Efficiency of Spiral Gears Calculator

✖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.ⓘ Spiral Angle of Gear Teeth for Gear 2 [α₂]			+10% -10%
✖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.ⓘ Angle of Friction [Φ]			+10% -10%
✖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.ⓘ Spiral Angle of Gear Teeth for Gear 1 [α₁]			+10% -10%

✖The Efficiency of an electric motor is defined as the ratio of usable shaft power to electric input power.ⓘ Efficiency of Spiral Gears [η]

⎘ Copy

👎

Formula

✖

Efficiency of Spiral Gears

Formula

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

Example

0.51371 = \frac{\cos (30.05 ° + 24 °) \cdot \cos (45 °)}{\cos (45 ° - 24 °) \cdot \cos (30.05 °)}

Calculator

LaTeX

Reset

👍

Download Theory of Machine Formula PDF PDF Image

Efficiency of Spiral Gears Solution

STEP 0: Pre-Calculation Summary

Formula Used

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))
η = (cos(α₂+Φ)*cos(α₁))/(cos(α₁-Φ)*cos(α₂))
This formula uses 1 Functions, 4 Variables

Functions Used

cos - Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle., cos(Angle)

Variables Used

Efficiency - The Efficiency of an electric motor is defined as the ratio of usable shaft power to electric input power.
Spiral Angle of Gear Teeth for Gear 2 - (Measured in Radian) - 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.
Angle of Friction - (Measured in Radian) - 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.
Spiral Angle of Gear Teeth for Gear 1 - (Measured in Radian) - 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.

STEP 1: Convert Input(s) to Base Unit

Spiral Angle of Gear Teeth for Gear 2: 30.05 Degree --> 0.524471440224197 Radian (Check conversion here)
Angle of Friction: 24 Degree --> 0.41887902047856 Radian (Check conversion here)
Spiral Angle of Gear Teeth for Gear 1: 45 Degree --> 0.785398163397301 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

η = (cos(α₂+Φ)*cos(α₁))/(cos(α₁-Φ)*cos(α₂)) --> (cos(0.524471440224197+0.41887902047856)*cos(0.785398163397301))/(cos(0.785398163397301-0.41887902047856)*cos(0.524471440224197))

Evaluating ... ...

η = 0.513710250745906

STEP 3: Convert Result to Output's Unit

0.513710250745906 --> No Conversion Required

FINAL ANSWER

0.513710250745906 ≈ 0.51371 <-- Efficiency

(Calculation completed in 00.004 seconds)

You are here -

Home » Physics » Theory of Machine » Toothed Gearing » Mechanical » Toothed Gear Terminologies » Efficiency of Spiral Gears

Credits

Created by Anshika Arya

National Institute Of Technology (NIT), Hamirpur

Anshika Arya has created this Calculator and 2000+ more calculators!

Verified by Team Softusvista

Softusvista Office (Pune), India

Team Softusvista has verified this Calculator and 1100+ more calculators!

< Toothed Gear Terminologies Calculators

Addendum of Pinion

Go Addendum of Pinion = Number of Teeth on Pinion/2*(sqrt(1+Number of Teeth on Wheel/Number of Teeth on Pinion*(Number of Teeth on Wheel/Number of Teeth on Pinion+2)*(sin(Pressure Angle of Gear))^2)-1)

Work Output on Driven

Go Work Output = Resultant Reaction at Point of Contact*cos(Spiral Angle of Gear Teeth for Gear 2+Angle of Friction)*pi*Pitch Circle Diameter of Gear 2*Speed of Gear 2

Work Output on Driver

Go Work Output = Resultant Reaction at Point of Contact*cos(Spiral Angle of Gear Teeth for Gear 1-Angle of Friction)*pi*Pitch Circle Diameter of Gear 1*Speed of Gear 1

Torque Exerted on Gear Shaft

Go Torque Exerted on Wheel = Tangential Force*Diameter of Pitch Circle/2

Efficiency of Spiral Gears Formula

What does efficiency mean?

Efficiency signifies a peak level of performance that uses the least amount of inputs to achieve the highest amount of output. It minimizes the waste of resources such as physical materials, energy, and time while accomplishing the desired output.

How to Calculate Efficiency of Spiral Gears?

Efficiency of Spiral Gears calculator 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 calculate the Efficiency, The efficiency of spiral gears signifies a level of performance that uses the least amount of inputs to achieve the highest amount of output. Efficiency is denoted by η symbol.

How to calculate Efficiency of Spiral Gears using this online calculator? To use this online calculator 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. Here is how the Efficiency of Spiral Gears calculation can be explained with given input values -> 0.51371 = (cos(0.524471440224197+0.41887902047856)*cos(0.785398163397301))/(cos(0.785398163397301-0.41887902047856)*cos(0.524471440224197)).

FAQ

What is Efficiency of Spiral Gears?

The efficiency of spiral gears signifies a level of performance that uses the least amount of inputs to achieve the highest amount of output and is represented as η = (cos(α₂+Φ)*cos(α₁))/(cos(α₁-Φ)*cos(α₂)) or 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)). 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, 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 & 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.

How to calculate Efficiency of Spiral Gears?

The efficiency of spiral gears signifies a level of performance that uses the least amount of inputs to achieve the highest amount of output is calculated using 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 calculate Efficiency of Spiral Gears, you need Spiral Angle of Gear Teeth for Gear 2 (α₂), Angle of Friction (Φ) & Spiral Angle of Gear Teeth for Gear 1 (α₁). With our tool, you need to enter the respective value for Spiral Angle of Gear Teeth for Gear 2, Angle of Friction & Spiral Angle of Gear Teeth for Gear 1 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 Efficiency?

In this formula, Efficiency uses Spiral Angle of Gear Teeth for Gear 2, Angle of Friction & Spiral Angle of Gear Teeth for Gear 1. We can use 2 other way(s) to calculate the same, which is/are as follows -

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)

Home

FREE PDFs

🔍 Search