Outside Diameter of Hollow Shaft based on Equivalent Twisting Moment Calculator

Hollow Shaft Outer Diameter Formula:

\[ d_o = \left( \frac{T_e \times 16}{\pi \times f_s \times (1 - k^4)} \right)^{1/3} \]

Equivalent Twisting Moment (T_e):

N·m

Torsional Shear Stress (f_s):

Ratio of Inner to Outer Diameter (k):

Hollow Shaft Outer Diameter (d_o):

1. What is Hollow Shaft Outer Diameter Calculator?

Definition: This calculator determines the required outer diameter of a hollow shaft based on equivalent twisting moment, torsional shear stress, and diameter ratio.

Purpose: It helps mechanical engineers design hollow shafts that can withstand specified torsional loads while maintaining safety factors.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ d_o = \left( \frac{T_e \times 16}{\pi \times f_s \times (1 - k^4)} \right)^{1/3} \]

Where:

\( d_o \) — Outer diameter of hollow shaft (meters)
\( T_e \) — Equivalent twisting moment (N·m)
\( f_s \) — Torsional shear stress (Pascals)
\( k \) — Ratio of inner to outer diameter (dimensionless, typically 0.85±5%)
\( \pi \) — Mathematical constant pi (~3.1416)

Explanation: The formula calculates the minimum outer diameter needed to resist the applied torque without exceeding the material's shear stress limit.

3. Importance of Shaft Diameter Calculation

Details: Proper shaft sizing ensures structural integrity, prevents failure under torsional loads, and optimizes material usage.

4. Using the Calculator

Tips: Enter the equivalent twisting moment in N·m, allowable shear stress in Pa, and diameter ratio (default 0.85). The ratio should be between 0 and 1.

5. Frequently Asked Questions (FAQ)

Q1: What is a typical value for diameter ratio (k)?
A: Common values range from 0.7 to 0.9, with 0.85±5% being typical for many applications.

Q2: How do I determine the equivalent twisting moment?
A: It's calculated considering combined loading conditions or taken as the maximum applied torque in pure torsion cases.

Q3: What affects the torsional shear stress limit?
A: Material properties, safety factors, and operating conditions determine the allowable shear stress.

Q4: Why is the ratio raised to the 4th power in the formula?
A: This accounts for the polar moment of inertia's dependence on diameter to the 4th power in hollow shafts.

Q5: Can I use this for solid shafts?
A: Yes, set k=0 for solid shafts (inner diameter = 0).