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

STEP 0: Pre-Calculation Summary
Formula Used
Number of Teeth on Pinion = (2*Addendum of Pinion)/(sqrt(1+Gear Ratio*(Gear Ratio+2)*(sin(Pressure Angle of Gear))^2)-1)
Zp = (2*Ap)/(sqrt(1+G*(G+2)*(sin(Φgear))^2)-1)
This formula uses 2 Functions, 4 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.
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.
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)
Gear Ratio: 3 --> No Conversion Required
Pressure Angle of Gear: 32 Degree --> 0.55850536063808 Radian (Check conversion here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
Zp = (2*Ap)/(sqrt(1+G*(G+2)*(sin(Φgear))^2)-1) --> (2*0.0225)/(sqrt(1+3*(3+2)*(sin(0.55850536063808))^2)-1)
Evaluating ... ...
Zp = 0.0350732824648497
STEP 3: Convert Result to Output's Unit
0.0350732824648497 --> No Conversion Required
FINAL ANSWER
0.0350732824648497 0.035073 <-- Number of Teeth on Pinion
(Calculation completed in 00.004 seconds)

Credits

Created by Anshika Arya
National Institute Of Technology (NIT), Hamirpur
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6 Minimum Number of Teeth Calculators

Minimum Teeth on Pinion to Avoid Interference given Addendum of Wheels
Go Minimum number of teeth on pinion = (2*Addendum of Wheel)/(Number of Teeth on Wheel/Number of Teeth on Pinion*(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
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
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
Go Number of Teeth on Pinion = (2*Addendum of Pinion)/(sqrt(1+3*(sin(Pressure Angle of Gear))^2)-1)
Minimum Teeth on Wheel to Avoid Interference if Pinion and Wheel have Equal Teeth
Go Number of Teeth on Wheel = (2*Addendum of Wheel)/(sqrt(1+3*(sin(Pressure Angle of Gear))^2)-1)
Minimum Number of Teeth on Pinion for Involute Rack to Avoid Interference
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 Addendum of Pinion Formula

Number of Teeth on Pinion = (2*Addendum of Pinion)/(sqrt(1+Gear Ratio*(Gear Ratio+2)*(sin(Pressure Angle of Gear))^2)-1)
Zp = (2*Ap)/(sqrt(1+G*(G+2)*(sin(Φgear))^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 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 to Avoid Interference given Addendum of Pinion?

Minimum Number of Teeth on Pinion to Avoid Interference given Addendum of Pinion calculator 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 calculate the Number of Teeth on Pinion, Minimum Number of Teeth on Pinion to avoid Interference given addendum of Pinion is the minimum number of teeth required on the pinion in order to avoid interference. Number of Teeth on Pinion is denoted by Zp symbol.

How to calculate Minimum Number of Teeth on Pinion to Avoid Interference given Addendum of Pinion using this online calculator? To use this online calculator for Minimum Number of Teeth on Pinion to Avoid Interference given Addendum of Pinion, enter Addendum of Pinion (Ap), Gear Ratio (G) & Pressure Angle of Gear gear) and hit the calculate button. Here is how the Minimum Number of Teeth on Pinion to Avoid Interference given Addendum of Pinion calculation can be explained with given input values -> 0.035073 = (2*0.0225)/(sqrt(1+3*(3+2)*(sin(0.55850536063808))^2)-1).

FAQ

What is 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 is the minimum number of teeth required on the pinion in order to avoid interference and is represented as Zp = (2*Ap)/(sqrt(1+G*(G+2)*(sin(Φgear))^2)-1) or Number of Teeth on Pinion = (2*Addendum of Pinion)/(sqrt(1+Gear Ratio*(Gear Ratio+2)*(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 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 & 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 Addendum of Pinion?
Minimum Number of Teeth on Pinion to avoid Interference given addendum of Pinion is the minimum number of teeth required on the pinion in order to avoid interference is calculated using Number of Teeth on Pinion = (2*Addendum of Pinion)/(sqrt(1+Gear Ratio*(Gear Ratio+2)*(sin(Pressure Angle of Gear))^2)-1). To calculate Minimum Number of Teeth on Pinion to Avoid Interference given Addendum of Pinion, you need Addendum of Pinion (Ap), Gear Ratio (G) & Pressure Angle of Gear gear). With our tool, you need to enter the respective value for Addendum of Pinion, Gear Ratio & 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, Gear Ratio & 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+3*(sin(Pressure Angle of Gear))^2)-1)
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