Minimum Teeth on Pinion to Avoid Interference given Addendum of Wheels 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%
✖Number of teeth on wheel is the count of teeths on the wheel.ⓘ Number of Teeth on Wheel [T]			+10% -10%
✖Number of teeth on pinion is the count of teeth on pinion.ⓘ Number of Teeth on Pinion [Z_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%

✖Minimum number of teeth on pinion is the count of teeth on pinion.ⓘ Minimum Teeth on Pinion to Avoid Interference given Addendum of Wheels [Z_min]

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

STEP 0: Pre-Calculation Summary

Formula Used

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))
Z_min = (2*A_w)/(T/Z_p*(sqrt(1+Z_p/T*(Z_p/T+2)*(sin(Φ_gear))^2)-1))
This formula uses 2 Functions, 5 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

Minimum Number of Teeth on Pinion - Minimum number of teeth on pinion is the count of teeth on pinion.
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.
Number of Teeth on Wheel - Number of teeth on wheel is the count of teeths on the wheel.
Number of Teeth on Pinion - Number of teeth on pinion is the count of teeth on 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 Wheel: 24.5 Millimeter --> 0.0245 Meter (Check conversion here)
Number of Teeth on Wheel: 0.13 --> No Conversion Required
Number of Teeth on Pinion: 0.09 --> No Conversion Required
Pressure Angle of Gear: 32 Degree --> 0.55850536063808 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

Z_min = (2*A_w)/(T/Z_p*(sqrt(1+Z_p/T*(Z_p/T+2)*(sin(Φ_gear))^2)-1)) --> (2*0.0245)/(0.13/0.09*(sqrt(1+0.09/0.13*(0.09/0.13+2)*(sin(0.55850536063808))^2)-1))

Evaluating ... ...

Z_min = 0.144806069702272

STEP 3: Convert Result to Output's Unit

0.144806069702272 --> No Conversion Required

FINAL ANSWER

0.144806069702272 ≈ 0.144806 <-- Minimum Number of Teeth on Pinion

(Calculation completed in 00.004 seconds)

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Home » Physics » Theory of Machine » Toothed Gearing » Mechanical » Minimum Number of Teeth » Minimum Teeth on Pinion to Avoid Interference given Addendum of Wheels

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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 Pinion to Avoid Interference given Addendum of Wheels Formula

LaTeX Go

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 Teeth on Pinion to Avoid Interference given Addendum of Wheels?

Minimum Teeth on Pinion to Avoid Interference given Addendum of Wheels calculator uses 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)) to calculate the Minimum Number of Teeth on Pinion, Minimum Teeth on Pinion to Avoid Interference given Addendum of Wheels formula is defined as the smallest number of teeth required on the pinion gear to prevent interference with the addendum of the mating wheels in a gear train, ensuring smooth and efficient power transmission. Minimum Number of Teeth on Pinion is denoted by Z_min symbol.

How to calculate Minimum Teeth on Pinion to Avoid Interference given Addendum of Wheels using this online calculator? To use this online calculator for Minimum Teeth on Pinion to Avoid Interference given Addendum of Wheels, enter Addendum of Wheel (A_w), Number of Teeth on Wheel (T), Number of Teeth on Pinion (Z_p) & Pressure Angle of Gear (Φ_gear) and hit the calculate button. Here is how the Minimum Teeth on Pinion to Avoid Interference given Addendum of Wheels calculation can be explained with given input values -> 0.144806 = (2*0.0245)/(0.13/0.09*(sqrt(1+0.09/0.13*(0.09/0.13+2)*(sin(0.55850536063808))^2)-1)).

FAQ

What is Minimum Teeth on Pinion to Avoid Interference given Addendum of Wheels?

Minimum Teeth on Pinion to Avoid Interference given Addendum of Wheels formula is defined as the smallest number of teeth required on the pinion gear to prevent interference with the addendum of the mating wheels in a gear train, ensuring smooth and efficient power transmission and is represented as Z_min = (2*A_w)/(T/Z_p*(sqrt(1+Z_p/T*(Z_p/T+2)*(sin(Φ_gear))^2)-1)) or 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)). 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, Number of teeth on wheel is the count of teeths on the wheel, Number of teeth on pinion is the count of teeth on 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 Teeth on Pinion to Avoid Interference given Addendum of Wheels?

Minimum Teeth on Pinion to Avoid Interference given Addendum of Wheels formula is defined as the smallest number of teeth required on the pinion gear to prevent interference with the addendum of the mating wheels in a gear train, ensuring smooth and efficient power transmission is calculated using 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)). To calculate Minimum Teeth on Pinion to Avoid Interference given Addendum of Wheels, you need Addendum of Wheel (A_w), Number of Teeth on Wheel (T), Number of Teeth on Pinion (Z_p) & Pressure Angle of Gear (Φ_gear). With our tool, you need to enter the respective value for Addendum of Wheel, Number of Teeth on Wheel, Number of Teeth on 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 Minimum Number of Teeth on Pinion?

In this formula, Minimum Number of Teeth on Pinion uses Addendum of Wheel, Number of Teeth on Wheel, Number of Teeth on Pinion & Pressure Angle of Gear. We can use 1 other way(s) to calculate the same, which is/are as follows -

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)

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