Normal Force on Shear Plane of Tool 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%

✖The Normal Force on Shear Plane is the force acting normal to the shear plane.ⓘ Normal Force on Shear Plane of Tool [F_ns]

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Formula

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Normal Force on Shear Plane of Tool

Formula

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

Example

`"448.4909N"="647.55N"*sin(("11.406°"+"52.43°"-"20°"))`

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Normal Force on Shear Plane of Tool Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

Functions Used

sin - Sine is a trigonometric function that describes the ratio of the length of the opposite side of a right triangle to the length of the hypotenuse., sin(Angle)

Variables Used

Normal Force on Shear Plane - (Measured in Newton) - The Normal Force on Shear Plane is the force acting normal to 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_ns = F_r*sin((ϕ+β-γ_ne)) --> 647.55*sin((0.199072254482436+0.915076126820455-0.3490658503988))

Evaluating ... ...

F_ns = 448.490884648176

STEP 3: Convert Result to Output's Unit

448.490884648176 Newton --> No Conversion Required

FINAL ANSWER

448.490884648176 ≈ 448.4909 Newton <-- Normal Force on Shear Plane

(Calculation completed in 00.004 seconds)

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

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Created by Parul Keshav

National Institute of Technology (NIT), Srinagar

Parul Keshav has created this Calculator and 300+ more calculators!

Verified by Anshika Arya

National Institute Of Technology (NIT), Hamirpur

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< 13 Forces and Friction Calculators

Normal stress due to tool

Go Normal stress = sin(Shear angle)*Resultant Cutting Force*sin((Shear angle+Mean Friction Angle on Tool Face-Working Normal Rake))/Cross-sectional Area of Uncut Chip

Normal Force on Shear Plane of Tool

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

Resultant Tool Force using Shear Force on Shear Plane

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

Rate of Energy Consumption during Machining given Specific Cutting Energy

Go Rate of Energy Consumption during Machining = Specific Cutting Energy in Machining*Metal removal rate

Specific cutting energy in machining

Go Specific Cutting Energy in Machining = Rate of Energy Consumption during Machining/Metal removal rate

Machining Power using Overall Efficiency

Go Machining Power = Overall Machining Efficiency*Electrical Power Available for Machining

Yield Pressure given Coefficient of Friction in metal cutting

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

Coefficient of friction in metal cutting

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

Area of contact given Total Frictional Force in metal cutting

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

Total frictional force in metal cutting

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

Cutting Speed using Rate of Energy Consumption during Machining

Go Cutting Speed = Rate of Energy Consumption during Machining/Cutting Force

Rate of Energy Consumption during Machining

Go Rate of Energy Consumption during Machining = Cutting Speed*Cutting Force

Plowing Force using Force required to remove Chip

Go Plowing Force = Resultant Cutting Force-Force Required to Remove Chip

Normal Force on Shear Plane of Tool Formula

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

What is normal Rake angle?

Normal Rake Angle (γN)—It is the angle of orientation of the tool's rake surface from the reference plane (πR) and measured on the normal plane (πN). Inclination Angle (λ)—It is the angle of inclination of the tool's principal cutting edge from the reference plane (πR) and measured on the cutting plane (πC).

How to Calculate Normal Force on Shear Plane of Tool?

Normal Force on Shear Plane of Tool calculator uses Normal Force on Shear Plane = Resultant Cutting Force*sin((Shear angle+Mean Friction Angle on Tool Face-Working Normal Rake)) to calculate the Normal Force on Shear Plane, Normal force on shear plane of tool formula is used to find the normal force acting on the shear plane of the tool. Normal Force on Shear Plane is denoted by F_ns symbol.

How to calculate Normal Force on Shear Plane of Tool using this online calculator? To use this online calculator for Normal Force on Shear Plane of Tool, 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 Normal Force on Shear Plane of Tool calculation can be explained with given input values -> 448.4909 = 647.55*sin((0.199072254482436+0.915076126820455-0.3490658503988)).

FAQ

What is Normal Force on Shear Plane of Tool?

Normal force on shear plane of tool formula is used to find the normal force acting on the shear plane of the tool and is represented as F_ns = F_r*sin((ϕ+β-γ_ne)) or Normal Force on Shear Plane = Resultant Cutting Force*sin((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 Normal Force on Shear Plane of Tool?

Normal force on shear plane of tool formula is used to find the normal force acting on the shear plane of the tool is calculated using Normal Force on Shear Plane = Resultant Cutting Force*sin((Shear angle+Mean Friction Angle on Tool Face-Working Normal Rake)). To calculate Normal Force on Shear Plane of Tool, 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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