MAE 322
Machine Design
Shafts -SummaryDr. Hodge Jenkins
Mercer University
Power Transmission
Nothing new, just calculate Torque, T, from power equation:
P = Tw
Careful with units!
Power (watts, ft-lb/s or hp)
Torque (N-m, lb-ft)
Angular velocity (RPM, rad/s or Hz)
Note: 1 HP = 550 ft-lb/s
fw 2 f = Hz or rev/s
Power, Speed and Torque
Shaft powered by 5 hp electric motor spins at 600 RPMS
[= 600revs/min = 10 Revs/sec = 10 Hz] ,
find Torque in shaft.
P = Tw
5 hp (550 ft-lb/s/hp) = 2,750 ft-lb/s
600 RPM=10 Hz (2 rad/rev) = 62.83 rad/s
T = 2750 ft-lb/s
62.83 rad/s
= 43.76 lb-ft
P
T
w
Shaft Stresses for Rotating Shaft
For rotating shaft with steady, alternating bending and torsion
◦ Bending stress is completely reversed (alternating), since a
stress element on the surface cycles from equal tension to
compression during each rotation (Ma) . Found from bending
moment diagrams
◦ Torsional stress is steady (constant or static Tm )
◦ Previous equations simplify with Mm and Ta equal to 0
Shigley’s Mechanical Engineering Design
Shaft Stresses
Standard stress equations can be customized for shafts for
convenience
Axial loads are generally small and constant, so will be ignored
in this section
Standard alternating and midrange stresses
Customized for round shafts
Shigley’s Mechanical Engineering Design
Shaft Stresses
Using modified Goodman line with DE,
Solving for d is convenient for design purposes
Shigley’s Mechanical Engineering Design
Shaft Stresses
DE-ASME Elliptic Minimum Diameter Calculation
Shigley’s Mechanical Engineering Design
Angular Deflection of Shafts
For stepped shaft with individual cylinder length li and torque Ti,
the angular deflection can be estimated from
For constant torque throughout homogeneous material
Experimental evidence shows that these equations slightly
underestimate the angular deflection.
Torsional stiffness of a stepped shaft is
Shigley’s Mechanical Engineering Design
Critical Speeds for Shafts
For a simply supported shaft of uniform diameter, the
first critical speed is
For an ensemble of attachments, Rayleigh’s method
for lumped masses gives
◦ wi is the weight of the ith location and yi is the static deflection at the ith body
location
Or Finite Element Model for modal analysis (later)
Shigley’s Mechanical Engineering Design
Standard Keys, Rectangular & Square
Shaft diameter
determines key
size
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Table 7–6
Keys
Failure of keys is by either direct shear or bearing stress
Key length is designed to provide desired factor of safety
Factor of safety should not be excessive, so the inexpensive key
is the weak link
Shigley’s Mechanical Engineering Design
Shigley’s Mechanical Engineering Design
Example 7–6
Shigley’s Mechanical Engineering Design
Fig. 7–19
Example 7–6 (continued)
Shigley’s Mechanical Engineering Design
Example 7–6 (continued)
Shigley’s Mechanical Engineering Design