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Pitch Circular Diameter of Gear given Virtual Number of Teeth Formula

GoPitch Circular Diameter of Gear given Virtual Gear Formula

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Diameter of Pitch Circle of Helical Gear is the diameter of the pitch circle of a gear that touches the meshing gear's pitch circle. Check FAQs

d = m n \cdot z' \cdot ({\cos (ψ)}^{2})

d - Diameter of Pitch Circle of Helical Gear?m_n - Normal Module of Helical Gear?z' - Virtual Number of Teeth on Helical Gear?ψ - Helix Angle of Helical Gear?

Pitch Circular Diameter of Gear given Virtual Number of Teeth Example

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Here is how the Pitch Circular Diameter of Gear given Virtual Number of Teeth equation looks like with Values.

Here is how the Pitch Circular Diameter of Gear given Virtual Number of Teeth equation looks like with Units.

Here is how the Pitch Circular Diameter of Gear given Virtual Number of Teeth equation looks like.

133.0658 = 3 \cdot 54 \cdot ({\cos (25)}^{2})

133.0658mm = 3mm \cdot 54 \cdot ({\cos (25°)}^{2})

133.0658 = 3 \cdot 54 \cdot ({\cos (25)}^{2})

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Pitch Circular Diameter of Gear given Virtual Number of Teeth Solution

Follow our step by step solution on how to calculate Pitch Circular Diameter of Gear given Virtual Number of Teeth?

FIRST Step Consider the formula

d = m n \cdot z' \cdot ({\cos (ψ)}^{2})

Next Step Substitute values of Variables

∴

d = 3mm \cdot 54 \cdot ({\cos (25°)}^{2})

Next Step Convert Units

∴

d = 0.003m \cdot 54 \cdot ({\cos (0.4363rad)}^{2})

Next Step Prepare to Evaluate

∴

d = 0.003 \cdot 54 \cdot ({\cos (0.4363)}^{2})

Next Step Evaluate

∴

d = 0.13306579638462m

Next Step Convert to Output's Unit

∴

d = 133.06579638462mm

LAST Step Rounding Answer

∴

d = 133.0658mm

Pitch Circular Diameter of Gear given Virtual Number of Teeth Formula Elements

Variables

Functions

Diameter of Pitch Circle of Helical Gear

Diameter of Pitch Circle of Helical Gear is the diameter of the pitch circle of a gear that touches the meshing gear's pitch circle.

Symbol: d

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Diameter of Pitch Circle 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

Virtual Number of Teeth on Helical Gear

The Virtual Number of Teeth on Helical Gear is defined as the number of teeth that are present on the virtual helical gear.

Symbol: z'

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Virtual Number of Teeth on 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 to find Diameter of Pitch Circle of Helical Gear

Go Pitch Circular Diameter of Gear given Virtual Gear

d = 2 \cdot r' \cdot {(\cos (ψ))}^{2}

Other formulas in Helix Geometry category

Go Normal Circular Pitch of Helical Gear

P N = p \cdot \cos (ψ)

Go Pitch of Helical Gear given Normal Circular Pitch

p = \frac{P N}{\cos (ψ)}

Go Helix Angle of Helical Gear given Normal Circular Pitch

ψ = a \cos (\frac{P N}{p})

Go Transverse Diametrical Pitch of Helical Gear given Transverse Module

P = \frac{1}{m}

How to Evaluate Pitch Circular Diameter of Gear given Virtual Number of Teeth?

Pitch Circular Diameter of Gear given Virtual Number of Teeth evaluator uses Diameter of Pitch Circle of Helical Gear = Normal Module of Helical Gear*Virtual Number of Teeth on Helical Gear*(cos(Helix Angle of Helical Gear)^2) to evaluate the Diameter of Pitch Circle of Helical Gear, The Pitch Circular Diameter of Gear given Virtual Number of Teeth formula is the diameter of the imaginary circle on the gear about which it may be supposed to roll without slipping with the pitch circle of another gear. The point of contact of the two pitch circles becomes the pitch point. Diameter of Pitch Circle of Helical Gear is denoted by d symbol.

How to evaluate Pitch Circular Diameter of Gear given Virtual Number of Teeth using this online evaluator? To use this online evaluator for Pitch Circular Diameter of Gear given Virtual Number of Teeth, enter Normal Module of Helical Gear (m_n), Virtual Number of Teeth on Helical Gear (z') & Helix Angle of Helical Gear (ψ) and hit the calculate button.

FAQs on Pitch Circular Diameter of Gear given Virtual Number of Teeth

What is the formula to find Pitch Circular Diameter of Gear given Virtual Number of Teeth?

The formula of Pitch Circular Diameter of Gear given Virtual Number of Teeth is expressed as Diameter of Pitch Circle of Helical Gear = Normal Module of Helical Gear*Virtual Number of Teeth on Helical Gear*(cos(Helix Angle of Helical Gear)^2). Here is an example- 133065.8 = 0.003*54*(cos(0.4363323129985)^2).

How to calculate Pitch Circular Diameter of Gear given Virtual Number of Teeth?

With Normal Module of Helical Gear (m_n), Virtual Number of Teeth on Helical Gear (z') & Helix Angle of Helical Gear (ψ) we can find Pitch Circular Diameter of Gear given Virtual Number of Teeth using the formula - Diameter of Pitch Circle of Helical Gear = Normal Module of Helical Gear*Virtual Number of Teeth on Helical Gear*(cos(Helix Angle of Helical Gear)^2). This formula also uses Cosine (cos) function(s).

What are the other ways to Calculate Diameter of Pitch Circle of Helical Gear?

Here are the different ways to Calculate Diameter of Pitch Circle of Helical Gear-

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

Can the Pitch Circular Diameter of Gear given Virtual Number of Teeth be negative?

No, the Pitch Circular Diameter of Gear given Virtual Number of Teeth, measured in Length cannot be negative.

Which unit is used to measure Pitch Circular Diameter of Gear given Virtual Number of Teeth?

Pitch Circular Diameter of Gear given Virtual Number of Teeth is usually measured using the Millimeter[mm] for Length. Meter[mm], Kilometer[mm], Decimeter[mm] are the few other units in which Pitch Circular Diameter of Gear given Virtual Number of Teeth can be measured.

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Pitch Circular Diameter of Gear given Virtual Number of Teeth Formula

​GoPitch Circular Diameter of Gear given Virtual Gear Formula

Pitch Circular Diameter of Gear given Virtual Number of Teeth Example

Pitch Circular Diameter of Gear given Virtual Number of Teeth Solution

Pitch Circular Diameter of Gear given Virtual Number of Teeth Formula Elements

Other Formulas to find Diameter of Pitch Circle of Helical Gear

Other formulas in Helix Geometry category

How to Evaluate Pitch Circular Diameter of Gear given Virtual Number of Teeth?

FAQs on Pitch Circular Diameter of Gear given Virtual Number of Teeth

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GoPitch Circular Diameter of Gear given Virtual Gear Formula