Cutting Ratio for given Shear Angle of Continuous chip Calculator

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

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Formula

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Cutting Ratio for given Shear Angle of Continuous chip

Formula

`"r"_{"c"} = tan("ϕ")/(cos("γ"_{"ne"})+(tan("ϕ")*sin("γ"_{"ne"})))`

Example

`"0.200006"=tan("11.406°")/(cos("20°")+(tan("11.406°")*sin("20°")))`

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Cutting Ratio for given Shear Angle of Continuous chip Solution

STEP 0: Pre-Calculation Summary

Formula Used

Cutting Ratio = tan(Shear angle)/(cos(Working Normal Rake)+(tan(Shear angle)*sin(Working Normal Rake)))
r_c = tan(ϕ)/(cos(γ_ne)+(tan(ϕ)*sin(γ_ne)))
This formula uses 3 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)

Variables Used

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

Shear angle: 11.406 Degree --> 0.199072254482436 Radian (Check conversion here)
Working Normal Rake: 20 Degree --> 0.3490658503988 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

r_c = tan(ϕ)/(cos(γ_ne)+(tan(ϕ)*sin(γ_ne))) --> tan(0.199072254482436)/(cos(0.3490658503988)+(tan(0.199072254482436)*sin(0.3490658503988)))

Evaluating ... ...

r_c = 0.200005649498844

STEP 3: Convert Result to Output's Unit

0.200005649498844 --> No Conversion Required

FINAL ANSWER

0.200005649498844 ≈ 0.200006 <-- Cutting Ratio

(Calculation completed in 00.006 seconds)

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Created by Parul Keshav

National Institute of Technology (NIT), Srinagar

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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

Cutting Ratio for given Shear Angle of Continuous chip Formula

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

What is Uncut Chip Thickness?

Uncut chip thickness is comparable to cutting edge radius in micromachining. If the uncut chip thickness is less than a critical value, there will be no chip formation. This critical value is termed as minimum uncut chip thickness.

How to Calculate Cutting Ratio for given Shear Angle of Continuous chip?

Cutting Ratio for given Shear Angle of Continuous chip calculator uses Cutting Ratio = tan(Shear angle)/(cos(Working Normal Rake)+(tan(Shear angle)*sin(Working Normal Rake))) to calculate the Cutting Ratio, The Cutting Ratio for given Shear Angle of Continuous chip is defined as the thickness of metal before cutting to the thickness of metal after cutting. Cutting Ratio is denoted by r_c symbol.

How to calculate Cutting Ratio for given Shear Angle of Continuous chip using this online calculator? To use this online calculator for Cutting Ratio for given Shear Angle of Continuous chip, enter Shear angle (ϕ) & Working Normal Rake (γ_ne) and hit the calculate button. Here is how the Cutting Ratio for given Shear Angle of Continuous chip calculation can be explained with given input values -> 0.200006 = tan(0.199072254482436)/(cos(0.3490658503988)+(tan(0.199072254482436)*sin(0.3490658503988))).

FAQ

What is Cutting Ratio for given Shear Angle of Continuous chip?

The Cutting Ratio for given Shear Angle of Continuous chip is defined as the thickness of metal before cutting to the thickness of metal after cutting and is represented as r_c = tan(ϕ)/(cos(γ_ne)+(tan(ϕ)*sin(γ_ne))) or Cutting Ratio = tan(Shear angle)/(cos(Working Normal Rake)+(tan(Shear angle)*sin(Working Normal Rake))). Shear angle is the inclination of the shear plane with the horizontal axis at machining point & 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 Cutting Ratio for given Shear Angle of Continuous chip?

The Cutting Ratio for given Shear Angle of Continuous chip is defined as the thickness of metal before cutting to the thickness of metal after cutting is calculated using Cutting Ratio = tan(Shear angle)/(cos(Working Normal Rake)+(tan(Shear angle)*sin(Working Normal Rake))). To calculate Cutting Ratio for given Shear Angle of Continuous chip, you need Shear angle (ϕ) & Working Normal Rake (γ_ne). With our tool, you need to enter the respective value for Shear angle & 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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