Experimental Analysis of Dynamic Characteristics of a Hybrid Aerostatic Bearing

2011 ◽  
Author(s):  
Laurent Rudloff ◽  
Mihai Arghir ◽  
Olivier Bonneau ◽  
Sebastien Guingo ◽  
Guillaume Chemla ◽  
...  
Keyword(s):  
Dynamic Characteristics ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Experimental Information ◽  
Rigid Rotor ◽  
Aerostatic Bearing ◽  
Test Rig ◽  
Impulse Turbine ◽  
Dynamic Coefficients ◽  
The Impact

The dynamic characteristics of a hybrid aerostatic bearing are experimentally investigated on a test rig consisting of a rigid rotor driven by an impulse turbine located at its midlength. The rotor is horizontally mounted and is supported by two identical aerostatic bearings at its ends. Both the impulse turbine and the aerostatic hybrid bearings are fed with air. The actually available resources enable to attain feeding pressures up to 5 bar in the bearings and rotation speeds up to 60 krpm. Under these conditions the dynamic load on the rotor is much larger than the static load engendered by its weight. Dynamic loads consist either of impacts provided by a hammer or of added unbalance masses. The test rig can measure the bearing feeding pressures, the rotation speed, the impact force, the displacements of the two bearings and the bearing housing accelerations. This experimental information together with the equations of motion of the rotor enables the identification of the dynamic coefficients of the bearings. A second identification procedure using the same impact hammer is enabled by the fact force transducers are mounted between the bearing housing and its support. The dynamic coefficients of the bearings can then be obtained from the equation of motion of its housing. Unbalance response provide a convenient way for verifying the accuracy of the identified dynamic coefficients. Therefore these coefficients are injected in the equations of motion of a four degrees of freedom rigid rotor and the theoretical results are compared with values measured on the test rig. Comparisons show that predictions are acceptable but become less accurate at high rotation speeds where large dynamic forces are needed for exciting the corresponding synchronous frequencies.

Experimental Analysis of the Dynamic Characteristics of a Hybrid Aerostatic Bearing

2012 ◽  
Vol 134 (8) ◽  
Author(s):  
Laurent Rudloff ◽  
Mihai Arghir ◽  
Olivier Bonneau ◽  
Sébastien Guingo ◽  
Guillaume Chemla ◽  
...  
Keyword(s):  
Dynamic Characteristics ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Measuring Instruments ◽  
Rigid Rotor ◽  
Aerostatic Bearing ◽  
Test Rig ◽  
Impulse Turbine ◽  
Dynamic Coefficients ◽  
The Impact

The dynamic characteristics of a hybrid aerostatic bearing are experimentally investigated on a test rig consisting of a rigid rotor driven by an impulse turbine. The rotor is horizontally mounted and is supported by two identical aerostatic bearings. Both the impulse turbine and the aerostatic hybrid bearings are fed with air. The feeding pressures in the bearings can be as high as 7 bars and rotation speeds can reach 60 krpm so the dynamic load on the rotor is much larger than the static load engendered by its weight. Excitations are applied either via an impact hammer or via unbalancing masses. The measuring instruments record the bearing feeding pressures, the rotation speed, the impact force, the displacements of the two bearings, and the bearing housing accelerations. The experimental data together with the equations of motion of the rotor enables the identification of the dynamic coefficients of the bearings. A second identification procedure using the same impact hammer is also possible as force transducers are mounted between the bearing housing and its support. The dynamic coefficients of the bearings can then be obtained from the equation of motion of its housing. Unbalance response provide a convenient way for verifying the accuracy of the identified dynamic coefficients. Therefore these coefficients are injected in the equations of motion of a four degrees of freedom rigid rotor and the theoretical results are compared with values measured on the test rig. Comparisons show that predictions are acceptable but become less accurate at high rotation speeds where large dynamic forces are needed for exciting the corresponding synchronous frequencies.

The Rotor Dynamic Coefficients of Eccentric Mechanical Face Seals

1996 ◽  
Vol 118 (1) ◽  
pp. 215-224 ◽  
Author(s):  
J. Wileman ◽  
I. Green
Keyword(s):  
Degrees Of Freedom ◽  
Reynolds Equation ◽  
Equations Of Motion ◽  
Shear Stresses ◽  
Dynamic Coefficients ◽  
Angular Deflection ◽  
Face Seals ◽  
Radial Forces ◽  
Rotor Dynamic ◽  
Additional Coupling

The Reynolds equation is extended to include the effects of radial deflection in a seal with two flexibly mounted rotors. The resulting pressures are used to obtain the forces and moments introduced in the axial and angular modes by the inclusion of eccentricity in the analysis. The rotor dynamic coefficients relating the forces and moments in these modes to the axial and angular deflection are shown to be the same as those presented in the literature for the concentric case. Additional coefficients are obtained to express the dependence of these forces and moments upon the radial deflections and velocities. The axial force is shown to be decoupled from both the angular and radial modes, but the angular and radial modes are coupled to one another by the dependence of the tilting moments upon the radial deflections. The shear stresses acting upon the element faces are derived and used to obtain the radial forces acting upon the rotors. These forces are used to obtain rotor dynamic coefficients for the two radial degrees of freedom of each rotor. The additional rotor dynamic coefficients can be used to obtain the additional equations of motion necessary to include the radial degrees of freedom in the dynamic analysis. These coefficients introduce additional coupling between the angular and radial degrees of freedom, but the axial degrees of freedom remain decoupled.

Dynamic Characteristics of Spiral-Grooved Opposed-Hemisphere Gas Bearings

2016 ◽  
Vol 139 (3) ◽  
Author(s):  
Guangwei Yang ◽  
Jianjun Du ◽  
Weiping Ge ◽  
Tun Liu ◽  
Xiaowei Yang
Keyword(s):  
Dynamic Characteristics ◽  
Degrees Of Freedom ◽  
Dynamic Stiffness ◽  
Translational Motion ◽  
Coupling Coefficients ◽  
Dynamic Coefficients ◽  
Large Eccentricity ◽  
The Stability ◽  
Stiffness And Damping ◽  
Gas Bearing

The traditional eight-coefficient bearing model only considers the translational motion of the bearings and neglects the tilting motion and coupling effects between them. In this paper, the dynamic characteristics of the spiral-grooved opposed-hemisphere gas bearing considering five degrees-of-freedom are studied, and 50 dynamic coefficients including the translational, tilting, and coupling components are completely calculated. The Reynolds equations and their perturbed equations are solved by the finite element method to obtain the dynamic stiffness and damping coefficients. The effects of the tilting motion on the dynamic coefficients and response are analyzed, respectively. The results show that the coupling coefficients between the translational and tilting motions, which have been neglected in most previous studies, are significant at large eccentricity ratio. But these coupling coefficients have little effect on the dynamic response. On the other hand, the influences of the tilting motion on the synchronous response and natural frequency are remarkable and will decrease the stability of the rotor bearing system.

Experimental Analyses of a First Generation Foil Bearing: Start-Up Torque and Dynamic Coefficients

2010 ◽  
Author(s):  
Laurent Rudloff ◽  
Mihai Arghir ◽  
Olivier Bonneau ◽  
Pierre Matta
Keyword(s):  
Dynamic Characteristics ◽  
Static Load ◽  
Excitation Frequency ◽  
Base Plate ◽  
Test Rig ◽  
Dynamic Coefficients ◽  
Foil Bearing ◽  
Start Up ◽  
Lift Off ◽  
Stiffness And Damping

The paper presents the results of the experimental analysis of static and dynamic characteristics of a generation 1 foil bearing of 38.1 mm diameter and L/D = 1. The test rig is of floating bearing type, the rigid shaft being mounted on ceramic ball bearings and driven up to 40 krpm. Two different casings are used for start-up and for measurement of dynamic coefficients. In its first configuration, the test rig is designed to measure the start-up torque. The foil bearing casing is made of two rings separated by a needle bearing for enabling an almost torque free rotation between the foil bearing and the static load. The basic results are the start up torque and the lift off speed. In its second configuration a different casing is used for measuring the impedances of the foil bearing. Misalignment is a problem that is minimized by using three flexible stingers connecting the foil bearing casing to the base plate of the test rig. The test rig enables the application of a static load and of the dynamic excitation on the journal bearing casing, and can measure displacements, forces and accelerations. Working conditions consisted of static loads comprised between 10 N and 50 N and rotation frequencies ranging from 260 Hz to 590 HZ. Excitation frequencies comprised between 100 Hz are 600 Hz are applied by two orthogonally mounted shakers for each working condition. Stiffness and damping coefficients are identified from the complex impedances and enable the calculation of natural frequencies. The experimental results show that the dynamic characteristics of the tested bearing have a weak dependence on the rotation speed but vary with the excitation frequency.

Experimental Analyses of a First Generation Foil Bearing: Startup Torque and Dynamic Coefficients

2011 ◽  
Vol 133 (9) ◽  
Author(s):  
Laurent Rudloff ◽  
Mihai Arghir ◽  
Olivier Bonneau ◽  
Pierre Matta
Keyword(s):  
Dynamic Characteristics ◽  
First Generation ◽  
Static Load ◽  
Excitation Frequency ◽  
Base Plate ◽  
Test Rig ◽  
Dynamic Coefficients ◽  
Foil Bearing ◽  
Lift Off ◽  
Stiffness And Damping

This paper presents the results of the experimental analysis of static and dynamic characteristics of a generation 1 foil bearing of 38.1 mm diameter and L/D=1. The test rig is of floating bearing type, the rigid shaft being mounted on ceramic ball bearings and driven up to 40 krpm. Two different casings are used for startup and for measurement of dynamic coefficients. In its first configuration, the test rig is designed to measure the startup torque. The foil bearing casing is made of two rings separated by a needle bearing to enable an almost torque free rotation between the foil bearing and the static load. The basic results are the startup torque and the lift-off speed. In its second configuration, a different casing is used to measure the impedances of the foil bearing. Misalignment is a problem that is minimized by using three flexible stingers connecting the foil bearing casing to the base plate of the test rig. The test rig enables the application of a static load and of the dynamic excitation on the journal bearing casing and can measure displacements, forces, and accelerations. Working conditions consisted of static loads comprised between 10 N and 50 N and rotation frequencies ranging from 260 Hz to 590 Hz. Excitation frequencies comprised between 100 Hz and 600 Hz are applied by two orthogonally mounted shakers for each working condition. Stiffness and damping coefficients are identified from the complex impedances and enable the calculation of natural frequencies. The experimental results show that the dynamic characteristics of the tested bearing have a weak dependence on the rotation speed but vary with the excitation frequency.

Dynamic Characteristics of an In-Contact Headslider Considering Meniscus Force: Part 1—Formulation and Application to the Disk With Sinusoidal Undulation

1999 ◽  
Vol 122 (3) ◽  
pp. 633-638 ◽  
Author(s):  
Takahisa Kato ◽  
Souta Watanabe ◽  
Hiroshige Matsuoka
Keyword(s):  
Dynamic Characteristics ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Disk Surface ◽  
Disk Interface ◽  
Meniscus Force ◽  
Calculation Results ◽  
Three Degrees Of Freedom

The authors present a three-degrees-of-freedom (3-DOF) model of an in-contact headslider/disk interface (HDI) system by which the dynamic characteristics of the in-contact headslider-suspension assembly can be obtained. Four regimes with respect to the interface of headslider and disk surface are shown to take the meniscus force of lubricant on the disk surface into account. The equations of motion of the in-contact headslider considering the meniscus force at each regime and the calculation results for the disk with sinusoidal undulation are described. [S0742-4787(00)01802-6]

Dynamic Characteristics of Sealed Squeeze Film Damper With a Central Feeding Groove

2005 ◽  
Vol 127 (1) ◽  
pp. 103-111 ◽  
Author(s):  
Keun-Joo Kim ◽  
Chong-Won Lee
Keyword(s):  
Dynamic Characteristics ◽  
Pressure Field ◽  
Dynamic Pressure ◽  
Magnetic Bearing ◽  
Active Magnetic Bearing ◽  
Field Analysis ◽  
Squeeze Film ◽  
Test Rig ◽  
Squeeze Film Damper ◽  
Dynamic Coefficients

In this paper, the dynamic characteristics of an oil-lubricated, sealed squeeze film damper (SFD) with a central feeding groove are analytically derived based on an enhanced dynamic pressure field analysis, accounting for the effect of the seal and feeding grooves, and its validity is experimentally verified. A test rig using an active magnetic bearing system as an exciter is introduced to identify the dynamic characteristics of SFDs with high accuracy and efficiency. Experiments are conducted with the seal gap varied, in order to investigate its effect on the dynamic characteristics of the SFD. The estimated and analytical damping and inertia coefficients for the sealed SFD with a groove are compared and it is found that the pressure field analysis, when neglecting the effect of the seal groove, tends to far underestimate the SFD dynamic coefficients.

Dynamic Analysis of a Motorized Spindle With Externally Pressurized Air Bearings

2015 ◽  
Vol 137 (4) ◽  
Author(s):  
Chundong Xu ◽  
Shuyun Jiang
Keyword(s):  
Dynamic Characteristics ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Forced Response ◽  
Air Bearings ◽  
Motorized Spindle ◽  
Static And Dynamic Characteristics ◽  
Rotating Speed ◽  
Rotor Bearing ◽  
Bearing System

The purpose of this paper is to investigate the dynamic characteristics of a motorized spindle with externally pressurized air bearings. The externally pressurized air bearings consist of a journal bearing and a double pad thrust bearing with orifice restrictors. The equations of motion for the rotor-bearing system are established considering five degrees-of-freedom (DOF). The perturbation method and the finite difference method are introduced to calculate the static and dynamic characteristics of the air bearings; and the effects of the rotating speed and tilt angle of the rotor on the dynamic characteristics of the air bearings are analyzed. With the dynamic coefficients of the air bearings and the 5DOF rotor-dynamic model obtained, the stability, the unbalance response, and the forced response of the rotor-bearing system are investigated. Finally, the static and dynamic characteristics of the spindle are verified by an experimental study.

Influence of Frame Stiffness and Rider Position on Bike Dynamics: Analytical Study

2015 ◽  
Author(s):  
Trevor Williams ◽  
Sudhir Kaul ◽  
Anoop Dhingra
Keyword(s):  
Dynamic Characteristics ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Critical Role ◽  
Rear Wheel ◽  
Front Wheel ◽  
Rigid Bodies ◽  
Limited Attention ◽  
Structural Stiffness ◽  
Bicycle Frame

Dynamic characteristics of a bicycle such as handling and stability can be studied during the design phase to comprehend specific aspects associated with the overall layout as well as the frame architecture. Bicycles demonstrate unique properties such as static instability that is overcome by getting them into motion with a minimum velocity threshold. The structural stiffness of a frame plays a critical role in the handling behavior of a bike. However, the influence of structural stiffness has received limited attention in the existing literature. This paper attempts to fill the gap by presenting analytical results from a study that includes the influence of rider positions on three bicycle layouts. The analytical model consists of four rigid bodies: rear frame, front frame (front fork and handle bar assembly), front wheel and rear wheel. The overall model exhibits three degrees-of-freedom: the roll angle of the frame, the steering of the front frame, and the rotation of the rear wheel with respect to the frame. The rear frame is divided into two parts, the rider and the bicycle frame, that are assumed to be rigidly connected. This is done in order to allow the model to account for varying rider positions. The influence of frame flexibility is studied by coupling the structural stiffness of the frame to the governing equations of motion. Layouts from a benchmark bicycle, a commercially manufactured bicycle, and a cargo bicycle are used for this study in conjunction with rider positions ranging from a relaxed position to an extreme prone position. All the results are analyzed and compared with some proven analytical and experimental results in the existing literature. Results indicate that some of the rider positions can play a significant role in influencing the dynamic characteristics of the bike. Structural stiffness is seen to significantly affect the weave mode, only when the stiffness is reduced substantially.

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