Resultant Tool Force using Shear Force on Shear Plane Calculator

✖Total Shear Force by Tool is the resultant shear force applied by the tool to the workpiece.ⓘ Total Shear Force by Tool [F_s]			+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 Resultant Cutting Force is the total force in the direction of cutting, the same direction as the cutting speed.ⓘ Resultant Tool Force using Shear Force on Shear Plane [F_r]

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Resultant Tool Force using Shear Force on Shear Plane

Formula

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

Example

`"1346.438N"="971.22N"/cos(("11.406°"+"52.43°"-"20°"))`

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Resultant Tool Force using Shear Force on Shear Plane Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

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.
Total Shear Force by Tool - (Measured in Newton) - Total Shear Force by Tool is the resultant shear force applied by the tool to the workpiece.
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

Total Shear Force by Tool: 971.22 Newton --> 971.22 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_r = F_s/cos((ϕ+β-γ_ne)) --> 971.22/cos((0.199072254482436+0.915076126820455-0.3490658503988))

Evaluating ... ...

F_r = 1346.43847320987

STEP 3: Convert Result to Output's Unit

1346.43847320987 Newton --> No Conversion Required

FINAL ANSWER

1346.43847320987 ≈ 1346.438 Newton <-- Resultant Cutting 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 » Forces and Friction » Resultant Tool Force using Shear Force on Shear Plane

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Created by Parul Keshav

National Institute of Technology (NIT), Srinagar

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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

Resultant Tool Force using Shear Force on Shear Plane Formula

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

What is resultant cutting force?

The resultant Cutting force is the resistance of the material against the intrusion of the cutting tool. The force directions and amplitudes differ in different cutting processes such as turning, milling, drilling, etc. performed in manufacturing machines –often CNC

How to Calculate Resultant Tool Force using Shear Force on Shear Plane?

Resultant Tool Force using Shear Force on Shear Plane calculator uses Resultant Cutting Force = Total Shear Force by Tool/cos((Shear angle+Mean Friction Angle on Tool Face-Working Normal Rake)) to calculate the Resultant Cutting Force, Resultant Tool Force using Shear force on shear plane formulas is used to find the force applied by the tool on the layer being removed and thus to the workpiece. Resultant Cutting Force is denoted by F_r symbol.

How to calculate Resultant Tool Force using Shear Force on Shear Plane using this online calculator? To use this online calculator for Resultant Tool Force using Shear Force on Shear Plane, enter Total Shear Force by Tool (F_s), Shear angle (ϕ), Mean Friction Angle on Tool Face (β) & Working Normal Rake (γ_ne) and hit the calculate button. Here is how the Resultant Tool Force using Shear Force on Shear Plane calculation can be explained with given input values -> 1346.438 = 971.22/cos((0.199072254482436+0.915076126820455-0.3490658503988)).

FAQ

What is Resultant Tool Force using Shear Force on Shear Plane?

Resultant Tool Force using Shear force on shear plane formulas is used to find the force applied by the tool on the layer being removed and thus to the workpiece and is represented as F_r = F_s/cos((ϕ+β-γ_ne)) or Resultant Cutting Force = Total Shear Force by Tool/cos((Shear angle+Mean Friction Angle on Tool Face-Working Normal Rake)). Total Shear Force by Tool is the resultant shear force applied by the tool to the workpiece, 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 Resultant Tool Force using Shear Force on Shear Plane?

Resultant Tool Force using Shear force on shear plane formulas is used to find the force applied by the tool on the layer being removed and thus to the workpiece is calculated using Resultant Cutting Force = Total Shear Force by Tool/cos((Shear angle+Mean Friction Angle on Tool Face-Working Normal Rake)). To calculate Resultant Tool Force using Shear Force on Shear Plane, you need Total Shear Force by Tool (F_s), 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 Total Shear Force by Tool, 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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