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

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The Number of Teeth on 1st Helical Gear is defined as the number of teeth that are present on gear 1. Check FAQs

z 1 = a c \cdot \frac{2 \cdot \cos (ψ)}{m n} - z 2

z₁ - Number of Teeth on 1st Helical Gear?a_c - Center to Center Distance of Helical Gears?ψ - Helix Angle of Helical Gear?m_n - Normal Module of Helical Gear?z₂ - Number of Teeth on 2nd Helical Gear?

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

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Here is how the Number of Teeth on First Gear given Center to Center Distance between Two Gears equation looks like with Values.

Here is how the Number of Teeth on First Gear given Center to Center Distance between Two Gears equation looks like with Units.

Here is how the Number of Teeth on First Gear given Center to Center Distance between Two Gears equation looks like.

17.9976 = 99.3 \cdot \frac{2 \cdot \cos (25)}{3} - 42

17.9976 = 99.3mm \cdot \frac{2 \cdot \cos (25°)}{3mm} - 42

17.9976 = 99.3 \cdot \frac{2 \cdot \cos (25)}{3} - 42

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

Follow our step by step solution on how to calculate Number of Teeth on First Gear given Center to Center Distance between Two Gears?

FIRST Step Consider the formula

z 1 = a c \cdot \frac{2 \cdot \cos (ψ)}{m n} - z 2

Next Step Substitute values of Variables

∴

z 1 = 99.3mm \cdot \frac{2 \cdot \cos (25°)}{3mm} - 42

Next Step Convert Units

∴

z 1 = 0.0993m \cdot \frac{2 \cdot \cos (0.4363rad)}{0.003m} - 42

Next Step Prepare to Evaluate

∴

z 1 = 0.0993 \cdot \frac{2 \cdot \cos (0.4363)}{0.003} - 42

Next Step Evaluate

∴

z 1 = 17.9975755018285

LAST Step Rounding Answer

∴

z 1 = 17.9976

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

Variables

Functions

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.

Symbol: z₁

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Number of Teeth on 1st Helical Gear

Center to Center Distance of Helical Gears

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.

Symbol: a_c

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Center to Center Distance of Helical Gears

Helix Angle of Helical Gear

Helix Angle of Helical Gear is the angle between any helical gear and an axial line on its right, circular cylinder, or cone.

Symbol: ψ

Measurement: AngleUnit: °

Note: Value should be greater than 0.

Formulas to find Helix Angle of Helical Gear

Normal Module of Helical Gear

The Normal Module of Helical Gear is defined as the unit of size that indicates how big or small is the helical gear.

Symbol: m_n

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Normal Module of 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.

Symbol: z₂

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Number of Teeth on 2nd Helical Gear

cos

Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle.

Syntax: cos(Angle)

Other formulas in Core Design Parameters category

Go Transverse Module of Helical Gear given Transverse Diametrical Pitch

m = \frac{1}{P}

Go Normal Module of Helical Gear

m n = m \cdot \cos (ψ)

Go Transverse Module of Helical Gear given Normal Module

m = \frac{m n}{\cos (ψ)}

Go Pitch Circle Diameter of Helical Gear

d = z \cdot \frac{m n}{\cos (ψ)}

How to Evaluate 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 evaluator 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 evaluate 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 evaluate Number of Teeth on First Gear given Center to Center Distance between Two Gears using this online evaluator? To use this online evaluator 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.

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

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

The formula of Number of Teeth on First Gear given Center to Center Distance between Two Gears is expressed as 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. Here is an example- 17.99758 = 0.0993*(2*cos(0.4363323129985))/0.003-42.

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

With 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) we can find Number of Teeth on First Gear given Center to Center Distance between Two Gears using the formula - 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. This formula also uses Cosine (cos) function(s).

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

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

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

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

Other formulas in Core Design Parameters category

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

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

Variable Name