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

✖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]

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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)

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

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Osmania University (OU), Hyderabad

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< Core Design Parameters Calculators

Pitch Circle Diameter of Helical Gear

LaTeX 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)

Transverse Module of Helical Gear given Normal Module

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

Normal Module of Helical Gear

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

Transverse Module of Helical Gear given Transverse Diametrical Pitch

LaTeX 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

LaTeX Go

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.

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