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 00.020 seconds)

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National Institute Of Technology (NIT), Hamirpur
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22 Toothed Gear Terminologies Calculators

Efficiency of Spiral Gears using Pitch Circle Diameter
Go 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 of Spiral Gears
Go 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))
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)
Addendum of Wheel
Go Addendum of Wheel = Number of Teeth on Wheel/2*(sqrt(1+Number of Teeth on Pinion/Number of Teeth on Wheel*(Number of Teeth on Pinion/Number of Teeth on Wheel+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
Maximum Efficiency of Spiral Gears
Go Efficiency = (cos(Shaft Angle+Angle of Friction)+1)/(cos(Shaft Angle-Angle of Friction)+1)
Resisting Force Acting Tangentially on Driven
Go Resisting Force acting Tangentially on Driven = Resultant Reaction at Point of Contact*cos(Spiral Angle of Gear Teeth for Gear 2+Angle of Friction)
Force Applied Tangentially on Driver
Go Force Applied Tangentially on Driver = Resultant Reaction at Point of Contact*cos(Spiral Angle of Gear Teeth for Gear 1-Angle of Friction)
Axial Thrust on Driven
Go Axial Thrust on Driven = Resisting Force acting Tangentially on Driven*tan(Spiral Angle of Gear Teeth for Gear 2)
Axial Thrust on Driver
Go Axial Thrust on Driver = Force Applied Tangentially on Driver*tan(Spiral Angle of Gear Teeth for Gear 1)
Radius of Base Circle of Pinion
Go Radius of Base Circle of Pinion = Radius of Pitch Circle of Pinion*cos(Pressure Angle of Gear)
Radius of Base Circle of Wheel
Go Radius of Base Circle of Wheel = Radius of Pitch Circle of Wheel*cos(Pressure Angle of Gear)
Addendum of Rack
Go Addendum of Rack = (Number of Teeth on Pinion*(sin(Pressure Angle of Gear))^2)/2
Tangential Force on Gear Shaft
Go Tangential Force = Maximum Tooth Pressure*cos(Pressure Angle of Gear)
Normal Force on Gear Shaft
Go Normal Force = Maximum Tooth Pressure*sin(Pressure Angle of Gear)
Shaft Angle
Go Shaft Angle = Spiral Angle of Gear Teeth for Gear 1+Spiral Angle of Gear Teeth for Gear 2
Gear Ratio
Go Gear Ratio = Radius of Pitch Circle of Wheel/Radius of Pitch Circle of Pinion
Torque Exerted on Gear Shaft
Go Torque Exerted on Wheel = Tangential Force*Diameter of Pitch Circle/2
Gear Ratio given Number of Teeth on Wheel and Pinion
Go Gear Ratio = Number of Teeth on Wheel/Number of Teeth on Pinion
Module
Go Module = Diameter of Pitch Circle/Number of Teeth on Wheel
Contact Ratio
Go Contact Ratio = Path of Contact/Circular Pitch

Efficiency of Spiral Gears using Pitch Circle Diameter 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)
η = (cos(α2+Φ)*d2*N2)/(cos(α1-Φ)*d1*N1)

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 signifies the 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 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 2), Angle of Friction (Φ), Pitch Circle Diameter of Gear 2 (d2), Speed of Gear 2 (N2), Spiral Angle of Gear Teeth for Gear 1 1), 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 signifies the 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)*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 signifies the 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)*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 2), Angle of Friction (Φ), Pitch Circle Diameter of Gear 2 (d2), Speed of Gear 2 (N2), Spiral Angle of Gear Teeth for Gear 1 1), 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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