Shaft Diameter Given Compressive Stress In Key Calculator

Formula Used:

\[ d_s = \frac{4 \times M_t}{\sigma_c \times l \times h} \]

Transmitted Torque by Keyed Shaft (M_t):

N·m

Compressive Stress in Key (σ_c):

Length of Key (l):

Height of Key (h):

Diameter of Shaft using Key (d_s):

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1. What is the Shaft Diameter Given Compressive Stress In Key Formula?

The Shaft Diameter Given Compressive Stress In Key formula calculates the required diameter of a shaft based on transmitted torque, key dimensions, and allowable compressive stress in the key. This ensures proper mechanical design and prevents key failure.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ d_s = \frac{4 \times M_t}{\sigma_c \times l \times h} \]

Where:

\( d_s \) — Diameter of shaft using key (m)
\( M_t \) — Transmitted torque by keyed shaft (N·m)
\( \sigma_c \) — Compressive stress in key (Pa)
\( l \) — Length of key (m)
\( h \) — Height of key (m)

Explanation: The formula calculates the minimum shaft diameter required to safely transmit torque without exceeding the allowable compressive stress in the key.

3. Importance of Shaft Diameter Calculation

Details: Proper shaft diameter calculation is crucial for mechanical design to ensure sufficient strength, prevent key failure, and maintain system reliability under operating conditions.

4. Using the Calculator

Tips: Enter transmitted torque in N·m, compressive stress in Pa, and key dimensions in meters. All values must be positive and non-zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is the typical range for compressive stress in keys?
A: Compressive stress values vary by material, but typically range from 70-140 MPa for steel keys in general applications.

Q2: How does key length affect shaft diameter?
A: Longer keys allow for smaller shaft diameters as the stress is distributed over a larger area, reducing compressive stress.

Q3: What safety factors should be considered?
A: Typical safety factors range from 1.5 to 3.0 depending on application criticality, material properties, and operating conditions.

Q4: Can this formula be used for different key shapes?
A: This formula is specifically for rectangular or square parallel keys. Other key types (Woodruff, tapered) require different calculations.

Q5: How does torque affect shaft diameter requirements?
A: Higher torque transmission requires larger shaft diameters to maintain safe stress levels and prevent mechanical failure.