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

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Worm Gear Efficiency is simply the ratio of output power from the worm gear to the Input power to the gear. Check FAQs

η = \frac{\cos (Φ) - μ \cdot \tan (γ)}{\cos (Φ) + μ \cdot \cot (γ)}

η - Worm Gear Efficiency?Φ - Pressure Angle of Worm Gear?μ - Coefficient of Friction for Worm Gear?γ - Lead Angle of Worm?

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

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Here is how the Efficiency of Worm Gear given lead angle, pressure angle and coefficient of friction equation looks like with Values.

Here is how the Efficiency of Worm Gear given lead angle, pressure angle and coefficient of friction equation looks like with Units.

Here is how the Efficiency of Worm Gear given lead angle, pressure angle and coefficient of friction equation looks like.

0.4897 = \frac{\cos (30) - 0.2 \cdot \tan (14.03)}{\cos (30) + 0.2 \cdot \cot (14.03)}

0.4897 = \frac{\cos (30°) - 0.2 \cdot \tan (14.03°)}{\cos (30°) + 0.2 \cdot \cot (14.03°)}

0.4897 = \frac{\cos (30) - 0.2 \cdot \tan (14.03)}{\cos (30) + 0.2 \cdot \cot (14.03)}

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

Follow our step by step solution on how to calculate Efficiency of Worm Gear given lead angle, pressure angle and coefficient of friction?

FIRST Step Consider the formula

η = \frac{\cos (Φ) - μ \cdot \tan (γ)}{\cos (Φ) + μ \cdot \cot (γ)}

Next Step Substitute values of Variables

∴

η = \frac{\cos (30°) - 0.2 \cdot \tan (14.03°)}{\cos (30°) + 0.2 \cdot \cot (14.03°)}

Next Step Convert Units

∴

η = \frac{\cos (0.5236rad) - 0.2 \cdot \tan (0.2449rad)}{\cos (0.5236rad) + 0.2 \cdot \cot (0.2449rad)}

Next Step Prepare to Evaluate

∴

η = \frac{\cos (0.5236) - 0.2 \cdot \tan (0.2449)}{\cos (0.5236) + 0.2 \cdot \cot (0.2449)}

Next Step Evaluate

∴

η = 0.489708646447362

LAST Step Rounding Answer

∴

η = 0.4897

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

Variables

Functions

Worm Gear Efficiency

Worm Gear Efficiency is simply the ratio of output power from the worm gear to the Input power to the gear.

Symbol: η

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Worm Gear Efficiency

Pressure Angle of Worm Gear

Pressure Angle of Worm Gear is known as the angle of obliquity is the angle between the tooth face and the gear wheel tangent.

Symbol: Φ

Measurement: AngleUnit: °

Note: Value should be greater than 0.

Formulas to find Pressure Angle of Worm Gear

Coefficient of Friction for Worm Gear

Coefficient of Friction for Worm Gear is the ratio defining the force that resists the motion of one body in relation to another body in contact with it.

Symbol: μ

Measurement: NAUnit: Unitless

Note: Value should be between 0 to 1.

Formulas to find Coefficient of Friction for Worm Gear

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

cos

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

Syntax: cos(Angle)

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)

cot

Cotangent is a trigonometric function that is defined as the ratio of the adjacent side to the opposite side in a right triangle.

Syntax: cot(Angle)

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

γ = a \tan (\frac{l w}{π \cdot d 1})

How to Evaluate Efficiency of Worm Gear given lead angle, pressure angle and coefficient of friction?

Efficiency of Worm Gear given lead angle, pressure angle and coefficient of friction evaluator uses 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)) to evaluate the Worm Gear Efficiency, Efficiency of Worm Gear given lead angle, pressure angle and coefficient of friction is simply calculated as the [output shaft power /Input shaft power]. The output power is the (input power - power losses). Power losses in gear systems are associated primarily with tooth friction and lubrication churning losses. Worm Gear Efficiency is denoted by η symbol.

How to evaluate Efficiency of Worm Gear given lead angle, pressure angle and coefficient of friction using this online evaluator? To use this online evaluator for Efficiency of Worm Gear given lead angle, pressure angle and coefficient of friction, enter Pressure Angle of Worm Gear (Φ), Coefficient of Friction for Worm Gear (μ) & Lead Angle of Worm (γ) and hit the calculate button.

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

What is the formula to find Efficiency of Worm Gear given lead angle, pressure angle and coefficient of friction?

The formula of Efficiency of Worm Gear given lead angle, pressure angle and coefficient of friction is expressed as 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)). Here is an example- 0.489709 = (cos(0.5235987755982)-0.2*tan(0.244869694054758))/(cos(0.5235987755982)+0.2*cot(0.244869694054758)).

How to calculate Efficiency of Worm Gear given lead angle, pressure angle and coefficient of friction?

With Pressure Angle of Worm Gear (Φ), Coefficient of Friction for Worm Gear (μ) & Lead Angle of Worm (γ) we can find Efficiency of Worm Gear given lead angle, pressure angle and coefficient of friction using the formula - 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)). This formula also uses Cosine (cos)Tangent (tan), Cotangent (cot) function(s).

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

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

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

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

Other formulas in Design of Worm Gears category

How to Evaluate Efficiency of Worm Gear given lead angle, pressure angle and coefficient of friction?

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

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