Resultant Bending Moment In Side Crankshaft At TDC Position Below Flywheel Given Shaft Diameter Calculator

Formula Used:

\[ M_b = \frac{\pi \times D_s^3 \times \sigma_b}{32} \]

Bending Moment at Crankshaft Under Flywheel (M_b):

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1. What is the Bending Moment Formula?

The formula calculates the bending moment at the crankshaft under the flywheel based on shaft diameter and bending stress. It's derived from fundamental beam bending theory and is essential for crankshaft design and analysis.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ M_b = \frac{\pi \times D_s^3 \times \sigma_b}{32} \]

Where:

\( M_b \) — Bending Moment at Crankshaft Under Flywheel (N·m)
\( D_s \) — Diameter of Shaft under Flywheel (m)
\( \sigma_b \) — Bending Stress in Shaft Under Flywheel (Pa)
\( \pi \) — Archimedes' constant (approximately 3.1416)

Explanation: The formula relates bending moment to shaft diameter and bending stress, considering the circular cross-section of the shaft.

3. Importance of Bending Moment Calculation

Details: Accurate bending moment calculation is crucial for crankshaft design, ensuring structural integrity, preventing failure, and optimizing material usage in engine components.

4. Using the Calculator

Tips: Enter shaft diameter in meters and bending stress in Pascals. Both values must be positive numbers for valid calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is bending moment in mechanical engineering?
A: Bending moment is the internal moment that causes a structural element to bend when external forces are applied.

Q2: Why is shaft diameter cubed in the formula?
A: The moment of inertia for a circular cross-section is proportional to the fourth power of diameter, making bending moment proportional to the cube of diameter.

Q3: What are typical values for crankshaft bending stress?
A: Bending stress values vary by material and application, but typically range from 50-400 MPa for steel crankshafts in automotive engines.

Q4: Can this formula be used for non-circular shafts?
A: No, this specific formula is derived for circular cross-sections. Different formulas apply to other cross-sectional shapes.

Q5: How does flywheel position affect bending moment?
A: The flywheel's mass and position create additional bending moments that must be considered in crankshaft design and analysis.