Ratio of Diameter Given Torsional Shear Stress in Hollow Shaft Calculator

Formula Used:

\[ C = \left(1 - \frac{16 \cdot M_{t_{hollowshaft}}}{\pi \cdot d_o^3 \cdot \tau_h}\right)^{1/4} \]

Torsional Moment in Hollow Shaft:

N·m

Outer Diameter of Hollow Shaft:

Torsional Shear Stress in Hollow Shaft:

Ratio of Inner to Outer Diameter of Hollow Shaft:

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1. What is the Ratio of Inner to Outer Diameter of Hollow Shaft?

The Ratio of Inner to Outer Diameter of Hollow Shaft is defined as the inner diameter of the shaft divided by the outer diameter. This ratio is crucial in determining the torsional strength and stress distribution in hollow shafts under torsional loading.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ C = \left(1 - \frac{16 \cdot M_{t_{hollowshaft}}}{\pi \cdot d_o^3 \cdot \tau_h}\right)^{1/4} \]

Where:

\( C \) — Ratio of Inner to Outer Diameter of Hollow Shaft
\( M_{t_{hollowshaft}} \) — Torsional Moment in Hollow Shaft (N·m)
\( d_o \) — Outer Diameter of Hollow Shaft (m)
\( \tau_h \) — Torsional Shear Stress in Hollow Shaft (Pa)
\( \pi \) — Archimedes' constant (approximately 3.1416)

Explanation: The formula calculates the diameter ratio based on the torsional moment, outer diameter, and allowable torsional shear stress in the hollow shaft.

3. Importance of Diameter Ratio Calculation

Details: Accurate calculation of the diameter ratio is essential for designing hollow shafts that can withstand specific torsional loads while maintaining optimal material usage and weight efficiency.

4. Using the Calculator

Tips: Enter torsional moment in N·m, outer diameter in meters, and torsional shear stress in Pascals. All values must be positive and valid for accurate results.

5. Frequently Asked Questions (FAQ)

Q1: Why is the diameter ratio important in shaft design?
A: The diameter ratio affects the shaft's torsional strength, weight, and material efficiency. A proper ratio ensures optimal performance under torsional loads.

Q2: What are typical values for diameter ratios in hollow shafts?
A: Typical ratios range from 0.5 to 0.9, depending on application requirements and material properties.

Q3: How does torsional shear stress affect the diameter ratio?
A: Higher allowable torsional shear stress allows for smaller diameter ratios, while lower stress requirements may necessitate larger ratios for safety.

Q4: Are there limitations to this formula?
A: This formula assumes uniform material properties and applies to circular hollow shafts under pure torsion. It may not be accurate for complex loading conditions or non-uniform materials.

Q5: Can this calculator be used for solid shafts?
A: No, this formula is specifically designed for hollow shafts. For solid shafts, different formulas apply as the inner diameter is zero.