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

pRoBLEmS
p6.18 The gear train system shown in Figure P6.18/19 includes
shafts (1) and (2), which are solid 15 mm diameter steel shafts. The
allowable shear stress of each shaft is 85 MPa. The diameter of gear
B is D B = 200 mm, and the diameter of gear C is D C = 150 mm. The
bearings shown allow the shafts to rotate freely. Determine the
maximum torque T D that can be applied to the system without exceeding
the allowable shear stress in either shaft.
are solid and made of steel [G = 11,500 ksi]. The shaft lengths are
L 1 = 15 ft and L 2 = 9 ft, respectively. If the angle of twist in each shaft
must not exceed 3.0°, calculate the minimum diameter required for
each shaft.
A
FIGURE p6.18/19
p6.19 The gear train system shown in Figure P6.18/19 includes
shafts (1) and (2), which are solid 0.75 in. diameter steel shafts. The
diameter of gear B is D B = 8 in., and the diameter of gear C is D C =
5 in. The bearings shown allow the shafts to rotate freely. An external
torque T D = 45 lb ⋅ ft is applied at gear D. Determine the maximum
shear stress produced in shafts (1) and (2).
p6.20 In the system shown in Figure P6.20, the motor applies a
torque T A = 40 N ⋅ m to the pulley at A. Through a sequence of pulleys
and belts, this torque is amplified to drive a gear at E. The
pulleys have diameters D A = 50 mm, D B = 150 mm, D C = 50 mm,
and D D = 250 mm.
(a) Calculate the torque T E that is produced at gear E.
(b) Shaft (2) is to be a solid shaft, and the maximum shear stress
must be limited to 60 MPa. What is the minimum diameter
that may be used for shaft (2)?
A
(1)
D A
FIGURE p6.20
B
D C
D B
D
D B
C
D C
p6.21 A motor provides a torque of 1,500 lb · ft to gear B of the
system shown in Figure P6.21. Gear A takes off 900 lb · ft from shaft
(1), and gear C takes off the remaining torque. Both shafts (1) and (2)
C
B
D D
(1)
(2)
(2)
T D
T E
E
D
TA
FIGURE p6.21
p6.22 Two solid steel shafts are connected by the gears shown in
Figure P6.22/23. The design requirements for the system specify (1)
that both shafts must have the same diameter, (2) that the maximum
shear stress in each shaft must be less than 10,000 psi, and (3) that
the rotation angle of gear D must not exceed 8°. Determine the minimum
required diameter of the shafts if the torque applied at gear D
is T D = 350 lb ⋅ ft. The shaft lengths are L 1 = 78 in. and L 2 = 60 in. The
number of teeth on gears B and C are N B = 90 and N C = 52, respectively.
Assume that the shear modulus of both shafts is G = 11,500 ksi
and that the bearings shown allow free rotation of the shafts.
A
T D
A B C
D
FIGURE p6.22/23
(1) (2)
L1
L2
p6.23 Two solid 120 mm diameter steel shafts are connected by
the gears shown in Figure P6.22/23. The shaft lengths are L 1 = 4 m
and L 2 = 3 m. The number of teeth on gears B and C are N B = 200 and
N C = 115, respectively. Assume that the shear modulus of both shafts
is G = 80 MPa and that the bearings shown allow free rotation of the
shafts. If the torque applied at gear D is T D = 6,000 N ⋅ m, determine
(a) the internal torques T 1 and T 2 in the two shafts.
(b) the angles of twist φ 1 and φ 2 .
(c) the rotation angles φ B and φ C of gears B and C.
(d) the rotation angle of gear D.
L 1
(1)
(2)
L 2
N B
C
B
N C
TC
x
x'
160