Accurately calculate the angular deflection, or twist, of a hollow shaft under various torque loads. This essential engineering tool helps determine the torsional deformation based on shaft length, shear modulus, and both inner and outer diameters, crucial for machinery design, structural integrity, and ensuring components operate within acceptable stress limits.
Formula:
The angular deflection (θ) of a hollow shaft is calculated using the formula:
θ = (T * L) / (G * J)
Where:
- θ = Angular Deflection (radians)
- T = Applied Torque (N·m or lb·ft)
- L = Length of Shaft (m or in)
- G = Shear Modulus of Elasticity (Pa or psi)
- J = Polar Moment of Inertia of a hollow shaft (m4 or in4)
The Polar Moment of Inertia (J) for a hollow shaft is given by:
J = (π/32) * (OD4 - ID4)
Where:
- OD = Outer Diameter
- ID = Inner Diameter