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

Formula Used:

\[ M_{br} = \frac{\pi \times d_s^3 \times \sigma_{bf}}{32} \]

Total Bending Moment in Crankshaft under Flywheel (M_br):

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1. What is the Resultant Bending Moment Formula?

The formula calculates the total bending moment in the crankshaft under the flywheel at TDC position, based on the shaft diameter and bending stress. This is essential for determining the structural integrity and load-bearing capacity of the crankshaft.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ M_{br} = \frac{\pi \times d_s^3 \times \sigma_{bf}}{32} \]

Where:

\( M_{br} \) — Total Bending Moment in Crankshaft under Flywheel (N·m)
\( d_s \) — Diameter of Shaft under Flywheel (m)
\( \sigma_{bf} \) — Bending Stress in Shaft Under Flywheel (Pa)
\( \pi \) — Archimedes' constant (≈3.14159)

Explanation: The formula derives from beam bending theory where the bending moment is proportional to the cube of the shaft diameter and the bending stress, with a constant factor of π/32.

3. Importance of Bending Moment Calculation

Details: Accurate bending moment calculation is crucial for crankshaft design, ensuring it can withstand operational loads without failure, and for determining appropriate safety factors in mechanical engineering applications.

4. Using the Calculator

Tips: Enter shaft diameter in meters and bending stress in pascals. Both values must be positive numbers. The calculator will compute the resultant bending moment in newton-meters.

5. Frequently Asked Questions (FAQ)

Q1: Why is the shaft diameter raised to the third power?
A: The bending moment resistance is proportional to the moment of inertia, which for a circular shaft is proportional to the diameter to the fourth power, but in this formula it appears as d³ due to the relationship with bending stress.

Q2: What are typical values for crankshaft bending stress?
A: Bending stress values vary based on material and design, but typically range from 50-400 MPa for steel crankshafts in automotive applications.

Q3: How does flywheel position affect bending moment?
A: The flywheel's mass creates significant bending moments, particularly at TDC position where inertial forces are maximized, making this calculation critical for crankshaft design.

Q4: Are there limitations to this formula?
A: This formula assumes a uniform, circular shaft and doesn't account for stress concentrations, fatigue loading, or complex geometries that may be present in actual crankshaft designs.

Q5: Can this formula be used for other shaft types?
A: While derived for crankshaft applications, the fundamental bending moment calculation can be applied to any circular shaft under bending stress, though specific applications may require additional considerations.