Gear Ratio given Number of Teeth on Wheel and Pinion Solution

STEP 0: Pre-Calculation Summary
Formula Used
Gear Ratio = Number of Teeth on Wheel/Number of Teeth on Pinion
G = T/Zp
This formula uses 3 Variables
Variables Used
Gear Ratio - The Gear Ratio is the ratio of output gear speed to the input gear speed or the ratio of number of teeth on gear to that on the pinion.
Number of Teeth on Wheel - Number of teeth on wheel is the count of teeths on the wheel.
Number of Teeth on Pinion - Number of teeth on pinion is the count of teeth on pinion.
STEP 1: Convert Input(s) to Base Unit
Number of Teeth on Wheel: 12 --> No Conversion Required
Number of Teeth on Pinion: 8 --> No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
G = T/Zp --> 12/8
Evaluating ... ...
G = 1.5
STEP 3: Convert Result to Output's Unit
1.5 --> No Conversion Required
FINAL ANSWER
1.5 <-- Gear Ratio
(Calculation completed in 00.004 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

Gear Ratio given Number of Teeth on Wheel and Pinion Formula

Gear Ratio = Number of Teeth on Wheel/Number of Teeth on Pinion
G = T/Zp

What is a good gearing ratio?

A gearing ratio higher than 50% is typically considered highly levered or geared. A gearing ratio lower than 25% is typically considered low-risk by both investors and lenders. A gearing ratio between 25% and 50% is typically considered optimal or normal for well-established companies.

How to Calculate Gear Ratio given Number of Teeth on Wheel and Pinion?

Gear Ratio given Number of Teeth on Wheel and Pinion calculator uses Gear Ratio = Number of Teeth on Wheel/Number of Teeth on Pinion to calculate the Gear Ratio, Gear Ratio given number of Teeth on Wheel and Pinion is the ratio of the number of teeth in the gear to the number of teeth in the pinion, the pinion being the smaller of the two gears in mesh. Gear Ratio is denoted by G symbol.

How to calculate Gear Ratio given Number of Teeth on Wheel and Pinion using this online calculator? To use this online calculator for Gear Ratio given Number of Teeth on Wheel and Pinion, enter Number of Teeth on Wheel (T) & Number of Teeth on Pinion (Zp) and hit the calculate button. Here is how the Gear Ratio given Number of Teeth on Wheel and Pinion calculation can be explained with given input values -> 1.5 = 12/8.

FAQ

What is Gear Ratio given Number of Teeth on Wheel and Pinion?
Gear Ratio given number of Teeth on Wheel and Pinion is the ratio of the number of teeth in the gear to the number of teeth in the pinion, the pinion being the smaller of the two gears in mesh and is represented as G = T/Zp or Gear Ratio = Number of Teeth on Wheel/Number of Teeth on Pinion. Number of teeth on wheel is the count of teeths on the wheel & Number of teeth on pinion is the count of teeth on pinion.
How to calculate Gear Ratio given Number of Teeth on Wheel and Pinion?
Gear Ratio given number of Teeth on Wheel and Pinion is the ratio of the number of teeth in the gear to the number of teeth in the pinion, the pinion being the smaller of the two gears in mesh is calculated using Gear Ratio = Number of Teeth on Wheel/Number of Teeth on Pinion. To calculate Gear Ratio given Number of Teeth on Wheel and Pinion, you need Number of Teeth on Wheel (T) & Number of Teeth on Pinion (Zp). With our tool, you need to enter the respective value for Number of Teeth on Wheel & Number of Teeth on Pinion 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 Gear Ratio?
In this formula, Gear Ratio uses Number of Teeth on Wheel & Number of Teeth on Pinion. We can use 1 other way(s) to calculate the same, which is/are as follows -
  • Gear Ratio = Radius of Pitch Circle of Wheel/Radius of Pitch Circle of Pinion
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