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

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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 = \frac{2}{{(\sin (Φ))}^{2}}

Example

7.76412 = \frac{2}{{(\sin (30.5 °))}^{2}}

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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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Created by Ojas Kulkarni

Sardar Patel College of Engineering (SPCE), Mumbai

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Verified by Vishal Anand

Indian Institute of Technology Kharagpur (IIT KGP), Kharagpur

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< 5 Design of Spur Gears Calculators

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

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

Module of Gear given Pitch Circle Diameter

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

Diametral Pitch of Gear given Circular Pitch

Go Diametral Pitch of Spur Gear = pi/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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