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.

Calculation of Stiffness and Damping Properties of Gas Bearings

1968 ◽  
Vol 90 (4) ◽  
pp. 793-803 ◽  
Author(s):  
J. W. Lund
Keyword(s):  
Static Load ◽  
Journal Bearing ◽  
Computational Method ◽  
Gas Bearings ◽  
Rotating Speed ◽  
Damping Coefficients ◽  
Tilting Pad ◽  
Stiffness And Damping ◽  
Tilting Pad Journal Bearing ◽  
Gas Bearing

The dynamic characteristics of a gas bearing can be represented by a set of spring and damping coefficients (impedances) which are functions of the static load on the bearing, the rotating speed and the whirl frequency of the journal. For a rotor supported in gas bearings, these coefficients can be used directly in a critical speed calculation or an unbalance response calculation. In addition, the coefficients can be employed in a stability investigation. The paper gives the computational method for obtaining the spring and damping coefficients and, also, describes how they are used in rotor calculations and stability studies. Numerical results are given in graphical and tabular form for a tilting pad journal bearing and a three-lobe journal bearing.

Measurements Versus Predictions for Rotordynamic Characteristics of a Flexure Pivot-Pad Tilting Pad Bearing in an LBP Condition at Higher Unit Loads

2008 ◽  
Author(s):  
J. Eric Hensley ◽  
Dara Childs
Keyword(s):  
Static Load ◽  
Dynamic Stiffness ◽  
Random Excitation ◽  
Test Rig ◽  
Load Direction ◽  
Rotordynamic Coefficients ◽  
Tilting Pad ◽  
Mass Coefficient ◽  
Static Performance ◽  
Added Mass Coefficient

Dynamic and static performance data are presented for a 117 mm diameter flexure-pivot tilting pad bearing in a load-between-pad configuration for speeds between 6000 and 12000 rpm and unit loads between 1–2.2 MPa. The present work is a continuation of 2005 tests on the same bearing by Al-Ghasem and Childs with unit loads at 0–1 Mpa. The rotordynamic coefficients are measured via a test rig that uses hydraulic shakers to excite the bearing stator. A psuedo-random excitation method is used to measure the complex direct and cross-coupled dynamic stiffness coefficients over a frequency range. The real and imaginary parts of coefficients are curve fitted to produce a constant-coefficient [K][C][M] bearing model. For the static load direction y, the direct added-mass coefficient Myy was needed to model the bearing’ “frequency dependence”. The direct unloaded mass coefficients Mxx was generally near zero. The analytical model generally predicted the correct trends for the change in rotordynamic coefficients with increasing loads but did not predict the measured orthotropy between results in the loaded and unloaded directions.

Numerical Analysis on Dynamic Coefficients of Self-Acting Gas-Lubricated Tilting-Pad Journal Bearings

2007 ◽  
Vol 130 (1) ◽  
Author(s):  
Yang Lihua ◽  
Qi Shemiao ◽  
Yu Lie
Keyword(s):  
Dynamic Stiffness ◽  
Cross Coupling ◽  
Damping Coefficients ◽  
Dynamic Coefficients ◽  
Stiffness Coefficients ◽  
Tilting Pad ◽  
Coupling Stiffness ◽  
Perturbation Frequency ◽  
Stiffness And Damping ◽  
Gas Bearing

Although gas-lubricated tilting-pad bearings are widely used in high-speed turbomachinery, the theoretical prediction of the dynamic characteristics of tilting-pad gas bearings is also a very difficult problem because of its structural complexity. Several approaches have been proposed to solve this problem such as the pad assembly method and the small perturbation method. A numerical method by combining the partial derivative method with the equivalent coefficient method is presented in this paper to evaluate the dynamic stiffness and damping coefficients of self-acting tilting-pad gas bearing. The dynamic coefficients with the pads fixed and with the pads perturbation are, respectively, obtained for a typical self-acting tilting-pad gas bearing by using the proposed method to mainly explain the dependency of the bearing dynamic coefficients on the perturbation frequency. For bearings with the pads perturbation, the cross-coupling stiffness and damping coefficients are almost negligible compared with the direct ones. At lower perturbation frequency, the stiffness coefficients increase, while the damping coefficients decrease with an increasing frequency. The higher perturbation frequencies have very little effects on the bearing dynamic coefficients. Dynamic stiffness coefficients approach to the constant and damping coefficients to zero. However, with the pads fixed, in a low range of frequency, the absolute values of cross-coupling stiffness coefficients decrease with frequency. Furthermore, the cross-coupling coefficients are not negligible compared with the direct ones. In addition, the effects of pad inertia on dynamic coefficients are studied and compared with the results of pad inertia neglected.

Dynamic Analysis of Tilting-Pad Journal Bearing—Influence of Pad Deformations

1994 ◽  
Vol 116 (3) ◽  
pp. 621-627 ◽  
Author(s):  
H. Desbordes ◽  
M. Fillon ◽  
C. Chan Hew Wai ◽  
J. Frene
Keyword(s):  
Film Thickness ◽  
Pressure Field ◽  
Journal Bearing ◽  
Maximum Pressure ◽  
Tilting Pad ◽  
Minimum Film Thickness ◽  
Dimensional Finite Element ◽  
The One ◽  
Tilting Pad Journal Bearing ◽  
Tilting Pad Journal Bearings

A theoretical nonlinear analysis of tilting-pad journal bearings is presented for small and large unbalance loads under isothermal conditions. The radial displacements of internal pad surface due to pressure field are determined by a two-dimensional finite element method in order to define the actual film thickness. The influence of pad deformations on the journal orbit, on the minimum film thickness and on the maximum pressure is studied. The effects of pad displacements are to decrease the minimum film thickness and to increase the maximum pressure. The orbit amplitude is also increased by 20 percent for the large unbalance load compared to the one obtained for rigid pad.

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.

Measured Static and Rotordynamic Coefficient Results for a Rocker-Pivot, Tilting-Pad Bearing With 50 and 60% Offsets

2012 ◽  
Vol 134 (5) ◽  
Author(s):  
Chris D. Kulhanek ◽  
Dara W. Childs
Keyword(s):  
Dynamic Stiffness ◽  
Mass Matrix ◽  
Excitation Frequency ◽  
Quadratic Function ◽  
Added Mass ◽  
Damping Coefficients ◽  
Stiffness Coefficients ◽  
Tilting Pad ◽  
Frequency Independent ◽  
Direct Stiffness

Static and rotordynamic coefficients are measured for a rocker-pivot, tilting-pad journal bearing (TPJB) with 50 and 60% offset pads in a load-between-pad (LBP) configuration. The bearing uses leading-edge-groove direct lubrication and has the following characteristics: 5-pads, 101.6 mm (4.0 in) nominal diameter,0.0814 -0.0837 mm (0.0032–0.0033 in) radial bearing clearance, 0.25 to 0.27 preload, and 60.325 mm (2.375 in) axial pad length. Tests were performed on a floating bearing test rig with unit loads from 0 to 3101 kPa (450 psi) and speeds from 7 to 16 krpm. Dynamic tests were conducted over a range of frequencies (20 to 320 Hz) to obtain complex dynamic stiffness coefficients as functions of excitation frequency. For most test conditions, the real dynamic stiffness functions were well fitted with a quadratic function with respect to frequency. This curve fit allowed for the stiffness frequency dependency to be captured by including an added mass matrix [M] to a conventional [K][C] model, yielding a frequency independent [K][C][M] model. The imaginary dynamic stiffness coefficients increased linearly with frequency, producing frequency-independent direct damping coefficients. Direct stiffness coefficients were larger for the 60% offset bearing at light unit loads. At high loads, the 50% offset configuration had a larger stiffness in the loaded direction, while the unloaded direct stiffness was approximately the same for both pivot offsets. Cross-coupled stiffness coefficients were positive and significantly smaller than direct stiffness coefficients. Negative direct added-mass coefficients were obtained for both offsets, especially in the unloaded direction. Cross-coupled added-mass coefficients are generally positive and of the same sign. Direct damping coefficients were mostly independent of load and speed, showing no appreciable difference between pivot offsets. Cross-coupled damping coefficients had the same sign and were much smaller than direct coefficients. Measured static eccentricities suggested cross coupling stiffness exists for both pivot offsets, agreeing with dynamic measurements. Static stiffness measurements showed good agreement with the loaded, direct dynamic stiffness coefficients.

Tilting Pad Journal Bearings: A Discussion on Stability Calculation, Frequency Dependence, and Pad and Pivot Flexibility

2012 ◽  
Author(s):  
Jason C. Wilkes ◽  
Dara W. Childs
Keyword(s):  
Degrees Of Freedom ◽  
Journal Bearing ◽  
Operating Temperature ◽  
Excitation Frequency ◽  
Full Model ◽  
Stability Calculation ◽  
Damping Coefficients ◽  
Tilting Pad ◽  
Stiffness And Damping ◽  
Tilting Pad Journal Bearing

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.

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.

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