Timken Super Precision Bearings for Machine Tool Applications

A
ENGINEERING
BEARING REACTIONS
Calculation equations
Symbols used
a e Effective bearing spread mm, in.
A, B, ... Bearing position, used as subscripts
c 1, c 2, ... Linear distance (positive or negative) mm, in.
D pG Pitch diameter of the gear mm, in.
F Applied force N, lbf
F r Radial bearing load N, lbf
h
Horizontal (used as subscript)
M Moment N-mm, lbf-in.
v
Vertical (used as subscript)
1
Gear mesh angle relative to plane
of reference defined in the figure below
deg, rad
2
3
1
2
3
Plane of
Reference
F aG
Angle of applied force relative to plane
of reference defined in the figure below
Angle of applied moment relative to plane
of reference defined in the figure below
F sG
F sG
F tG F
F aG F tG
F
Plane of Moment
Bearing A
Fig. 42. Bearing radial reactions.
F rA h
F rA v
c 1
c 2
a e
M
deg, rad
deg, rad
Bearing B
F rB h
F rB v
Centrifugal force
Centrifugal force resulting from imbalance in a rotating member:
F c =
=
Shock loads
F w r n 2
8.94 x 10 5
F w r n 2
3.52 x 10 4
(newtons)
(pounds-force)
It is difficult to determine the exact effect that shock loading has
on bearing life. The magnitude of the shock load depends on the
masses of the colliding bodies, their velocities, and deformations
at impact.
The effect on the bearing depends on how much of the shock is
absorbed between the point of impact and the bearings, as well as
whether the shock load is great enough to cause bearing damage.
It also is dependent on frequency and duration of shock loads.
At a minimum, a suddenly applied load is equivalent to twice its
static value. It may be considerably more than this, depending on
the velocity of impact.
Shock involves a number of variables that generally are not known
or easily determined. Therefore, it is good practice to rely on
experience. The Timken Company has years of experience with
many types of equipment under the most severe loading conditions.
Your Timken representative should be consulted on any application
involving unusual loading or service requirements.
Vertical reaction component at bearing position B:
F rB v = 1 c 1 (F sG cos 1 + F tG sin 1) + 1 (DpG - b sin G) F aG cos 1 +c 2 F cos 2 + M cos 3
a e 2
(
Horizontal reaction component at bearing position B:
F rB h = 1 c 1 (F sG sin 1 - F tG cos 1) + 1 (DpG - b sin G) F aG sin 1 +c 2 F sin 2 + M sin 3
a e 2
(
Vertical reaction component at bearing position A:
F rAv = F sG cos 1 + F tG sin 1 + F cos 2 - F rBv
Horizontal reaction component at bearing position A:
F rA h = F sG sin 1 - F tG cos 1 + F sin 2 - F rB h
Resultant radial reaction: F rA = [(F rA v) 2 + (F rA h) 2 ] 1/2 F rB = [(F rB v) 2 + (F rB h) 2 ] 1/2
Resultant axial reaction: F aA = F aG (fixed position) F aB = O (float position)
(
(
42 TIMKEN MACHINE TOOL CATALOG