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POWER TRANSMISSION SHAFTING
Shaft design:
It consists of the determination of the correct shaft diameter to ensure satisfactory strength and rigidity when the shaft is transmitting power under various operating and loading conditions. Shafts are usually circular in cross-section, and may be either hollow or solid.
Design of shafts:
For ductile materials, based on strength, is controlled by the maximum-shear theory. Shafts of brittle materials would be designed on the basis of the maximum-normal-stress theory. Shafts are usually subjected to torsion, bending, and axial loads.
1)-For torsional loads:
The torsional stress, xy is: xy = (Mtr)/J = (16Mt)/d3 For solid shafts
or xy = (16Mtdo)/(do4-di4) For hollow shafts
2)-For bending loads:
The bending stress σb (tension or compression) is:
σb =(Mbr)/I = 32Mb/d3 For solid shafts
σb = (32Mbdo)/(do4-di4) For hollow hafts
3)-For axial load:
The tensile or compressive stress σa is:
σa = 4Fa/d2 For solid shafts
σa =4Fa/(do2-di2) For hollow shafts
The ASME code equation for hollow shaft combines torsion, bending, and axial loads by applying the maximum-shear equation modified by introducing shock, fatigue, and column factor as follows:
For solid shaft having little or no axial loading, the equation is:
Where:
K=di/do
s= allowable shear stress, N/m2= 30% of the elastic limit but not over 18% of the ultimate strength in tension for shafts without keyways. These values are to be reduced by 25% if keyways are present.
do= shaft outside diameter, m
di = shaft inside diameter, m
kb = combined shock and fatigue factor applied to bending moment
kt = combined shock and fatigue factor applied to torsional moment
The following table gives the values of the factors kb and kt for different loading conditions of the stationary and rotating shafts.
For stationary shafts kb kt
Load gradually applied 1.0 1.0
Load suddenly applied 1.5 to 2.0 1.5 to 2.0
For rotating shafts
Load gradually applied 1.5 1.0
Load suddenly applied (minor shock) 1.5 to 2.0 1.0 to 1.5
Load suddenly applied (heavy shock) 2.0 to 3.0 1.5 to 3.0
*For commercial steel shafting:
σs(allowable) = 8000 psi (55MPa) for shaft without keyway
= 6000 psi (40MPa) for hafts with keyway
 = Column-action factor. The column-action factor is unity for a tensile load. For a compressive load,  may be computed by:
Where:
n = 1 for hinged ends or 2.25 for fixed ends and 1.6 for ends partly restrained, as bearings.
k = radius of gyration, m
σy = yield stress in compression, N/m2 .
Design of shafts for torsional rigidity:
It is based on the permissible angle of twist. The amount of twist permissible depends on the particular application, and varies about 0.3 degree/m for machine tool shafts to about 3.0 degree/m for line shafting
For solid circular shaft:
For hollow circular shaft:
Where:
Ө = angle of twist, deg. L = length of shaft, m
G = torsional modulus of elasticity, N/m2.
Standard sizes of shafting:
These sizes vary according to material specifications and supplier. Typical sizes for solid shafts are:
Up to 25 mm in 0.5 mm increments
25 to 50 mm in 1.0 mm increments
50 to 100 mm in 2.0 mm increments
100 to 200 mm in 5 mm increments
Bending and torsional moment:
These are the main factors influencing shaft design. One of the first steps in shaft design is to draw the bending moment diagram for the loaded shaft or the combined bending moment diagram if the loads acting on the shaft are in more than one axial plane. From the bending moment diagram, the points of critical bending stress can be determined.
The torsional moment acting on the shaft can be determined from:
For belt drive:
The torque is found from:
Mt = (T1 – T2)Rp Nm
Where:
T1 = tight side of belt on pulley, N
T2 = loose side of belt on pulley, N
Rp = radius of pulley, m
For gear drive:
The torque is found from:
Mt = Ft.Rg Nm
Fr = Ft.tan
Where:
Ft = tangential force at the pitch radius, N
Fr = radial force, N
Rg = pitch radius, m
= gear pitch angle, degrees