Timken Super Precision Bearings for Machine Tool Applications

ENGINEERING
A
HEAT GENERATION AND DISSIPATION
TAPERED ROLLER BEARINGS
Heat Generation
Under normal operating conditions, most of the torque and heat
generated by the bearing is due to the elastohydrodynamic losses
at the contact area between rollers and races.
The following equation is used to calculate the heat generated by
the bearing:
Q gen = k 4n M
M = k 1G 1 (nμ) 0.62 (P eq) 0.3
Where:
Q gen = generated heat (W or Btu/min)
M = running torque N.m or lbf-in.
n = rotational speed (RPM)
G 1 = geometry factor from bearing data tables
μ = viscosity at operating temperature (cP)
P eq = dynamic equivalent load (N or lbf)
k 1 = bearing torque constant
= 2.56 x 10 -6 for M in N-m
Fig. 67. Determination of combined load factors f 1 and f 2.
= 3.54 x 10 -5 for M in lbf-in.
k 4 = dimensional factor to calculate heat generation rate
= 0.105 for Qgen in W when M in N-m
= 6.73 x 10 -4 for Qgen in Btu/min when M in lbf-in.
The generated heat will be underestimated if operating speed:
n
k 2
( f2 x ) Fr 0.66 RPM
G 2 x μ K
Where:
G 2 = geometry factor (from bearing data tables)
k 2 = 625 (metric) or 1700 (inch)
K = K factor of the bearing (from bearing data tables)
f 2 = combined load factor (Figure 67)
Design
(thrust f ae onto A)
Thrust condition Net axial load Dynamic equivalent
load P eq
Bearing A Bearing B
F aA = 0.47 x FrB + F
0.47 x F ae
rA 0.47 x F rB
≤
+ Fae
K B
K A K B
0.47 x FrB
F aB =
K B
P eq =
( f1 x )
Fr Fae
K
FrA
FrB
Bearing A
Bearing B
0.47 x FrA
F aA =
0.47 x F rA
>
0.47 x F rB + Fae
K A
K A
K B
F aB = 0.47 x FrA - F ae
Fae
K A
FrA
FrB
Combined Load Factors, f1 and f2
2.8
2.6
2.4
2.2
2.0
1.8
1.6
1.4
1.2
1.0
0.8
0.6
0.4
0.2
0
0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0
KF a /F r
f 2
f 1
if K x Fa
> 2.0
Fr
if K x Fa
= 0.47
Fr
f1 = K x Fa
Fr
{
f2 = f1 + 0.8
K x Fa
if 0.47 < < 2.0: Use graph
- Fr -
{
f1 = 0.06
f2 = 1.78
f 1 = combined load factor
(see Figure 67)
64 TIMKEN MACHINE TOOL CATALOG