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Lead angle of Worm Gear given lead of worm and pitch circle diameter of worm Formula

GoLead angle of Worm Gear given number of starts and diametral quotient Formula

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The Lead Angle of Worm is defined as the angle between a tangent to the thread at the pitch diameter and a plane normal to the worm axis. Check FAQs

γ = a \tan (\frac{l w}{π \cdot d 1})

γ - Lead Angle of Worm?l_w - Lead of Worm?d₁ - Pitch Circle Diameter of Worm Gear?π - Archimedes' constant?

Lead angle of Worm Gear given lead of worm and pitch circle diameter of worm Example

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Here is how the Lead angle of Worm Gear given lead of worm and pitch circle diameter of worm equation looks like with Values.

Here is how the Lead angle of Worm Gear given lead of worm and pitch circle diameter of worm equation looks like with Units.

Here is how the Lead angle of Worm Gear given lead of worm and pitch circle diameter of worm equation looks like.

14.2866 = a \tan (\frac{40}{3.1416 \cdot 50})

14.2866° = a \tan (\frac{40mm}{3.1416 \cdot 50mm})

14.2866 = a \tan (\frac{40}{3.1416 \cdot 50})

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Lead angle of Worm Gear given lead of worm and pitch circle diameter of worm Solution

Follow our step by step solution on how to calculate Lead angle of Worm Gear given lead of worm and pitch circle diameter of worm?

FIRST Step Consider the formula

γ = a \tan (\frac{l w}{π \cdot d 1})

Next Step Substitute values of Variables

∴

γ = a \tan (\frac{40mm}{π \cdot 50mm})

Next Step Substitute values of Constants

∴

γ = a \tan (\frac{40mm}{3.1416 \cdot 50mm})

Next Step Convert Units

∴

γ = a \tan (\frac{0.04m}{3.1416 \cdot 0.05m})

Next Step Prepare to Evaluate

∴

γ = a \tan (\frac{0.04}{3.1416 \cdot 0.05})

Next Step Evaluate

∴

γ = 0.249348359011174rad

Next Step Convert to Output's Unit

∴

γ = 14.2866085998558°

LAST Step Rounding Answer

∴

γ = 14.2866°

Lead angle of Worm Gear given lead of worm and pitch circle diameter of worm Formula Elements

Variables

Constants

Functions

Lead Angle of Worm

The Lead Angle of Worm is defined as the angle between a tangent to the thread at the pitch diameter and a plane normal to the worm axis.

Symbol: γ

Measurement: AngleUnit: °

Note: Value should be greater than 0.

Formulas to find Lead Angle of Worm

Lead of Worm

The Lead of Worm is defined as the distance that a point on the helical profile will move when the worm is rotated through one revolution.

Symbol: l_w

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Lead of Worm

Pitch Circle Diameter of Worm Gear

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

Symbol: d₁

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Pitch Circle Diameter of Worm Gear

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

tan

The tangent of an angle is a trigonometric ratio of the length of the side opposite an angle to the length of the side adjacent to an angle in a right triangle.

Syntax: tan(Angle)

atan

Inverse tan is used to calculate the angle by applying the tangent ratio of the angle, which is the opposite side divided by the adjacent side of the right triangle.

Syntax: atan(Number)

Other Formulas to find Lead Angle of Worm

Go Lead angle of Worm Gear given number of starts and diametral quotient

γ = a \tan (\frac{z 1}{q})

Other formulas in Design of Worm Gears category

Go Diametral Quotient of Worm Gear

q = \frac{d 1}{m a}

Go Lead of Worm Gear given axial pitch and number of starts on worm

l w = p x \cdot z 1

Go Lead of Worm Gear given axial module and number of starts on worm

l w = π \cdot m a \cdot z 1

Go Rubbing speed of Worm Gear

v = π \cdot d 1 \cdot \frac{N}{60 \cdot \cos (γ)}

How to Evaluate Lead angle of Worm Gear given lead of worm and pitch circle diameter of worm?

Lead angle of Worm Gear given lead of worm and pitch circle diameter of worm evaluator uses Lead Angle of Worm = atan(Lead of Worm/(pi*Pitch Circle Diameter of Worm Gear)) to evaluate the Lead Angle of Worm, Lead angle of Worm Gear given lead of worm and pitch circle diameter of worm formula is defined as the angle between a tangent to the thread at the pitch diameter and a plane normal to the worm axis. Lead Angle of Worm is denoted by γ symbol.

How to evaluate Lead angle of Worm Gear given lead of worm and pitch circle diameter of worm using this online evaluator? To use this online evaluator for Lead angle of Worm Gear given lead of worm and pitch circle diameter of worm, enter Lead of Worm (l_w) & Pitch Circle Diameter of Worm Gear (d₁) and hit the calculate button.

FAQs on Lead angle of Worm Gear given lead of worm and pitch circle diameter of worm

What is the formula to find Lead angle of Worm Gear given lead of worm and pitch circle diameter of worm?

The formula of Lead angle of Worm Gear given lead of worm and pitch circle diameter of worm is expressed as Lead Angle of Worm = atan(Lead of Worm/(pi*Pitch Circle Diameter of Worm Gear)). Here is an example- 818.5624 = atan(0.04/(pi*0.05)).

How to calculate Lead angle of Worm Gear given lead of worm and pitch circle diameter of worm?

With Lead of Worm (l_w) & Pitch Circle Diameter of Worm Gear (d₁) we can find Lead angle of Worm Gear given lead of worm and pitch circle diameter of worm using the formula - Lead Angle of Worm = atan(Lead of Worm/(pi*Pitch Circle Diameter of Worm Gear)). This formula also uses Archimedes' constant and , Tangent (tan), Inverse Tan (atan) function(s).

What are the other ways to Calculate Lead Angle of Worm?

Here are the different ways to Calculate Lead Angle of Worm-

Lead Angle of Worm=atan(Number of Starts on Worm/Diametral Quotient)

Can the Lead angle of Worm Gear given lead of worm and pitch circle diameter of worm be negative?

No, the Lead angle of Worm Gear given lead of worm and pitch circle diameter of worm, measured in Angle cannot be negative.

Which unit is used to measure Lead angle of Worm Gear given lead of worm and pitch circle diameter of worm?

Lead angle of Worm Gear given lead of worm and pitch circle diameter of worm is usually measured using the Degree[°] for Angle. Radian[°], Minute[°], Second[°] are the few other units in which Lead angle of Worm Gear given lead of worm and pitch circle diameter of worm can be measured.

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Lead angle of Worm Gear given lead of worm and pitch circle diameter of worm Formula

​GoLead angle of Worm Gear given number of starts and diametral quotient Formula

Lead angle of Worm Gear given lead of worm and pitch circle diameter of worm Example

Lead angle of Worm Gear given lead of worm and pitch circle diameter of worm Solution

Lead angle of Worm Gear given lead of worm and pitch circle diameter of worm Formula Elements

Other Formulas to find Lead Angle of Worm

Other formulas in Design of Worm Gears category

How to Evaluate Lead angle of Worm Gear given lead of worm and pitch circle diameter of worm?

FAQs on Lead angle of Worm Gear given lead of worm and pitch circle diameter of worm

Variable Name

GoLead angle of Worm Gear given number of starts and diametral quotient Formula