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

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Design of Gears

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Design of Spur Gears

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✖Pressure Angle of Spur Gear also known as the angle of obliquity is the angle between the tooth face and the gear wheel tangent.ⓘ Pressure Angle of Spur Gear [Φ]

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✖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.ⓘ Minimum Number of Teeth on Gear to Avoid Interference given Pressure Angle [z_min]

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Formula

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

Formula

`"z"_{"min"} = 2/(sin("Φ"))^2`

Example

`"7.76412"=2/(sin("30.5°"))^2`

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Download Design of Spur Gears Formulas PDF

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
z_min = 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

z_min = 2/(sin(Φ))^2 --> 2/(sin(0.53232542185817))^2

Evaluating ... ...

z_min = 7.76412013344262

STEP 3: Convert Result to Output's Unit

7.76412013344262 --> No Conversion Required

FINAL ANSWER

7.76412013344262 ≈ 7.76412 <-- Minimum Number of Teeth on Spur Gear

(Calculation completed in 00.004 seconds)

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Home » Physics » Design of Machine Elements » Design of Gears » Design of Spur Gears » Minimum Number of Teeth on Gear to Avoid Interference given Pressure Angle

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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

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< 25 Design of Spur Gears Calculators

Center to Center Distance between Spur Gears

Go 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

Go Circular Pitch of Spur Gear = pi*Pitch Circle Diameter of Spur Gear/Number of Teeth on Spur Gear

Resultant Force on Gear

Go 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

Go 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

Go 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

Go 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

Go 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

Go 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

Go Torque transmitted by spur gear = Tangential Force on Spur Gear*Pitch Circle Diameter of Spur Gear/2

Addendum Circle Diameter of Medium Size Gear Diameter given Addendum

Go 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

Go 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

Go 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

Go Diametral Pitch of Spur Gear = Number of Teeth on Spur Gear/Pitch Circle Diameter of Spur Gear

Dedendum Circle Diameter of Large Size Gear

Go 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

Go 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

Go Pitch Circle Diameter of Spur Gear = Module of Spur Gear*Number of Teeth on Spur Gear

Module of Gear given Pitch Circle Diameter

Go Module of Spur Gear = Pitch Circle Diameter of Spur Gear/Number of Teeth on Spur Gear

Maximum Torque of Gear given Service Factor

Go Maximum Torque on Spur Gear = Service Factor for Spur Gear*Rated Torque of Spur Gear

Service Factor for Gear given Torque

Go Service Factor for Spur Gear = Maximum Torque on Spur Gear/Rated Torque of Spur Gear

Gear Ratio given Number of Teeth

Go Gear Ratio of Spur Gear = Number of Teeth on Spur Gear/Number of Teeth on Pinion

Gear Ratio given Speed

Go Gear Ratio of Spur Gear = Speed of Spur Pinion/Speed of Spur Gear

Diametral Pitch of Gear given Circular Pitch

Go Diametral Pitch of Spur Gear = pi/Circular Pitch of Spur Gear

Outer Diameter of Hub of Large Size Gear

Go Outer Diameter of Spur Gear Hub = 2*Diameter of Spur Gear Shaft

Thickness of Rim of Large Size Gear

Go Thickness of Spur Gear Rim = 0.56*Circular Pitch of Spur Gear

Module of Gear given Diametral Pitch

Go 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
z_min = 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 z_min 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 z_min = 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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