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Center to Center distance between Two Gears Formula

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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. Check FAQs

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

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

Center to Center distance between Two Gears Example

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Here is how the Center to Center distance between Two Gears equation looks like with Values.

Here is how the Center to Center distance between Two Gears equation looks like with Units.

Here is how the Center to Center distance between Two Gears equation looks like.

99.304 = 3 \cdot \frac{18 + 42}{2 \cdot \cos (25)}

99.304mm = 3mm \cdot \frac{18 + 42}{2 \cdot \cos (25°)}

99.304 = 3 \cdot \frac{18 + 42}{2 \cdot \cos (25)}

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Center to Center distance between Two Gears Solution

Follow our step by step solution on how to calculate Center to Center distance between Two Gears?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

a c = 3mm \cdot \frac{18 + 42}{2 \cdot \cos (25°)}

Next Step Convert Units

∴

a c = 0.003m \cdot \frac{18 + 42}{2 \cdot \cos (0.4363rad)}

Next Step Prepare to Evaluate

∴

a c = 0.003 \cdot \frac{18 + 42}{2 \cdot \cos (0.4363)}

Next Step Evaluate

∴

a c = 0.0993040127066204m

Next Step Convert to Output's Unit

∴

a c = 99.3040127066204mm

LAST Step Rounding Answer

∴

a c = 99.304mm

Center to Center distance between Two Gears Formula Elements

Variables

Functions

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

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 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

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

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

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 Center to Center distance between Two Gears?

Center to Center distance between Two Gears evaluator uses 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)) to evaluate the Center to Center Distance of Helical Gears, Center to Center distance between two Gears formula is defined as the distance between the centers of the two gears that are taken into consideration. Center to Center Distance of Helical Gears is denoted by a_c symbol.

How to evaluate Center to Center distance between Two Gears using this online evaluator? To use this online evaluator for Center to Center distance between Two Gears, enter Normal Module of Helical Gear (m_n), Number of Teeth on 1st Helical Gear (z₁), Number of Teeth on 2nd Helical Gear (z₂) & Helix Angle of Helical Gear (ψ) and hit the calculate button.

FAQs on Center to Center distance between Two Gears

What is the formula to find Center to Center distance between Two Gears?

The formula of Center to Center distance between Two Gears is expressed as 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)). Here is an example- 99304.01 = 0.003*(18+42)/(2*cos(0.4363323129985)).

How to calculate Center to Center distance between Two Gears?

With Normal Module of Helical Gear (m_n), Number of Teeth on 1st Helical Gear (z₁), Number of Teeth on 2nd Helical Gear (z₂) & Helix Angle of Helical Gear (ψ) we can find Center to Center distance between Two Gears using the formula - 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)). This formula also uses Cosine (cos) function(s).

Can the Center to Center distance between Two Gears be negative?

No, the Center to Center distance between Two Gears, measured in Length cannot be negative.

Which unit is used to measure Center to Center distance between Two Gears?

Center to Center distance between Two Gears is usually measured using the Millimeter[mm] for Length. Meter[mm], Kilometer[mm], Decimeter[mm] are the few other units in which Center to Center distance between Two Gears can be measured.

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Center to Center distance between Two Gears Formula

Center to Center distance between Two Gears Example

Center to Center distance between Two Gears Solution

Center to Center distance between Two Gears Formula Elements

Other formulas in Core Design Parameters category

How to Evaluate Center to Center distance between Two Gears?

FAQs on Center to Center distance between Two Gears

Variable Name