Efficiency of Spiral Gears using Pitch Circle Diameter 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%
✖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.ⓘ Pitch Circle Diameter of Gear 2 [d₂]			+10% -10%
✖Speed of gear 2 is speed of revolution.ⓘ Speed of Gear 2 [N₂]			+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%
✖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.ⓘ Pitch Circle Diameter of Gear 1 [d₁]			+10% -10%
✖Speed of gear 1 is speed of revolution.ⓘ Speed of Gear 1 [N₁]			+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 using Pitch Circle Diameter [η]

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Efficiency of Spiral Gears using Pitch Circle Diameter Solution

STEP 0: Pre-Calculation Summary

Formula Used

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)
η = (cos(α₂+Φ)*d₂*N₂)/(cos(α₁-Φ)*d₁*N₁)
This formula uses 1 Functions, 8 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.
Pitch Circle Diameter of Gear 2 - (Measured in Meter) - 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.
Speed of Gear 2 - (Measured in Hertz) - Speed of gear 2 is speed of revolution.
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.
Pitch Circle Diameter of Gear 1 - (Measured in Meter) - 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.
Speed of Gear 1 - (Measured in Hertz) - Speed of gear 1 is speed of revolution.

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)
Pitch Circle Diameter of Gear 2: 10.004 Millimeter --> 0.010004 Meter (Check conversion here)
Speed of Gear 2: 28 Revolution per Minute --> 0.466666666666667 Hertz (Check conversion here)
Spiral Angle of Gear Teeth for Gear 1: 45 Degree --> 0.785398163397301 Radian (Check conversion here)
Pitch Circle Diameter of Gear 1: 22 Millimeter --> 0.022 Meter (Check conversion here)
Speed of Gear 1: 20 Revolution per Minute --> 0.333333333333333 Hertz (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

η = (cos(α₂+Φ)*d₂*N₂)/(cos(α₁-Φ)*d₁*N₁) --> (cos(0.524471440224197+0.41887902047856)*0.010004*0.466666666666667)/(cos(0.785398163397301-0.41887902047856)*0.022*0.333333333333333)

Evaluating ... ...

η = 0.400335282122144

STEP 3: Convert Result to Output's Unit

0.400335282122144 --> No Conversion Required

FINAL ANSWER

0.400335282122144 ≈ 0.400335 <-- Efficiency

(Calculation completed in 00.004 seconds)

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Home » Physics » Theory of Machine » Toothed Gearing » Mechanical » Toothed Gear Terminologies » Efficiency of Spiral Gears using Pitch Circle Diameter

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< Toothed Gear Terminologies Calculators

Addendum of Pinion

LaTeX 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

LaTeX 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

LaTeX 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

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

Efficiency of Spiral Gears using Pitch Circle Diameter Formula

LaTeX Go

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 using Pitch Circle Diameter?

Efficiency of Spiral Gears using Pitch Circle Diameter calculator 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 calculate 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 calculate Efficiency of Spiral Gears using Pitch Circle Diameter using this online calculator? To use this online calculator 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. Here is how the Efficiency of Spiral Gears using Pitch Circle Diameter calculation can be explained with given input values -> 0.400335 = (cos(0.524471440224197+0.41887902047856)*0.010004*0.466666666666667)/(cos(0.785398163397301-0.41887902047856)*0.022*0.333333333333333).

FAQ

What is Efficiency of Spiral Gears using Pitch Circle Diameter?

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 and is represented as η = (cos(α₂+Φ)*d₂*N₂)/(cos(α₁-Φ)*d₁*N₁) or 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). 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, 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, Speed of gear 2 is speed of revolution, 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, 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 & Speed of gear 1 is speed of revolution.

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

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 is calculated using 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 calculate Efficiency of Spiral Gears using Pitch Circle Diameter, you need 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). With our tool, you need to enter the respective value for Spiral Angle of Gear Teeth for Gear 2, Angle of Friction, Pitch Circle Diameter of Gear 2, Speed of Gear 2, Spiral Angle of Gear Teeth for Gear 1, Pitch Circle Diameter of Gear 1 & Speed of 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, Pitch Circle Diameter of Gear 2, Speed of Gear 2, Spiral Angle of Gear Teeth for Gear 1, Pitch Circle Diameter of Gear 1 & Speed of 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)*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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