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

✖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.ⓘ Addendum of Pinion [A_p]			+10% -10%
✖The pressure angle of gear also known as the angle of obliquity is the angle between the tooth face and the gear wheel tangent.ⓘ Pressure Angle of Gear [Φ_gear]			+10% -10%

✖Number of teeth on pinion is the count of teeth on pinion.ⓘ Minimum Number of Teeth on Pinion to Avoid Interference given Pinion and Wheel have Equal Teeth [Z_p]

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

STEP 0: Pre-Calculation Summary

Formula Used

Number of Teeth on Pinion = (2*Addendum of Pinion)/(sqrt(1+3*(sin(Pressure Angle of Gear))^2)-1)
Z_p = (2*A_p)/(sqrt(1+3*(sin(Φ_gear))^2)-1)
This formula uses 2 Functions, 3 Variables

Functions Used

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., 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., sqrt(Number)

Variables Used

Number of Teeth on Pinion - Number of teeth on pinion is the count of teeth on pinion.
Addendum of Pinion - (Measured in Meter) - 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.
Pressure Angle of Gear - (Measured in Radian) - The pressure angle of gear also known as the angle of obliquity is the angle between the tooth face and the gear wheel tangent.

STEP 1: Convert Input(s) to Base Unit

Addendum of Pinion: 22.5 Millimeter --> 0.0225 Meter (Check conversion here)
Pressure Angle of Gear: 32 Degree --> 0.55850536063808 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

Z_p = (2*A_p)/(sqrt(1+3*(sin(Φ_gear))^2)-1) --> (2*0.0225)/(sqrt(1+3*(sin(0.55850536063808))^2)-1)

Evaluating ... ...

Z_p = 0.125921217683036

STEP 3: Convert Result to Output's Unit

0.125921217683036 --> No Conversion Required

FINAL ANSWER

0.125921217683036 ≈ 0.125921 <-- Number of Teeth on Pinion

(Calculation completed in 00.012 seconds)

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Home » Physics » Theory of Machine » Toothed Gearing » Mechanical » Minimum Number of Teeth » Minimum Number of Teeth on Pinion to Avoid Interference given Pinion and Wheel have Equal Teeth

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National Institute Of Technology (NIT), Hamirpur

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< Minimum Number of Teeth Calculators

Minimum Number of Teeth on Pinion to Avoid Interference

LaTeX Go Minimum Number of Teeth on Pinion = (2*Addendum of Wheel)/(sqrt(1+Number of Teeth on Pinion/Number of Teeth on Wheel*(Number of Teeth on Pinion/Number of Teeth on Wheel+2)*(sin(Pressure Angle of Gear))^2)-1)

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

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

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

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

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

LaTeX Go Number of Teeth on Pinion = (2*Addendum of Rack)/(sin(Pressure Angle of Gear))^2

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

LaTeX Go

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

What do you understand by Interference in gears?

When two gears are in mesh at one instant there is a chance to mate involute portion with non-involute portion of mating gear. This phenomenon is known as "interference" and occurs when the number of teeth on the smaller of the two meshing gears is less than a required minimum.

What is the law of gearing?

The common normal at the point of contact between a pair of teeth must always pass through the pitch point. This is the fundamental condition which must be satisfied while designing the profiles for the teeth of gear wheels. It is also known as law of gearing.

How to Calculate Minimum Number of Teeth on Pinion to Avoid Interference given Pinion and Wheel have Equal Teeth?

Minimum Number of Teeth on Pinion to Avoid Interference given Pinion and Wheel have Equal Teeth calculator uses Number of Teeth on Pinion = (2*Addendum of Pinion)/(sqrt(1+3*(sin(Pressure Angle of Gear))^2)-1) to calculate the Number of Teeth on Pinion, Minimum Number of Teeth on Pinion to Avoid Interference given Pinion and Wheel have Equal Teeth formula is defined as the smallest number of teeth required on the pinion gear to prevent interference with the wheel gear when they have the same number of teeth, ensuring smooth operation and avoiding mechanical failure. Number of Teeth on Pinion is denoted by Z_p symbol.

How to calculate Minimum Number of Teeth on Pinion to Avoid Interference given Pinion and Wheel have Equal Teeth using this online calculator? To use this online calculator for Minimum Number of Teeth on Pinion to Avoid Interference given Pinion and Wheel have Equal Teeth, enter Addendum of Pinion (A_p) & Pressure Angle of Gear (Φ_gear) and hit the calculate button. Here is how the Minimum Number of Teeth on Pinion to Avoid Interference given Pinion and Wheel have Equal Teeth calculation can be explained with given input values -> 0.125921 = (2*0.0225)/(sqrt(1+3*(sin(0.55850536063808))^2)-1).

FAQ

What is Minimum Number of Teeth on Pinion to Avoid Interference given Pinion and Wheel have Equal Teeth?

Minimum Number of Teeth on Pinion to Avoid Interference given Pinion and Wheel have Equal Teeth formula is defined as the smallest number of teeth required on the pinion gear to prevent interference with the wheel gear when they have the same number of teeth, ensuring smooth operation and avoiding mechanical failure and is represented as Z_p = (2*A_p)/(sqrt(1+3*(sin(Φ_gear))^2)-1) or Number of Teeth on Pinion = (2*Addendum of Pinion)/(sqrt(1+3*(sin(Pressure Angle of Gear))^2)-1). 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 & The pressure angle of gear also known as the angle of obliquity is the angle between the tooth face and the gear wheel tangent.

How to calculate Minimum Number of Teeth on Pinion to Avoid Interference given Pinion and Wheel have Equal Teeth?

Minimum Number of Teeth on Pinion to Avoid Interference given Pinion and Wheel have Equal Teeth formula is defined as the smallest number of teeth required on the pinion gear to prevent interference with the wheel gear when they have the same number of teeth, ensuring smooth operation and avoiding mechanical failure is calculated using Number of Teeth on Pinion = (2*Addendum of Pinion)/(sqrt(1+3*(sin(Pressure Angle of Gear))^2)-1). To calculate Minimum Number of Teeth on Pinion to Avoid Interference given Pinion and Wheel have Equal Teeth, you need Addendum of Pinion (A_p) & Pressure Angle of Gear (Φ_gear). With our tool, you need to enter the respective value for Addendum of Pinion & Pressure Angle of Gear and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Number of Teeth on Pinion?

In this formula, Number of Teeth on Pinion uses Addendum of Pinion & Pressure Angle of Gear. We can use 2 other way(s) to calculate the same, which is/are as follows -

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+Gear Ratio*(Gear Ratio+2)*(sin(Pressure Angle of Gear))^2)-1)

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