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Efficiency of Spiral Gears Formula

GoEfficiency of Spiral Gears using Pitch Circle Diameter Formula

GoMaximum Efficiency of Spiral Gears Formula

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The Efficiency of an electric motor is defined as the ratio of usable shaft power to electric input power. Check FAQs

η = \frac{\cos (α 2 + Φ) \cdot \cos (α 1)}{\cos (α 1 - Φ) \cdot \cos (α 2)}

η - Efficiency?α₂ - Spiral Angle of Gear Teeth for Gear 2?Φ - Angle of Friction?α₁ - Spiral Angle of Gear Teeth for Gear 1?

Efficiency of Spiral Gears Example

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Here is how the Efficiency of Spiral Gears equation looks like with Values.

Here is how the Efficiency of Spiral Gears equation looks like with Units.

Here is how the Efficiency of Spiral Gears equation looks like.

0.5137 = \frac{\cos (30.05 + 24) \cdot \cos (45)}{\cos (45 - 24) \cdot \cos (30.05)}

0.5137 = \frac{\cos (30.05° + 24°) \cdot \cos (45°)}{\cos (45° - 24°) \cdot \cos (30.05°)}

0.5137 = \frac{\cos (30.05 + 24) \cdot \cos (45)}{\cos (45 - 24) \cdot \cos (30.05)}

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Efficiency of Spiral Gears Solution

Follow our step by step solution on how to calculate Efficiency of Spiral Gears?

FIRST Step Consider the formula

η = \frac{\cos (α 2 + Φ) \cdot \cos (α 1)}{\cos (α 1 - Φ) \cdot \cos (α 2)}

Next Step Substitute values of Variables

∴

η = \frac{\cos (30.05° + 24°) \cdot \cos (45°)}{\cos (45° - 24°) \cdot \cos (30.05°)}

Next Step Convert Units

∴

η = \frac{\cos (0.5245rad + 0.4189rad) \cdot \cos (0.7854rad)}{\cos (0.7854rad - 0.4189rad) \cdot \cos (0.5245rad)}

Next Step Prepare to Evaluate

∴

η = \frac{\cos (0.5245 + 0.4189) \cdot \cos (0.7854)}{\cos (0.7854 - 0.4189) \cdot \cos (0.5245)}

Next Step Evaluate

∴

η = 0.513710250745906

LAST Step Rounding Answer

∴

η = 0.5137

Efficiency of Spiral Gears Formula Elements

Variables

Functions

Efficiency

The Efficiency of an electric motor is defined as the ratio of usable shaft power to electric input power.

Symbol: η

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Efficiency

Spiral Angle of Gear Teeth for Gear 2

The spiral angle of gear teeth for gear 2 is the angle between the tooth trace and an element of the pitch cone and corresponds to the helix angle in helical teeth.

Symbol: α₂

Measurement: AngleUnit: °

Note: Value can be positive or negative.

Formulas to find Spiral Angle of Gear Teeth for Gear 2

Angle of Friction

The angle of friction is the angle of a plane to the horizontal when a body placed on the plane will just start to slide.

Symbol: Φ

Measurement: AngleUnit: °

Note: Value should be greater than 0.

Formulas to find Angle of Friction

Spiral Angle of Gear Teeth for Gear 1

The spiral angle of gear teeth for gear 1 is the angle between the tooth trace and an element of the pitch cone and corresponds to the helix angle in helical teeth.

Symbol: α₁

Measurement: AngleUnit: °

Note: Value can be positive or negative.

Formulas to find Spiral Angle of Gear Teeth for Gear 1

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 Efficiency

Go Efficiency of Spiral Gears using Pitch Circle Diameter

η = \frac{\cos (α 2 + Φ) \cdot d 2 \cdot N 2}{\cos (α 1 - Φ) \cdot d 1 \cdot N 1}

Go Maximum Efficiency of Spiral Gears

η = \frac{\cos (θ + Φ) + 1}{\cos (θ - Φ) + 1}

Other formulas in Toothed Gear Terminologies category

Go Torque Exerted on Gear Shaft

τ = P t \cdot \frac{d pitch circle}{2}

Go Work Output on Driven

w = R \cdot \cos (α 2 + Φ) \cdot π \cdot d 2 \cdot N 2

Go Work Output on Driver

w = R \cdot \cos (α 1 - Φ) \cdot π \cdot d 1 \cdot N 1

Go Addendum of Pinion

A p = \frac{Z p}{2} \cdot (\sqrt{1 + \frac{T}{Z p} \cdot (\frac{T}{Z p} + 2) \cdot {(\sin (Φ gear))}^{2}} - 1)

How to Evaluate Efficiency of Spiral Gears?

Efficiency of Spiral Gears evaluator uses Efficiency = (cos(Spiral Angle of Gear Teeth for Gear 2+Angle of Friction)*cos(Spiral Angle of Gear Teeth for Gear 1))/(cos(Spiral Angle of Gear Teeth for Gear 1-Angle of Friction)*cos(Spiral Angle of Gear Teeth for Gear 2)) to evaluate the Efficiency, Efficiency of Spiral Gears formula is defined as a measure of the effectiveness of spiral gears in transmitting power, taking into account the angle of pressure and the friction angle, to provide a quantitative value of the gear's performance in mechanical systems. Efficiency is denoted by η symbol.

How to evaluate Efficiency of Spiral Gears using this online evaluator? To use this online evaluator for Efficiency of Spiral Gears, enter Spiral Angle of Gear Teeth for Gear 2 (α₂), Angle of Friction (Φ) & Spiral Angle of Gear Teeth for Gear 1 (α₁) and hit the calculate button.

FAQs on Efficiency of Spiral Gears

What is the formula to find Efficiency of Spiral Gears?

The formula of Efficiency of Spiral Gears is expressed as Efficiency = (cos(Spiral Angle of Gear Teeth for Gear 2+Angle of Friction)*cos(Spiral Angle of Gear Teeth for Gear 1))/(cos(Spiral Angle of Gear Teeth for Gear 1-Angle of Friction)*cos(Spiral Angle of Gear Teeth for Gear 2)). Here is an example- 0.51371 = (cos(0.524471440224197+0.41887902047856)*cos(0.785398163397301))/(cos(0.785398163397301-0.41887902047856)*cos(0.524471440224197)).

How to calculate Efficiency of Spiral Gears?

With Spiral Angle of Gear Teeth for Gear 2 (α₂), Angle of Friction (Φ) & Spiral Angle of Gear Teeth for Gear 1 (α₁) we can find Efficiency of Spiral Gears using the formula - Efficiency = (cos(Spiral Angle of Gear Teeth for Gear 2+Angle of Friction)*cos(Spiral Angle of Gear Teeth for Gear 1))/(cos(Spiral Angle of Gear Teeth for Gear 1-Angle of Friction)*cos(Spiral Angle of Gear Teeth for Gear 2)). This formula also uses Cosine (cos) function(s).

What are the other ways to Calculate Efficiency?

Here are the different ways to Calculate Efficiency-

Efficiency=(cos(Spiral Angle of Gear Teeth for Gear 2+Angle of Friction)*Pitch Circle Diameter of Gear 2*Speed of Gear 2)/(cos(Spiral Angle of Gear Teeth for Gear 1-Angle of Friction)*Pitch Circle Diameter of Gear 1*Speed of Gear 1)
Efficiency=(cos(Shaft Angle+Angle of Friction)+1)/(cos(Shaft Angle-Angle of Friction)+1)

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: Unit

Efficiency of Spiral Gears Formula

​GoEfficiency of Spiral Gears using Pitch Circle Diameter Formula

​GoMaximum Efficiency of Spiral Gears Formula

Efficiency of Spiral Gears Example

Efficiency of Spiral Gears Solution

Efficiency of Spiral Gears Formula Elements

Other Formulas to find Efficiency

Other formulas in Toothed Gear Terminologies category

How to Evaluate Efficiency of Spiral Gears?

FAQs on Efficiency of Spiral Gears

Variable Name

GoEfficiency of Spiral Gears using Pitch Circle Diameter Formula

GoMaximum Efficiency of Spiral Gears Formula