## Minimum Number of Teeth on Gear to Avoid Interference given Pressure Angle Solution

STEP 0: Pre-Calculation Summary
Formula Used
Minimum Number of Teeth on Spur Gear = 2/(sin(Pressure Angle of Spur Gear))^2
zmin = 2/(sin(Φ))^2
This formula uses 1 Functions, 2 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
Minimum Number of Teeth on Spur Gear - Minimum Number of Teeth on Spur Gear to avoid interference is defined as the least number of teeth that should be made on a gear to avoid interference of gear teeth.
Pressure Angle of Spur Gear - (Measured in Radian) - Pressure Angle of Spur 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
Pressure Angle of Spur Gear: 30.5 Degree --> 0.53232542185817 Radian (Check conversion ​here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
zmin = 2/(sin(Φ))^2 --> 2/(sin(0.53232542185817))^2
Evaluating ... ...
zmin = 7.76412013344262
STEP 3: Convert Result to Output's Unit
7.76412013344262 --> No Conversion Required
7.76412013344262 7.76412 <-- Minimum Number of Teeth on Spur Gear
(Calculation completed in 00.004 seconds)
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## Credits

Created by Ojas Kulkarni
Sardar Patel College of Engineering (SPCE), Mumbai
Ojas Kulkarni has created this Calculator and 10+ more calculators!
Verified by Vishal Anand
Indian Institute of Technology Kharagpur (IIT KGP), Kharagpur
Vishal Anand has verified this Calculator and 6 more calculators!

## < 25 Design of Spur Gears Calculators

Center to Center Distance between Spur Gears
Distance between Spur Gear Centres = Module of Spur Gear*((Number of Teeth on Pinion+Number of Teeth on Spur Gear)/2)
Circular Pitch of Gear given Diameter and Number of Teeth
Circular Pitch of Spur Gear = pi*Pitch Circle Diameter of Spur Gear/Number of Teeth on Spur Gear
Resultant Force on Gear
Resultant Force on Spur Gear = Tangential Force on Spur Gear/cos(Pressure Angle of Spur Gear)
Radial Force of Gear given Tangential Force and Pressure Angle
Radial Force on Spur Gear = Tangential Force on Spur Gear*tan(Pressure Angle of Spur Gear)
Tangential Force on Gear given Radial Force and Pressure Angle
Tangential Force on Spur Gear = Radial Force on Spur Gear*cot(Pressure Angle of Spur Gear)
Pitch Circle Diameter of holes of Medium Size Gear
Pitch Circle Diameter of Holes in Gear = (Inner Diameter of Rim of Spur Gear+Outer Diameter of Spur Gear Hub)/2
Diameter of Holes in Gear Web of Medium Size Diameter
Diameter of Holes in Spur Gear Web = (Inner Diameter of Rim of Spur Gear-Outer Diameter of Spur Gear Hub)/4
Inner Diameter of Rim of Large Size Gear
Inner Diameter of Rim of Spur Gear = Dedendum Circle Diameter of Spur Gear-2*Thickness of Spur Gear Rim
Torque Transmitted by Gear given Tangential Force and Pitch Circle Diameter
Torque transmitted by spur gear = Tangential Force on Spur Gear*Pitch Circle Diameter of Spur Gear/2
Addendum Circle Diameter of Spur Gear = Pitch Circle Diameter of Spur Gear+(2*Addendum of spur gear)
Tangential Force on Gear given Torque and Pitch Circle Diameter
Tangential Force on Spur Gear = 2*Torque transmitted by spur gear/Pitch Circle Diameter of Spur Gear
Dedendum Circle Diameter of Medium Size Gear given Dedundum
Dedendum Circle Diameter of Spur Gear = Pitch Circle Diameter of Spur Gear-(2*Dedundum of Spur Gear)
Diametral Pitch of Gear given Number of teeth and Pitch Circle Diameter
Diametral Pitch of Spur Gear = Number of Teeth on Spur Gear/Pitch Circle Diameter of Spur Gear
Dedendum Circle Diameter of Large Size Gear
Dedendum Circle Diameter of Spur Gear = Module of Spur Gear*(Number of Teeth on Spur Gear-2.5)
Addendum Circle Diameter of Large Size Gear
Addendum Circle Diameter of Spur Gear = Module of Spur Gear*(Number of Teeth on Spur Gear+2)
Pitch Circle Diameter of Gear given Module and Number of Teeth
Pitch Circle Diameter of Spur Gear = Module of Spur Gear*Number of Teeth on Spur Gear
Module of Gear given Pitch Circle Diameter
Module of Spur Gear = Pitch Circle Diameter of Spur Gear/Number of Teeth on Spur Gear
Maximum Torque of Gear given Service Factor
Maximum Torque on Spur Gear = Service Factor for Spur Gear*Rated Torque of Spur Gear
Service Factor for Gear given Torque
Service Factor for Spur Gear = Maximum Torque on Spur Gear/Rated Torque of Spur Gear
Gear Ratio given Number of Teeth
Gear Ratio of Spur Gear = Number of Teeth on Spur Gear/Number of Teeth on Pinion
Gear Ratio given Speed
Gear Ratio of Spur Gear = Speed of Spur Pinion/Speed of Spur Gear
Diametral Pitch of Gear given Circular Pitch
Diametral Pitch of Spur Gear = pi/Circular Pitch of Spur Gear
Outer Diameter of Hub of Large Size Gear
Outer Diameter of Spur Gear Hub = 2*Diameter of Spur Gear Shaft
Thickness of Rim of Large Size Gear
Thickness of Spur Gear Rim = 0.56*Circular Pitch of Spur Gear
Module of Gear given Diametral Pitch
Module of Spur Gear = 1/Diametral Pitch of Spur Gear

## Minimum Number of Teeth on Gear to Avoid Interference given Pressure Angle Formula

Minimum Number of Teeth on Spur Gear = 2/(sin(Pressure Angle of Spur Gear))^2
zmin = 2/(sin(Φ))^2

## What is interference in gears?

When two gears mesh, involute and non-involute portions of gear come into contact due to clearance present in the dedendum of gear which leads to cutting the tooth narrower. Such a phenomenon is called interference.

## How to Calculate Minimum Number of Teeth on Gear to Avoid Interference given Pressure Angle?

Minimum Number of Teeth on Gear to Avoid Interference given Pressure Angle calculator uses Minimum Number of Teeth on Spur Gear = 2/(sin(Pressure Angle of Spur Gear))^2 to calculate the Minimum Number of Teeth on Spur Gear, Minimum Number of Teeth on Gear to avoid interference given pressure angle is defined as the least number of teeth that should be made on gear to avoid interference of its teeth. Minimum Number of Teeth on Spur Gear is denoted by zmin symbol.

How to calculate Minimum Number of Teeth on Gear to Avoid Interference given Pressure Angle using this online calculator? To use this online calculator for Minimum Number of Teeth on Gear to Avoid Interference given Pressure Angle, enter Pressure Angle of Spur Gear (Φ) and hit the calculate button. Here is how the Minimum Number of Teeth on Gear to Avoid Interference given Pressure Angle calculation can be explained with given input values -> 7.76412 = 2/(sin(0.53232542185817))^2.

### FAQ

What is Minimum Number of Teeth on Gear to Avoid Interference given Pressure Angle?
Minimum Number of Teeth on Gear to avoid interference given pressure angle is defined as the least number of teeth that should be made on gear to avoid interference of its teeth and is represented as zmin = 2/(sin(Φ))^2 or Minimum Number of Teeth on Spur Gear = 2/(sin(Pressure Angle of Spur Gear))^2. Pressure Angle of Spur 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 Gear to Avoid Interference given Pressure Angle?
Minimum Number of Teeth on Gear to avoid interference given pressure angle is defined as the least number of teeth that should be made on gear to avoid interference of its teeth is calculated using Minimum Number of Teeth on Spur Gear = 2/(sin(Pressure Angle of Spur Gear))^2. To calculate Minimum Number of Teeth on Gear to Avoid Interference given Pressure Angle, you need Pressure Angle of Spur Gear (Φ). With our tool, you need to enter the respective value for Pressure Angle of Spur 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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