Tutorial 7 - Design of a Journal Bearing

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Tutorial 7 - Design of a Journal Bearing
Goals Design a journal bearing. Calculate
important operating parameters of hydrodynamic
bearings.
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Problem Statement
Given A heated roll is used to evaporate water
from pulp in the production of paper. This roll
is mounted onto a two inch diameter shaft for
which a journal bearing needs to be designed.
The roller sees a total load of 1500 pounds,
which is distributed evenly between two identical
bearings. The roll speed is 2000 rev/min and SAE
10 oil is readily available (it is used
throughout the paper mill and is in abundant
supply). The oil inlet temperature is thought
to be around 110F. Because of clearance issues,
the bearing width must be one inch or
less. Find 1.) The radial clearance of the
bearing for optimum load carrying capacity. 2.)
The surface finish required on the bearing. 3.)
The temperature rise, friction coefficient,
flow rate and side flow rate of oil through the
bearing. (These are needed to prescribe heat
exchangers for the oil reservoir.) 4.)Comment on
the importance of the inlet temperature, that
is, what effect on the bearing performance would
occur if the inlet temperature were 130 F?
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Solution Outline

• Preliminary Calculations
• Determination of Bearing Characteristic Number
• Determination of required clearance
• Determination of bearing parameters and surface
  roughness
• Effect of inlet oil temperatures
• Concluding Remarks

Note The approach presented is only one of many
approaches which can be pursued. Although the
indicated steps are in a logical order, they are
not to be considered the essential order.
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Preliminary Calculations
Since the bearing width is restricted to one inch
or less, it will be taken as one inch. The
reason for this is that there is no advantage
from an operating standpoint to have a smaller
width, and if the bearing will be manufactured
through a grinding operation, the cost of
finishing a one inch wide surface on a large
roller is insignificantly larger than a 0.75 inch
bearing, for example. Therefore, the diameter
to width ratio for the bearing is
2
in
?
?
?
2
1
in

j
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Determine the bearing characteristic number and
the dimensionless film thickness
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Determination of Bearing Characteristic Number
The bearing characteristic number is Bj0.35. The
dimensionless film thickness parameter is
hmin/c0.42.
See the Next Slide for details of the analysis!
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Analysis Details
These values can be directly read from Figure
2.28, since it is known that the diameter to
width ratio is 2 and the bearing is to be
designed for maximum load carrying
capability From the chart, the bearing
number Bj is approximately 0.35 and the
dimensionless film thickness variable is hmin/c
is 0.42. The bearing number will be used to
obtain the clearance once the average viscosity
is calculated.
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Determine the dimensionless coefficient of
friction variable for the bearing.
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Dimensionless Coefficient of Friction Variable
The dimensionless coefficient of friction
variable is rbm/c9.5.
See the Next Slide for details of the analysis!
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Analysis Details
The coefficient of friction can be read from
Figure 12.30, since the bearing number is known
to be 0.35 The dimensionless
coefficient of friction variable can be seen to
be around 9.5.
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Determine the dimensionless volume flow rate for
the bearing.
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Dimensionless Volume Flow Rate
The dimensionless volume flow rate is Q5.1.
See the Next Slide for details of the analysis!
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Analysis Details
The dimensionless volume flow rate is obtained
from Figure 12.31 The dimensionless
volumetric flow is 5.1.
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Determine the side-leakage flow ratio.
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Side Leakage Flow Variable
The side leakage flow variable is qs/q0.73.
See the Next Slide for details of the analysis!
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Analysis Details
The side leakage flow variable can be obtained
from Figure 12.32 The value is qs/q0.73.
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Calculate the temperature rise in the lubricant
in the bearing and the average lubricant
viscosity.
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Temperature Rise and Lubricant Viscosity
The temperature rise is 113F. The average
lubricant viscosity in the bearing is µ1.16 x
10-6 lbf-s/in2.
See the Next Slide for details of the analysis!
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Analysis Details
The dimensionless load on the bearing
is Therefore the temperature rise can be
calculated from Equation (12.91b)
The average lubricant temperature is then 110F
113F/2166F 74C. The oil viscosity is from
Figure 8.13, µ00.008Ns/m2, or using the
conversion from Table 8.2, µ01.16 x 10-6
lbf-s/in2.
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Calculate the required radial clearance, the
minimum film thickness and the required shaft
surface roughness.
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Journal Information
The required radial clearance is 540 µin. The
minimum film thickness is 230 µin. The maximum
surface roughness is 23 µin.
See the Next Slide for details of the analysis!
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Analysis Details
The required radial clearance, now that the
viscosity is known, is obtained from the Bearing
number (Equation 12.85) The minimum film
thickness is obtained from the dimensionless film
thickness parameter previously determined To
maintain full film lubrication, the surface
finish should be at most one-tenth the film
thickness, or 23µin. Fortunately, this is
obtainable through standard grinding operations
(see Table 8.1).
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Calculate the friction coefficient of the journal
bearing.
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Friction Coefficient
The friction coefficient is 0.005.
See the Next Slide for details of the analysis!
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Analysis Details
The dimensionless friction coefficient has been
previously obtained as rbµ/c9.5. Since the
bearing radius is 1 in and the clearance is 540
µin, the coefficient of friction is simply 0.005.
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Comment on the importance of the inlet oil
temperature. Specifically, what effect would an
inlet temperature of 130F have on the bearing
performance?
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Inlet Temperature Importance
As can be seen from Figure 8.13, the effect of
increasing the oil temperature would be minimal
for such a small temperature rise. However, if
the viscosity were to fall significantly, then
the film thickness would be small enough to allow
the film to break down and have
surface-to-surface contact. This would lead to
quick failure of the bearing. Also, care must
be taken so that the lubricant does not become
excessively heated and degrade chemically.
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Concluding Remarks
The design of the bearing was relatively easy,
using the figures from the textbook.
Fortunately, this problem did not require
consideration of a number of different bearing
widths, which is normally the case in design.
Also, this problem resulted in clearances,
surface finishes and bearing dimensions which
were reasonable and easily obtained, so the
bearing design did not require successive
iterations.