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Turbulence in a tilting-pad thrust bearing
NOTES FROM THE FRANKLIN INSTITUTE LABORATORIES FOR RESEARCH AND DEVELOPMENT NICOL H . SMITH, DIRECTOR
TURBULENCE IN A TILTING-PAD THRUST BEARING BY
STANLEY ABRAMOVITZ
During experiments with a tilting-pad thrust bearing (see Fig . 1) using water as a lubricant, we found that friction torque increased abnormally when the rubbing speed exceeded what appeared to be a critical
U RUNNER
/////////////////i/////////
FIG. 1. value . To examine this in further detail, tests were conducted over a range of water temperatures (i5 to 200° F .) and bearing velocities (25 to 100 fps .) . With the torque values obtained, a plot of coefficient of friction versus µ U/PB was made ; its deviation from the classic, straight-line, log-plotted relationship was clear . It was interesting to find that when the plotted values were grouped by constant temperatures, the result appeared to be a family of curves with fluid temperature (viscosity) as the parameter. Upon reviewing the literature it was found that G . I . Taylor (I, z), had investigated fluid stability in the annulus between two concentric rotating cylinders . In applying Taylor's analysis for a film of constant thickness to a tilting-pad thrust bearing, the following relationship was derived from Newton's law of viscous flow :
l Ul \KU'p/ H
)
where Hp is horsepower absorbed ; h= minimum film thickness, in . ; U=velocity at mean diameter, ips . ; K2 is a constant ; p=mass density, lb-sec 2/in? ; v=kinematic viscosity, in 2/sec . This is an abstract from a paper that was presented at the Annual ASME/ASLE Lubrication Conference in Baltimore, Md . on October 18, 1954 . It is being published by the ASME in complete form . 61
62
FRANKLIN INSTITUTE LABORATORIES NOTES
[J . F. I .
Since this is the equation for an equilateral hyperbola, a log-log plot of the two {dimensionless} terms in parentheses would yield a straight line whose slope is ---45 Some error is introduced, in using this relationship for a tiltingpad bearing . For instance, the film thickness in a tilting-pad bearing is certainly not constant ; variations in filmm thickness occur due to changes in speed and viscosity, and also due to pad inclination . Other points to consider are surface configuration and interrupted flow between pad segments, which do not allow strict comparison to Taylor's work with concentric cylinders . Nevertheless, using Taylor's criterion, we obtained some interesting and perhaps significant conclusions,
FIG. Z . The test machine used for this research was designed and built by The Franklin Institute (Fig . 2) . Using this machine, thrust bearings can be tested over wide ranges of load, speed, and fluid temperature . To obtain an accurate measure of the fluid shear between runner and pads, a rather ingenious method was derived using a hydrostatically supported disk in combination with an elastic arm and a differential transformer, The shear force and fluid temperature and pressure were continuously recorded . The dimensionless values of the equation are plotted in Fig . 3 . The experimental points follow the theoretical curve for laminar flow until a critical value of Reynolds number is reached . Above this value the horsepower increases and shows what appears to be a transition region a then the curve approaches a horizontal asymptote .
]an .,
FRANKLIN INSTITUTE LABORATORIES NOTES
Ig55 .1
6
The general shape of the experimental curve is similar to the curves obtained by Nikuradse (3) from his investigation of the variation of the resistance coefficient with Reynolds number for artifically roughened pipes . Nikuradse's system of curves is dependent on a pipe roughness parameter . If a correlation can be made between the Nikuradse experiments and ours, the effect of roughness would define the final shape and magnitude of the Taylor plot above the critical value for film instability . Figure 3 shows that the region in which film instability occurs is between Reynolds numbers 5$o and 800 . This can be compared with ~ .5
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,
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REYNOLDS
s NUMBER,
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values obtained by D . I . Fuller ; in his experiments with a journal
bearing using liquid freon 11 as a lubricant ; based on the rubbing velocity at which the torque started to increase abnormally, the calculated Reynolds number was about 970 . In conclusion, this investigation has shown an abnormal increase in pourer above a critical Reynolds number, and has indicated the presence of film instability in a tilting-pad thrust bearing . Actually, further research on this subject is needed . For this particular experiment a more variable speed range would yield a family of curves with film thickness as the parameter . It would be interesting to use different pad and runner materials (glass for example ) , and a fluid lubricant 1 Professor of Mechanical Engineering, Columbia University ; and Chief, Friction and Lubrication Section, Franklin Institute Laboratories .
FRANKLIN INSTITUTE LABORATORIES NOTES
64
[J • F. I .
other than water but of comparable viscosity ; this would be a means of exploring the effects of adhesion, if any . Lastly, the effect of surface roughness should be investigated . REFERENCES (1) G . I . TAYLOR, "Stability of a Viscous Liquid Contained Between Two Rotating Cylinders,"
Trans. Roy. .S'oc. London, England, Series A, Vol . 223, p . 289 (1923) . (2) G . I . TAYLOR,
"Fluid Friction Between Rotating Cylinders," .Pros . Roy. Soc . London,
England, Series A, Vol . 157, p. 546 (1936) . (3) .Forschungsheft, Vol . 4, p. 361 (1933) . See Also D . F . VILCOCK, "{ Turbulence in High Speed Journal Bearings," pp . 825--834 (1950) .
`raps . ASME, VoL 72,
TURBULENCE IN A TILTING-PAD THRUST BEARING BY
STANLEY ABRAMOVITZ
During experiments with a tilting-pad thrust bearing (see Fig . 1) using water as a lubricant, we found that friction torque increased abnormally when the rubbing speed exceeded what appeared to be a critical
U RUNNER
/////////////////i/////////
FIG. 1. value . To examine this in further detail, tests were conducted over a range of water temperatures (i5 to 200° F .) and bearing velocities (25 to 100 fps .) . With the torque values obtained, a plot of coefficient of friction versus µ U/PB was made ; its deviation from the classic, straight-line, log-plotted relationship was clear . It was interesting to find that when the plotted values were grouped by constant temperatures, the result appeared to be a family of curves with fluid temperature (viscosity) as the parameter. Upon reviewing the literature it was found that G . I . Taylor (I, z), had investigated fluid stability in the annulus between two concentric rotating cylinders . In applying Taylor's analysis for a film of constant thickness to a tilting-pad thrust bearing, the following relationship was derived from Newton's law of viscous flow :
l Ul \KU'p/ H
)
where Hp is horsepower absorbed ; h= minimum film thickness, in . ; U=velocity at mean diameter, ips . ; K2 is a constant ; p=mass density, lb-sec 2/in? ; v=kinematic viscosity, in 2/sec . This is an abstract from a paper that was presented at the Annual ASME/ASLE Lubrication Conference in Baltimore, Md . on October 18, 1954 . It is being published by the ASME in complete form . 61
62
FRANKLIN INSTITUTE LABORATORIES NOTES
[J . F. I .
Since this is the equation for an equilateral hyperbola, a log-log plot of the two {dimensionless} terms in parentheses would yield a straight line whose slope is ---45 Some error is introduced, in using this relationship for a tiltingpad bearing . For instance, the film thickness in a tilting-pad bearing is certainly not constant ; variations in filmm thickness occur due to changes in speed and viscosity, and also due to pad inclination . Other points to consider are surface configuration and interrupted flow between pad segments, which do not allow strict comparison to Taylor's work with concentric cylinders . Nevertheless, using Taylor's criterion, we obtained some interesting and perhaps significant conclusions,
FIG. Z . The test machine used for this research was designed and built by The Franklin Institute (Fig . 2) . Using this machine, thrust bearings can be tested over wide ranges of load, speed, and fluid temperature . To obtain an accurate measure of the fluid shear between runner and pads, a rather ingenious method was derived using a hydrostatically supported disk in combination with an elastic arm and a differential transformer, The shear force and fluid temperature and pressure were continuously recorded . The dimensionless values of the equation are plotted in Fig . 3 . The experimental points follow the theoretical curve for laminar flow until a critical value of Reynolds number is reached . Above this value the horsepower increases and shows what appears to be a transition region a then the curve approaches a horizontal asymptote .
]an .,
FRANKLIN INSTITUTE LABORATORIES NOTES
Ig55 .1
6
The general shape of the experimental curve is similar to the curves obtained by Nikuradse (3) from his investigation of the variation of the resistance coefficient with Reynolds number for artifically roughened pipes . Nikuradse's system of curves is dependent on a pipe roughness parameter . If a correlation can be made between the Nikuradse experiments and ours, the effect of roughness would define the final shape and magnitude of the Taylor plot above the critical value for film instability . Figure 3 shows that the region in which film instability occurs is between Reynolds numbers 5$o and 800 . This can be compared with ~ .5
M
IQ 3
a N
w
O V 2
.∎∎Ii• Ui!
fl ;aJ f_:l ~
__
∎
4 3
l
,
Z 0
`...
f-~-~--I
2
.
oo-
f'
∎
y f { I
._---
! .5
I-
i
U
I
8
B
1 .5
ti
T 2
~
-
3
4
REYNOLDS
s NUMBER,
2
u
3
,
Frc= . 3 .
values obtained by D . I . Fuller ; in his experiments with a journal
bearing using liquid freon 11 as a lubricant ; based on the rubbing velocity at which the torque started to increase abnormally, the calculated Reynolds number was about 970 . In conclusion, this investigation has shown an abnormal increase in pourer above a critical Reynolds number, and has indicated the presence of film instability in a tilting-pad thrust bearing . Actually, further research on this subject is needed . For this particular experiment a more variable speed range would yield a family of curves with film thickness as the parameter . It would be interesting to use different pad and runner materials (glass for example ) , and a fluid lubricant 1 Professor of Mechanical Engineering, Columbia University ; and Chief, Friction and Lubrication Section, Franklin Institute Laboratories .
FRANKLIN INSTITUTE LABORATORIES NOTES
64
[J • F. I .
other than water but of comparable viscosity ; this would be a means of exploring the effects of adhesion, if any . Lastly, the effect of surface roughness should be investigated . REFERENCES (1) G . I . TAYLOR, "Stability of a Viscous Liquid Contained Between Two Rotating Cylinders,"
Trans. Roy. .S'oc. London, England, Series A, Vol . 223, p . 289 (1923) . (2) G . I . TAYLOR,
"Fluid Friction Between Rotating Cylinders," .Pros . Roy. Soc . London,
England, Series A, Vol . 157, p. 546 (1936) . (3) .Forschungsheft, Vol . 4, p. 361 (1933) . See Also D . F . VILCOCK, "{ Turbulence in High Speed Journal Bearings," pp . 825--834 (1950) .
`raps . ASME, VoL 72,