reviewed here and results are compared. Excellent agreement in results obtained from the two methods was achieved. Equivalent viscous damping coefficients as high as 1050N.s∕cm(600lbf.s∕in) were obtained at low frequencies. Dynamic stiffness was shown to be fairly constant with frequency.


Author(s):  
Mohsen Salehi ◽  
Hooshang Heshmat ◽  
James F. Walton

This paper presents the results of an experimental investigation into the dynamic structural stiffness and damping characteristics of a 21.6 cm (8.5inch) diameter compliant surface foil journal bearing. The goal of this development was to achieve high levels of damping without the use of oil, as is used in squeeze film dampers, while maintaining a nearly constant dynamic stiffness over a range of frequencies and amplitudes of motion. In the experimental work described herein, a full compliant foil bearing was designed, fabricated and tested. The test facility included a non-rotating journal located inside the bearing. The journal was connected to an electrodynamic shaker so that dynamic forces simulating expected operating conditions could be applied to the structurally compliant bump foil elements. Excitation test frequencies to a maximum of 400 Hz at amplitudes of motion between 25.4μm to 102μm were applied to the damper assembly. During testing, both compressive preload and unidirectional static loads of up to 1335N and 445N, respectively, were applied to the damper assembly. The experimental data from these tests were analyzed using both a single degree of freedom model and an energy method. These methods of data analysis are reviewed here and results are compared. Excellent agreement in results obtained from the two methods was achieved. Equivalent viscous damping coefficients as high as 1050 N.s/cm (600 lbf.s/in) were obtained at low frequencies. Dynamic stiffness was shown to be fairly constant with frequency.


1994 ◽  
Vol 116 (3) ◽  
pp. 257-262 ◽  
Author(s):  
C. P. Roger Ku ◽  
H. Heshmat

This paper describes an experimental investigation into the structural dynamic characteristics of corrugated foil (bump foil) strips used in one type of compliant surface foil journal bearings and dampers. The nonrotating journal was supported by a compliant foil journal bearing and driven by two shakers which were used to simulate dynamic forces acting on the bump foil strips. The dynamic structural stiffness and equivalent viscous damping coefficients were calculated based on the experimental measurements for a wide range of operating conditions. The results were compared to the analytical predictions obtained by a theoretical model developed earlier, and the agreement is considered reasonably well. Both experimental and theoretical results show that the direct structural stiffness and damping coefficients increase with increasing bearing static load.


Author(s):  
Luis San Andrés ◽  
Thomas Abraham Chirathadam ◽  
Tae-Ho Kim

Engineered metal mesh foil bearings (MMFBs) are a promising low cost bearing technology for oil-free microturbomachinery. In a MMFB, a ring shaped metal mesh provides a soft elastic support to a smooth arcuate foil wrapped around a rotating shaft. This paper details the construction of a MMFB and the static and dynamic load tests conducted on the bearing for estimation of its structural stiffness and equivalent viscous damping. The 28.00 mm diameter 28.05 mm long bearing, with a metal mesh ring made of 0.3 mm copper wire and compactness of 20%, is installed on a test shaft with a slight preload. Static load versus bearing deflection measurements display a cubic nonlinearity with large hysteresis. The bearing deflection varies linearly during loading, but nonlinearly during the unloading process. An electromagnetic shaker applies on the test bearing loads of controlled amplitude over a frequency range. In the frequency domain, the ratio of applied force to bearing deflection gives the bearing mechanical impedance, whose real part and imaginary part give the structural stiffness and damping coefficients, respectively. As with prior art published in the literature, the bearing stiffness decreases significantly with the amplitude of motion and shows a gradual increasing trend with frequency. The bearing equivalent viscous damping is inversely proportional to the excitation frequency and motion amplitude. Hence, it is best to describe the mechanical energy dissipation characteristics of the MMFB with a structural loss factor (material damping). The experimental results show a loss factor as high as 0.7 though dependent on the amplitude of motion. Empirically based formulas, originally developed for metal mesh rings, predict bearing structural stiffness and damping coefficients that agree well with the experimentally estimated parameters. Note, however, that the metal mesh ring, after continuous operation and various dismantling and re-assembly processes, showed significant creep or sag that resulted in a gradual decrease in its structural force coefficients.


Author(s):  
Luis San Andre´s ◽  
Thomas Abraham Chirathadam ◽  
Tae-Ho Kim

Engineered Metal Mesh Foil Bearings (MMFB) are a promising low cost bearing technology for oil-free microturbomachinery. In a MMFB, a ring shaped metal mesh (MM) provides a soft elastic support to a smooth arcuate foil wrapped around a rotating shaft. The paper details the construction of a MMFB and the static and dynamic load tests conducted on the bearing for estimation of its structural stiffness and equivalent viscous damping. The 28.00 mm diameter, 28.05 mm long bearing, with a metal mesh ring made of 0.3 mm Copper wire and compactness of 20%, is installed on a test shaft with a slight preload. Static load versus bearing deflection measurements display a cubic nonlinearity with large hysteresis. The bearing deflection varies linearly during loading, but nonlinearly during the unloading process. An electromagnetic shaker applies on the test bearing loads of controlled amplitude over a frequency range. In the frequency domain, the ratio of applied force to bearing deflection gives the bearing mechanical impedance, whose real part and imaginary part give the structural stiffness and damping coefficients, respectively. As with prior art published in the literature, the bearing stiffness decreases significantly with the amplitude of motion and shows a gradual increasing trend with frequency. The bearing equivalent viscous damping is inversely proportional to the excitation frequency and motion amplitude. Hence, it is best to describe the mechanical energy dissipation characteristics of the MMFB with a structural loss factor (material damping). The experimental results show a loss factor as high as 0.7 though dependent on the amplitude of motion. Empirically based formulas, originally developed for metal mesh rings, predict bearing structural stiffness and damping coefficients agreeing well with the experimentally estimated parameters. Note, however, that the metal mesh ring, after continuous operation and various dismantling and reassembly processes, showed significant creep or sag that resulted in a gradual decrease of its structural force coefficients.


Author(s):  
Kai Feng ◽  
Xueyuan Zhao ◽  
Zhiyang Guo

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.


1997 ◽  
Vol 119 (1) ◽  
pp. 132-141 ◽  
Author(s):  
J. T. Sawicki ◽  
R. J. Capaldi ◽  
M. L. Adams

This paper describes an experimental and theoretical investigation of a four-pocket, oil-fed, orifice-compensated hydrostatic bearing including the hybrid effects of journal rotation. The test apparatus incorporates a double-spool-shaft spindle which permits independent control over the journal spin speed and the frequency of an adjustable-magnitude circular orbit, for both forward and backward whirling. This configuration yields data that enables determination of the full linear anisotropic rotordynamic model. The dynamic force measurements were made simultaneously with two independent systems, one with piezoelectric load cells and the other with strain gage load cells. Theoretical predictions are made for the same configuration and operating conditions as the test matrix using a finite-difference solver of Reynolds lubrication equation. The computational results agree well with test results, theoretical predictions of stiffness and damping coefficients are typically within thirty percent of the experimental results.


2017 ◽  
Vol 140 (2) ◽  
Author(s):  
Christopher G. Cooley ◽  
Tan Chai

This study investigates the vibration of and power harvested by typical electromagnetic and piezoelectric vibration energy harvesters when applied to vibrating host systems that rotate at constant speed. The governing equations for these electromechanically coupled devices are derived using Newtonian mechanics and Kirchhoff's voltage law. The natural frequency for these devices is speed-dependent due to the centripetal acceleration from their constant rotation. Resonance diagrams are used to identify excitation frequencies and speeds where these energy harvesters have large amplitude vibration and power harvested. Closed-form solutions are derived for the steady-state response and power harvested. These devices have multifrequency dynamic response due to the combined vibration and rotation of the host system. Multiple resonances are possible. The average power harvested over one oscillation cycle is calculated for a wide range of operating conditions. Electromagnetic devices have a local maximum in average harvested power that occurs near a specific excitation frequency and rotation speed. Piezoelectric devices, depending on their mechanical damping, can have two local maxima of average power harvested. Although these maxima are sensitive to small changes in the excitation frequency, they are much less sensitive to small changes in rotation speed.


Author(s):  
Jason C. Wilkes ◽  
Dara W. Childs

For several years, researchers have presented predictions showing that using a full tilting-pad journal bearing (TPJB) model (retaining all of the pad degrees of freedom) is necessary to accurately perform stability calculations for a shaft operating on TPJBs. This paper will discuss this issue, discuss the importance of pad and pivot flexibility in predicting impedance coefficients for the tilting-pad journal bearing, present measured changes in bearing clearance with operating temperature, and summarize the differences between measured and predicted frequency dependence of dynamic impedance coefficients. The current work presents recent test data for a 100 mm (4 in) five-pad TPJB tested in load on pad (LOP) configuration. Measured results include bearing clearance as a function of operating temperature, pad clearance and radial displacement of the loaded pad (the pad having the static load vector directed through its pivot), and frequency dependent stiffness and damping. Measured hot bearing clearances are approximately 30% smaller than measured cold bearing clearances and are inversely proportional to pad surface temperature; predicting bearing impedances with a rigid pad and pivot model using these reduced clearances results in overpredicted stiffness and damping coefficients that are several times larger than previous comparisons. The effect of employing a full bearing model versus a reduced bearing model (where only journal degrees of freedom are retained) in a stability calculation for a realistic rotor-bearing system is assessed. For the bearing tested, the bearing coefficients reduced at the frequency of the unstable eigenvalue (subsynchronously reduced) predicted a destabilizing cross-coupled stiffness coefficient at the onset of instability within 1% of the full model, while synchronously reduced coefficients for the lightly loaded bearing required 25% more destabilizing cross-coupled stiffness than the full model to cause system instability. The same stability calculation was performed using measured stiffness and damping coefficients at synchronous and subsynchronous frequencies. These predictions showed that both the synchronously measured stiffness and damping and predictions using the full bearing model were more conservative than the model using subsynchronously measured stiffness and damping, an outcome that is completely opposite from conclusions reached by comparing different prediction models. This contrasting outcome results from a predicted increase in damping with increasing excitation frequency at all speeds and loads; however, this increase in damping with increasing excitation frequency was only measured at the most heavily loaded conditions.


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