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Width of Key given Compressive Stress in Key Formula

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The Width of Key is the measurement of the key's thickness, which ensures proper fit and function within a mechanical assembly, preventing slippage and ensuring torque transmission. Check FAQs

b k = \sqrt{2} \cdot \frac{Mt k}{d s \cdot σ c \cdot l}

b_k - Width of Key?Mt_k - Transmitted Torque by Kennedy Key?d_s - Diameter of Shaft using Key?σ_c - Compressive Stress in Key?l - Length of Key?

Width of Key given Compressive Stress in Key Example

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Here is how the Width of Key given Compressive Stress in Key equation looks like with Values.

Here is how the Width of Key given Compressive Stress in Key equation looks like with Units.

Here is how the Width of Key given Compressive Stress in Key equation looks like.

5.0011 = \sqrt{2} \cdot \frac{712763.6}{44.99 \cdot 128 \cdot 35}

5.0011mm = \sqrt{2} \cdot \frac{712763.6N*mm}{44.99mm \cdot 128N/mm² \cdot 35mm}

5.0011 = \sqrt{2} \cdot \frac{712763.6}{44.99 \cdot 128 \cdot 35}

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Width of Key given Compressive Stress in Key Solution

Follow our step by step solution on how to calculate Width of Key given Compressive Stress in Key?

FIRST Step Consider the formula

b k = \sqrt{2} \cdot \frac{Mt k}{d s \cdot σ c \cdot l}

Next Step Substitute values of Variables

∴

b k = \sqrt{2} \cdot \frac{712763.6N*mm}{44.99mm \cdot 128N/mm² \cdot 35mm}

Next Step Convert Units

∴

b k = \sqrt{2} \cdot \frac{712.7636N*m}{0.045m \cdot 1.3E+8Pa \cdot 0.035m}

Next Step Prepare to Evaluate

∴

b k = \sqrt{2} \cdot \frac{712.7636}{0.045 \cdot 1.3E+8 \cdot 0.035}

Next Step Evaluate

∴

b k = 0.00500111333265342m

Next Step Convert to Output's Unit

∴

b k = 5.00111333265342mm

LAST Step Rounding Answer

∴

b k = 5.0011mm

Width of Key given Compressive Stress in Key Formula Elements

Variables

Functions

Width of Key

The Width of Key is the measurement of the key's thickness, which ensures proper fit and function within a mechanical assembly, preventing slippage and ensuring torque transmission.

Symbol: b_k

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Width of Key

Transmitted Torque by Kennedy Key

The Transmitted Torque by Kennedy Key is the torque that a Kennedy key can effectively transmit between two connected machine components without slipping or failure.

Symbol: Mt_k

Measurement: TorqueUnit: N*mm

Note: Value should be greater than 0.

Formulas to find Transmitted Torque by Kennedy Key

Diameter of Shaft using Key

The Diameter of Shaft using Key is the measurement across the widest part of a shaft that accommodates a key for secure attachment and torque transmission.

Symbol: d_s

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Diameter of Shaft using Key

Compressive Stress in Key

The Compressive Stress in Key is the internal stress experienced by a key due to axial loads, affecting its performance and stability in mechanical assemblies.

Symbol: σ_c

Measurement: StressUnit: N/mm²

Note: Value should be greater than 0.

Formulas to find Compressive Stress in Key

Length of Key

The Length of Key is the measurement of the key used in mechanical systems to secure components and transmit torque between shafts and hubs.

Symbol: l

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Length of Key

sqrt

A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number.

Syntax: sqrt(Number)

Other formulas in Design of Kennedy Key category

Go Shear Stress in Kennedy Key

𝜏 = \frac{Mt k}{\sqrt{2} \cdot d s \cdot b k \cdot l}

Go Torque Transmitted by Kennedy Key given Shear Stress in Key

Mt k = 𝜏 \cdot \sqrt{2} \cdot d s \cdot b k \cdot l

Go Diameter of Shaft given Shear Stress in Kennedy Key

d s = \frac{Mt k}{\sqrt{2} \cdot 𝜏 \cdot b k \cdot l}

Go Length of Kennedy Key given Shear Stress in Key

l = \frac{Mt k}{\sqrt{2} \cdot d s \cdot b k \cdot 𝜏}

How to Evaluate Width of Key given Compressive Stress in Key?

Width of Key given Compressive Stress in Key evaluator uses Width of Key = sqrt(2)*Transmitted Torque by Kennedy Key/(Diameter of Shaft using Key*Compressive Stress in Key*Length of Key) to evaluate the Width of Key, Width of Key given Compressive Stress in Key formula is defined as a method to determine the necessary width of a key in mechanical design, ensuring it can withstand compressive stress without failure. This is crucial for the reliability and efficiency of mechanical components. Width of Key is denoted by b_k symbol.

How to evaluate Width of Key given Compressive Stress in Key using this online evaluator? To use this online evaluator for Width of Key given Compressive Stress in Key, enter Transmitted Torque by Kennedy Key (Mt_k), Diameter of Shaft using Key (d_s), Compressive Stress in Key (σ_c) & Length of Key (l) and hit the calculate button.

FAQs on Width of Key given Compressive Stress in Key

What is the formula to find Width of Key given Compressive Stress in Key?

The formula of Width of Key given Compressive Stress in Key is expressed as Width of Key = sqrt(2)*Transmitted Torque by Kennedy Key/(Diameter of Shaft using Key*Compressive Stress in Key*Length of Key). Here is an example- 5001.113 = sqrt(2)*712.7636/(0.04498998*128000000*0.035).

How to calculate Width of Key given Compressive Stress in Key?

With Transmitted Torque by Kennedy Key (Mt_k), Diameter of Shaft using Key (d_s), Compressive Stress in Key (σ_c) & Length of Key (l) we can find Width of Key given Compressive Stress in Key using the formula - Width of Key = sqrt(2)*Transmitted Torque by Kennedy Key/(Diameter of Shaft using Key*Compressive Stress in Key*Length of Key). This formula also uses Square Root (sqrt) function(s).

Can the Width of Key given Compressive Stress in Key be negative?

No, the Width of Key given Compressive Stress in Key, measured in Length cannot be negative.

Which unit is used to measure Width of Key given Compressive Stress in Key?

Width of Key given Compressive Stress in Key is usually measured using the Millimeter[mm] for Length. Meter[mm], Kilometer[mm], Decimeter[mm] are the few other units in which Width of Key given Compressive Stress in Key can be measured.

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Width of Key given Compressive Stress in Key Formula

Width of Key given Compressive Stress in Key Example

Width of Key given Compressive Stress in Key Solution

Width of Key given Compressive Stress in Key Formula Elements

Other formulas in Design of Kennedy Key category

How to Evaluate Width of Key given Compressive Stress in Key?

FAQs on Width of Key given Compressive Stress in Key

Variable Name