Diameter Of Crank Pin Of Centre Crankshaft For Max Torque Given Bending And Torsional Moment Calculator

Formula Used:

\[ dc = \left( \frac{16}{\pi \cdot \tau} \cdot \sqrt{(Mb^2) + (Mt^2)} \right)^{1/3} \]

Shear Stress in Central Plane of Crank Pin (τ):

Bending Moment at Central Plane of Crankpin (Mb):

N·m

Torsional Moment at Central Plane of Crankpin (Mt):

N·m

Diameter of Crank Pin (dc):

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1. What is the Diameter of Crank Pin Formula?

The diameter of crank pin formula calculates the required diameter of the crank pin in a centre crankshaft under maximum torque conditions, considering both bending and torsional moments. This ensures the crank pin can withstand the combined stresses without failure.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ dc = \left( \frac{16}{\pi \cdot \tau} \cdot \sqrt{(Mb^2) + (Mt^2)} \right)^{1/3} \]

Where:

\( dc \) — Diameter of crank pin (m)
\( \tau \) — Shear stress in central plane of crank pin (Pa)
\( Mb \) — Bending moment at central plane of crankpin (N·m)
\( Mt \) — Torsional moment at central plane of crankpin (N·m)
\( \pi \) — Mathematical constant pi (approximately 3.14159)

Explanation: The formula combines both bending and torsional moments using the square root of the sum of their squares, then calculates the required diameter to withstand the combined stress.

3. Importance of Crank Pin Diameter Calculation

Details: Proper crank pin diameter calculation is crucial for ensuring the crankshaft can withstand maximum torque conditions without failure. An undersized crank pin may lead to mechanical failure, while an oversized one adds unnecessary weight and cost.

4. Using the Calculator

Tips: Enter shear stress in Pascals, bending moment in Newton-meters, and torsional moment in Newton-meters. All values must be positive numbers with shear stress greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: Why is both bending and torsional moment considered?
A: Under maximum torque conditions, the crank pin experiences combined stresses from both bending and torsion. Considering both ensures the design accounts for the worst-case loading scenario.

Q2: What is a typical shear stress value for crank pin material?
A: Typical shear stress values range from 20-60 MPa for steel crank pins, depending on the material grade and safety factors used in the design.

Q3: How does this formula relate to maximum shear stress theory?
A: The formula is derived from the maximum shear stress theory (Tresca criterion), which states that yielding occurs when the maximum shear stress reaches the shear yield strength of the material.

Q4: Can this calculator be used for other shaft components?
A: While the principle is similar, this specific formula is tailored for crank pins in centre crankshafts. Other shaft components may require different formulas based on their specific loading conditions.

Q5: What safety factors should be considered?
A: Engineering designs typically include safety factors ranging from 1.5 to 3.0, depending on the application, material properties, and operating conditions.