Timken Super Precision Bearings for Machine Tool Applications

ENGINEERING
A
FrA
Bearing A
Fae
Bearing A
FrA
Design Thrust condition Axial load
Bearing B
Fae
Bearing B
FrB
Design (external axial load, F ae,
onto bearing A)
FrB
F aA = 0.47 F
P OB = F rB
rB
+ F
0.47 F rA 0.47 F ae
rB
≤
+ F ae
K B
K A K B
F aB = 0.47 F rB
K B
F aA = 0.47 F rA
0.47 F rA 0.47 F rB K
>
+ F A
ae
K A K B F aB = 0.47 F rA
K A
- Fae
Static equivalent
radial load
for F aA < 0.6 F rA / K A
P OA = 1.6 F rA - 1.269 K A F aA
for F aA < 0.6 F rA / K A
P OA = 0.5 F rA + 0.564 K A F aA
for F aB < 0.6 F rB / K B
P OB = 0.5 F rB + 0.564 K B F aB
for F aB < 0.6 F rB / K B
P OB = 1.6 F rB - 1.269 K B F aB
P OA = F rA
Use the values of P O calculated for comparison with the static rating (C O), even if P O is less than the radial applied F r.
Where:
F r = applied radial load
F a = net bearing axial load. F aA and F aB calculated from equations
Fig. 43. Static equivalent load equations, single-row tapered roller bearing.
Static Equivalent Radial Load (Two-Row Bearings)
The bearing data tables do not include static rating for two-row
bearings. The two-row static radial rating can be estimated as:
Where:
C o(2) = 2C o
C o(2) = two-row static radial rating
C o = static radial load rating of a single-row bearing,
type TS, from the same series.
Dynamic Equivalent Radial Bearing Loads (P r )
To calculate the L 10 life, it is necessary to calculate a dynamic
equivalent radial load, designated by P r. The dynamic equivalent
radial load is defined as a single radial load that, if applied to the
bearing, will result in the same life as the combined loading under
which the bearing operates.
P r = XF r + YF a
Where:
P r = dynamic equivalent radial load
F r = applied radial load
F a = applied axial load
X = radial load factor
Y = axial load factor
Tapered roller bearings use the equations based on the number of
rows and type of mounting utilized. For single-row bearings in direct
or indirect mounting, the figure on page 46 can be used based on the
direction of the externally applied axial load. Once the appropriate
design is chosen, review the table and check the thrust condition
to determine which axial load and dynamic equivalent radial load
calculations apply.
For ball bearings, the dynamic equivalent radial load can be found
in the table below.
Bearing
description
(ref.)
Bearing type
and or series
MM9300K
MM9100K
MM200K
MM300K
2MMV9300WI
2MM9300WI
2MMV9100WI
2MM99100WI
2MV9100WI
2MMV200WI
2MM200WI
2MV300WI
Contact
angle
Single-row
and tandem mountings
Double-row
and preload pair
mountings
K T =
F a
K T = Fa
(# of bearings) x C o C o
Radial type ball bearings – use larger of resulting “P r” value (1)
0° P r = F r or
P r = 0.56F r + Y 1F a
Angular contact ball bearings – use larger of resulting “P r” value
2MMV9300HX
2MV9300WI
2MMV9100HX
2MM9100WI
2MV200WI
2MMV300WI
2MM300WI
15°
P r = F r
or
P r = 0.44F r +Y 2F a
2MM9100WO 15° P r = F r
or
P r = 0.44F r + Y 3F a
3MMV9300WI
3MM9300WI
3MMV9100WI
3MM9100WI
3MM99100WI
3MMV200WI
3MM200WI
3MV300WI
3MMV9300HX
3MV9300WI
3MMV9100HX
3MV9100WI
3MV200WI
3MM300WI
3MV300WI
25° P r = F r
or
P r = 0.41F r +0.87F a
P r = F r + 1.20Y 1F a or
P r = 0.78F r + 1.625Y 1F a
P r = F r + 1.124Y 2F a
or
P r = 0.72F r + 1.625Y 2F a
P r = F r + 1.124Y 3F a
or
P r = 0.72F r + 1.625Y 3F a
P r = F r + 0.92F a
or
P r = 0.67F r + 1.41F a
(1) If Pr > Co or Pr > 1/2 Ce consult with your Timken representative on Life Calculations.
Table 7. Dynamic equivalent load equations.
44 TIMKEN MACHINE TOOL CATALOG