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Efficiency of Spiral Gears using Pitch Circle Diameter Formula

GoEfficiency of Spiral Gears 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 d 2 \cdot N 2}{\cos (α 1 - Φ) \cdot d 1 \cdot N 1}

η - Efficiency?α₂ - Spiral Angle of Gear Teeth for Gear 2?Φ - Angle of Friction?d₂ - Pitch Circle Diameter of Gear 2?N₂ - Speed of Gear 2?α₁ - Spiral Angle of Gear Teeth for Gear 1?d₁ - Pitch Circle Diameter of Gear 1?N₁ - Speed of Gear 1?

Efficiency of Spiral Gears using Pitch Circle Diameter Example

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Here is how the Efficiency of Spiral Gears using Pitch Circle Diameter equation looks like with Values.

Here is how the Efficiency of Spiral Gears using Pitch Circle Diameter equation looks like with Units.

Here is how the Efficiency of Spiral Gears using Pitch Circle Diameter equation looks like.

0.4003 = \frac{\cos (30.05 + 24) \cdot 10.004 \cdot 28}{\cos (45 - 24) \cdot 22 \cdot 20}

0.4003 = \frac{\cos (30.05° + 24°) \cdot 10.004mm \cdot 28rev/min}{\cos (45° - 24°) \cdot 22mm \cdot 20rev/min}

0.4003 = \frac{\cos (30.05 + 24) \cdot 10.004 \cdot 28}{\cos (45 - 24) \cdot 22 \cdot 20}

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Home » Physics » Mechanical » Theory of Machine » Efficiency of Spiral Gears using Pitch Circle Diameter

Efficiency of Spiral Gears using Pitch Circle Diameter Solution

Follow our step by step solution on how to calculate Efficiency of Spiral Gears using Pitch Circle Diameter?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

η = \frac{\cos (30.05° + 24°) \cdot 10.004mm \cdot 28rev/min}{\cos (45° - 24°) \cdot 22mm \cdot 20rev/min}

Next Step Convert Units

∴

η = \frac{\cos (0.5245rad + 0.4189rad) \cdot 0.01m \cdot 0.4667Hz}{\cos (0.7854rad - 0.4189rad) \cdot 0.022m \cdot 0.3333Hz}

Next Step Prepare to Evaluate

∴

η = \frac{\cos (0.5245 + 0.4189) \cdot 0.01 \cdot 0.4667}{\cos (0.7854 - 0.4189) \cdot 0.022 \cdot 0.3333}

Next Step Evaluate

∴

η = 0.400335282122144

LAST Step Rounding Answer

∴

η = 0.4003

Efficiency of Spiral Gears using Pitch Circle Diameter 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.

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.

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.

Pitch Circle Diameter of Gear 2

Pitch circle diameter of gear 2 is the diameter of the circle which passes through the centre of all the studs, wheel bolts or wheel rim holes.

Symbol: d₂

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Speed of Gear 2

Speed of gear 2 is speed of revolution.

Symbol: N₂

Measurement: FrequencyUnit: rev/min

Note: Value should be greater than 0.

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.

Pitch Circle Diameter of Gear 1

Pitch circle diameter of gear 1 is the diameter of the circle which passes through the centre of all the studs, wheel bolts or wheel rim holes.

Symbol: d₁

Measurement: LengthUnit: mm

Note: Value can be positive or negative.

Speed of Gear 1

Speed of gear 1 is speed of revolution.

Symbol: N₁

Measurement: FrequencyUnit: rev/min

Note: Value should be greater than 0.

cos

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

Syntax: cos(Angle)

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Created by Anshika Arya

National Institute Of Technology (NIT), Hamirpur

Anshika Arya has created this Formula and 2000+ more formulas!

Verified by Team Softusvista

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Other Formulas to find Efficiency

Go Efficiency of Spiral Gears

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

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

How to Evaluate Efficiency of Spiral Gears using Pitch Circle Diameter?

Efficiency of Spiral Gears using Pitch Circle Diameter evaluator uses 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) to evaluate the Efficiency, Efficiency of Spiral Gears using Pitch Circle Diameter formula is defined as a measure of the effectiveness of spiral gears in transmitting power, taking into account the pitch circle diameter, pressure angle, and number of teeth, to determine the optimal gear design for maximum power transmission efficiency. Efficiency is denoted by η symbol.

How to evaluate Efficiency of Spiral Gears using Pitch Circle Diameter using this online evaluator? To use this online evaluator for Efficiency of Spiral Gears using Pitch Circle Diameter, enter Spiral Angle of Gear Teeth for Gear 2 (α₂), Angle of Friction (Φ), Pitch Circle Diameter of Gear 2 (d₂), Speed of Gear 2 (N₂), Spiral Angle of Gear Teeth for Gear 1 (α₁), Pitch Circle Diameter of Gear 1 (d₁) & Speed of Gear 1 (N₁) and hit the calculate button.

FAQs on Efficiency of Spiral Gears using Pitch Circle Diameter

What is the formula to find Efficiency of Spiral Gears using Pitch Circle Diameter?

The formula of Efficiency of Spiral Gears using Pitch Circle Diameter is expressed as 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). Here is an example- 0.400335 = (cos(0.524471440224197+0.41887902047856)*0.010004*0.466666666666667)/(cos(0.785398163397301-0.41887902047856)*0.022*0.333333333333333).

How to calculate Efficiency of Spiral Gears using Pitch Circle Diameter?

With Spiral Angle of Gear Teeth for Gear 2 (α₂), Angle of Friction (Φ), Pitch Circle Diameter of Gear 2 (d₂), Speed of Gear 2 (N₂), Spiral Angle of Gear Teeth for Gear 1 (α₁), Pitch Circle Diameter of Gear 1 (d₁) & Speed of Gear 1 (N₁) we can find Efficiency of Spiral Gears using Pitch Circle Diameter using the formula - 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). 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)*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))
Efficiency=(cos(Shaft Angle+Angle of Friction)+1)/(cos(Shaft Angle-Angle of Friction)+1)

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Efficiency of Spiral Gears using Pitch Circle Diameter Formula

​GoEfficiency of Spiral Gears Formula

​GoMaximum Efficiency of Spiral Gears Formula

Efficiency of Spiral Gears using Pitch Circle Diameter Example

Efficiency of Spiral Gears using Pitch Circle Diameter Solution

Efficiency of Spiral Gears using Pitch Circle Diameter Formula Elements

Credits

Other Formulas to find Efficiency

Other formulas in Toothed Gear Terminologies category

How to Evaluate Efficiency of Spiral Gears using Pitch Circle Diameter?

FAQs on Efficiency of Spiral Gears using Pitch Circle Diameter

Variable Name

GoEfficiency of Spiral Gears Formula

GoMaximum Efficiency of Spiral Gears Formula