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

✖Addendum of rack 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 Rack [A_R]			+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 for Involute Rack to Avoid Interference [Z_p]

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

STEP 0: Pre-Calculation Summary

Formula Used

Number of Teeth on Pinion = (2*Addendum of Rack)/(sin(Pressure Angle of Gear))^2
Z_p = (2*A_R)/(sin(Φ_gear))^2
This formula uses 1 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)

Variables Used

Number of Teeth on Pinion - Number of teeth on pinion is the count of teeth on pinion.
Addendum of Rack - (Measured in Meter) - Addendum of rack 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 Rack: 13 Millimeter --> 0.013 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_R)/(sin(Φ_gear))^2 --> (2*0.013)/(sin(0.55850536063808))^2

Evaluating ... ...

Z_p = 0.0925878357258983

STEP 3: Convert Result to Output's Unit

0.0925878357258983 --> No Conversion Required

FINAL ANSWER

0.0925878357258983 ≈ 0.092588 <-- Number of Teeth on Pinion

(Calculation completed in 00.004 seconds)

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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 for Involute Rack to Avoid Interference Formula

LaTeX Go

Number of Teeth on Pinion = (2*Addendum of Rack)/(sin(Pressure Angle of Gear))^2
Z_p = (2*A_R)/(sin(Φ_gear))^2

What do you understand by Interference in gears?

When two gears are in mesh at one instant there is a chance to mate an involute portion with a non-involute portion of the 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 that must be satisfied while designing the profiles for the teeth of gear wheels. It is also known as the law of gearing.

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

Minimum Number of Teeth on Pinion for Involute Rack to Avoid Interference calculator uses Number of Teeth on Pinion = (2*Addendum of Rack)/(sin(Pressure Angle of Gear))^2 to calculate the Number of Teeth on Pinion, Minimum Number of Teeth on Pinion for Involute Rack to Avoid Interference formula is defined as the lowest number of teeth required on a pinion gear to prevent interference with an involute rack, ensuring smooth and efficient gear operation without tooth overlap or jamming. Number of Teeth on Pinion is denoted by Z_p symbol.

How to calculate Minimum Number of Teeth on Pinion for Involute Rack to Avoid Interference using this online calculator? To use this online calculator for Minimum Number of Teeth on Pinion for Involute Rack to Avoid Interference, enter Addendum of Rack (A_R) & Pressure Angle of Gear (Φ_gear) and hit the calculate button. Here is how the Minimum Number of Teeth on Pinion for Involute Rack to Avoid Interference calculation can be explained with given input values -> 0.092588 = (2*0.013)/(sin(0.55850536063808))^2.

FAQ

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

Minimum Number of Teeth on Pinion for Involute Rack to Avoid Interference formula is defined as the lowest number of teeth required on a pinion gear to prevent interference with an involute rack, ensuring smooth and efficient gear operation without tooth overlap or jamming and is represented as Z_p = (2*A_R)/(sin(Φ_gear))^2 or Number of Teeth on Pinion = (2*Addendum of Rack)/(sin(Pressure Angle of Gear))^2. Addendum of rack 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 for Involute Rack to Avoid Interference?

Minimum Number of Teeth on Pinion for Involute Rack to Avoid Interference formula is defined as the lowest number of teeth required on a pinion gear to prevent interference with an involute rack, ensuring smooth and efficient gear operation without tooth overlap or jamming is calculated using Number of Teeth on Pinion = (2*Addendum of Rack)/(sin(Pressure Angle of Gear))^2. To calculate Minimum Number of Teeth on Pinion for Involute Rack to Avoid Interference, you need Addendum of Rack (A_R) & Pressure Angle of Gear (Φ_gear). With our tool, you need to enter the respective value for Addendum of Rack & 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 Rack & 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 Pinion)/(sqrt(1+3*(sin(Pressure Angle of Gear))^2)-1)
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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