Length Of Key Given Compressive Stress In Key Calculator

Formula Used:

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

Transmitted Torque by Keyed Shaft (M_t):

N·m

Diameter of Shaft using Key (d_s):

Compressive Stress in Key (σ_c):

Height of Key (h):

Length of Key (l):

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

The Length of Key Given Compressive Stress in Key is a calculation used in mechanical engineering to determine the required length of a key that can safely transmit torque from a shaft to a hub without exceeding the compressive stress limit of the key material.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

\( l \) — Length of Key (m)
\( M_t \) — Transmitted Torque by Keyed Shaft (N·m)
\( d_s \) — Diameter of Shaft using Key (m)
\( \sigma_c \) — Compressive Stress in Key (Pa)
\( h \) — Height of Key (m)

Explanation: This formula calculates the minimum key length required to prevent failure due to compressive stress when transmitting a specific torque through a keyed shaft connection.

3. Importance of Key Length Calculation

Details: Proper key length calculation ensures mechanical components can transmit required torque without failure, prevents equipment damage, and maintains operational safety in machinery and rotating equipment.

4. Using the Calculator

Tips: Enter all values in consistent SI units. Torque in Newton-meters, dimensions in meters, and stress in Pascals. All input values must be positive numbers greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: What is a key in mechanical engineering?
A: A key is a machine element used to connect a rotating machine element to a shaft, preventing relative rotation between them and enabling torque transmission.

Q2: Why is compressive stress important in key design?
A: Compressive stress determines the key's ability to withstand the crushing forces generated during torque transmission without permanent deformation or failure.

Q3: What are typical materials used for keys?
A: Keys are typically made from medium carbon steel, alloy steel, or stainless steel, chosen for their strength and wear resistance properties.

Q4: How does shaft diameter affect key length?
A: Larger shaft diameters generally require longer keys to distribute the compressive stress over a larger area and maintain safe stress levels.

Q5: What safety factors should be considered?
A: Engineering design typically includes safety factors of 1.5-3.0 to account for dynamic loads, material variations, and unexpected operating conditions.