Page 369 - Analysis and Design of Machine Elements

12.3.3 Heat Balance Analysis Sliding Bearings 347
The viscosity of lubricant is a crucial parameter for the performance of sliding bearing.
In the previous analysis, the viscosity is assumed to be constant as the lubricant flows
through the bearing. However, oil temperature is actually higher when the lubricant
leaves the loading zone than it was on entry [1], and the viscosity drops off significantly
with the rise of temperature. It is thus important to estimate oil film temperature at
equilibrium operating conditions so as to use proper viscosity at operating temperature
in the analysis.
Under equilibrium operating conditions, the rate at which heat is generated by friction
must be equal to the rate at which heat is removed from the bearing so as to prevent
continued temperature rise to an unsatisfactory level. The removed heat includes the
heat takenawaybylubricant flowand theheatdissipatedfromthe exposedmetal surface
area of bearing housing to the ambient environment. Therefore

H = H + H 2 (12.25)
1
H –heat generated by friction per second, or frictional power rate, calculated by
H = fFv
H 1 –heat removed by lubricant flow per second H = cQ (t −t )
i
o
1
H 2 –heat dissipated from the bearing housing per second H = dB(t −t )
i
o
2
s
Therefore, we have
fFv = cQ (t − t )+ dB(t − t )
0 i s 0 i
Then
fFv f
fFv vBd p
Δt = t − t = = = (12.26)
o
i
d
Qc + dB Q c + s dB 2c C + s
s
vBd vBd B Q v
where
3 −1
Q –volumetric flow rate of lubricant, m s ;
−3
–lubricant density, for mineral oils = 850∼900 kg m ;
∘
−1
c –specific heat of lubricant, for mineral oils c = 1675∼2090 J (kg C) ;
∘
t o –outlet oil temperature, C;
∘
t i –inlet oil temperature, t = 35∼45 C;
i
s –heat transfer coefficient. It depends on many factors, such as bearing
material, surface geometry, the temperature difference between the
housing and surrounding, and ventilation. For light loaded bearings, or
2 ∘ −1
high ambient temperature, select = 50 W (m C) ; for medium-sized
s
bearings and general ventilation, select = 80 W (m 2 ∘ C) −1 and for heavy
s
bearings and good ventilation, select = 140 W (m 2 ∘ C) −1 [5].
s
Q
C = –coefficient of oil flow. Table 12.3 lists the values of C for various values
Q d 3 Q
of eccentricity radio and width to diameter ratio B/d when pressure
∘
generates within 180 arc between the journal and liner.
f
C = –coefficient of friction variable. Table 12.4 lists the value of C for various
f f
values of eccentricity radio and width to diameter ratio B/d when
∘
pressure generates within 180 arc between the journal and liner.