Height Of Key Given Compressive Stress In Key Calculator

Formula Used:

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

Transmitted Torque by Keyed Shaft (Mt):

N·m

Diameter of Shaft using Key (ds):

Length of Key (l):

Compressive Stress in Key (σc):

Height of Key (h):

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1. What is Height of Key given Compressive Stress in Key?

Height of Key is defined as the vertical length of the key that is used to transmit the torque produced and to restrict the relative movement between two rotating elements. It is calculated based on the transmitted torque, shaft diameter, key length, and compressive stress in the key.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

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

Explanation: The formula calculates the required height of a key based on the transmitted torque and the allowable compressive stress in the key material.

3. Importance of Height of Key Calculation

Details: Accurate calculation of key height is crucial for ensuring proper torque transmission and preventing key failure due to excessive compressive stress. It helps in designing reliable power transmission systems.

4. Using the Calculator

Tips: Enter transmitted torque in N·m, shaft diameter in meters, key length in meters, and compressive stress in Pascals. All values must be positive and non-zero.

5. Frequently Asked Questions (FAQ)

Q1: What is the purpose of a key in mechanical systems?
A: A key is used to prevent relative rotation between a shaft and a connected component (like gears or pulleys) and to transmit torque between them.

Q2: What factors affect key height calculation?
A: Key height depends on transmitted torque, shaft diameter, key length, and the allowable compressive stress of the key material.

Q3: What are typical materials used for keys?
A: Keys are typically made from medium carbon steel (C45) or alloy steels that can withstand high compressive stresses.

Q4: How does compressive stress affect key design?
A: The compressive stress must be kept below the yield strength of the key material to prevent permanent deformation and failure.

Q5: Can this formula be used for different key types?
A: This formula is primarily for rectangular or square parallel keys. Other key types (Woodruff, taper, etc.) may require different calculations.