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Minimum Number of Teeth on Pinion to Avoid Interference given Addendum of Pinion Formula

GoMinimum Number of Teeth on Pinion for Involute Rack to Avoid Interference Formula

GoMinimum Number of Teeth on Pinion to Avoid Interference given Pinion and Wheel have Equal Teeth Formula

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Number of teeth on pinion is the count of teeth on pinion. Check FAQs

Z p = \frac{2 \cdot A p}{\sqrt{1 + G \cdot (G + 2) \cdot {(\sin (Φ gear))}^{2}} - 1}

Z_p - Number of Teeth on Pinion?A_p - Addendum of Pinion?G - Gear Ratio?Φ_gear - Pressure Angle of Gear?

Minimum Number of Teeth on Pinion to Avoid Interference given Addendum of Pinion Example

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Here is how the Minimum Number of Teeth on Pinion to Avoid Interference given Addendum of Pinion equation looks like with Values.

Here is how the Minimum Number of Teeth on Pinion to Avoid Interference given Addendum of Pinion equation looks like with Units.

Here is how the Minimum Number of Teeth on Pinion to Avoid Interference given Addendum of Pinion equation looks like.

0.0351 = \frac{2 \cdot 22.5}{\sqrt{1 + 3 \cdot (3 + 2) \cdot {(\sin (32))}^{2}} - 1}

0.0351 = \frac{2 \cdot 22.5mm}{\sqrt{1 + 3 \cdot (3 + 2) \cdot {(\sin (32°))}^{2}} - 1}

0.0351 = \frac{2 \cdot 22.5}{\sqrt{1 + 3 \cdot (3 + 2) \cdot {(\sin (32))}^{2}} - 1}

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Minimum Number of Teeth on Pinion to Avoid Interference given Addendum of Pinion Solution

Follow our step by step solution on how to calculate Minimum Number of Teeth on Pinion to Avoid Interference given Addendum of Pinion?

FIRST Step Consider the formula

Z p = \frac{2 \cdot A p}{\sqrt{1 + G \cdot (G + 2) \cdot {(\sin (Φ gear))}^{2}} - 1}

Next Step Substitute values of Variables

∴

Z p = \frac{2 \cdot 22.5mm}{\sqrt{1 + 3 \cdot (3 + 2) \cdot {(\sin (32°))}^{2}} - 1}

Next Step Convert Units

∴

Z p = \frac{2 \cdot 0.0225m}{\sqrt{1 + 3 \cdot (3 + 2) \cdot {(\sin (0.5585rad))}^{2}} - 1}

Next Step Prepare to Evaluate

∴

Z p = \frac{2 \cdot 0.0225}{\sqrt{1 + 3 \cdot (3 + 2) \cdot {(\sin (0.5585))}^{2}} - 1}

Next Step Evaluate

∴

Z p = 0.0350732824648497

LAST Step Rounding Answer

∴

Z p = 0.0351

Minimum Number of Teeth on Pinion to Avoid Interference given Addendum of Pinion Formula Elements

Variables

Functions

Number of Teeth on Pinion

Number of teeth on pinion is the count of teeth on pinion.

Symbol: Z_p

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Number of Teeth on Pinion

Addendum of Pinion

Addendum of pinion is the height by which a tooth of a gear projects beyond (outside for external, or inside for internal) the standard pitch circle or pitch line.

Symbol: A_p

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Addendum of Pinion

Gear Ratio

The Gear Ratio is the ratio of output gear speed to the input gear speed or the ratio of number of teeth on gear to that on the pinion.

Symbol: G

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Gear Ratio

Pressure Angle of Gear

The pressure angle of gear also known as the angle of obliquity is the angle between the tooth face and the gear wheel tangent.

Symbol: Φ_gear

Measurement: AngleUnit: °

Note: Value should be greater than 0.

Formulas to find Pressure Angle of 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)

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 Number of Teeth on Pinion

Go Minimum Number of Teeth on Pinion for Involute Rack to Avoid Interference

Z p = \frac{2 \cdot A R}{{(\sin (Φ gear))}^{2}}

Go Minimum Number of Teeth on Pinion to Avoid Interference given Pinion and Wheel have Equal Teeth

Z p = \frac{2 \cdot A p}{\sqrt{1 + 3 \cdot {(\sin (Φ gear))}^{2}} - 1}

Other formulas in Minimum Number of Teeth category

Go Minimum Number of Teeth on Pinion to Avoid Interference

Z min = \frac{2 \cdot A w}{\sqrt{1 + \frac{Z p}{T} \cdot (\frac{Z p}{T} + 2) \cdot {(\sin (Φ gear))}^{2}} - 1}

Go Minimum Teeth on Pinion to Avoid Interference given Addendum of Wheels

Z min = \frac{2 \cdot A w}{\frac{T}{Z p} \cdot (\sqrt{1 + \frac{Z p}{T} \cdot (\frac{Z p}{T} + 2) \cdot {(\sin (Φ gear))}^{2}} - 1)}

Go Minimum Teeth on Wheel to Avoid Interference if Pinion and Wheel have Equal Teeth

T = \frac{2 \cdot A w}{\sqrt{1 + 3 \cdot {(\sin (Φ gear))}^{2}} - 1}

How to Evaluate Minimum Number of Teeth on Pinion to Avoid Interference given Addendum of Pinion?

Minimum Number of Teeth on Pinion to Avoid Interference given Addendum of Pinion evaluator uses Number of Teeth on Pinion = (2*Addendum of Pinion)/(sqrt(1+Gear Ratio*(Gear Ratio+2)*(sin(Pressure Angle of Gear))^2)-1) to evaluate the Number of Teeth on Pinion, Minimum Number of Teeth on Pinion to Avoid Interference given Addendum of Pinion formula is defined as the smallest number of teeth required on the pinion gear to prevent interference with the mating gear in an engagement, ensuring smooth and efficient power transmission. Number of Teeth on Pinion is denoted by Z_p symbol.

How to evaluate Minimum Number of Teeth on Pinion to Avoid Interference given Addendum of Pinion using this online evaluator? To use this online evaluator for Minimum Number of Teeth on Pinion to Avoid Interference given Addendum of Pinion, enter Addendum of Pinion (A_p), Gear Ratio (G) & Pressure Angle of Gear (Φ_gear) and hit the calculate button.

FAQs on Minimum Number of Teeth on Pinion to Avoid Interference given Addendum of Pinion

What is the formula to find Minimum Number of Teeth on Pinion to Avoid Interference given Addendum of Pinion?

The formula of Minimum Number of Teeth on Pinion to Avoid Interference given Addendum of Pinion is expressed as Number of Teeth on Pinion = (2*Addendum of Pinion)/(sqrt(1+Gear Ratio*(Gear Ratio+2)*(sin(Pressure Angle of Gear))^2)-1). Here is an example- 0.035073 = (2*0.0225)/(sqrt(1+3*(3+2)*(sin(0.55850536063808))^2)-1).

How to calculate Minimum Number of Teeth on Pinion to Avoid Interference given Addendum of Pinion?

With Addendum of Pinion (A_p), Gear Ratio (G) & Pressure Angle of Gear (Φ_gear) we can find Minimum Number of Teeth on Pinion to Avoid Interference given Addendum of Pinion using the formula - Number of Teeth on Pinion = (2*Addendum of Pinion)/(sqrt(1+Gear Ratio*(Gear Ratio+2)*(sin(Pressure Angle of Gear))^2)-1). This formula also uses Sine (sin), Square Root (sqrt) function(s).

What are the other ways to Calculate Number of Teeth on Pinion?

Here are the different ways to Calculate Number of Teeth on Pinion-

Number of Teeth on Pinion=(2*Addendum of Rack)/(sin(Pressure Angle of Gear))^2
Number of Teeth on Pinion=(2*Addendum of Pinion)/(sqrt(1+3*(sin(Pressure Angle of Gear))^2)-1)

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Minimum Number of Teeth on Pinion to Avoid Interference given Addendum of Pinion Formula

​GoMinimum Number of Teeth on Pinion for Involute Rack to Avoid Interference Formula

​GoMinimum Number of Teeth on Pinion to Avoid Interference given Pinion and Wheel have Equal Teeth Formula

Minimum Number of Teeth on Pinion to Avoid Interference given Addendum of Pinion Example

Minimum Number of Teeth on Pinion to Avoid Interference given Addendum of Pinion Solution

Minimum Number of Teeth on Pinion to Avoid Interference given Addendum of Pinion Formula Elements

Other Formulas to find Number of Teeth on Pinion

Other formulas in Minimum Number of Teeth category

How to Evaluate Minimum Number of Teeth on Pinion to Avoid Interference given Addendum of Pinion?

FAQs on Minimum Number of Teeth on Pinion to Avoid Interference given Addendum of Pinion

Variable Name

GoMinimum Number of Teeth on Pinion for Involute Rack to Avoid Interference Formula

GoMinimum Number of Teeth on Pinion to Avoid Interference given Pinion and Wheel have Equal Teeth Formula