SHAFTIN
G
REVIEW IN MACHINE DESIGN
SHAFTING
DEFINITION OF TERMS
■ SHAFT – a rotating member, usually of circular section, used
to transmit power or motion. Its primary load is torsion
■ AXLE – a non rotating member which carries no torque and
is used to support wheels, pulleys and the like. It is primarily
loaded with bending.
■ SPINDLE – a short shaft or axle
SHAFTING
DEFINITION OF TERMS
■ Terms such as LINESHAFT, HEADSHAFT,
TRANSMISSION SHAFT, MACHINERY SHAFT,
COUNTERSHAFT AND FLEXIBLE SHAFT are names
associated with special usage
■ Most machine design books generally use the term
shaft to mean all of the above.
SHAFT UNDER
CONCEPTS AND FORMULAS
PURE
TORSION
■SOLID SHAFT
■ HOLLOW SHAFT
SHAFT UNDER
CONCEPTS AND FORMULAS
PURE
TORSION
■
■MAXIMUM TORSIONAL STRESS
– SOLID SHAFT
WHERE:
SS = MAXIMUM
TORSIONAL STRESS
T = MAXIMUM
– HOLLOW SHAFT TORQUE
D = OUTSIDE
DIAMETER
d = INSIDE
DIAMETER
SHAFT UNDER
CONCEPTS AND FORMULAS
PURE
TORSION
■
■TORSIONAL DEFLECTION
– ANGLE OF TWIST
WHERE:
SS = MAXIMUM
TORSIONAL STRESS
T = MAXIMUM
– POLAR MOMENT OF INERTIA TORQUE
D = OUTSIDE
■ J, FOR SOLID SHAFT DIAMETER
■ J, FOR SOLID SHAFT d = INSIDE
DIAMETER
SHAFT UNDER
CONCEPTS AND FORMULAS
PURE
BENDING
■
■MAXIMUM FLEXURAL STRESS
– SOLID SHAFT
WHERE:
SS = MAXIMUM
TORSIONAL STRESS
T = MAXIMUM
– HOLLOW SHAFT TORQUE
D = OUTSIDE
DIAMETER
d = INSIDE
DIAMETER
SHAFT UNDER
CONCEPTS AND FORMULAS
PURE
BENDING
■
■SHAFT DEFLECTION FOR SPECIAL CASES
– CASES A: CANTILEVER WITH LOAD P AT FREE END
■
– CASE B: SIMPLY SUPPORTED WITH LOAD P AT
MIDSPAN
■
SHAFT UNDER
CONCEPTS AND FORMULAS
PURE
BENDING
■
■SHAFT DEFLECTION FOR SPECIAL CASES
– CASE C: FIXED SUPPORT WITH LOAD P AT MIDSPAN
■
CLASSIFICATION OF
SHAFTS
CONCEPTS AND FORMULAS
■TRANSMISSION SHAFT – shaft that
connects a prime mover to a machine
■Machinery shaft – shaft that is an
integral part of a machine
ASME FORMULAS
SHAFT DESIGN STRESSES (ONLY Sy AND Su ARE
KNOWN)
■NORMAL DESIGN STRESS
■Sd= 0.6 Sy WHICHEVER IS
SMALLER: IF SHAFT
■Sd= 0.36 SU HAS A KEY WAY,
CONSIDER A
■SHEAR DESIGN STRESS STRENGTH
REDUCTION FACTOR
■Ssd =0.3Sy OF 0.75
■Ssd = 0.18 SU
ASME FORMULAS
SHAFT DESIGN STRESSES (ANGLE OF TWIST)
■
■TRANSMISSION SHAFT:
■ IF L=20D
■MACHINERY SHAFT
ASME FORMULAS
SHAFT DESIGN STRESSES (TRANSVERSE DEFLECTION)
■
■TRANSMISSION SHAFT:
■MACHINERY SHAFT
COMBINED STRESSES
SHAFT DESIGN STRESSES
■
■MAXIMUM SHEAR STRESS
■MAXIMUM NORMAL STRESS
NOTE: IF Km AND KS ARE NOT SPECIFIED, USE Km = KS = 1.0
TRANSMISSION SHAFTS FROM
PSME CODE
POWER FORMULAS
■
■MAIN POWER
TRANSMITTING SHAFT
(MAIN SHAFT)
■LINE SHAFTS
CARRYING PULLEYS
TRANSMISSION SHAFTS FROM
PSME CODE
POWER FORMULAS
■
■SMALL, SHORT AND
COUNTERSHAFT
EMPIRICAL FORMULAS FROM MACHINERY
HANDBOOK
REQUIRED SHAFT DIAMETER
■
■FOR ALLOWABLE ANGLE OF TWIST NOT EXCEEDING 0.08 0 PER
FOOT OF LENGTH
■FOR AN ALLOWABLE ANGLE OF TWIST NOT EXCEEDING 1 0 IN A
LENGTH OF L=20D
■FOR SHORT, SOLID SHAFT SUBJECTED ONLY TO HEAVY
TRANSVERSE SHEAR
EMPIRICAL FORMULAS FROM MACHINERY
HANDBOOK
SHAFT SUPPORTED LENGTH VS SHAFT DIAMETER
■
■NO BENDING ACTION EXCEPT KITS OWN
WEIGHT
■SUBJECTED TO BENDING ACTION DUE TO
PULLEYS
EMPIRICAL FORMULAS FROM MACHINERY
HANDBOOK
SHAFT SUPPORTED LENGTH VS SHAFT DIAMETER
■
■NO BENDING ACTION EXCEPT KITS OWN
WEIGHT
■SUBJECTED TO BENDING ACTION DUE TO
PULLEYS
SAMPLE
SHAFTING
PROBLEMS
The shear strength of a shaft not
exceed 30 Mpa. The shaft is 100
mm. What is the greatest torque
that can be place on it?
ANS: 5900 J
SAMPLE
SHAFTING
PROBLEMS
A steel shaft 1.4375 inches in diameter
transmits 40 hp at 1400 rpm.
Assuming a modulus of rigidity of 12 x
106 psi, find the torsional deflection of
the shaft in degrees per foot in length.
ANS: 0.246
SAMPLE
SHAFTING
PROBLEMS
Find the torsional stress in MPa. If a
40 mm diameter shaft that
transmits 20.53 kW at 600 rpm.
ANS: 26 MPa
SAMPLE
SHAFTING
PROBLEMS
A round steel shaft transmits 50 kW
and rotates at 150 rad/s. Find the
angle twist for a 3 meters length
shaft if allowable shearing stress of
40 MPa and G = 69 GPa.
ANS: 5.7 deg
SAMPLE
SHAFTING
PROBLEMS
Compute the polar section
modulus of a solid shaft with a
diameter of 101.6 mm.
ANS: 205.9 cm3
SAMPLE
SHAFTING
PROBLEMS
A line shaft runs at 360 rpm. An 18” pulley on
the same shaft is belt connected to a 12” pulley
on the countershaft. From a 15” pulley on the
countershaft motion is transmitted to the
machine. Compute/check the required size of
the pulley on the machine to give a spindle
speed of 660 rpm
ANS: 12.25 in
SAMPLE
SHAFTING
PROBLEMS
A solid circular shaft is used to transmit 200 hp at
1000 rpm. If a hollow shaft is used having an
inside diameter equal to the diameter of the solid
shaft determine what must be the outside
diameter of this shaft if the angular twist of the
hollow and solid shaft is to be equal? The
allowable maximum shearing stress is 20,000 psi.
ANS: 1.755 in
SAMPLE
SHAFTING
PROBLEMS
A 3“diameter short shaft carrying
two pulleys close to the bearings
transmit. How much horse power if
the shaft makes 280 rpm?
ANS: 199 Hp
SAMPLE
SHAFTING
PROBLEMS
A solid cylindrical shaft 48.2 cm
long is used for a transmission of
mechanical power at rate of 37 kW
running at 1760 rpm. The Ss is
8.13 MPa. Calculate the diameter.
ANS: 50 mm
SAMPLE
SHAFTING
PROBLEMS
A steel shafting transmit 50 hp at 1400 rpm.
If the allowable stress is 5000 psi. find the
shaft diameter.
ANS: 1.32 in.
SAMPLE
SHAFTING
PROBLEMS
Compute the twisting moment in in-lb
developed when a shaft delivers 20 Hp at
1200 rpm.
ANS: 1050 in-lb
SAMPLE
SHAFTING
PROBLEMS
A hollow shaft has an inner diameter of
0.035 m and outer diameter of 0.06 m.
Determine the polar moment of inertia of
the hollow shaft. Compute for the torque
if the shear stress is not to exceed 120
MPa in Nm.
ANS: 1.125 x 10-6 m, 4500 N-m
SAMPLE
SHAFTING
PROBLEMS
The shaft whose torque varies from
2000 to 6000 in-lb has 1 ½ in in
diameter and 60000 psi yield
strength. Compute for the shaft
mean average stress
ANS: 6036 psi
SAMPLE
SHAFTING
PROBLEMS
The torsional deformation of a SAE 1040
steel shaft is to 0.8 o in a length of ½
meter. The shear stress is 69 Mpa.
Compute the diameter of the shaft in
millimeter. Steel modulus of elasticity is
79,300 Mpa or N/mm2
ANS: 62.3 mm
SAMPLE
SHAFTING
PROBLEMS
The maximum bending moment of a
beam simply supported at both
ends and subject to a total load W
uniformly distributed over its length
L is expressed by the formula.
ANS: wL2/8
SAMPLE
SHAFTING
PROBLEMS
The maximum moment induced in
a simply supported beam of 20 foot
span, by a 2,000 pound load at
midspan is.
ANS: 10 000 ft-lb
SAMPLE
SHAFTING
PROBLEMS
An axle 1m long is supported by bearing at
its end. It carries a flywheel weighing 30 kN
at the center. If the allowable design flexural
stress is not to exceed 60 Mpa, find the
diameter of the axle.
ANS: 108.4 mm
SAMPLE
SHAFTING
PROBLEMS
What is the limiting speed of a 63.42 mm
diameter shaft transmitting 75 kW if the
stress is not to exceed 26 MPa
ANS: 550 rpm
SAMPLE
SHAFTING
PROBLEMS
A 76 mm solid shaft is to be replaced by a
hollow shaft of equal torsional strength.
Determine the percent saving in weight by
using hollow shaft. The outside diameter of
the hollow shaft is 100mm.
ANS: 56.56%
SAMPLE
SHAFTING
PROBLEMS
Find the inside and outside diameter of the
hollow shaft which will replace a 76 mm solid
shaft made of the same material. The hollow
shaft should be strong in torsion but it weighs
only half as much as the solid per meter.
ANS: 74.35 mm, 91.74 mm
SAMPLE
SHAFTING
PROBLEMS
Compute for the diameter in inches of a SAE
1030 steel shaft to transmit 12 hp at 120
rpm with torsional deflection limited to only
about 0.08 deg / foot length as
recommended.
ANS: 2 -7/8 in, 2.6 in.
SAMPLE
SHAFTING
PROBLEMS
A marine propeller shaft is to transmit 3700 kW at
126 rpm with out exceeding a torsional stress of
42 MPa or twisting through more than 1 deg in a
length of 20 diameters. The modulus of rigidity is
taken as 83 GPa. Find the required shaft diameter
ANS: 340.38 mm
SAMPLE
SHAFTING
PROBLEMS
An SAE 1030 steel is used as a shaft in
transmitting 200 hp at 600 rpm. Considering
a shear yield strength of 36 ksi and a design
factor of 3, what shaft diameter is required?
ANS: 2-1/8 in
SAMPLE
SHAFTING
PROBLEMS
A solid steel shaft, whose S = 300
y
MPa and Su= 400 Mpa is used to
transmit 300 kW at 800 rpm.
Determine its diameter.
ANS: 65 mm
SAMPLE
SHAFTING
PROBLEMS
A 2 inch diameter steel shaft with S = 48 ksi
y
and Su= 65 ksi, is used as a 2 feet long
cantilever that supports a load at its free
end . Neglecting any torsional load,
determine the maximum value of F. consider
a combined shock and fatigue factor of 1.5
ANS: 510 lb
SAMPLE
SHAFTING
PROBLEMS
Find the power, in watts,
transmitted by a main shaft with a
diameter of 65 mm and a speed of
200 rpm.
ANS: 31,254
SAMPLE
SHAFTING
PROBLEMS
What is the diameter of the line
shaft that transmits 150 kw at 15
rps?
ANS: 58.1 mm
SAMPLE
SHAFTING
PROBLEMS
A 16ft steel line shaft has no
bending load except its own
weight. What power in Hp can the
shaft deliver at a speed of 200
rpm?
ANS: 51.1 Hp
SAMPLE
SHAFTING
PROBLEMS
Determine the size of a horizontal section of a
square bar, which is to be held firmly at one end
and to support a weight of 1600 kg at the other
end, the bar is to be 1m long and is to be made
from steel with a yield strength of 500 MPa. Use
a factor of safety of 3 and a concentration factor
of 1.3.
ANS: 90.23 x 90.23 mm
SAMPLE
SHAFTING
PROBLEMS
A small counter shaft, 1-1/2 inch in
diameter, has an allowable stress
of 8500 psi. find the horsepower
that can be safely delivered by the
shaft at a speed of 15.7 rad/sec.
ANS: 13.40 Hp
SAMPLE
SHAFTING
PROBLEMS
The shaft of a vertical turbo- generator set in a
hydroelectric power plant has an outside
diameter of 305 mm and an inside diameter of
254 mm. the shaft transmit 5000 Hp at 750 rpm.
The total weight of the shaft and the turbine
runner is 54 metric tons. Determine the
maximum normal stress in the shaft.
ANS: 32.08 MPa
SAMPLE
SHAFTING
PROBLEMS
The axle of a heavy duty tractor transmit 120
kW at 600 rpm. It acts as a cantilever
supporting a load of 280 N located 60 cm from
the fixed end. The allowable normal stress is
137 MPa and the allowable shear stress is 62
Mpa. If the axial load is negligible, find the the
axle diameter.
ANS: 54 mm
SAMPLE
SHAFTING
PROBLEMS
The shaft of a machine supported on bearing 6 feet
apart is to transmit 250 Hp at 200 rpm, while subjected
to a bending load of 1003.28 lb located at a distance of
2 ft from one bearing. Allow a maximum shearing stress
of shear stress of 6000 psi and maximum bending stress
of 12000 psi. Assume a combined shock and fatigue for
bending of 1.5 and a combined shock and fatigue factor
for shear of 1.0. Determine the shaft size.
ANS: 4.25 in.
