Maximum Efficiency of Spiral Gears Calculator

✖Shaft angle is the measurement of the angle formed between the obliquely oriented neck with the vertical shaft.ⓘ Shaft Angle [θ]			+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 Efficiency of an electric motor is defined as the ratio of usable shaft power to electric input power.ⓘ Maximum Efficiency of Spiral Gears [η]

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Formula

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Maximum Efficiency of Spiral Gears

Formula

`"η" = (cos("θ"+"Φ")+1)/(cos("θ"-"Φ")+1)`

Example

`"0.802434"=(cos("29°"+"24°")+1)/(cos("29°"-"24°")+1)`

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Maximum Efficiency of Spiral Gears Solution

STEP 0: Pre-Calculation Summary

Formula Used

Efficiency = (cos(Shaft Angle+Angle of Friction)+1)/(cos(Shaft Angle-Angle of Friction)+1)
η = (cos(θ+Φ)+1)/(cos(θ-Φ)+1)
This formula uses 1 Functions, 3 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.
Shaft Angle - (Measured in Radian) - Shaft angle is the measurement of the angle formed between the obliquely oriented neck with the vertical shaft.
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.

STEP 1: Convert Input(s) to Base Unit

Shaft Angle: 29 Degree --> 0.50614548307826 Radian (Check conversion here)
Angle of Friction: 24 Degree --> 0.41887902047856 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

η = (cos(θ+Φ)+1)/(cos(θ-Φ)+1) --> (cos(0.50614548307826+0.41887902047856)+1)/(cos(0.50614548307826-0.41887902047856)+1)

Evaluating ... ...

η = 0.802434263893915

STEP 3: Convert Result to Output's Unit

0.802434263893915 --> No Conversion Required

FINAL ANSWER

0.802434263893915 ≈ 0.802434 <-- Efficiency

(Calculation completed in 00.020 seconds)

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

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Created by Anshika Arya

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

Maximum Efficiency of Spiral Gears Formula

Efficiency = (cos(Shaft Angle+Angle of Friction)+1)/(cos(Shaft Angle-Angle of Friction)+1)
η = (cos(θ+Φ)+1)/(cos(θ-Φ)+1)

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 Maximum Efficiency of Spiral Gears?

Maximum Efficiency of Spiral Gears calculator uses Efficiency = (cos(Shaft Angle+Angle of Friction)+1)/(cos(Shaft Angle-Angle of Friction)+1) to calculate the Efficiency, The maximum efficiency of spiral gears signifies a peak 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 Maximum Efficiency of Spiral Gears using this online calculator? To use this online calculator for Maximum Efficiency of Spiral Gears, enter Shaft Angle (θ) & Angle of Friction (Φ) and hit the calculate button. Here is how the Maximum Efficiency of Spiral Gears calculation can be explained with given input values -> 0.802434 = (cos(0.50614548307826+0.41887902047856)+1)/(cos(0.50614548307826-0.41887902047856)+1).

FAQ

What is Maximum Efficiency of Spiral Gears?

The maximum efficiency of spiral gears signifies a peak level of performance that uses the least amount of inputs to achieve the highest amount of output and is represented as η = (cos(θ+Φ)+1)/(cos(θ-Φ)+1) or Efficiency = (cos(Shaft Angle+Angle of Friction)+1)/(cos(Shaft Angle-Angle of Friction)+1). Shaft angle is the measurement of the angle formed between the obliquely oriented neck with the vertical shaft & 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.

How to calculate Maximum Efficiency of Spiral Gears?

The maximum efficiency of spiral gears signifies a peak level of performance that uses the least amount of inputs to achieve the highest amount of output is calculated using Efficiency = (cos(Shaft Angle+Angle of Friction)+1)/(cos(Shaft Angle-Angle of Friction)+1). To calculate Maximum Efficiency of Spiral Gears, you need Shaft Angle (θ) & Angle of Friction (Φ). With our tool, you need to enter the respective value for Shaft Angle & Angle of Friction 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 Shaft Angle & Angle of Friction. 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(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)

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