1. What is Polar Modulus of Hollow Shaft?

The Polar Modulus of a hollow shaft section is equal to the ratio of the polar moment of inertia to the radius of the shaft. It is a measure of a shaft's ability to resist torsion and is denoted by Z_p.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( Z_p \) — Polar Modulus (m³)
• \( d_o \) — Outer Diameter of Shaft (m)
• \( d_i \) — Inner Diameter of Shaft (m)
• \( \pi \) — Mathematical constant (≈3.14159)

Explanation: The formula calculates the polar section modulus for a hollow circular shaft based on its outer and inner diameters.

3. Importance of Polar Modulus Calculation

Details: Polar modulus is crucial in mechanical engineering for designing shafts that can withstand torsional loads without failure. It helps determine the maximum torque a shaft can handle.

4. Using the Calculator

Tips: Enter outer diameter and inner diameter in meters. Both values must be positive, and inner diameter must be less than outer diameter.

5. Frequently Asked Questions (FAQ)

Q1: What is the difference between polar modulus and polar moment of inertia?
A: Polar modulus (Z_p) is the ratio of polar moment of inertia (J) to the radius (R) of the shaft (Z_p = J/R). It represents the shaft's resistance to torsion.

Q2: Why use hollow shafts instead of solid shafts?
A: Hollow shafts provide better strength-to-weight ratio, can handle higher torsional loads with less material, and are more efficient in many engineering applications.

Q3: What are the units of polar modulus?
A: Polar modulus is measured in cubic meters (m³) in the SI system.

Q4: Can the inner diameter be zero?
A: If inner diameter is zero, the shaft becomes solid, and the formula simplifies to Z_p = (π·d_o³)/16 for solid shafts.

Q5: What are typical applications of this calculation?
A: This calculation is used in designing drive shafts, propeller shafts, torque tubes, and any rotating machinery components that transmit torque.