Shaft Design: Shaft Dimension and Strength

Shaft Design: Shaft Dimension and Strength - Shaft is static or dynamic part having a round cross section, which is attached to elements such as gears, pulleys, steering wheel, crank, sprocket and other power transmission elements. Shaft can receive bending load, strength, pressure and torque, either alone or in combination with others.

The word shaft could include the term of axle and spindle. The term of axle more dedicated to the shaft that accepts torque load, while the spindle is dedicated to the reception of the short shaft around. Calculating the shaft load type also depends on the torque and deflection or both.

Torque load of shaft

The torque load occurs at the shaft rotation of the reception of the electric motor. The torque is the ratio of the power requirement and shaft speed by the formula:

Note: 

T = Torque (kg mm)

P_R  = Power Requirement (kW)

n = Shaft Speed (Rpm)

Power requirement is obtained from the power of electric motors after that is multiplied by a correction factor by the following formula:

Note:

P_R  = Power Requirement (kW)

P = Electric Motor Power(kW)

f_c  = Correction Factor

Correction factors have been taken according to the values of use of the transmission power as shown in the following table.

Note:

• Use the correction factor at average power if the shaft load is not constant and the calculated average load. This condition is the cause of the power consumption varies.
• Use the correction factor at maximum power if the calculated maximum loads on the shaft.
• Use the correction factor at normal power if the shaft load is constant or normal load

The shaft diameter with the torque load can be calculated by the equation:

Note:
d = Shaft Diameter (mm)
t  = Shear Stress (kg/mm)
T = Torque (kg mm)
f_T = Torque Factor
f_D = Deflection Factor

Torque factor and deflection factor are selected according to the type of load which is received by the shaft as in the following table:

Note:

• If the shaft certainly not accept a bending load, the deflection factor taken 1,0.
• If the shaft is provided for receiving the bending load, but its value is not known, a deflection factor value corresponding caught in the table above.
• If the shaft directly receives a bending load, and then use the calculation of torque and deflection load of shaft together.

Torque load will cause the deformation in the form of an angle of the torsion shaft. It is calculated by the equation:

Note:
θ      = Torsion angle (o)
T = Torque (Kg mm)
d = Shaft Diameter (mm)
l = Shaft Length (mm)
G = Modulus of Rigidity (Kg/mm2)

Shaft can be declared safe if the torsion angle less than 0,25 degree/m in the normal working conditions. If the calculation results show the value of the torsion angle of more than 0,25 degree/m, it should be redesigned to take a larger shaft diameter.

Bending load of shaft

Bending stress will occur in the static or dynamic shaft gets radial force in a region that has a distance from the fulcrum. Radial force is the force which is perpendicular to the axis of the shaft. The radial force caused by the external load or internal load of shaft.

The external load of shaft is caused by the force received by the machine element is mounted on the shaft like belt tension, gears tangential force, blade shear forces etc. The internal load of shaft is caused by weight of shaft and other component.

Its loads will cause a bending moment that can be calculated using the formula:

Note:

M = Bending Moment (Kg mm)

F = Radial Force or Load (Kg)

l = Distance of Force to Equilibrium Moment  (mm)

If a large number of forces acting on the shaft that the bending moment then be taken into account largest bending moment on the shaft by following equilibrium calculations.

If the static shaft receives a pure bending load, the shaft diameter can be calculated by the equation:

Note:

d = Shaft Diameter (mm)

t  = Shear Stress (kg/mm)

M = Bending Momen(kg mm)

f_D     = Deflection Factor

Bending load will cause the deformation in the form of deflection shaft. It is calculated by the equation:

Note:

y = Deflection (mm)

d = Shaft Diameter (mm)

F = Force (Kg)

l_A, l_B = Distance of Force to Bearing (mm)

l = Distance of Bearing to Bearing (mm)

Shaft can be declared safe if the shaft deflection less than 0,3 (mm/m) in the normal working conditions. If the shaft works in high speed or high precision, the shaft deflection must be less than 0,03 – 0,15 (mm/m). If the calculation results show the value of the deflection shaft of more than standard, it should be redesigned to take a larger shaft diameter.

Torque and bending load of shaft together

If the shaft receives the torque and deflection together, the shaft diameter can be calculated by the equation:

Note:
d  = Shaft Diameter (mm)
t = Shear Stress (kg/mm)
M = Bending Moment (kg mm)
T = Torque (kg mm)
f_T  = Torque Factor
f_D = Deflection Factor

Value of bending moment and torque can be calculated by previous equation. Shaft strength can be checked by calculation of torque angle and deflection shaft.

Shaft calculation formulas above is taken from the handbook of Design of Machine Elements by Sularso & Kiyokatsu Suga and Mechanical Engineering Design by Shigley & Mitchel

That is a description about Shaft Design: Shaft Dimension and Strength. If you find misconceptions in the shaft formula, please provide the correction in the comment box.