1. What is the Diameter of Shaft Formula?

The formula calculates the minimum diameter of a shaft required to safely transmit a given torque without exceeding the allowable shear stress. It's derived from the torsion formula for circular shafts.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( d_s \) — Diameter of shaft (m)
• \( T_{\text{shaft}} \) — Torque transmitted by shaft (N·m)
• \( \tau \) — Shear stress in shaft (Pa)
• \( \pi \) — Mathematical constant pi (approximately 3.1416)

Explanation: The formula ensures that the maximum shear stress in the shaft does not exceed the allowable shear stress for the material.

3. Importance of Shaft Diameter Calculation

Details: Proper shaft sizing is crucial for mechanical design to ensure sufficient strength to transmit torque while preventing failure due to excessive shear stress.

4. Using the Calculator

Tips: Enter torque in Newton-meters and shear stress in Pascals. Both values must be positive numbers greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: What is the significance of the 16/π factor?
A: This factor comes from the polar moment of inertia formula for a solid circular shaft (J = πd⁴/32) and the torsion formula (τ = T·r/J).

Q2: Can this formula be used for hollow shafts?
A: No, this specific formula is for solid circular shafts. Hollow shafts require a different formula accounting for inner and outer diameters.

Q3: What are typical shear stress values for shaft materials?
A: Typical values range from 40-60 MPa for mild steel, 80-100 MPa for alloy steels, but always consult material specifications for exact values.

Q4: Does this consider fatigue or dynamic loading?
A: No, this is a basic static strength calculation. For dynamic or fatigue loading, additional factors and safety margins must be considered.

Q5: How does shaft length affect this calculation?
A: Shaft length doesn't affect the diameter calculation for pure torsion, as shear stress depends only on torque and cross-sectional properties.