Contact Ratio Solution

STEP 0: Pre-Calculation Summary
Formula Used
Contact Ratio = Path of Contact/Circular Pitch
CR = P/Pc
This formula uses 3 Variables
Variables Used
Contact Ratio - The contact ratio represents the average number of teeth meshing at the same time.
Path of Contact - (Measured in Meter) - The path of contact is the path traced by the contact point of a pair of tooth profiles.
Circular Pitch - (Measured in Meter) - A circular pitch is the distance along the pitch circle or pitch line between corresponding profiles of adjacent teeth.
STEP 1: Convert Input(s) to Base Unit
Path of Contact: 18 Millimeter --> 0.018 Meter (Check conversion here)
Circular Pitch: 16 Millimeter --> 0.016 Meter (Check conversion here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
CR = P/Pc --> 0.018/0.016
Evaluating ... ...
CR = 1.125
STEP 3: Convert Result to Output's Unit
1.125 --> No Conversion Required
FINAL ANSWER
1.125 <-- Contact Ratio
(Calculation completed in 00.004 seconds)

Credits

Created by Anshika Arya
National Institute Of Technology (NIT), Hamirpur
Anshika Arya has created this Calculator and 2000+ more calculators!
Verified by Team Softusvista
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Team Softusvista has verified this Calculator and 1100+ more calculators!

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

Contact Ratio Formula

Contact Ratio = Path of Contact/Circular Pitch
CR = P/Pc

What is length of path of contact?

Path of contact is the locus of the point of contact on two mating teeth from the beginning of engagement to the end of it. Thus CD is the path of contact. It is also called as contact length. It is the tangent to both the base circles and passes through the pitch point.

How is circular pitch calculated?

Circular Circular pitch is the distance from a point on one tooth to the corresponding point on the next tooth measured along the pitch circle. Its value is equal to the circumference of the pitch circle divided by the number of teeth in the gear.

How to Calculate Contact Ratio?

Contact Ratio calculator uses Contact Ratio = Path of Contact/Circular Pitch to calculate the Contact Ratio, Contact ratio represents the average number of teeth meshing at the same time. Contact Ratio is denoted by CR symbol.

How to calculate Contact Ratio using this online calculator? To use this online calculator for Contact Ratio, enter Path of Contact (P) & Circular Pitch (Pc) and hit the calculate button. Here is how the Contact Ratio calculation can be explained with given input values -> 1.125 = 0.018/0.016.

FAQ

What is Contact Ratio?
Contact ratio represents the average number of teeth meshing at the same time and is represented as CR = P/Pc or Contact Ratio = Path of Contact/Circular Pitch. The path of contact is the path traced by the contact point of a pair of tooth profiles & A circular pitch is the distance along the pitch circle or pitch line between corresponding profiles of adjacent teeth.
How to calculate Contact Ratio?
Contact ratio represents the average number of teeth meshing at the same time is calculated using Contact Ratio = Path of Contact/Circular Pitch. To calculate Contact Ratio, you need Path of Contact (P) & Circular Pitch (Pc). With our tool, you need to enter the respective value for Path of Contact & Circular Pitch and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
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