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

✖Addendum of wheel 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 Wheel [A_w]			+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 wheel is the count of teeths on the wheel.ⓘ Minimum Teeth on Wheel to Avoid Interference if Pinion and Wheel have Equal Teeth [T]

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

STEP 0: Pre-Calculation Summary

Formula Used

Number of Teeth on Wheel = (2*Addendum of Wheel)/(sqrt(1+3*(sin(Pressure Angle of Gear))^2)-1)
T = (2*A_w)/(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 Wheel - Number of teeth on wheel is the count of teeths on the wheel.
Addendum of Wheel - (Measured in Meter) - Addendum of wheel 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 Wheel: 24.5 Millimeter --> 0.0245 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

T = (2*A_w)/(sqrt(1+3*(sin(Φ_gear))^2)-1) --> (2*0.0245)/(sqrt(1+3*(sin(0.55850536063808))^2)-1)

Evaluating ... ...

T = 0.137114214810417

STEP 3: Convert Result to Output's Unit

0.137114214810417 --> No Conversion Required

FINAL ANSWER

0.137114214810417 ≈ 0.137114 <-- Number of Teeth on Wheel

(Calculation completed in 00.004 seconds)

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Created by Anshika Arya

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 Teeth on Wheel to Avoid Interference if Pinion and Wheel have Equal Teeth Formula

LaTeX Go

Number of Teeth on Wheel = (2*Addendum of Wheel)/(sqrt(1+3*(sin(Pressure Angle of Gear))^2)-1)
T = (2*A_w)/(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 Teeth on Wheel to Avoid Interference if Pinion and Wheel have Equal Teeth?

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

How to calculate Minimum Teeth on Wheel to Avoid Interference if Pinion and Wheel have Equal Teeth using this online calculator? To use this online calculator for Minimum Teeth on Wheel to Avoid Interference if Pinion and Wheel have Equal Teeth, enter Addendum of Wheel (A_w) & Pressure Angle of Gear (Φ_gear) and hit the calculate button. Here is how the Minimum Teeth on Wheel to Avoid Interference if Pinion and Wheel have Equal Teeth calculation can be explained with given input values -> 0.137114 = (2*0.0245)/(sqrt(1+3*(sin(0.55850536063808))^2)-1).

FAQ

What is Minimum Teeth on Wheel to Avoid Interference if Pinion and Wheel have Equal Teeth?

Minimum Teeth on Wheel to Avoid Interference if Pinion and Wheel have Equal Teeth formula is defined as the smallest number of teeth required on a wheel to prevent interference when paired with a pinion of equal teeth, ensuring smooth gear operation and avoiding mechanical failure and is represented as T = (2*A_w)/(sqrt(1+3*(sin(Φ_gear))^2)-1) or Number of Teeth on Wheel = (2*Addendum of Wheel)/(sqrt(1+3*(sin(Pressure Angle of Gear))^2)-1). Addendum of wheel 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 Teeth on Wheel to Avoid Interference if Pinion and Wheel have Equal Teeth?

Minimum Teeth on Wheel to Avoid Interference if Pinion and Wheel have Equal Teeth formula is defined as the smallest number of teeth required on a wheel to prevent interference when paired with a pinion of equal teeth, ensuring smooth gear operation and avoiding mechanical failure is calculated using Number of Teeth on Wheel = (2*Addendum of Wheel)/(sqrt(1+3*(sin(Pressure Angle of Gear))^2)-1). To calculate Minimum Teeth on Wheel to Avoid Interference if Pinion and Wheel have Equal Teeth, you need Addendum of Wheel (A_w) & Pressure Angle of Gear (Φ_gear). With our tool, you need to enter the respective value for Addendum of Wheel & 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.

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