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

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Design of Gears

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Design of Worm Gears

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Design of Helical Gears

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✖The Number of starts on worm is defined as the number of thread starts of worm in one rotation.ⓘ Number of starts on worm [z₁]			+10% -10%
✖Diametral Quotient is defined as the ratio of pitch circle diameter of worm to the axial module of worm.ⓘ Diametral Quotient [q]			+10% -10%

✖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.ⓘ Lead angle of Worm Gear given number of starts and diametral quotient [γ]

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Formula

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

Formula

`"γ" = atan("z"_{"1"}/"q")`

Example

`"14.03624°"=atan("3"/"12")`

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

STEP 0: Pre-Calculation Summary

Formula Used

Lead Angle of Worm = atan(Number of starts on worm/Diametral Quotient)
γ = atan(z₁/q)
This formula uses 2 Functions, 3 Variables

Functions Used

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., 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., atan(Number)

Variables Used

Lead Angle of Worm - (Measured in Radian) - 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.
Number of starts on worm - The Number of starts on worm is defined as the number of thread starts of worm in one rotation.
Diametral Quotient - Diametral Quotient is defined as the ratio of pitch circle diameter of worm to the axial module of worm.

STEP 1: Convert Input(s) to Base Unit

Number of starts on worm: 3 --> No Conversion Required
Diametral Quotient: 12 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

γ = atan(z₁/q) --> atan(3/12)

Evaluating ... ...

γ = 0.244978663126864

STEP 3: Convert Result to Output's Unit

0.244978663126864 Radian -->14.0362434679291 Degree (Check conversion here)

FINAL ANSWER

14.0362434679291 ≈ 14.03624 Degree <-- Lead Angle of Worm

(Calculation completed in 00.004 seconds)

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< 7 Design of Worm Gears Calculators

Efficiency of Worm Gear given lead angle, pressure angle and coefficient of friction

Go Worm Gear Efficiency = (cos(Pressure Angle of Worm Gear)-Coefficient of Friction for Worm Gear*tan(Lead Angle of Worm))/(cos(Pressure Angle of Worm Gear)+Coefficient of Friction for Worm Gear*cot(Lead Angle of Worm))

Rubbing speed of Worm Gear

Go Rubbing Speed of Worm Gear = pi*Pitch Circle Diameter of Worm Gear*Speed of Worm Gear/(60*cos(Lead Angle of Worm))

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

Go Lead Angle of Worm = atan(Lead of Worm/(pi*Pitch Circle Diameter of Worm Gear))

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

Go Lead Angle of Worm = atan(Number of starts on worm/Diametral Quotient)

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

Go Lead of Worm = pi*Axial Module*Number of starts on worm

Diametral Quotient of Worm Gear

Go Diametral Quotient = Pitch Circle Diameter of Worm Gear/Axial Module

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

Go Lead of Worm = Axial Pitch of Worm*Number of starts on worm

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

Lead Angle of Worm = atan(Number of starts on worm/Diametral Quotient)
γ = atan(z₁/q)

What is the approximate condition for a self-locking gear drive?

The coefficient of friction between mating surfaces should be greater than the tangent of lead angle of worm.

How to Calculate Lead angle of Worm Gear given number of starts and diametral quotient?

Lead angle of Worm Gear given number of starts and diametral quotient calculator uses Lead Angle of Worm = atan(Number of starts on worm/Diametral Quotient) to calculate the Lead Angle of Worm, Lead angle of Worm Gear given number of starts and diametral quotient formula is defined as the distance that a point on the helical profile will move when the worm is rotated through one revolution. Lead Angle of Worm is denoted by γ symbol.

How to calculate Lead angle of Worm Gear given number of starts and diametral quotient using this online calculator? To use this online calculator for Lead angle of Worm Gear given number of starts and diametral quotient, enter Number of starts on worm (z₁) & Diametral Quotient (q) and hit the calculate button. Here is how the Lead angle of Worm Gear given number of starts and diametral quotient calculation can be explained with given input values -> 804.2175 = atan(3/12).

FAQ

What is Lead angle of Worm Gear given number of starts and diametral quotient?

Lead angle of Worm Gear given number of starts and diametral quotient formula is defined as the distance that a point on the helical profile will move when the worm is rotated through one revolution and is represented as γ = atan(z₁/q) or Lead Angle of Worm = atan(Number of starts on worm/Diametral Quotient). The Number of starts on worm is defined as the number of thread starts of worm in one rotation & Diametral Quotient is defined as the ratio of pitch circle diameter of worm to the axial module of worm.

How to calculate Lead angle of Worm Gear given number of starts and diametral quotient?

Lead angle of Worm Gear given number of starts and diametral quotient formula is defined as the distance that a point on the helical profile will move when the worm is rotated through one revolution is calculated using Lead Angle of Worm = atan(Number of starts on worm/Diametral Quotient). To calculate Lead angle of Worm Gear given number of starts and diametral quotient, you need Number of starts on worm (z₁) & Diametral Quotient (q). With our tool, you need to enter the respective value for Number of starts on worm & Diametral Quotient and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Lead Angle of Worm?

In this formula, Lead Angle of Worm uses Number of starts on worm & Diametral Quotient. We can use 1 other way(s) to calculate the same, which is/are as follows -

Lead Angle of Worm = atan(Lead of Worm/(pi*Pitch Circle Diameter of Worm Gear))

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