Length of Kennedy Key Given Compressive Stress in Key Calculator

Formula Used:

\[ l = \frac{\sqrt{2} \times M_{tk}}{d_s \times b_k \times \sigma_c} \]

Transmitted Torque by Kennedy Key (M_tk):

N·m

Diameter of Shaft using Key (d_s):

Width of Key (b_k):

Compressive Stress in Key (σ_c):

Length of Key (l):

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1. What is the Length of Kennedy Key Given Compressive Stress in Key Formula?

The formula calculates the required length of a Kennedy key based on transmitted torque, shaft diameter, key width, and allowable compressive stress. It ensures the key can safely transmit torque without excessive compressive stress.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ l = \frac{\sqrt{2} \times M_{tk}}{d_s \times b_k \times \sigma_c} \]

Where:

\( l \) — Length of Key (m)
\( M_{tk} \) — Transmitted Torque by Kennedy Key (N·m)
\( d_s \) — Diameter of Shaft using Key (m)
\( b_k \) — Width of Key (m)
\( \sigma_c \) — Compressive Stress in Key (Pa)

Explanation: The formula calculates the minimum key length required to safely transmit the specified torque while keeping compressive stress within allowable limits.

3. Importance of Key Length Calculation

Details: Proper key length calculation is essential for ensuring mechanical components can transmit torque safely without failure. An undersized key may fail under load, while an oversized key increases cost and weight unnecessarily.

4. Using the Calculator

Tips: Enter all values in the specified units. Ensure torque is in N·m, dimensions in meters, and stress in Pascals. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is a Kennedy key?
A: A Kennedy key is a type of parallel key used to connect rotating machine elements to shafts, transmitting torque through compressive forces.

Q2: Why is the √2 factor included in the formula?
A: The √2 factor accounts for the 45-degree orientation of the Kennedy key and the resulting force distribution.

Q3: What are typical compressive stress values for keys?
A: Compressive stress values vary by material, but typically range from 70-140 MPa for steel keys, depending on the application and safety factors.

Q4: Can this calculator be used for other key types?
A: This specific formula is designed for Kennedy keys. Other key types (Woodruff, saddle, etc.) have different calculation methods.

Q5: What safety factors should be considered?
A: Always apply appropriate safety factors based on the application. Typical safety factors range from 1.5 to 3 for mechanical keys depending on the criticality of the application.