Vibration Analysis for a 12-DOF Full Car Model with Hydraulic Engine Mounts of Frequency Dependent Stiffness and Damping

This paper presents measured frequency dependent stiffness and damping coefficients for 12-bladed and 8-bladed pocket damper seals (PDS) subdivided into four different seal configurations. Rotating experimental tests are presented for inlet pressures at 69 bar (1000 psi), a frequency excitation range of 20–300 Hz, and rotor speeds up to 20,200 rpm. The testing method used to determine direct and cross-coupled force coefficients was the mechanical impedance method, which required the measurement of external shaker forces, system accelerations, and motion in two orthogonal directions. In addition to the impedance measurements, dynamic pressure responses were measured for individual seal cavities of the eight-bladed PDS. Results of the frequency dependent force coefficients for the four PDS designs are compared. The conclusions of the tests show that the eight-bladed PDS possessed significantly more positive direct damping and negative direct stiffness than the 12-bladed seal. The results from the dynamic pressure response tests show that the diverging clearance design strongly influences the dynamic pressure phase and force density of the seal cavities. The tests also revealed the measurement of same-sign cross-coupled (cross-axis) stiffness coefficients for all seals, which indicate that the seals do not produce a destabilizing influence on rotor-bearing systems.

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Rotordynamic Force Coefficients of Pocket Damper Seals

Volume 5: Marine; Microturbines and Small Turbomachinery; Oil and Gas Applications; Structures and Dynamics, Parts A and B ◽

10.1115/gt2006-91058 ◽

2006 ◽

Cited By ~ 3

Author(s):

B. Ertas ◽

A. Gamal ◽

J. Vance

Keyword(s):

Dynamic Pressure ◽

Mechanical Impedance ◽

Impedance Method ◽

Force Density ◽

Frequency Dependent ◽

Force Coefficients ◽

Direct Stiffness ◽

Cross Axis ◽

Positive Direct ◽

Stiffness And Damping

This paper presents measured frequency dependent stiffness and damping coefficients for 12 and 8 bladed pocket damper seals (PDS) subdivided into 4 different seal configurations. Rotating experimental test are presented for inlet pressures at 69 bar (1,000 psi), a frequency excitation range of 20–300 Hz, and rotor speeds up to 20,200 rpm. The testing method used to determine direct and cross-coupled force coefficients was the mechanical impedance method, which required the measurement of external shaker forces, system accelerations, and motion in two orthogonal directions. In addition to the impedance measurements, dynamic pressure responses were measured for individual seal cavities of the 8 bladed PDS. Results of the frequency dependent force coefficients for the 4 PDS designs are compared. The conclusions of the test show that the 8 bladed PDS possessed significantly more positive direct damping and negative direct stiffness than the 12 bladed seal. The results from the dynamic pressure response tests show that the diverging clearance design strongly influences the dynamic pressure phase and force density of the seal cavities. The tests also revealed the measurement of same-sign cross-coupled (cross-axis) stiffness coefficients for all seals, which indicate that the seals do not produce a de-stabilizing influence on rotor-bearing systems.

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Vibration analysis of a half-car model with semi-active damping

Journal of Theoretical and Applied Mechanics ◽

10.15632/jtam-pl.54.2.321 ◽

2016 ◽

pp. 321 ◽

Cited By ~ 4

Author(s):

Urszula Ferdek ◽

Jan Łuczko

Keyword(s):

Vibration Analysis ◽

Active Damping ◽

Car Model

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Energy harvesting from car suspension system: Mathematical approach for half car model

JOURNAL OF MECHANICAL ENGINEERING AND SCIENCES ◽

10.15282/jmes.15.1.2021.07.0607 ◽

2021 ◽

Vol 15 (1) ◽

pp. 7695-7714

Author(s):

Tariq Darabseh ◽

Doaa Al-Yafeai ◽

Abdel-Hamid Ismail Mourad

Keyword(s):

Significant Contribution ◽

Excitation Frequency ◽

Harmonic Excitation ◽

Suspension System ◽

Ride Quality ◽

Car Model ◽

Car Suspension ◽

In Series ◽

Piezoelectric Stacks ◽

Stiffness And Damping

A significant contribution of this paper is developing a half car model with a built-in piezoelectric stack to evaluate the potential of harvesting power from the car suspension system. The regenerative car suspension system is modelled mathematically using Laplace transformation and simulated using MATLAB/Simulink. Two piezoelectric stacks are installed in series with the front and rear suspension springs to maintain the performance of the original suspension system in ride quality and comfortability. Half car model is subjected under harmonic excitation with acceleration of 0.5 g and velocity of 9.17 rad/s. The harvested voltage and power are tested in both time, and frequency domain approaches. The influence of the different parameters of the piezoelectric stack (number of stack layers and area to thickness) and car suspension (sprung and unsprung stiffness and damping coefficients) are examined. Also, the effect of road amplitude unevenness is considered. The results illustrate that the maximum generated voltage and power at the excitation frequency of 1.46 Hz are 33.51 V and 56.25 mW, respectively.

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Optimization of improved suspension system with inerter device of the quarter-car model in vibration analysis

Archive of Applied Mechanics ◽

10.1007/s00419-010-0492-x ◽

2010 ◽

Vol 81 (10) ◽

pp. 1427-1437 ◽

Cited By ~ 27

Author(s):

Alexey Kuznetsov ◽

Musa Mammadov ◽

Ibrahim Sultan ◽

Eldar Hajilarov

Keyword(s):

Vibration Analysis ◽

Suspension System ◽

Quarter Car Model ◽

Car Model ◽

Quarter Car

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Vibration Analysis of Statically Indeterminate Rotors With Hydrodynamic Bearings

Journal of Tribology ◽

10.1115/1.2833779 ◽

1998 ◽

Vol 120 (4) ◽

pp. 781-788 ◽

Cited By ~ 8

Author(s):

N. S. Feng ◽

E. J. Hahn

Keyword(s):

Vibration Analysis ◽

Operating Conditions ◽

System Stability ◽

Hydrodynamic Bearings ◽

Hydrodynamic Bearing ◽

Unbalance Response ◽

Tilting Pad ◽

The Stability ◽

Rotor Bearings ◽

Stiffness And Damping

In statically indeterminate rotor bearings systems, where the rotor is supported by one or more hydrodynamic bearings, the reactions at each hydrodynamic bearing, and hence its stiffness and damping properties depend not only on the bearing type, the operating conditions and the bearing dimensions but also on the relative lateral alignment between the journal and the bearing housing; the alignment, therefore, has a significant influence on the system stability and unbalance response. Additional complications arise if nonsymmetric bearing types such as elliptic or tilting pad bearings are present. An iterative procedure is outlined which enables the bearing reactions to be determined at any speed, thereby enabling even large systems such as turbomachinery to be rapidly analyzed in conjunction with existing linear rotor bearing vibration analysis software. Sample numerical examples show how misalignment and bearing type can affect the natural frequencies, the stability threshold, and the unbalance response of such statically indeterminate systems.

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Predictions for Non-Contacting Mechanical Face Seal Vibration With External Excitation From Pump Vibration: Part I — Flexibly Mounted Stator

Volume 7B: Structures and Dynamics ◽

10.1115/gt2018-77198 ◽

2018 ◽

Author(s):

Clay S. Norrbin ◽

Dara W. Childs

Keyword(s):

Excitation Frequency ◽

Mechanical Seal ◽

Seal Ring ◽

External Excitation ◽

Frequency Dependent ◽

Frequency Independent ◽

Mechanical Face Seal ◽

Stiffness And Damping ◽

Damping Model ◽

Independent Model

Stability and response predictions are presented for a Flexibly Mounted Stator (FMS) mechanical seal ring using the model developed by Childs in 2018. The seal ring is excited by external vibration from the rotor/housing. The model includes a frequency dependent stiffness and damping model for the O-ring and a frequency independent model for the fluid film. The dynamic coefficients depend on both speed and excitation frequency. Data used in defining the model are representative of a typical FMS mechanical seal. Parameters for radius and O-Ring placement are varied. The predictions show an insignificant dependency on speed. The predictions are strongly frequency dependent with a critical speed of 90 kRPM. The FMS is predicted to be stable to frequencies below 140 kRPM. The distance between the O-Ring and seal ring inertia center doz couples lateral and pitch-yaw motion of the seal ring. Overall, if doz is kept small, the seal ring is predicted to not have any stability or response issues.

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