Resultant Bending Moment At Side Crankshaft Below Flywheel At Max Torque Given Bearing Reactions Calculator

Formula Used:

\[ M_{br} = \sqrt{ \left( \left( P_r \cdot (b + c_1) - c_1 \cdot (R_{1v} + R'_{1v}) \right)^2 + \left( P_t \cdot (b + c_1) - c_1 \cdot (R_{1h} + R'_{1h}) \right)^2 \right) } \]

Radial Force at Crank Pin (P_r):

Overhang Distance of Piston Force From Bearing1 (b):

Side Crankshaft Bearing1 Gap From Flywheel (c₁):

Vertical Reaction at Bearing 1 Due to Radial Force (R_1v):

Vertical Reaction at Bearing 1 Due to Flywheel (R'_1v):

Tangential Force at Crank Pin (P_t):

Horizontal Force at Bearing1 By Tangential Force (R_1h):

Horizontal Reaction at Bearing 1 Due to Belt (R'_1h):

Total Bending Moment in Crankshaft Under Flywheel (M_br):

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1. What is the Resultant Bending Moment in Crankshaft?

The resultant bending moment in the crankshaft under the flywheel is the combined effect of bending moments in both horizontal and vertical planes. It represents the total bending stress experienced by the crankshaft section below the flywheel at maximum torque conditions, considering various bearing reactions.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ M_{br} = \sqrt{ \left( \left( P_r \cdot (b + c_1) - c_1 \cdot (R_{1v} + R'_{1v}) \right)^2 + \left( P_t \cdot (b + c_1) - c_1 \cdot (R_{1h} + R'_{1h}) \right)^2 \right) } \]

Where:

\( M_{br} \) — Total bending moment in crankshaft under flywheel (N·m)
\( P_r \) — Radial force at crank pin (N)
\( b \) — Overhang distance of piston force from bearing1 (m)
\( c_1 \) — Side crankshaft bearing1 gap from flywheel (m)
\( R_{1v} \) — Vertical reaction at bearing 1 due to radial force (N)
\( R'_{1v} \) — Vertical reaction at bearing 1 due to flywheel (N)
\( P_t \) — Tangential force at crank pin (N)
\( R_{1h} \) — Horizontal force at bearing1 by tangential force (N)
\( R'_{1h} \) — Horizontal reaction at bearing 1 due to belt (N)

Explanation: The formula calculates the resultant bending moment by combining the effects of both vertical and horizontal bending moments using vector addition.

3. Importance of Bending Moment Calculation

Details: Accurate calculation of bending moments is crucial for crankshaft design and analysis. It helps determine stress levels, fatigue life, and ensures the crankshaft can withstand operational loads without failure.

4. Using the Calculator

Tips: Enter all values in appropriate units (N for forces, m for distances). Ensure all values are positive and within reasonable ranges for mechanical systems.

5. Frequently Asked Questions (FAQ)

Q1: Why is the resultant bending moment important in crankshaft design?
A: It determines the maximum stress the crankshaft experiences, which is critical for ensuring structural integrity and preventing fatigue failure.

Q2: What factors influence the bending moment in a crankshaft?
A: Engine torque, piston forces, flywheel weight, bearing reactions, and geometric dimensions all contribute to the bending moment.

Q3: How does flywheel position affect bending moments?
A: The flywheel's weight and position create additional moments that must be considered in the overall bending moment calculation.

Q4: Are there safety factors applied to these calculations?
A: Yes, engineering designs typically include safety factors to account for dynamic loads, material variations, and unexpected operating conditions.

Q5: Can this calculator be used for different engine configurations?
A: While the formula is general, specific engine configurations may require additional considerations or modified calculations.