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Diameter of Shaft given Shear Stress in Kennedy Key Formula

GoDiameter of Shaft given Compressive Stress in Kennedy Key Formula

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

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

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

Diameter of Shaft given Shear Stress in Kennedy Key Example

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Here is how the Diameter of Shaft given Shear Stress in Kennedy Key equation looks like with Values.

Here is how the Diameter of Shaft given Shear Stress in Kennedy Key equation looks like with Units.

Here is how the Diameter of Shaft given Shear Stress in Kennedy Key equation looks like.

40.1532 = \frac{635000}{\sqrt{2} \cdot 63.9 \cdot 5 \cdot 35}

40.1532mm = \frac{635000N*mm}{\sqrt{2} \cdot 63.9N/mm² \cdot 5mm \cdot 35mm}

40.1532 = \frac{635000}{\sqrt{2} \cdot 63.9 \cdot 5 \cdot 35}

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Diameter of Shaft given Shear Stress in Kennedy Key Solution

Follow our step by step solution on how to calculate Diameter of Shaft given Shear Stress in Kennedy Key?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

d s = \frac{635000N*mm}{\sqrt{2} \cdot 63.9N/mm² \cdot 5mm \cdot 35mm}

Next Step Convert Units

∴

d s = \frac{635N*m}{\sqrt{2} \cdot 6.4E+7Pa \cdot 0.005m \cdot 0.035m}

Next Step Prepare to Evaluate

∴

d s = \frac{635}{\sqrt{2} \cdot 6.4E+7 \cdot 0.005 \cdot 0.035}

Next Step Evaluate

∴

d s = 0.0401531684375996m

Next Step Convert to Output's Unit

∴

d s = 40.1531684375996mm

LAST Step Rounding Answer

∴

d s = 40.1532mm

Diameter of Shaft given Shear Stress in Kennedy Key Formula Elements

Variables

Functions

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

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

Shear Stress in Key

Shear Stress in Key is the force per unit area tending to cause deformation of the key by slippage along a plane or planes parallel to the imposed stress.

Symbol: 𝜏

Measurement: StressUnit: N/mm²

Note: Value should be greater than 0.

Formulas to find Shear Stress in Key

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

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 to find Diameter of Shaft using Key

Go Diameter of Shaft given Compressive Stress in Kennedy Key

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

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 Length of Kennedy Key given Shear Stress in Key

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

Go Compressive Stress in Kennedy Key

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

How to Evaluate Diameter of Shaft given Shear Stress in Kennedy Key?

Diameter of Shaft given Shear Stress in Kennedy Key evaluator uses Diameter of Shaft using Key = Transmitted Torque by Kennedy Key/(sqrt(2)*Shear Stress in Key*Width of Key*Length of Key) to evaluate the Diameter of Shaft using Key, Diameter of Shaft given Shear Stress in Kennedy Key formula is defined as a method to determine the appropriate diameter of a shaft based on the shear stress experienced in a Kennedy key design. This ensures the shaft can safely transmit torque without failure. Diameter of Shaft using Key is denoted by d_s symbol.

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

FAQs on Diameter of Shaft given Shear Stress in Kennedy Key

What is the formula to find Diameter of Shaft given Shear Stress in Kennedy Key?

The formula of Diameter of Shaft given Shear Stress in Kennedy Key is expressed as Diameter of Shaft using Key = Transmitted Torque by Kennedy Key/(sqrt(2)*Shear Stress in Key*Width of Key*Length of Key). Here is an example- 50500.99 = 712.7636/(sqrt(2)*63900000*0.005*0.035).

How to calculate Diameter of Shaft given Shear Stress in Kennedy Key?

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

What are the other ways to Calculate Diameter of Shaft using Key?

Here are the different ways to Calculate Diameter of Shaft using Key-

Diameter of Shaft using Key=sqrt(2)*Transmitted Torque by Kennedy Key/(Compressive Stress in Key*Width of Key*Length of Key)

Can the Diameter of Shaft given Shear Stress in Kennedy Key be negative?

No, the Diameter of Shaft given Shear Stress in Kennedy Key, measured in Length cannot be negative.

Which unit is used to measure Diameter of Shaft given Shear Stress in Kennedy Key?

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

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Diameter of Shaft given Shear Stress in Kennedy Key Formula

​GoDiameter of Shaft given Compressive Stress in Kennedy Key Formula

Diameter of Shaft given Shear Stress in Kennedy Key Example

Diameter of Shaft given Shear Stress in Kennedy Key Solution

Diameter of Shaft given Shear Stress in Kennedy Key Formula Elements

Other Formulas to find Diameter of Shaft using Key

Other formulas in Design of Kennedy Key category

How to Evaluate Diameter of Shaft given Shear Stress in Kennedy Key?

FAQs on Diameter of Shaft given Shear Stress in Kennedy Key

Variable Name

GoDiameter of Shaft given Compressive Stress in Kennedy Key Formula