Shear Angle of Continuous Chip Formation Calculator

✖The Cutting Ratio is defined as the thickness of metal before cutting to the thickness of metal after cutting.ⓘ Cutting Ratio [r_c]			+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 angle is the inclination of the shear plane with the horizontal axis at machining point.ⓘ Shear Angle of Continuous Chip Formation [ϕ]

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Formula

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Shear Angle of Continuous Chip Formation

Formula

`"ϕ" = atan(("r"_{"c"}*cos("γ"_{"ne"}))/(1-("r"_{"c"}*sin("γ"_{"ne"}))))`

Example

`"11.40566°"=atan(("0.2"*cos("20°"))/(1-("0.2"*sin("20°"))))`

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Shear Angle of Continuous Chip Formation Solution

STEP 0: Pre-Calculation Summary

Formula Used

Shear angle = atan((Cutting Ratio*cos(Working Normal Rake))/(1-(Cutting Ratio*sin(Working Normal Rake))))
ϕ = atan((r_c*cos(γ_ne))/(1-(r_c*sin(γ_ne))))
This formula uses 4 Functions, 3 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)
cos - Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle., cos(Angle)
tan - The tangent of an angle is a trigonometric ratio of the length of the side opposite an angle to the length of the side adjacent to an angle in a right triangle., tan(Angle)
atan - Inverse tan is used to calculate the angle by applying the tangent ratio of the angle, which is the opposite side divided by the adjacent side of the right triangle., atan(Number)

Variables Used

Shear angle - (Measured in Radian) - Shear angle is the inclination of the shear plane with the horizontal axis at machining point.
Cutting Ratio - The Cutting Ratio is defined as the thickness of metal before cutting to the thickness of metal after cutting.
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

Cutting Ratio: 0.2 --> No Conversion Required
Working Normal Rake: 20 Degree --> 0.3490658503988 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

ϕ = atan((r_c*cos(γ_ne))/(1-(r_c*sin(γ_ne)))) --> atan((0.2*cos(0.3490658503988))/(1-(0.2*sin(0.3490658503988))))

Evaluating ... ...

ϕ = 0.199066376665285

STEP 3: Convert Result to Output's Unit

0.199066376665285 Radian -->11.4056632258845 Degree (Check conversion here)

FINAL ANSWER

11.4056632258845 ≈ 11.40566 Degree <-- Shear angle

(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 Angle of Continuous Chip Formation

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

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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 Angle of Continuous Chip Formation Formula

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

What is the Significance of Shear Angle?

The shear angle is of fundamental importance in chip formation. The smaller the shear angle the larger the strain, the machining forces, and the power requirements. There is nothing in the geometry of the tool that dictates what the shear angle should be.

How to Calculate Shear Angle of Continuous Chip Formation?

Shear Angle of Continuous Chip Formation calculator uses Shear angle = atan((Cutting Ratio*cos(Working Normal Rake))/(1-(Cutting Ratio*sin(Working Normal Rake)))) to calculate the Shear angle, The Shear Angle of Continuous Chip Formation is the angle between the horizontal plane and the shear plane. Shear angle is denoted by ϕ symbol.

How to calculate Shear Angle of Continuous Chip Formation using this online calculator? To use this online calculator for Shear Angle of Continuous Chip Formation, enter Cutting Ratio (r_c) & Working Normal Rake (γ_ne) and hit the calculate button. Here is how the Shear Angle of Continuous Chip Formation calculation can be explained with given input values -> 653.4964 = atan((0.2*cos(0.3490658503988))/(1-(0.2*sin(0.3490658503988)))).

FAQ

What is Shear Angle of Continuous Chip Formation?

The Shear Angle of Continuous Chip Formation is the angle between the horizontal plane and the shear plane and is represented as ϕ = atan((r_c*cos(γ_ne))/(1-(r_c*sin(γ_ne)))) or Shear angle = atan((Cutting Ratio*cos(Working Normal Rake))/(1-(Cutting Ratio*sin(Working Normal Rake)))). The Cutting Ratio is defined as the thickness of metal before cutting to the thickness of metal after cutting & 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 Angle of Continuous Chip Formation?

The Shear Angle of Continuous Chip Formation is the angle between the horizontal plane and the shear plane is calculated using Shear angle = atan((Cutting Ratio*cos(Working Normal Rake))/(1-(Cutting Ratio*sin(Working Normal Rake)))). To calculate Shear Angle of Continuous Chip Formation, you need Cutting Ratio (r_c) & Working Normal Rake (γ_ne). With our tool, you need to enter the respective value for Cutting Ratio & 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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