Calculation and Measurement of the Stiffness and Damping Coefficients for a Low Impedance Hydrodynamic Bearing

1997 ◽  
Vol 119 (1) ◽  
pp. 57-63 ◽  
Author(s):  
M. J. Goodwin ◽  
P. J. Ogrodnik ◽  
M. P. Roach ◽  
Y. Fang
Keyword(s):  
Experimental Data ◽  
Dynamic Stiffness ◽  
Perturbation Technique ◽  
The Novel ◽  
Oil Film ◽  
Hydrodynamic Bearing ◽  
Damping Coefficients ◽  
Stiffness And Damping ◽  
Film Stiffness ◽  
Novel Design

This paper describes a combined theoretical and experimental investigation of the eight oil film stiffness and damping coefficients for a novel low impedance hydrodynamic bearing. The novel design incorporates a recess in the bearing surface which is connected to a standard commercial gas bag accumulator; this arrangement reduces the oil film dynamic stiffness and leads to improved machine response and stability. A finite difference method was used to solve Reynolds equation and yield the pressure distribution in the bearing oil film. Integration of the pressure profile then enabled the fluid film forces to be evaluated. A perturbation technique was used to determine the dynamic pressure components, and hence to determine the eight oil film stiffness and damping coefficients. Experimental data was obtained from a laboratory test rig in which a test bearing, floating on a rotating shaft, was excited by a multi-frequency force signal. Measurements of the resulting relative movement between bearing and journal enabled the oil film coefficients to be measured. The results of the work show good agreement between theoretical and experimental data, and indicate that the oil film impedance of the novel design is considerably lower than that of a conventional bearing.

The Surface Roughness Effect on the Dynamic Stiffness and Damping Characteristics of the Hydrostatic Thrust Spherical Bearings: Part 5 of 5 — Clearance Type of Bearings

2007 ◽  
Author(s):  
Ahmad W. Yacout
Keyword(s):  
Surface Roughness ◽  
Capillary Tube ◽  
Dynamic Stiffness ◽  
Dynamic Performance ◽  
Major Effect ◽  
Design Parameters ◽  
Compressibility Effect ◽  
Damping Coefficients ◽  
Stiffness And Damping ◽  
Fluid Compressibility

This study has theoretically analyzed the surface roughness, centripetal inertia and recess volume fluid compressibility effects on the dynamic behavior of a restrictor compensated hydrostatic thrust spherical clearance type of bearing. The stochastic Reynolds equation, with centripetal inertia effect, and the recess flow continuity equation with recess volume fluid compressibility effect have been derived to take into account the presence of roughness on the bearing surfaces. On the basis of a small perturbations method, the dynamic stiffness and damping coefficients have been evaluated. In addition to the usual bearing design parameters the results for the dynamic stiffness and damping coefficients have been calculated for various frequencies of vibrations or squeeze parameter (frequency parameter) and recess volume fluid compressibility parameter. The study shows that both of the surface roughness and the centripetal inertia have slight effects on the stiffness coefficient and remarkable effects on the damping coefficient while the recess volume fluid compressibility parameter has the major effect on the bearing dynamic characteristics. The cross dynamic stiffness showed the bearing self-aligning property and the ability to oppose whirl movements. The orifice restrictor showed better dynamic performance than that of the capillary tube.

scholarly journals Study on dynamic characteristics of gas films of spherical spiral groove hybrid gas bearings

2019 ◽  
Vol 233 (8) ◽  
pp. 1169-1181
Author(s):  
Chenhui Jia ◽  
Haijiang Zhang ◽  
Shijun Guo ◽  
Ming Qiu ◽  
Wensuo Ma ◽  
...  
Keyword(s):  
Pressure Effect ◽  
Dynamic Pressure ◽  
Iteration Algorithm ◽  
Unstable State ◽  
Gas Bearings ◽  
Damping Coefficients ◽  
The Stability ◽  
Stiffness And Damping ◽  
Film Stiffness ◽  
Gas Bearing

According to the gas film force variation law, when the bearing axis is slightly displaced from the static equilibrium position, displacement and velocity disturbance relation expressions for the gas film force increment are constructed. Moreover, combined with the bearing rotor system motion equation, calculation model equations for the gas film stiffness and damping coefficients are established. The axial and radial vibration and velocity of the gas bearings during operation are collected. The instantaneous stiffness and damping coefficients of the gas film are calculated by the rolling iteration algorithm using MATLAB. The dynamic changes in the gas film stiffness and damping under different motion states are analyzed, and the mechanism of the gas film vortex and oscillation is studied. The results demonstrate the following: (1) When the gas bearing is running in the linear steady state in cycle 1, the dynamic pressure effect is enhanced and the stability is improved by increasing the eccentricity; when the gas supply pressure is increased, the static pressure effect is enhanced and the gas film vortex is reduced, but the oscillation is strengthened. (2) With the increase in rotational speed, the gas film vortex force gradually exceeds the gas film damping force, and the stability gradually worsens, causing a fluctuation in the gas film stiffness and damping, following which singularity occurs and a half-speed vortex is formed. Meanwhile, the gas film oscillation is intensified, and the rotor enters the nonlinear stable cycle 2 state operation. (3) As the fluctuation of the film force increases, the instantaneous stiffness and damping oscillation of the film intensifies, most of the stiffness and damping coefficients exhibit distortion, and the rotor operation will enter a chaotic or unstable state. Therefore, the gas bearing stiffness and damping variation characteristics can be used to study and predict the gas bearing operating state. Finally, measures for reducing the vortex and oscillation of the gas film and improving the stability of the gas bearing operation are proposed.

Development of an Efficient Oil Film Damper for Improving the Control of Rotor Vibration

1991 ◽  
Vol 113 (4) ◽  
pp. 557-562 ◽  
Author(s):  
Shiping Zhang ◽  
Litang Yan
Keyword(s):  
High Speed ◽  
Porous Metal ◽  
Porous Matrix ◽  
Squeeze Film ◽  
Oil Film ◽  
Squeeze Film Damper ◽  
Outer Race ◽  
Typical Experiment ◽  
Stiffness And Damping ◽  
Film Stiffness

An efficient oil film damper known as a porous squeeze film damper (PSFD) was developed for more effective and reliable vibration control of high-speed rotors based on the conventional squeeze film damper (SFD). The outer race of the PSFD is made of permeable sintered porous metal materials. The permeability allows some of the oil to permeate into and seep out of the porous matrix, with remarkable improvement of the squeeze film damping properties. The characteristics of PSFD oil film stiffness and damping coefficients and permeability, and also, the steady-state unbalance response of a simple rigid rotor and flexible Jeffcott’s rotor supported on PSFD and SFD are investigated. A typical experiment is presented. Investigations show that the nonlinear vibration characteristics of the unpressurized SFD system such as bistable jump phenomena and “lockup” at rotor pin-pin critical speeds could be avoided and virtually disappear under much greater unbalance levels with properly designed PSFD system. PSFD has the potential advantage of operating effectively under relatively large unbalance conditions.

Simple Method for Dynamic Interaction between Two Rigid Foundations

2011 ◽  
Vol 250-253 ◽  
pp. 2225-2228
Author(s):  
Bin Yan ◽  
Ying Hui Lv ◽  
Ping Hu
Keyword(s):  
Dynamic Stiffness ◽  
Dynamic Interaction ◽  
Foundation Soil ◽  
Simple Method ◽  
Damping Coefficients ◽  
The Past ◽  
Calculating Method ◽  
Interaction Factors ◽  
Two Parameters ◽  
Stiffness And Damping

In the past many researchers studied dynamic stiffness and damping coefficients of surface and embedded rigid foundations of arbitrary shapes in the elastic homogenous half space. Dynamic stiffness and damping coefficients were obtained by using regularly shaped foundations instead of arbitrarily shaped ones. Obviously, the calculating methods were not perfect. In addition, the two parameters mentioned above were calculated only in the case of a single foundation. But the cases of two or more foundations were not presented because the interactions between foundations were not considered in all present papers. This paper eliminates two faults named above by using the assumption of the plane strain and of dynamic foundation-soil interaction factors. The calculating method of dynamic impedances presented by the paper proved to be accurate and practical.

scholarly journals A valid method of gas foil bearing parameter estimation: A model anchored on experimental data

2016 ◽  
Vol 232 (24) ◽  
pp. 4510-4527 ◽  
Author(s):  
Robert Hoffmann ◽  
Oliver Munz ◽  
Tomasz Pronobis ◽  
Enrico Barth ◽  
Robert Liebich
Keyword(s):  
Experimental Data ◽  
Dynamic Stiffness ◽  
Linear Structure ◽  
Order Equation ◽  
Design Stage ◽  
Frictional Contacts ◽  
Foil Bearing ◽  
Non Linear ◽  
Stiffness And Damping ◽  
The Impact

Gas foil bearings are a smart green technology and suitable for the next generation of small turbo machinery e.g. turbochargers, micro gas turbines, range extenders and compressors of fuel cells. A combination of low power loss, high speed operation and the omission of an oil system are the major advantages. To enable access to this technology, it is essential to evaluate critical speeds and onset speeds of subharmonic vibration of the rotor system in the first design stage. Hence, robust and valid models are necessary, which correctly describe the fluid structure interaction between the lubrication film and the elastic bearing structure. In the past three decades several experimental and numerical investigations of bearing parameters have been published. But the number of sophisticated models is small and there is still a lack of validation towards experimental works. To make it easy for designers dealing with this issue, the bearing parameters are often linearised about certain operating points. In this paper a method for calculating linearised bearing parameters (stiffness and damping) of gas foil bearing is presented. Experimental data are used for validation of the model. The linearised stiffness and damping values are calculated using a perturbation method. The pressure field is coupled with a two-dimensional plate model, while the non-linear bump structure is simplified by a link-spring model. It includes Coulomb friction effects inside the elastic corrugated structure and captures the interaction between the single bumps. For solving the separated perturbed Reynolds equation a static stiffness is used for the 0. order equation (stationary case) and a dynamic stiffness is applied for 1. order equation (dynamic case). Therefore, an additional dynamic structural model is applied to calculate the dynamic stiffness. The results depend on the load level and friction state of each bump. Different case studies including the impact of clearance, frictional contacts and the comparison of a linear and non-linear structure are carried out for infinitesimal perturbations. The results show, that the linear structure underestimates main and cross-coupling effects. The impact of the clearance is notable, while the impact of the overall frictional contacts is small due to relatively small loadings. The infinitely small perturbation model is adapted to the experimental setup by using a superposition of two resulting bearing parameters identifications of two total loadings including shaker forces. Due to this adaptation a good correlation with the experimental results of the bearing parameters is achieved.

Technical Note: Rolling dynamic stiffness and damping characteristics of small-sized pneumatic tyres

2000 ◽  
Vol 214 (3) ◽  
pp. 243-248 ◽  
Author(s):  
V. H. Saran ◽  
V. K. Goel
Keyword(s):  
Normal Load ◽  
Dynamic Stiffness ◽  
Technical Note ◽  
Inflation Pressure ◽  
Laboratory Technique ◽  
Damping Coefficients ◽  
Damping Characteristics ◽  
Stiffness And Damping

In this paper, a laboratory technique for determination of rolling dynamic stiffness and damping coefficients of small-sized, bias-ply tyres has been discussed. The effect of normal load, inflation pressure and speed on four different tyres has been reported. The results show similar trends to those reported by other investigators.

An Experimental Study of Nonlinear Oil-Film Forces in a Tilting-Pad Journal Bearing

2015 ◽  
Author(s):  
Phuoc Vinh Dang ◽  
Steven Chatterton ◽  
Paolo Pennacchi ◽  
Andrea Vania ◽  
Filippo Cangioli
Keyword(s):  
High Speed ◽  
Nonlinear Models ◽  
Reaction Force ◽  
Taylor Series Expansion ◽  
Test Model ◽  
Oil Film ◽  
Hydrodynamic Bearing ◽  
Dynamic Coefficients ◽  
Stiffness And Damping ◽  
Tilting Pad Journal Bearing

Journal bearings have been widely used in high-speed rotating machinery. The dynamic coefficients of oil-film force affect the machine unbalance response and machine stability. The oil-film force of hydrodynamic bearing is often characterized by a set of linear stiffness and damping coefficients. However the linear oil-film coefficients with respect to an equilibrium position of the journal are inaccurate when the bearing system vibrates with large amplitudes due to a dynamic load. The study on nonlinear oil-film forces is still rare and most papers are confined to theoretical analyses. The purpose of this paper is to derive some new non-linear force models (28-co., 24-co. and 36-co. models) to identify these dynamic coefficients based on experimental data. The fundamental test model is obtained from a Taylor series expansion of bearing reaction force. Tests were performed with a nominal diameter of 100mm and a length–to–diameter ratio of 0.7 using a suitable test rig in which it is possible to apply the static load in any direction. The results show that these three models are feasible to identify the oil-film forces in which the second-order oil-film coefficients received from the 24-co. model are more stable compared to those of other two nonlinear models.

Behavior of Tilting–Pad Journal Bearings With Large Machining Error on Pads

2016 ◽  
Author(s):  
Phuoc Vinh Dang ◽  
Steven Chatterton ◽  
Paolo Pennacchi ◽  
Andrea Vania ◽  
Filippo Cangioli
Keyword(s):  
Static Load ◽  
Dynamic Stiffness ◽  
Maximum Pressure ◽  
Load Direction ◽  
Machining Error ◽  
Damping Coefficients ◽  
Machining Errors ◽  
Tilting Pad ◽  
Stiffness And Damping ◽  
Tilting Pad Journal Bearings

The use of tilting pad journal bearings (TPJBs) has increased in recent years due to their stabilizing effects on the rotor bearing system. Most of the studies addressing steady state and dynamic behaviors of TPJBs have been evaluated by means of thermo-hydrodynamic (THD) models, assuming nominal dimensions for the bearing, (i.e., the physical dimensions of all pads are identical and loads applied along the vertical direction). However machining errors could lead to actual bearing geometry and dimensions different from the nominal ones. In particular, for TPJB the asymmetry of the bearing geometry has not been well-investigated and can lead to an unexpected behavior of the bearing. The asymmetry of the bearing geometry can arise from large machining errors on only one or more pads, as a consequence of a pivot failure or after bad-mounting of the pads during assembly. These conditions can sometimes be detected by high values of the pad temperature, as measured by the temperature probes installed on the bearing pads, or by the abnormal vibration caused by pad-flutter phenomena. In this paper the authors investigate large machining errors on the pad thickness for a five-pad TPJB and analyze their effects on the bearing operating characteristics. Pad thickness errors correspond to a different preload factor or clearance for each pad. A sensitivity analysis was performed for several combinations of pad thickness using a THD model and the behavior of the bearing was analyzed, including dynamic stiffness and damping coefficients, clearance profile, shaft locus, minimum oil-film thickness, power loss, flow rate, and maximum pressure. The experimental case of a five pads TPJB with an intentional large machining error on the thickness of the pads is also described in the paper. The bearing has a nominal diameter of 100 mm, a diameter to length ratio (L/D) equal to 0.7 and can run at up to 3000 rpm. The experimental measurements are compared with the results obtained from the analytical model. The results show that the effects of asymmetry of the bearing geometry are more evident if the direction of the static load applied on the rotor bearing system, which is different from the vertical load, is also considered. For instance, the shape of shaft locus obtained by experimental tests changing the static load direction at a constant speed is an irregular pentagon if it is compared to the case of the nominal bearing. Based on our findings, we concludes that the machining error on the pads has a large influence on the shaft locus, minimum oil-film thickness and maximum pressure on pads, especially at high rotational speed, but has little effect on the flow rate and power loss. In addition, this error significantly affects the dynamic stiffness and damping coefficients, both in terms of rotational speed and load direction.

scholarly journals Modeling of Flexible Rotor Machines Supported With Hydrostatic Bearings

1993 ◽  
Author(s):  
R. N. Headifen ◽  
W. F. Weldon
Keyword(s):  
Dynamic Stiffness ◽  
Iteration Scheme ◽  
Flexible Rotor ◽  
Fem Model ◽  
Damping Coefficients ◽  
Rotating Machine ◽  
Hydrostatic Bearings ◽  
Newton Raphson ◽  
Stiffness And Damping ◽  
Raphson Iteration

In this paper a method is described that takes the nonlinear dynamic stiffness and damping coefficients for multiple hydrostatic bearings and incorporates them into a rotordynamic FEM model for a rotating machine. A Newton-Raphson iteration scheme is presented that uses updated bearing coefficients at every iteration to the solution. A non-linear computer program was written using the method described which models transient and synchronous response and calculates damped eigenvalues.

Sign in / Sign up

Export Citation Format

Share Document