Ratio Factor for Internal Gears Solution

STEP 0: Pre-Calculation Summary
Formula Used
Ratio Factor = 2*Number of Teeth of Gear/(Number of Teeth of Gear-Number of Teeth on Spur Pinion)
Qg = 2*Zg/(Zg-zp)
This formula uses 3 Variables
Variables Used
Ratio Factor - The Ratio Factor for Gear is the ratio of twice gear teeth to the sum of gear and pinion of gear teeth, considering a formative number of teeth.
Number of Teeth of Gear - The number of teeth of Gear is defined as the number of teeth on gear.
Number of Teeth on Spur Pinion - Number of Teeth on Spur Pinion is the total number of teeth on the periphery of the smaller gear or also known as the pinion.
STEP 1: Convert Input(s) to Base Unit
Number of Teeth of Gear: 30 --> No Conversion Required
Number of Teeth on Spur Pinion: 12 --> No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
Qg = 2*Zg/(Zg-zp) --> 2*30/(30-12)
Evaluating ... ...
Qg = 3.33333333333333
STEP 3: Convert Result to Output's Unit
3.33333333333333 --> No Conversion Required
FINAL ANSWER
3.33333333333333 3.333333 <-- Ratio Factor
(Calculation completed in 00.004 seconds)

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21 Design of Machine Elements Calculators

Factor of Safety for Tri-axial State of Stress
Go Factor of Safety = Tensile Yield Strength/sqrt(1/2*((Normal Stress 1-Normal Stress 2)^2+(Normal Stress 2-Normal Stress 3)^2+(Normal Stress 3-Normal Stress 1)^2))
Equivalent Stress by Distortion Energy Theory
Go Equivalent Stress = 1/sqrt(2)*sqrt((Normal Stress 1-Normal Stress 2)^2+(Normal Stress 2-Normal Stress 3)^2+(Normal Stress 3-Normal Stress 1)^2)
Collar Friction Torque in Accordance of Uniform Pressure Theory
Go Collar Friction Torque = ((Coefficient of Friction*Load)*(Outer Diameter of Collar^3-Inner Diameter of Collar^3))/(3*(Outer Diameter of Collar^2-Inner Diameter of Collar^2))
Factor of Safety for Bi-Axial State of Stress
Go Factor of Safety = Tensile Yield Strength/(sqrt(Normal Stress 1^2+Normal Stress 2^2-Normal Stress 1*Normal Stress 2))
Tensile Stress in Spigot
Go Tensile Stress = Tensile Force on Rods/((pi/4*Diameter of Spigot^(2))-(Diameter of Spigot*Thickness of Cotter))
Unit Bearing Pressure
Go Unit Bearing Pressure = (4*Force on Unit)/(pi*Number of Threads*(Nominal Diameter^2-Core Diameter^2))
Shear Stress on Flat Key
Go Shear Stress = (2*Torque Transmitted by Shaft)/(Width of Key*Diameter of Shaft*Length of Key)
Polar Moment of Inertia of Hollow Circular Shaft
Go Polar Moment of Inertia of shaft = (pi*(Outer Diameter of Shaft^(4)-Inner Diameter of Shaft^(4)))/32
Ratio Factor for External Gears
Go Ratio Factor = 2*Number of Teeth of Gear/(Number of Teeth of Gear+Number of Teeth on Spur Pinion)
Ratio Factor for Internal Gears
Go Ratio Factor = 2*Number of Teeth of Gear/(Number of Teeth of Gear-Number of Teeth on Spur Pinion)
Permissible Shear Stress for Cotter
Go Permissible Shear Stress = Tensile Force on Rods/(2*Mean Width of Cotter*Thickness of Cotter)
Compressive Stress of Spigot
Go Compressive Stress in Spigot = Load on Cotter Joint/(Thickness of Cotter*Spigot Diameter)
Permissible Shear Stress for Spigot
Go Permissible Shear Stress = Tensile Force on Rods/(2*Spigot Distance*Diameter of Spigot)
Pitchline Velocity of Meshing Gears
Go Velocity = pi*Diameter of Pitch Circle*Speed in RPM/60
Power Transmitted
Go Shaft Power = 2*pi*Speed of Rotation*Torque applied
Stress Amplitude
Go Stress Amplitude = (Maximum Stress at Crack Tip-Minimum Stress)/2
Polar Moment of Inertia of Solid Circular Shaft
Go Polar Moment of Inertia = (pi*Diameter of Shaft^4)/32
Factor of Safety given Ultimate Stress and Working Stress
Go Factor of Safety = Fracture Stress/Working Stress
Thickness of Cotter Joint
Go Thickness of Cotter = 0.31*Diameter of Rod of Cotter Joint
Shear Yield Strength by Maximum Distortion Energy Theory
Go Shear Yield Strength = 0.577*Tensile Yield Strength
Shear Yield Strength by Maximum Shear Stress Theory
Go Shear Yield Strength = Tensile Yield Strength/2

Ratio Factor for Internal Gears Formula

Ratio Factor = 2*Number of Teeth of Gear/(Number of Teeth of Gear-Number of Teeth on Spur Pinion)
Qg = 2*Zg/(Zg-zp)

What are internal gears?

An internal gear is a gear which has its teeth formed on the inner surface of a cylinder or cone. The teeth of an internal spur gear point inwards the center.

How to Calculate Ratio Factor for Internal Gears?

Ratio Factor for Internal Gears calculator uses Ratio Factor = 2*Number of Teeth of Gear/(Number of Teeth of Gear-Number of Teeth on Spur Pinion) to calculate the Ratio Factor, The ratio factor for internal gears is defined as the ratio of number of teeth on gear to the difference of number of teeth on gear and pinion. Ratio Factor is denoted by Qg symbol.

How to calculate Ratio Factor for Internal Gears using this online calculator? To use this online calculator for Ratio Factor for Internal Gears, enter Number of Teeth of Gear (Zg) & Number of Teeth on Spur Pinion (zp) and hit the calculate button. Here is how the Ratio Factor for Internal Gears calculation can be explained with given input values -> 3.333333 = 2*30/(30-12).

FAQ

What is Ratio Factor for Internal Gears?
The ratio factor for internal gears is defined as the ratio of number of teeth on gear to the difference of number of teeth on gear and pinion and is represented as Qg = 2*Zg/(Zg-zp) or Ratio Factor = 2*Number of Teeth of Gear/(Number of Teeth of Gear-Number of Teeth on Spur Pinion). The number of teeth of Gear is defined as the number of teeth on gear & Number of Teeth on Spur Pinion is the total number of teeth on the periphery of the smaller gear or also known as the pinion.
How to calculate Ratio Factor for Internal Gears?
The ratio factor for internal gears is defined as the ratio of number of teeth on gear to the difference of number of teeth on gear and pinion is calculated using Ratio Factor = 2*Number of Teeth of Gear/(Number of Teeth of Gear-Number of Teeth on Spur Pinion). To calculate Ratio Factor for Internal Gears, you need Number of Teeth of Gear (Zg) & Number of Teeth on Spur Pinion (zp). With our tool, you need to enter the respective value for Number of Teeth of Gear & Number of Teeth on Spur 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 Ratio Factor?
In this formula, Ratio Factor uses Number of Teeth of Gear & Number of Teeth on Spur Pinion. We can use 1 other way(s) to calculate the same, which is/are as follows -
  • Ratio Factor = 2*Number of Teeth of Gear/(Number of Teeth of Gear+Number of Teeth on Spur Pinion)
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