Timothy A. Philpot - Mechanics of materials _ an integrated learning system-John Wiley (2017)

m6.17 A motor shaft is being designed to transmit 40 kW
of power at 900 rpm. If the shearing stress in the shaft must
be limited to 75 MPa, determine
(a) the minimum diameter required for a solid shaft.
(b) the minimum outside diameter required for a hollow
shaft if the inside diameter of the shaft is assumed to be
80 percent of its outside diameter.
(2) is a solid 1.50 in. diameter shaft. Both shafts are made of
steel [G = 12,000 ksi]. The bearings shown permit free rotation
of the shafts. Determine
(a) the maximum shear stress produced in each shaft.
(b) the rotation angle of gear D with respect to flange A.
m6.18 The motor shown supplies 15 hp at 1,800 rpm at
flange A. Shaft (1) is a solid 0.75 in. diameter shaft, and shaft
′
ExAmpLE 6.7
Two solid 25 mm diameter steel shafts are connected by the gears
shown. A motor supplies 20 kW at 15 Hz to the system at A. The
bearings shown permit free rotation of the shafts. Determine
(a) the torque available at gear D.
(b) the maximum shear stress magnitudes in each shaft.
Plan the Solution
The torque in shaft (1) can be calculated from the power transmission
equation. The torque in shaft (2) can then be determined
from the gear ratio. Once the torques are known, the
maximum shear stress magnitudes will be determined from the
elastic torsion formula.
SOLUTION
The torque in shaft (1) can be calculated from the power transmission equation. The
power supplied by the motor is 20 kW, so
⎛ 1, 000 W ⎞
P = (20 kW) 20,000 W 20,000 Nm ⋅
⎝
⎜
1kW ⎠
⎟ = =
s
The motor rotates at 15 Hz. This rotation speed must be converted to units of rad/s:
15 rev 2π
rad
ω = 15 Hz = ⎛ 94.24778 rad
⎝ ⎜ ⎞
s ⎠
⎟ ⎛ ⎝ ⎜ ⎞
1rev ⎠
⎟ =
s
The torque in shaft (1) is therefore
T
1
P 20,000 N⋅m/s
= =
= 212.2066 Nm ⋅
ω 94.24778 rad/s
The torque in shaft (2) will be increased because gear C is larger than gear B. Use the
number of teeth on each gear to establish the gear ratio, and compute the magnitude of
the torque in shaft (2) as
⎛ 48 teeth⎞
T 2 = (212.2066 Nm) ⋅
339.5306 Nm
⎝
⎜
30 teeth⎠
⎟ = ⋅
A
(1)
48 teeth
C
30 teeth
B
(2)
T D
D
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