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Shaft Diameter given Compressive Stress in Key Formula

GoShaft Diameter given Force on 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 = 4 \cdot \frac{M t}{σ c \cdot l \cdot h}

d_s - Diameter of Shaft using Key?M_t - Transmitted Torque by Keyed Shaft?σ_c - Compressive Stress in Key?l - Length of Key?h - Height of Key?

Shaft Diameter given Compressive Stress in Key Example

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

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

Here is how the Shaft Diameter given Compressive Stress in Key equation looks like.

44.5437 = 4 \cdot \frac{224500}{128 \cdot 35 \cdot 4.5}

44.5437mm = 4 \cdot \frac{224500N*mm}{128N/mm² \cdot 35mm \cdot 4.5mm}

44.5437 = 4 \cdot \frac{224500}{128 \cdot 35 \cdot 4.5}

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Shaft Diameter given Compressive Stress in Key Solution

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

FIRST Step Consider the formula

d s = 4 \cdot \frac{M t}{σ c \cdot l \cdot h}

Next Step Substitute values of Variables

∴

d s = 4 \cdot \frac{224500N*mm}{128N/mm² \cdot 35mm \cdot 4.5mm}

Next Step Convert Units

∴

d s = 4 \cdot \frac{224.5N*m}{1.3E+8Pa \cdot 0.035m \cdot 0.0045m}

Next Step Prepare to Evaluate

∴

d s = 4 \cdot \frac{224.5}{1.3E+8 \cdot 0.035 \cdot 0.0045}

Next Step Evaluate

∴

d s = 0.0445436507936508m

Next Step Convert to Output's Unit

∴

d s = 44.5436507936508mm

LAST Step Rounding Answer

∴

d s = 44.5437mm

Shaft Diameter given Compressive Stress in Key Formula Elements

Variables

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 Keyed Shaft

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

Symbol: M_t

Measurement: TorqueUnit: N*mm

Note: Value should be greater than 0.

Formulas to find Transmitted Torque by Keyed Shaft

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

Height of 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.

Symbol: h

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Height of Key

Other Formulas to find Diameter of Shaft using Key

Go Shaft Diameter given Force on Key

d s = 2 \cdot \frac{M t}{F}

Other formulas in Design of Square and Flat Keys category

Go Force on Key

F = 2 \cdot \frac{M t}{d s}

Go Torque Transmitted by Keyed Shaft given Force on Keys

M t = F \cdot \frac{d s}{2}

Go Shear Stress in given Force on Key

𝜏 = \frac{F}{b k \cdot l}

Go Width of Key given Shear Stress in Key

b k = \frac{F}{𝜏 \cdot l}

How to Evaluate Shaft Diameter given Compressive Stress in Key?

Shaft Diameter given Compressive Stress in Key evaluator uses Diameter of Shaft using Key = 4*Transmitted Torque by Keyed Shaft/(Compressive Stress in Key*Length of Key*Height of Key) to evaluate the Diameter of Shaft using Key, Shaft Diameter given Compressive Stress in Key formula is defined as a method to determine the appropriate diameter of a shaft based on the compressive stress experienced by the key. This ensures the shaft can withstand the applied loads without failure, enhancing mechanical reliability. Diameter of Shaft using Key is denoted by d_s symbol.

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

FAQs on Shaft Diameter given Compressive Stress in Key

What is the formula to find Shaft Diameter given Compressive Stress in Key?

The formula of Shaft Diameter given Compressive Stress in Key is expressed as Diameter of Shaft using Key = 4*Transmitted Torque by Keyed Shaft/(Compressive Stress in Key*Length of Key*Height of Key). Here is an example- 44543.65 = 4*224.5/(128000000*0.035*0.0045).

How to calculate Shaft Diameter given Compressive Stress in Key?

With Transmitted Torque by Keyed Shaft (M_t), Compressive Stress in Key (σ_c), Length of Key (l) & Height of Key (h) we can find Shaft Diameter given Compressive Stress in Key using the formula - Diameter of Shaft using Key = 4*Transmitted Torque by Keyed Shaft/(Compressive Stress in Key*Length of Key*Height of Key).

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=2*Transmitted Torque by Keyed Shaft/Force on Key

Can the Shaft Diameter given Compressive Stress in Key be negative?

No, the Shaft Diameter given Compressive Stress in Key, measured in Length cannot be negative.

Which unit is used to measure Shaft Diameter given Compressive Stress in Key?

Shaft Diameter 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 Shaft Diameter given Compressive Stress in Key can be measured.

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Shaft Diameter given Compressive Stress in Key Formula

​GoShaft Diameter given Force on Key Formula

Shaft Diameter given Compressive Stress in Key Example

Shaft Diameter given Compressive Stress in Key Solution

Shaft Diameter given Compressive Stress in Key Formula Elements

Other Formulas to find Diameter of Shaft using Key

Other formulas in Design of Square and Flat Keys category

How to Evaluate Shaft Diameter given Compressive Stress in Key?

FAQs on Shaft Diameter given Compressive Stress in Key

Variable Name

GoShaft Diameter given Force on Key Formula