Length of Shaft Given Angle of Twist of Hollow Shaft on Basis of Torsional Rigidity Calculator

Formula Used:

\[ L_h = \frac{\theta_{hollow} \times (G_h \times d_o^4 \times (1 - C^4))}{584 \times M_{t_{hollowshaft}}} \]

Angle of Twist of Hollow Shaft (θ):

rad

Modulus of Rigidity of Hollow Shaft (G):

Outer Diameter of Hollow Shaft (dₒ):

Ratio of Inner to Outer Diameter of Hollow Shaft (C):

Torsional Moment in Hollow Shaft (Mₜ):

N·m

Length of Hollow Shaft (Lₕ):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is Length of Shaft Given Angle of Twist of Hollow Shaft on Basis of Torsional Rigidity?

This calculation determines the length of a hollow shaft based on its angle of twist under torsional loading, using the material's modulus of rigidity, shaft dimensions, and applied torsional moment.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ L_h = \frac{\theta_{hollow} \times (G_h \times d_o^4 \times (1 - C^4))}{584 \times M_{t_{hollowshaft}}} \]

Where:

\( L_h \) — Length of Hollow Shaft (m)
\( \theta_{hollow} \) — Angle of Twist of Hollow Shaft (rad)
\( G_h \) — Modulus of Rigidity of Hollow Shaft (Pa)
\( d_o \) — Outer Diameter of Hollow Shaft (m)
\( C \) — Ratio of Inner to Outer Diameter of Hollow Shaft
\( M_{t_{hollowshaft}} \) — Torsional Moment in Hollow Shaft (N·m)

Explanation: This formula calculates the length of a hollow shaft that would produce a specific angle of twist under given torsional loading conditions, considering the shaft's material properties and geometry.

3. Importance of Length Calculation

Details: Accurate length calculation is crucial for designing shafts in mechanical systems to ensure they can withstand torsional loads without excessive twisting that could affect performance or cause failure.

4. Using the Calculator

Tips: Enter all values in appropriate units (angle in radians, modulus in Pascals, diameters in meters, moment in Newton-meters). The diameter ratio must be between 0 and 1.

5. Frequently Asked Questions (FAQ)

Q1: What is modulus of rigidity?
A: Modulus of rigidity (or shear modulus) is a material property that measures its resistance to shearing deformation under applied shear stress.

Q2: Why is the diameter ratio important?
A: The ratio of inner to outer diameter affects the shaft's polar moment of inertia, which significantly influences its torsional stiffness and strength.

Q3: What are typical values for modulus of rigidity?
A: For steel: ~79.3 GPa, for aluminum: ~26 GPa, for brass: ~40 GPa. Actual values vary by specific alloy and treatment.

Q4: When is this calculation particularly important?
A: In applications where precise angular positioning is critical, such as in precision machinery, robotics, or where torsional vibrations must be minimized.

Q5: What factors can affect the accuracy of this calculation?
A: Material homogeneity, temperature effects, manufacturing tolerances, and non-uniform loading conditions can all affect the actual performance compared to theoretical calculations.