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1n Given: FS = 2,s yp = 340 MPa s e = 220 MPa
n Section at shoulder may be deduced to be critical.
n Moment at section at shoulder is:
M = (P/2) x 0.18 = 45/2 x 0.18 = 4.05 kNm
n Take q = 1, Kf = Kt = 1.34
Solution to Tutorial Q1:
( ) 223132
TMKFSd
fyp
e
yp += ss
sp
n Part (a):
n From Soderberg equation: T = 0. Therefore,
MKFS
MKFSd
fe
fe
yp
yp ss
s
sp
== )(32
31
n Since T = 0,
-
22
3331
220
101005.434.1232
mmN
Nmmd =
p
n Giving d1 = 79.15 mm
d2 = 1.5d1 = 118.73 mm
r = 0.25d1 = 19.79 mm
( ) 223132
TMKFSd
fyp
e
yp += ss
sp
n Part (b):
n P = 45 kN and T = 6.8 kNm
n From Soderberg equation:
( ) 23323322034031 )10108.6(101005.434.1
3402
32+=
dp
-
3n Giving d1 = 86.48 mm
d2 = 1.5d1 = 129.72 mm
r = 0.25d1 = 21.62 mm
n Check at section directly under load P:
n M = (P/2) x 0.38 = 45/2 x 0.38 = 8.55 kNm
( ) 23323322034032 )10108.6(101055.81
3402
32+=
dp
n Giving d2 = 96.20 mm (which is smaller than 129.72 mm
calculated earlier for the shoulder section).
n Hence, section directly under load P is not critical.
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4n From what are given:
Solution to Tutorial Q2:
n Consider lower bearing:
Radial load = 1.83 kN
Axial load = 900 N (assume all axial load taken by lower bearing
since axial load here is lower)
n Number of rev. in 9000 hrs
= 9000 x 300 x 60 = 162x106 rev
n Hence, L = 162.
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5For ball bearing:
From L = (C/P)p = (C/P)3
(C/P) = (162)1/3 = 5.45
Assume Fa = 0, and P = Fr = 1.83 kN
C = 5.45 x 1.83 = 9.97 kN
Nearest bearing = 6206 with C = 14.9, C0 = 10.0 and diameter of
bore = 30mm (which is > shaft diameter of 24mm)
Since Fa/Fr > e, cannot neglect axial load
29.0090.00.10
9.0 === eCF
o
a 492.083.19.0 ==
r
a
FF
X = 0.56, Y = 1.5
P = 0.56Fr + 1.5Fa= 0.56x1.83 + 1.5x0.9 = 2.375 kN
Hence, C = 5.45x2.375 = 12.94 kN
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6Note that this 12.94 kN is < C for 6206 of 14.90 kN, hence,
selection of 6206 is OK !
n Consider upper bearing:
n L = 162, C/P = 5.45, Fa = 0.
Hence P = Fr = 3.67 kN,
giving C = 5.45 x 3.67 = 19.98 kN
n From catalogue, select bearing 6306, with C = 21.4 kN and and
diameter of bore = 30mm (which is > shaft diameter of 24mm)
n Summary:
Upper bearing = 6306 (d = 30mm)
Lower bearing = 6206 (d = 30mm
Shaft diameter = 24mm (given)
