Replacement Shaft Sizing Calculator

Shaft Diameter Formula:

\[ d = \left[ \frac{16}{\pi \tau} \times \sqrt{ (K_b T_b)^2 + (K_t T_t)^2 } \right]^{1/3} \]

Allowable Shear Stress (τ):

Bending Factor (K_b):

Bending Torque (T_b):

Torsional Factor (K_t):

Torsional Torque (T_t):

Shaft Diameter (d):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is Shaft Sizing Calculation?

The shaft sizing calculation determines the appropriate diameter for a mechanical shaft subjected to combined bending and torsion loads. This ensures the shaft can withstand applied stresses without failure while maintaining structural integrity.

2. How Does the Calculator Work?

The calculator uses the shaft diameter formula:

\[ d = \left[ \frac{16}{\pi \tau} \times \sqrt{ (K_b T_b)^2 + (K_t T_t)^2 } \right]^{1/3} \]

Where:

\( d \) — Shaft diameter (m)
\( \tau \) — Allowable shear stress (Pa)
\( K_b \) — Bending factor (unitless)
\( T_b \) — Bending torque (Nm)
\( K_t \) — Torsional factor (unitless)
\( T_t \) — Torsional torque (Nm)
\( \pi \) — 3.1416

Explanation: The formula calculates the minimum shaft diameter required to safely handle combined bending and torsional loads based on material properties and applied forces.

3. Importance of Shaft Sizing

Details: Proper shaft sizing is crucial for mechanical system reliability, preventing shaft failure, minimizing deflection, and ensuring efficient power transmission in rotating machinery.

4. Using the Calculator

Tips: Enter allowable shear stress in Pascals, bending and torsional factors (typically 1.0-2.0), and corresponding torques in Newton-meters. All values must be positive and non-zero.

5. Frequently Asked Questions (FAQ)

Q1: What is allowable shear stress?
A: Allowable shear stress is the maximum shear stress a material can withstand without permanent deformation, typically based on material yield strength and safety factors.

Q2: How do I determine K_b and K_t factors?
A: These factors account for stress concentrations and loading conditions. Common values range from 1.0 for steady loads to 2.0 for shock loads. Consult engineering handbooks for specific applications.

Q3: What units should I use?
A: Use consistent SI units: meters for diameter, Pascals for stress, and Newton-meters for torque. Ensure all inputs are in correct units for accurate results.

Q4: When is this formula applicable?
A: This formula is suitable for solid circular shafts under combined bending and torsion. For hollow shafts or other loading conditions, different formulas may be required.

Q5: What safety factors should I consider?
A: Typical safety factors range from 1.5 to 4.0 depending on application criticality, material variability, and load uncertainty. Always apply appropriate safety margins.