Timken Super Precision Bearings for Machine Tool Applications

A
ENGINEERING
ALTERNATE APPROACH FOR DETERMINING
DYNAMIC EQUIVALENT RADIAL LOADS
The following is a general approach to determining the dynamic
equivalent radial loads. Here, a factor “m” has to be defined as
+1 for direct-mounted single-row or two-row bearings, or -1 for
indirect mounted bearings. Also, a sign convention is necessary
for the external axial load F ae as follows:
• In case of external axial load applied to the shaft (typical
rotating cone application), F ae to the right is positive; to the left
is negative.
• When external axial load is applied to the housing (typical
rotating cup application), F ae to the right is negative; to the left
is positive.
Design Thrust condition Axial load
Dynamic equivalent
radial load
Indirect Mounting (m = -1)
Bearing A Bearing B
–F ae
+F ae
F rA
F rB
Direct Mounting (m = +1)
Bearing A
Bearing B
F rA
–F ae
+F ae
F rB
P A = 0.4 F rA + K A F aA
0.47 x F rA
≤ 0.47 x FrB - m F ae
F aA = 0.47 x F rB - m Fae
K B
K A K B F aB = 0.47 x F rA
+ m F ae P B = 0.4 F rB + K B F aB
K A K B
F aB = 0.47 x F rB
P B = F rB
K B
F aA = 0.47 x F rA
0.47 x F rA
> 0.47 x FrB - m F ae
K A
P A = F rA
K A
If P A < F rA, use P A = F rA or if P B < F rB, use P B = F rB.
Fig. 44. Dynamic equivalent radial load equations, single-row tapered roller bearing mounting.
Design
Thrust condition
Dynamic equivalent
radial load
Bearing A
F rAB
Bearing B
F ae ≤
0.6 x FrAB
K (1) P A =
K A
(F rAB - 1.67 m K B F ae)
K A + K B
Fixed Bearing
Indirect Mounting (m = -1)
–F ae
+F ae
P B =
K B
K A + K B
(F rAB + 1.67 m K A F ae)
F rAB
Bearing A
Bearing B
F ae >
0.6 x FrAB
K (1)
P A = 0.4 F rAB - m K A F ae
P B = 0.4 F rAB + m K B F ae
–F ae
+Fae
Fixed Bearing
Direct Mounting (m = +1)
(1) If "m F ae" is positive, K = K A; If "m F ae" is negative, K = K B.
F rAB is the radial load on the two-row assembly. The single-row basic dynamic radial load rating, C 90, is to be applied when calculating
life based on the above equations.
Fig. 45. Dynamic equivalent radial load equations, two-row tapered roller bearing mounting – fixed bearing with external axial load,
F ae (similar or dissimilar series).
46 TIMKEN MACHINE TOOL CATALOG