Area of contact given Frictional Force Solution

STEP 0: Pre-Calculation Summary
Formula Used
Real Area of Contact = Force of Friction/((Proportion of Area of Metallic Contact*Shear Strength of Softer Metal)+((1-Proportion of Area of Metallic Contact)*Shear Strength of Softer Lubricant Layer))
Ar = Ffriction/((γm*τ1)+((1-γm)*τ2))
This formula uses 5 Variables
Variables Used
Real Area of Contact - (Measured in Square Meter) - Real area of contact is defined as the actual or real area that is in actual contact with the other part.
Force of Friction - (Measured in Newton) - Force of friction, used in merchant circle where the friction force is equal to the product of coefficient of friction and normal force.
Proportion of Area of Metallic Contact - The proportion of area of metallic contact is defined as the proportion of the area supporting the load in which metal came in contact.
Shear Strength of Softer Metal - (Measured in Pascal) - Shear Strength of Softer Metal is the shear strength of the softer metal.
Shear Strength of Softer Lubricant Layer - (Measured in Pascal) - Shear Strength of Softer Lubricant Layer is the shear strength of the softer material.
STEP 1: Convert Input(s) to Base Unit
Force of Friction: 25 Newton --> 25 Newton No Conversion Required
Proportion of Area of Metallic Contact: 0.5 --> No Conversion Required
Shear Strength of Softer Metal: 0.03 Newton per Square Millimeter --> 30000 Pascal (Check conversion here)
Shear Strength of Softer Lubricant Layer: 0.01 Newton per Square Millimeter --> 10000 Pascal (Check conversion here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
Ar = Ffriction/((γm1)+((1-γm)*τ2)) --> 25/((0.5*30000)+((1-0.5)*10000))
Evaluating ... ...
Ar = 0.00125
STEP 3: Convert Result to Output's Unit
0.00125 Square Meter -->1250 Square Millimeter (Check conversion here)
FINAL ANSWER
1250 Square Millimeter <-- Real Area of Contact
(Calculation completed in 00.004 seconds)

Credits

Created by Parul Keshav
National Institute of Technology (NIT), Srinagar
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Indian Institute of Information Technology, Design and Manufacturing (IIITDM), Jabalpur
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17 Cutting Fluid and Surface Roughness Calculators

Frictional Force required to continuously shear junction between surfaces
Go Force of Friction = Real Area of Contact*((Proportion of Area of Metallic Contact*Shear Strength of Softer Metal)+((1-Proportion of Area of Metallic Contact)*Shear Strength of Softer Lubricant Layer))
Shear Strength of Softer Lubricant layer given Frictional force
Go Shear Strength of Softer Lubricant Layer = ((Force of Friction/Real Area of Contact)-(Proportion of Area of Metallic Contact*Shear Strength of Softer Metal))/(1-Proportion of Area of Metallic Contact)
Area of contact given Frictional Force
Go Real Area of Contact = Force of Friction/((Proportion of Area of Metallic Contact*Shear Strength of Softer Metal)+((1-Proportion of Area of Metallic Contact)*Shear Strength of Softer Lubricant Layer))
Proportion of Area in which metallic contact occurs given Frictional Force
Go Proportion of Area of Metallic Contact = ((Force of Friction/Real Area of Contact)-Shear Strength of Softer Lubricant Layer)/(Shear Strength of Softer Metal-Shear Strength of Softer Lubricant Layer)
Shear Strength of Softer Metal given Frictional force
Go Shear Strength of Softer Metal = ((Force of Friction/Real Area of Contact)-(1-Proportion of Area of Metallic Contact)*Shear Strength of Softer Lubricant Layer)/Proportion of Area of Metallic Contact
Working major cutting edge Angle given Roughness value
Go Working Major Cutting-Edge Angle = (acot((Feed/(4*Roughness Value))-cot(Working Minor Cutting Edge)))
Working minor cutting edge Angle given Roughness value
Go Working Minor Cutting Edge = (acot((Feed/(4*Roughness Value))-cot(Working Major Cutting-Edge Angle)))
Roughness Value
Go Roughness Value = Feed/(4*(cot(Working Major Cutting-Edge Angle)+cot(Working Minor Cutting Edge)))
Feed given Roughness value
Go Feed = 4*(cot(Working Major Cutting-Edge Angle)+cot(Working Minor Cutting Edge))*Roughness Value
Rotational Frequency of Cutter given Roughness Value
Go Rotational Frequency of Cutter = sqrt(0.0642/(Roughness Value*Diameter of Cutter))*Feed Speed
Feed speed given Roughness value
Go Feed Speed = sqrt(Roughness Value*Diameter of Cutter/0.0642)*Rotational Frequency of Cutter
Diameter of Cutter given Roughness Value
Go Diameter of Cutter = (0.0642*(Feed Speed)^2)/(Roughness Value*(Rotational Frequency of Cutter)^2)
Roughness value given feed speed
Go Roughness Value = (0.0642*(Feed Speed)^2)/(Diameter of Cutter*(Rotational Frequency of Cutter)^2)
Feed given Roughness Value and corner radius
Go Feed = (Roughness Value*Corner Radius of Tool/0.0321)^(1/2)
Corner Radius given Roughness value
Go Corner Radius of Tool = 0.0321*(Feed)^2/Roughness Value
Roughness value given corner radius
Go Roughness Value = 0.0321*(Feed)^2/Corner Radius of Tool
Roughness value of tool
Go Roughness Value = 0.0321*(Feed)^2/Corner Radius of Tool

Area of contact given Frictional Force Formula

Real Area of Contact = Force of Friction/((Proportion of Area of Metallic Contact*Shear Strength of Softer Metal)+((1-Proportion of Area of Metallic Contact)*Shear Strength of Softer Lubricant Layer))
Ar = Ffriction/((γm*τ1)+((1-γm)*τ2))

what is friction force?

The friction force is the force exerted by a surface as an object moves across it or makes an effort to move across it. There are at least two types of friction force - sliding and static friction. Though it is not always the case, the friction force often opposes the motion of an object.

How to Calculate Area of contact given Frictional Force?

Area of contact given Frictional Force calculator uses Real Area of Contact = Force of Friction/((Proportion of Area of Metallic Contact*Shear Strength of Softer Metal)+((1-Proportion of Area of Metallic Contact)*Shear Strength of Softer Lubricant Layer)) to calculate the Real Area of Contact, The Area of contact given Frictional Force is defined as the real area that is in the actual contact between the two surfaces. Real Area of Contact is denoted by Ar symbol.

How to calculate Area of contact given Frictional Force using this online calculator? To use this online calculator for Area of contact given Frictional Force, enter Force of Friction (Ffriction), Proportion of Area of Metallic Contact m), Shear Strength of Softer Metal 1) & Shear Strength of Softer Lubricant Layer 2) and hit the calculate button. Here is how the Area of contact given Frictional Force calculation can be explained with given input values -> 1.3E+9 = 25/((0.5*30000)+((1-0.5)*10000)).

FAQ

What is Area of contact given Frictional Force?
The Area of contact given Frictional Force is defined as the real area that is in the actual contact between the two surfaces and is represented as Ar = Ffriction/((γm1)+((1-γm)*τ2)) or Real Area of Contact = Force of Friction/((Proportion of Area of Metallic Contact*Shear Strength of Softer Metal)+((1-Proportion of Area of Metallic Contact)*Shear Strength of Softer Lubricant Layer)). Force of friction, used in merchant circle where the friction force is equal to the product of coefficient of friction and normal force, The proportion of area of metallic contact is defined as the proportion of the area supporting the load in which metal came in contact, Shear Strength of Softer Metal is the shear strength of the softer metal & Shear Strength of Softer Lubricant Layer is the shear strength of the softer material.
How to calculate Area of contact given Frictional Force?
The Area of contact given Frictional Force is defined as the real area that is in the actual contact between the two surfaces is calculated using Real Area of Contact = Force of Friction/((Proportion of Area of Metallic Contact*Shear Strength of Softer Metal)+((1-Proportion of Area of Metallic Contact)*Shear Strength of Softer Lubricant Layer)). To calculate Area of contact given Frictional Force, you need Force of Friction (Ffriction), Proportion of Area of Metallic Contact m), Shear Strength of Softer Metal 1) & Shear Strength of Softer Lubricant Layer 2). With our tool, you need to enter the respective value for Force of Friction, Proportion of Area of Metallic Contact, Shear Strength of Softer Metal & Shear Strength of Softer Lubricant Layer 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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