Number of Teeth on First Gear given Center to Center Distance between Two Gears Calculator

↳

⤿

Design of Gears

Basics Of Machine Design

Design of Coupling

⤿

Design of Helical Gears

Design of Bevel Gears

Design of Spur Gears

Design of Worm Gears

⤿

Core Design Parameters

Helix Geometry

✖Center to Center Distance of Helical Gears is defined as the distance in between the centers of the two helical gears that are taken in consideration.ⓘ Center to Center Distance of Helical Gears [a_c]			+10% -10%
✖Helix Angle of Helical Gear is the angle between any helical gear and an axial line on its right, circular cylinder, or cone.ⓘ Helix Angle of Helical Gear [ψ]			+10% -10%
✖The Normal Module of Helical Gear is defined as the unit of size that indicates how big or small is the helical gear.ⓘ Normal Module of Helical Gear [m_n]			+10% -10%
✖The Number of Teeth on 2nd Helical Gear is defined as the number of teeth that are present on gear 2.ⓘ Number of Teeth on 2nd Helical Gear [z₂]			+10% -10%

✖The Number of Teeth on 1st Helical Gear is defined as the number of teeth that are present on gear 1.ⓘ Number of Teeth on First Gear given Center to Center Distance between Two Gears [z₁]

⎘ Copy

👎

Formula

✖

Number of Teeth on First Gear given Center to Center Distance between Two Gears

Formula

`"z"_{"1"} = "a"_{"c"}*(2*cos("ψ"))/"m"_{"n"}-"z"_{"2"}`

Example

`"17.99758"="99.3mm"*(2*cos("25°"))/"3mm"-"42"`

Calculator

LaTeX

Reset

👍

Download Design of Helical Gears Formulas PDF

Number of Teeth on First Gear given Center to Center Distance between Two Gears Solution

STEP 0: Pre-Calculation Summary

Formula Used

Number of Teeth on 1st Helical Gear = Center to Center Distance of Helical Gears*(2*cos(Helix Angle of Helical Gear))/Normal Module of Helical Gear-Number of Teeth on 2nd Helical Gear
z₁ = a_c*(2*cos(ψ))/m_n-z₂
This formula uses 1 Functions, 5 Variables

Functions Used

cos - Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle., cos(Angle)

Variables Used

Number of Teeth on 1st Helical Gear - The Number of Teeth on 1st Helical Gear is defined as the number of teeth that are present on gear 1.
Center to Center Distance of Helical Gears - (Measured in Meter) - Center to Center Distance of Helical Gears is defined as the distance in between the centers of the two helical gears that are taken in consideration.
Helix Angle of Helical Gear - (Measured in Radian) - Helix Angle of Helical Gear is the angle between any helical gear and an axial line on its right, circular cylinder, or cone.
Normal Module of Helical Gear - (Measured in Meter) - The Normal Module of Helical Gear is defined as the unit of size that indicates how big or small is the helical gear.
Number of Teeth on 2nd Helical Gear - The Number of Teeth on 2nd Helical Gear is defined as the number of teeth that are present on gear 2.

STEP 1: Convert Input(s) to Base Unit

Center to Center Distance of Helical Gears: 99.3 Millimeter --> 0.0993 Meter (Check conversion here)
Helix Angle of Helical Gear: 25 Degree --> 0.4363323129985 Radian (Check conversion here)
Normal Module of Helical Gear: 3 Millimeter --> 0.003 Meter (Check conversion here)
Number of Teeth on 2nd Helical Gear: 42 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

z₁ = a_c*(2*cos(ψ))/m_n-z₂ --> 0.0993*(2*cos(0.4363323129985))/0.003-42

Evaluating ... ...

z₁ = 17.9975755018285

STEP 3: Convert Result to Output's Unit

17.9975755018285 --> No Conversion Required

FINAL ANSWER

17.9975755018285 ≈ 17.99758 <-- Number of Teeth on 1st Helical Gear

(Calculation completed in 00.004 seconds)

You are here -

Home » Physics » Design of Machine Elements » Design of Gears » Design of Helical Gears » Core Design Parameters » Number of Teeth on First Gear given Center to Center Distance between Two Gears

Credits

Created by Kethavath Srinath

Osmania University (OU), Hyderabad

Kethavath Srinath has created this Calculator and 1000+ more calculators!

Verified by Urvi Rathod

Vishwakarma Government Engineering College (VGEC), Ahmedabad

Urvi Rathod has verified this Calculator and 1900+ more calculators!

< 25 Core Design Parameters Calculators

Normal Module of Helical Gear given Center to Center Distance between Two Gears

Go Normal Module of Helical Gear = Center to Center Distance of Helical Gears*(2*cos(Helix Angle of Helical Gear))/(Number of Teeth on 1st Helical Gear+Number of Teeth on 2nd Helical Gear)

Center to Center distance between Two Gears

Go Center to Center Distance of Helical Gears = Normal Module of Helical Gear*(Number of Teeth on 1st Helical Gear+Number of Teeth on 2nd Helical Gear)/(2*cos(Helix Angle of Helical Gear))

Number of Teeth on Second Helical Gear given Center to Center Distance between Two Gears

Go Number of Teeth on 2nd Helical Gear = Center to Center Distance of Helical Gears*(2*cos(Helix Angle of Helical Gear))/Normal Module of Helical Gear-Number of Teeth on 1st Helical Gear

Number of Teeth on First Gear given Center to Center Distance between Two Gears

Go Number of Teeth on 1st Helical Gear = Center to Center Distance of Helical Gears*(2*cos(Helix Angle of Helical Gear))/Normal Module of Helical Gear-Number of Teeth on 2nd Helical Gear

Normal Module of Helical Gear given Virtual Number of Teeth

Go Normal Module of Helical Gear = Diameter of Pitch Circle of Helical Gear/Virtual Number of Teeth on Helical Gear*(cos(Helix Angle of Helical Gear)^2)

Addendum Circle Diameter of Gear

Go Addendum Circle Diameter of Helical Gear = Normal Module of Helical Gear*((Number of Teeth on Helical Gear/cos(Helix Angle of Helical Gear))+2)

Normal Module of Helical Gear given Addendum Circle Diameter

Go Normal Module of Helical Gear = Addendum Circle Diameter of Helical Gear/(Number of Teeth on Helical Gear/cos(Helix Angle of Helical Gear)+2)

Number of Teeth on Gear given Addendum Circle Diameter

Go Number of Teeth on Helical Gear = (Addendum Circle Diameter of Helical Gear/Normal Module of Helical Gear-2)*cos(Helix Angle of Helical Gear)

Normal Module of Helical Gear given Pitch Circle Diameter

Go Normal Module of Helical Gear = Diameter of Pitch Circle of Helical Gear*cos(Helix Angle of Helical Gear)/Number of Teeth on Helical Gear

Number of Teeth on Gear given Pitch Circle Diameter

Go Number of Teeth on Helical Gear = Diameter of Pitch Circle of Helical Gear*cos(Helix Angle of Helical Gear)/Normal Module of Helical Gear

Pitch Circle Diameter of Helical Gear

Go Diameter of Pitch Circle of Helical Gear = Number of Teeth on Helical Gear*Normal Module of Helical Gear/cos(Helix Angle of Helical Gear)

Virtual Number of Teeth on Helical Gear

Go Virtual Number of Teeth on Helical Gear = 2*pi*Virtual Pitch Circle Radius for Helical Gear/Normal Circular Pitch of Helical Gear

Pitch Circle Diameter of Gear given Radius of Curvature at Point

Go Diameter of Pitch Circle of Helical Gear = 2*Radius of Curvature of Helical Gear*(cos(Helix Angle of Helical Gear))^2

Virtual Number of Teeth on Helical Gear given Actual Number of Teeth

Go Virtual Number of Teeth on Helical Gear = Number of Teeth on Helical Gear/(cos(Helix Angle of Helical Gear))^3

Transverse Module of Helical Gear given Normal Module

Go Transverse Module of Helical Gear = Normal Module of Helical Gear/cos(Helix Angle of Helical Gear)

Normal Module of Helical Gear

Go Normal Module of Helical Gear = Transverse Module of Helical Gear*cos(Helix Angle of Helical Gear)

Addendum of Gear given Addendum Circle Diameter

Go Addendum of Helical Gear = (Addendum Circle Diameter of Helical Gear-Diameter of Pitch Circle of Helical Gear)/2

Addendum Circle Diameter of Gear given Pitch Circle Diameter

Go Addendum Circle Diameter of Helical Gear = 2*Addendum of Helical Gear+Diameter of Pitch Circle of Helical Gear

Pitch Circle Diameter of Gear given Addendum Circle Diameter

Go Diameter of Pitch Circle of Helical Gear = Addendum Circle Diameter of Helical Gear-2*Addendum of Helical Gear

Number of Teeth on Helical Gear given Speed Ratio for Helical Gears

Go Number of Teeth on Helical Gear = Number of Teeth on Helical Pinion*Helical Gear Speed Ratio

Number of Teeth on Pinion given Speed Ratio

Go Number of Teeth on Helical Pinion = Number of Teeth on Helical Gear/Helical Gear Speed Ratio

Angular Velocity of Pinion given Speed Ratio

Go Speed of Pinion Helical Gear = Helical Gear Speed Ratio*Speed of Helical Gear

Angular Velocity of Gear given Speed Ratio

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

Speed Ratio for Helical Gears

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

Transverse Module of Helical Gear given Transverse Diametrical Pitch

Go Transverse Module of Helical Gear = 1/Transverse Diametrical Pitch of Helical Gear

Number of Teeth on First Gear given Center to Center Distance between Two Gears Formula

Define Helical Gears

A helical gear has a cylindrical pitch surface and teeth that follow a helix on the pitch cylinder. External helical gears have teeth that project outwards, whereas internal helical gears have teeth that project inwards.

How to Calculate Number of Teeth on First Gear given Center to Center Distance between Two Gears?

Number of Teeth on First Gear given Center to Center Distance between Two Gears calculator uses Number of Teeth on 1st Helical Gear = Center to Center Distance of Helical Gears*(2*cos(Helix Angle of Helical Gear))/Normal Module of Helical Gear-Number of Teeth on 2nd Helical Gear to calculate the Number of Teeth on 1st Helical Gear, Number of Teeth on first Gear given center to center distance between two Gears formula is defined as the number of protrusions onto the periphery of a Gear that mesh with the teeth of another Gear to transmit motion. Number of Teeth on 1st Helical Gear is denoted by z₁ symbol.

How to calculate Number of Teeth on First Gear given Center to Center Distance between Two Gears using this online calculator? To use this online calculator for Number of Teeth on First Gear given Center to Center Distance between Two Gears, enter Center to Center Distance of Helical Gears (a_c), Helix Angle of Helical Gear (ψ), Normal Module of Helical Gear (m_n) & Number of Teeth on 2nd Helical Gear (z₂) and hit the calculate button. Here is how the Number of Teeth on First Gear given Center to Center Distance between Two Gears calculation can be explained with given input values -> 17.99758 = 0.0993*(2*cos(0.4363323129985))/0.003-42.

FAQ

What is Number of Teeth on First Gear given Center to Center Distance between Two Gears?

Number of Teeth on first Gear given center to center distance between two Gears formula is defined as the number of protrusions onto the periphery of a Gear that mesh with the teeth of another Gear to transmit motion and is represented as z₁ = a_c*(2*cos(ψ))/m_n-z₂ or Number of Teeth on 1st Helical Gear = Center to Center Distance of Helical Gears*(2*cos(Helix Angle of Helical Gear))/Normal Module of Helical Gear-Number of Teeth on 2nd Helical Gear. Center to Center Distance of Helical Gears is defined as the distance in between the centers of the two helical gears that are taken in consideration, Helix Angle of Helical Gear is the angle between any helical gear and an axial line on its right, circular cylinder, or cone, The Normal Module of Helical Gear is defined as the unit of size that indicates how big or small is the helical gear & The Number of Teeth on 2nd Helical Gear is defined as the number of teeth that are present on gear 2.

How to calculate Number of Teeth on First Gear given Center to Center Distance between Two Gears?

Number of Teeth on first Gear given center to center distance between two Gears formula is defined as the number of protrusions onto the periphery of a Gear that mesh with the teeth of another Gear to transmit motion is calculated using Number of Teeth on 1st Helical Gear = Center to Center Distance of Helical Gears*(2*cos(Helix Angle of Helical Gear))/Normal Module of Helical Gear-Number of Teeth on 2nd Helical Gear. To calculate Number of Teeth on First Gear given Center to Center Distance between Two Gears, you need Center to Center Distance of Helical Gears (a_c), Helix Angle of Helical Gear (ψ), Normal Module of Helical Gear (m_n) & Number of Teeth on 2nd Helical Gear (z₂). With our tool, you need to enter the respective value for Center to Center Distance of Helical Gears, Helix Angle of Helical Gear, Normal Module of Helical Gear & Number of Teeth on 2nd Helical Gear and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

Home

FREE PDFs

🔍 Search