Shear Force on Shear Plane Calculator

✖The Resultant Cutting Force is the total force in the direction of cutting, the same direction as the cutting speed.ⓘ Resultant Cutting Force [F_r]			+10% -10%
✖Shear angle is the inclination of the shear plane with the horizontal axis at machining point.ⓘ Shear angle [ϕ]			+10% -10%
✖The Mean Friction Angle on Tool Face corresponds to the maximum static friction force between the tool face and workpiece.ⓘ Mean Friction Angle on Tool Face [β]			+10% -10%
✖The Working Normal Rake angle is the angle of orientation of the tool's rake surface from the reference plane and measured on a normal plane.ⓘ Working Normal Rake [γ_ne]			+10% -10%

✖Shear Force is the force which causes shear deformation to occur in the shear plane.ⓘ Shear Force on Shear Plane [F_shear]

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Formula

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Shear Force on Shear Plane

Formula

`"F"_{"shear"} = "F"_{"r"}*cos(("ϕ"+"β"-"γ"_{"ne"}))`

Example

`"467.0941N"="647.55N"*cos(("11.406°"+"52.43°"-"20°"))`

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Shear Force on Shear Plane Solution

STEP 0: Pre-Calculation Summary

Formula Used

Shear Force = Resultant Cutting Force*cos((Shear angle+Mean Friction Angle on Tool Face-Working Normal Rake))
F_shear = F_r*cos((ϕ+β-γ_ne))
This formula uses 1 Functions, 5 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

Shear Force - (Measured in Newton) - Shear Force is the force which causes shear deformation to occur in the shear plane.
Resultant Cutting Force - (Measured in Newton) - The Resultant Cutting Force is the total force in the direction of cutting, the same direction as the cutting speed.
Shear angle - (Measured in Radian) - Shear angle is the inclination of the shear plane with the horizontal axis at machining point.
Mean Friction Angle on Tool Face - (Measured in Radian) - The Mean Friction Angle on Tool Face corresponds to the maximum static friction force between the tool face and workpiece.
Working Normal Rake - (Measured in Radian) - The Working Normal Rake angle is the angle of orientation of the tool's rake surface from the reference plane and measured on a normal plane.

STEP 1: Convert Input(s) to Base Unit

Resultant Cutting Force: 647.55 Newton --> 647.55 Newton No Conversion Required
Shear angle: 11.406 Degree --> 0.199072254482436 Radian (Check conversion here)
Mean Friction Angle on Tool Face: 52.43 Degree --> 0.915076126820455 Radian (Check conversion here)
Working Normal Rake: 20 Degree --> 0.3490658503988 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

F_shear = F_r*cos((ϕ+β-γ_ne)) --> 647.55*cos((0.199072254482436+0.915076126820455-0.3490658503988))

Evaluating ... ...

F_shear = 467.094132790701

STEP 3: Convert Result to Output's Unit

467.094132790701 Newton --> No Conversion Required

FINAL ANSWER

467.094132790701 ≈ 467.0941 Newton <-- Shear Force

(Calculation completed in 00.004 seconds)

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Home » Engineering » Production Engineering » Metal Machining » Metal Machining Dynamics » Theory of Ernst and Merchant » Shear » Shear Force on Shear Plane

Credits

Created by Kethavath Srinath

Osmania University (OU), Hyderabad

Kethavath Srinath has created this Calculator and 1000+ more calculators!

Verified by Anshika Arya

National Institute Of Technology (NIT), Hamirpur

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< 9 Shear Calculators

Cutting Ratio for given Shear Angle of Continuous chip

Go Cutting Ratio = tan(Shear angle)/(cos(Working Normal Rake)+(tan(Shear angle)*sin(Working Normal Rake)))

Shear Angle of Continuous Chip Formation

Go Shear angle = atan((Cutting Ratio*cos(Working Normal Rake))/(1-(Cutting Ratio*sin(Working Normal Rake))))

Total Shear force by tool

Go Total Shear Force by Tool = (Cutting Force*cos(Shear angle))+(Thrust force*sin(Shear angle))

Shear Force on Shear Plane

Go Shear Force = Resultant Cutting Force*cos((Shear angle+Mean Friction Angle on Tool Face-Working Normal Rake))

Shear Force on Shear Plane using Shear Strength

Go Total Shear Force by Tool = Shear Strength of Material*Cross-sectional Area of Uncut Chip/sin(Shear angle)

Area of Shear

Go Area of Shear = Cross-sectional Area of Uncut Chip/sin(Shear angle)

Shear Strength given Coefficient of Friction in Metal Cutting

Go Shear Strength of Material = Coefficient of Friction*Yield Pressure of Softer Material

Shear Strength of Material given Total Frictional force in metal cutting

Go Shear Strength of Material = Total Frictional Force by Tool/Area of Contact

Shear Strength of Material on Shear Plane

Go Shear Strength of Material = Total Shear Force by Tool/Area of Shear

Shear Force on Shear Plane Formula

Shear Force = Resultant Cutting Force*cos((Shear angle+Mean Friction Angle on Tool Face-Working Normal Rake))
F_shear = F_r*cos((ϕ+β-γ_ne))

Define Shear Force?

Shear force is force that makes one surface of a substance move over another parallel surface.Tensile and compressive force acts perpendicular to a structure's surface whereas shear force acts parallel to the surface. Shear force is force that makes one surface of a substance move over another parallel surface.

How to Calculate Shear Force on Shear Plane?

Shear Force on Shear Plane calculator uses Shear Force = Resultant Cutting Force*cos((Shear angle+Mean Friction Angle on Tool Face-Working Normal Rake)) to calculate the Shear Force, The Shear Force on Shear Plane formula is defined as the force that makes one surface of a substance move over another parallel surface. Shear Force is denoted by F_shear symbol.

How to calculate Shear Force on Shear Plane using this online calculator? To use this online calculator for Shear Force on Shear Plane, enter Resultant Cutting Force (F_r), Shear angle (ϕ), Mean Friction Angle on Tool Face (β) & Working Normal Rake (γ_ne) and hit the calculate button. Here is how the Shear Force on Shear Plane calculation can be explained with given input values -> 467.0941 = 647.55*cos((0.199072254482436+0.915076126820455-0.3490658503988)).

FAQ

What is Shear Force on Shear Plane?

The Shear Force on Shear Plane formula is defined as the force that makes one surface of a substance move over another parallel surface and is represented as F_shear = F_r*cos((ϕ+β-γ_ne)) or Shear Force = Resultant Cutting Force*cos((Shear angle+Mean Friction Angle on Tool Face-Working Normal Rake)). The Resultant Cutting Force is the total force in the direction of cutting, the same direction as the cutting speed, Shear angle is the inclination of the shear plane with the horizontal axis at machining point, The Mean Friction Angle on Tool Face corresponds to the maximum static friction force between the tool face and workpiece & The Working Normal Rake angle is the angle of orientation of the tool's rake surface from the reference plane and measured on a normal plane.

How to calculate Shear Force on Shear Plane?

The Shear Force on Shear Plane formula is defined as the force that makes one surface of a substance move over another parallel surface is calculated using Shear Force = Resultant Cutting Force*cos((Shear angle+Mean Friction Angle on Tool Face-Working Normal Rake)). To calculate Shear Force on Shear Plane, you need Resultant Cutting Force (F_r), Shear angle (ϕ), Mean Friction Angle on Tool Face (β) & Working Normal Rake (γ_ne). With our tool, you need to enter the respective value for Resultant Cutting Force, Shear angle, Mean Friction Angle on Tool Face & Working Normal Rake 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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