Torque Transmitted By Pulley Given Bending Stress In Arm Calculator

Formula Used:

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

Bending Stress in Pulley's Arm (σ_b):

Number of Arms in Pulley (N):

Minor Axis of Pulley Arm (a):

Torque Transmitted by Pulley (M_t):

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1. What is Torque Transmitted by Pulley?

Torque Transmitted by Pulley refers to the rotational force that a pulley can transfer from one shaft to another through its arms. It is a critical parameter in mechanical design and power transmission systems.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

\( M_t \) — Torque Transmitted by Pulley (N·m)
\( \sigma_b \) — Bending stress in pulley's arm (Pa)
\( \pi \) — Mathematical constant (approximately 3.1416)
\( N \) — Number of Arms in Pulley
\( a \) — Minor Axis of Pulley Arm (m)

Explanation: This formula calculates the maximum torque a pulley can transmit based on the bending stress capacity of its arms, considering the number of arms and their cross-sectional dimensions.

3. Importance of Torque Calculation

Details: Accurate torque calculation is essential for designing reliable power transmission systems, ensuring pulley arms can withstand operational stresses without failure, and optimizing mechanical efficiency.

4. Using the Calculator

Tips: Enter bending stress in Pascals, number of arms (must be at least 1), and minor axis in meters. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is bending stress in pulley arms?
A: Bending stress is the internal stress caused by bending moments in the pulley arms when torque is applied. It must be kept below the material's yield strength to prevent failure.

Q2: How does the number of arms affect torque transmission?
A: More arms generally allow higher torque transmission as the load is distributed among more supporting elements, reducing stress on individual arms.

Q3: What is the minor axis of a pulley arm?
A: The minor axis refers to the smaller dimension of the elliptical cross-section of the pulley arm, which is critical in determining the arm's resistance to bending.

Q4: Are there limitations to this formula?
A: This formula assumes uniform stress distribution and may not account for dynamic loads, material imperfections, or complex geometries. Professional engineering analysis is recommended for critical applications.

Q5: Can this calculator be used for all pulley types?
A: This calculator is specifically designed for pulleys with elliptical cross-section arms. Different arm geometries may require different calculation methods.