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Minimum Number of Teeth on Gear to Avoid Interference given Pressure Angle Formula

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Minimum Number of Teeth on Spur Gear to avoid interference is defined as the least number of teeth that should be made on a gear to avoid interference of gear teeth. Check FAQs

z min = \frac{2}{{(\sin (Φ))}^{2}}

z_min - Minimum Number of Teeth on Spur Gear?Φ - Pressure Angle of Spur Gear?

Minimum Number of Teeth on Gear to Avoid Interference given Pressure Angle Example

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Here is how the Minimum Number of Teeth on Gear to Avoid Interference given Pressure Angle equation looks like with Values.

Here is how the Minimum Number of Teeth on Gear to Avoid Interference given Pressure Angle equation looks like with Units.

Here is how the Minimum Number of Teeth on Gear to Avoid Interference given Pressure Angle equation looks like.

7.7641 = \frac{2}{{(\sin (30.5))}^{2}}

7.7641 = \frac{2}{{(\sin (30.5°))}^{2}}

7.7641 = \frac{2}{{(\sin (30.5))}^{2}}

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Minimum Number of Teeth on Gear to Avoid Interference given Pressure Angle Solution

Follow our step by step solution on how to calculate Minimum Number of Teeth on Gear to Avoid Interference given Pressure Angle?

FIRST Step Consider the formula

z min = \frac{2}{{(\sin (Φ))}^{2}}

Next Step Substitute values of Variables

∴

z min = \frac{2}{{(\sin (30.5°))}^{2}}

Next Step Convert Units

∴

z min = \frac{2}{{(\sin (0.5323rad))}^{2}}

Next Step Prepare to Evaluate

∴

z min = \frac{2}{{(\sin (0.5323))}^{2}}

Next Step Evaluate

∴

z min = 7.76412013344262

LAST Step Rounding Answer

∴

z min = 7.7641

Minimum Number of Teeth on Gear to Avoid Interference given Pressure Angle Formula Elements

Variables

Functions

Minimum Number of Teeth on Spur Gear

Minimum Number of Teeth on Spur Gear to avoid interference is defined as the least number of teeth that should be made on a gear to avoid interference of gear teeth.

Symbol: z_min

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Minimum Number of Teeth on Spur Gear

Pressure Angle of Spur Gear

Pressure Angle of Spur Gear also known as the angle of obliquity is the angle between the tooth face and the gear wheel tangent.

Symbol: Φ

Measurement: AngleUnit: °

Note: Value should be greater than 0.

Formulas to find Pressure Angle of Spur Gear

sin

Sine is a trigonometric function that describes the ratio of the length of the opposite side of a right triangle to the length of the hypotenuse.

Syntax: sin(Angle)

Other formulas in Parameters of Spur Gear category

Go Circular Pitch of Gear given Diameter and Number of Teeth

P c = π \cdot \frac{d}{z}

Go Diametral Pitch of Gear given Number of teeth and Pitch Circle Diameter

P d = \frac{z}{d}

Go Diametral Pitch of Gear given Circular Pitch

P d = \frac{π}{P c}

Go Module of Gear given Diametral Pitch

m = \frac{1}{P d}

How to Evaluate Minimum Number of Teeth on Gear to Avoid Interference given Pressure Angle?

Minimum Number of Teeth on Gear to Avoid Interference given Pressure Angle evaluator uses Minimum Number of Teeth on Spur Gear = 2/(sin(Pressure Angle of Spur Gear))^2 to evaluate the Minimum Number of Teeth on Spur Gear, Minimum Number of Teeth on Gear to avoid interference given pressure angle is defined as the least number of teeth that should be made on gear to avoid interference of its teeth. Minimum Number of Teeth on Spur Gear is denoted by z_min symbol.

How to evaluate Minimum Number of Teeth on Gear to Avoid Interference given Pressure Angle using this online evaluator? To use this online evaluator for Minimum Number of Teeth on Gear to Avoid Interference given Pressure Angle, enter Pressure Angle of Spur Gear (Φ) and hit the calculate button.

FAQs on Minimum Number of Teeth on Gear to Avoid Interference given Pressure Angle

What is the formula to find Minimum Number of Teeth on Gear to Avoid Interference given Pressure Angle?

The formula of Minimum Number of Teeth on Gear to Avoid Interference given Pressure Angle is expressed as Minimum Number of Teeth on Spur Gear = 2/(sin(Pressure Angle of Spur Gear))^2. Here is an example- 7.76412 = 2/(sin(0.53232542185817))^2.

How to calculate Minimum Number of Teeth on Gear to Avoid Interference given Pressure Angle?

With Pressure Angle of Spur Gear (Φ) we can find Minimum Number of Teeth on Gear to Avoid Interference given Pressure Angle using the formula - Minimum Number of Teeth on Spur Gear = 2/(sin(Pressure Angle of Spur Gear))^2. This formula also uses Sine function(s).

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