Normal stress due to tool Calculator

✖Shear angle is the inclination of the shear plane with the horizontal axis at machining point.ⓘ Shear angle [ϕ]			+10% -10%
✖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%
✖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 Cross-sectional Area of Uncut Chip is the area enclosed within the outer surface of the workpiece and the line of cut followed by the single-point cutting edge. It is calculated for one pass.ⓘ Cross-sectional Area of Uncut Chip [A_c]			+10% -10%

✖Normal stress is stress that occurs when a member is loaded by an axial force.ⓘ Normal stress due to tool [σ_n]

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Formula

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Normal stress due to tool

Formula

`"σ"_{"n"} = sin("ϕ")*"F"_{"r"}*sin(("ϕ"+"β"-"γ"_{"ne"}))/"A"_{"c"}`

Example

`"197.0968N/mm²"=sin("11.406°")*"647.55N"*sin(("11.406°"+"52.43°"-"20°"))/"0.45mm²"`

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Normal stress due to tool Solution

STEP 0: Pre-Calculation Summary

Formula Used

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
σ_n = sin(ϕ)*F_r*sin((ϕ+β-γ_ne))/A_c
This formula uses 1 Functions, 6 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 stress - (Measured in Pascal) - Normal stress is stress that occurs when a member is loaded by an axial force.
Shear angle - (Measured in Radian) - Shear angle is the inclination of the shear plane with the horizontal axis at machining point.
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.
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.
Cross-sectional Area of Uncut Chip - (Measured in Square Meter) - The Cross-sectional Area of Uncut Chip is the area enclosed within the outer surface of the workpiece and the line of cut followed by the single-point cutting edge. It is calculated for one pass.

STEP 1: Convert Input(s) to Base Unit

Shear angle: 11.406 Degree --> 0.199072254482436 Radian (Check conversion here)
Resultant Cutting Force: 647.55 Newton --> 647.55 Newton No Conversion Required
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)
Cross-sectional Area of Uncut Chip: 0.45 Square Millimeter --> 4.5E-07 Square Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

σ_n = sin(ϕ)*F_r*sin((ϕ+β-γ_ne))/A_c --> sin(0.199072254482436)*647.55*sin((0.199072254482436+0.915076126820455-0.3490658503988))/4.5E-07

Evaluating ... ...

σ_n = 197096787.182499

STEP 3: Convert Result to Output's Unit

197096787.182499 Pascal -->197.096787182499 Newton per Square Millimeter (Check conversion here)

FINAL ANSWER

197.096787182499 ≈ 197.0968 Newton per Square Millimeter <-- Normal stress

(Calculation completed in 00.020 seconds)

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Home » Engineering » Production Engineering » Metal Machining » Metal Machining Dynamics » Theory of Ernst and Merchant » Forces and Friction » Normal stress due to tool

Credits

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

Anshika Arya has verified this Calculator and 2500+ more calculators!

< 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 stress due to tool Formula

What is normal stress and shear stress?

There are two types of stress that a structure can experience: 1. Normal Stress and 2. Shear Stress. When a force acts perpendicular (or "normal") to the surface of an object, it exerts a normal stress. When a force acts parallel to the surface of an object, it exerts a shear stress.

How to Calculate Normal stress due to tool?

Normal stress due to tool calculator uses 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 to calculate the Normal stress, Normal stress due to tool is when a force acts perpendicular (or "normal") to the surface of a workpiece, it exerts normal stress. Normal stress is denoted by σ_n symbol.

How to calculate Normal stress due to tool using this online calculator? To use this online calculator for Normal stress due to tool, enter Shear angle (ϕ), Resultant Cutting Force (F_r), Mean Friction Angle on Tool Face (β), Working Normal Rake (γ_ne) & Cross-sectional Area of Uncut Chip (A_c) and hit the calculate button. Here is how the Normal stress due to tool calculation can be explained with given input values -> 0.000197 = sin(0.199072254482436)*647.55*sin((0.199072254482436+0.915076126820455-0.3490658503988))/4.5E-07.

FAQ

What is Normal stress due to tool?

Normal stress due to tool is when a force acts perpendicular (or "normal") to the surface of a workpiece, it exerts normal stress and is represented as σ_n = sin(ϕ)*F_r*sin((ϕ+β-γ_ne))/A_c or 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. Shear angle is the inclination of the shear plane with the horizontal axis at machining point, The Resultant Cutting Force is the total force in the direction of cutting, the same direction as the cutting speed, 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 & The Cross-sectional Area of Uncut Chip is the area enclosed within the outer surface of the workpiece and the line of cut followed by the single-point cutting edge. It is calculated for one pass.

How to calculate Normal stress due to tool?

Normal stress due to tool is when a force acts perpendicular (or "normal") to the surface of a workpiece, it exerts normal stress is calculated using 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. To calculate Normal stress due to tool, you need Shear angle (ϕ), Resultant Cutting Force (F_r), Mean Friction Angle on Tool Face (β), Working Normal Rake (γ_ne) & Cross-sectional Area of Uncut Chip (A_c). With our tool, you need to enter the respective value for Shear angle, Resultant Cutting Force, Mean Friction Angle on Tool Face, Working Normal Rake & Cross-sectional Area of Uncut Chip 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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