Shaft:
A shaft is a rotating or stationary member, usually of circular cross-section,
having mounted upon it such elements as gears, pulleys, flywheels, cranks,
sprockets and other power-transmitting elements. The shafts are relatively long
and may be subjected to bending, tension, compression or torsional loads, acting
singly or in combination with one another. When they are combined, one may
expect to find both static and fatigue strengths to be important design
consideration, since a single shaft may be subjected to static stresses, completely
reversed stresses and repeated stresses, all acting at the same time.
a) Transmission shaft – It is used to transmit power between the power source
and the machines absorbing power. It is generally subjected to torque,
bending moment and axial load in combination e.g. line shaft, counter
shaft, head shaft and all factory shafts.
b) Machine shaft – It is integral part of a machine. It is used to transfer motion
and power within the machine e.g. crank shaft, gear shaft.
c) Axle – It is a stationary or rotating shaft. It does not carry any torsional
load. It is subjected to bending moment due to transverse load only. It is
used to support rotating parts e.g. axles of automobiles.
d) Spindle – It is a short rotating shafts used to impart motion either to cutting
tool or work piece e.g. lathe spindle, drill press spindle.
Materials: Commonly adopted materials are mild steel. In addition, different
types of alloy steels are also used for shafts, depending on situation and types of
application.
Deflection restraints: δ = L/1200, where δ and L are maximum transverse
deflection of the shaft and length of shaft between bearing supports respectively.
Twist restraint: Maximum twist is 2.5-3.5 degree per meter of shaft length for line
shaft. It is with 0.25 degree per meter of machine shaft.
Problem:
A solid horizontal steel shaft is to run in self-aligning bearings A and B,
2500mm apart. The shaft is driven from the right of right-hand bearing with an
electric motor. The power is supplied to a machine from the shaft through a 500-
mm diameter pulley, mounted on the shaft through a rectangular key at 1200mm
from the left-hand bearing. The belt tensions are 1800N and 840N and they are
parallel to each other and at 64O to the horizontal. The weight of the pulley is
500N. Determine the diameter of the shaft.
Use the following data:
Material = FeE 200; Factor of safety = 2.5;
Combined shock and fatigue factor for bending = 1.6;
Combined shock and fatigue factor for torsion = 1.2;
Allowable tensile stress for key material = 120MPa
Note: From the above discussion, it is understood that the calculated diameter of
the shaft depends on the computed values of Te and [τ]. With the appropriately
selected values of Km and Kt, the value of Te depends on the values of T and M.
It is clear that values of T and M varies from location to location on the same
shaft. The values of allowable shear stress also not same along the shaft. The
diameter of the shaft is to be calculated at all critical locations and design decision
is to be taken based on engineering judgement.
Type of Loading Cm Ct
Stationary Shaft :
Load applied gradually 1.0 1.0
Load applied suddenly 1.5-2.0 1.5-2.0
Rotating Shaft:
Load applied gradually 1.5 1.0
Steady Loads 1.5 1.0
Loads applied gradually with minor 1.5-2.0 1.0-1.5
shocks 2.0-3.0 1.5-3.0
Loads applied suddenly with heavy shocks
Note: In some books, Cm and Ct are denoted as Km and Kt respectively.
Calculation of average torque Tav from rated power [kW] of motor with rpm n:
(2πn × Tav)/60 = 1000 × [kW];
Tav = (60 × 1000) / (2πn) × [kW] N-m = (9549.296586/n) N-m ≈ (9550/n) × [kW] N-m
Tav = (9550/n) × 103 × [kW] N-mm.
Design Torque Td = Tav × Cs.
Problem:
Q.1. A solid shaft and a hollow shaft are to be of equal strength. The hollow shaft is to be
10% larger than the solid shaft. What will be the ratio of the weight of the hollow shaft to that
of the solid shaft? Both the shafts are to be made of the same material.
Q.2. A Hollow shaft, 500mm outside diameter and 300mm inside diameter, is supported in
two bearings 6m apart. The shaft is driven by a flexible coupling at one end and drives a ship’s
propeller at 100rpm. The maximum trust on the propeller is 500kN when the shaft is
transmitting 6000kW. Determine the factor of safety. Give your comment on the result obtained
by you.
Use the following data:
Material = 40C8
Combined shock and fatigue factor for bending = 1.5
Combined shock and fatigue factor for torsion = 1.0
Acceleration due to gravity = 9.8m/sec2.
Density of material = 8.1 gms/cc.
