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Width of Key given Compressive Stress in Key Formula

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Width of Key is defined as the width of the key that is fixed in between the shaft and the hub to prevent relative movement between a power transmitting shaft and an attached component. 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.

4.4545 = \sqrt{2} \cdot \frac{635000}{45 \cdot 128 \cdot 35}

4.4545mm = \sqrt{2} \cdot \frac{635000N*mm}{45mm \cdot 128N/mm² \cdot 35mm}

4.4545 = \sqrt{2} \cdot \frac{635000}{45 \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{635000N*mm}{45mm \cdot 128N/mm² \cdot 35mm}

Next Step Convert Units

∴

b k = \sqrt{2} \cdot \frac{635N*m}{0.045m \cdot 1.3E+8Pa \cdot 0.035m}

Next Step Prepare to Evaluate

∴

b k = \sqrt{2} \cdot \frac{635}{0.045 \cdot 1.3E+8 \cdot 0.035}

Next Step Evaluate

∴

b k = 0.00445449212354621m

Next Step Convert to Output's Unit

∴

b k = 4.45449212354621mm

LAST Step Rounding Answer

∴

b k = 4.4545mm

Width of Key given Compressive Stress in Key Formula Elements

Variables

Functions

Width of Key

Width of Key is defined as the width of the key that is fixed in between the shaft and the hub to prevent relative movement between a power transmitting shaft and an attached component.

Symbol: b_k

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Width of Key

Transmitted Torque by Kennedy Key

Transmitted Torque by Kennedy Key is defined as the amount of torque or the rotating power transferred from a shaft using a key into it.

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

Diameter of Shaft using Key is defined as the external surface diameter of a shaft (a rotating machine element) using a key into it.

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

Compressive Stress in Key is the force per unit area of a key cross-section that is responsible for the deformation of the material such that the volume of the material reduces.

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 defined as the length of the key which is used to prevent rotation of a machine component or it is the major dimension of the key.

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