Bending Stress in Arm of Belt Driven Pulley Given Torque Transmitted by Pulley Calculator

Formula Used:

\[ \sigma_b = \frac{16 \times M_t}{\pi \times N \times a^3} \]

Bending Stress in Pulley's Arm (σ_b):

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1. What is Bending Stress in Pulley's Arm?

Bending stress in pulley's arm is the normal stress that is induced at a point in the arms of a pulley subjected to loads that cause it to bend. It's a critical factor in pulley design to ensure structural integrity and prevent failure.

2. How Does the Calculator Work?

The calculator uses the bending stress formula:

\[ \sigma_b = \frac{16 \times M_t}{\pi \times N \times a^3} \]

Where:

\( \sigma_b \) — Bending stress in pulley's arm (Pa)
\( M_t \) — Torque transmitted by pulley (N·m)
\( N \) — Number of arms in pulley
\( a \) — Minor axis of pulley arm (m)
\( \pi \) — Mathematical constant (approximately 3.1416)

Explanation: The formula calculates the bending stress based on the torque distribution across multiple pulley arms and the cross-sectional dimensions of the arms.

3. Importance of Bending Stress Calculation

Details: Accurate bending stress calculation is crucial for designing pulleys that can withstand operational loads without failure, ensuring safety and reliability in belt-driven systems.

4. Using the Calculator

Tips: Enter torque in Newton-meters, number of arms (must be at least 1), and minor axis dimension in meters. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is the significance of the minor axis in this calculation?
A: The minor axis dimension (cubed in the denominator) significantly affects bending stress. Smaller cross-sections result in higher stress concentrations.

Q2: How does the number of arms affect bending stress?
A: More arms distribute the torque load more evenly, reducing the bending stress on individual arms.

Q3: What are typical safe bending stress values for pulley arms?
A: Safe stress values depend on the material used (steel, cast iron, etc.) and should be below the material's yield strength with appropriate safety factors.

Q4: Can this formula be used for pulleys with different arm cross-sections?
A: This specific formula is designed for arms with elliptical cross-sections where the minor axis is specified.

Q5: How does torque transmission affect bending stress?
A: Higher torque values directly increase bending stress proportionally, making proper torque calculation essential for design.