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Cutting Ratio for given Shear Angle of Continuous chip Formula

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The Cutting Ratio is defined as the thickness of metal before cutting to the thickness of metal after cutting. Check FAQs

r c = \frac{\tan (ϕ)}{\cos (γ ne) + (\tan (ϕ) \cdot \sin (γ ne))}

r_c - Cutting Ratio?ϕ - Shear Angle?γ_ne - Working Normal Rake?

Cutting Ratio for given Shear Angle of Continuous chip Example

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Here is how the Cutting Ratio for given Shear Angle of Continuous chip equation looks like with Values.

Here is how the Cutting Ratio for given Shear Angle of Continuous chip equation looks like with Units.

Here is how the Cutting Ratio for given Shear Angle of Continuous chip equation looks like.

0.2 = \frac{\tan (11.406)}{\cos (20) + (\tan (11.406) \cdot \sin (20))}

0.2 = \frac{\tan (11.406°)}{\cos (20°) + (\tan (11.406°) \cdot \sin (20°))}

0.2 = \frac{\tan (11.406)}{\cos (20) + (\tan (11.406) \cdot \sin (20))}

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Cutting Ratio for given Shear Angle of Continuous chip Solution

Follow our step by step solution on how to calculate Cutting Ratio for given Shear Angle of Continuous chip?

FIRST Step Consider the formula

r c = \frac{\tan (ϕ)}{\cos (γ ne) + (\tan (ϕ) \cdot \sin (γ ne))}

Next Step Substitute values of Variables

∴

r c = \frac{\tan (11.406°)}{\cos (20°) + (\tan (11.406°) \cdot \sin (20°))}

Next Step Convert Units

∴

r c = \frac{\tan (0.1991rad)}{\cos (0.3491rad) + (\tan (0.1991rad) \cdot \sin (0.3491rad))}

Next Step Prepare to Evaluate

∴

r c = \frac{\tan (0.1991)}{\cos (0.3491) + (\tan (0.1991) \cdot \sin (0.3491))}

Next Step Evaluate

∴

r c = 0.200005649498844

LAST Step Rounding Answer

∴

r c = 0.2

Cutting Ratio for given Shear Angle of Continuous chip Formula Elements

Variables

Functions

Cutting Ratio

The Cutting Ratio is defined as the thickness of metal before cutting to the thickness of metal after cutting.

Symbol: r_c

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Cutting Ratio

Shear Angle

Shear Angle is the inclination of the shear plane with the horizontal axis at machining point.

Symbol: ϕ

Measurement: AngleUnit: °

Note: Value should be greater than 0.

Formulas to find Shear Angle

Working Normal Rake

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.

Symbol: γ_ne

Measurement: AngleUnit: °

Note: Value can be positive or negative.

Formulas to find Working Normal Rake

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.

Syntax: sin(Angle)

cos

Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle.

Syntax: 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.

Syntax: tan(Angle)

Other formulas in Shear category

Go Area of Shear

A s = \frac{A c}{\sin (ϕ)}

Go Shear Force on Shear Plane

F shear = F r \cdot \cos ((ϕ + β - γ ne))

Go Shear Force on Shear Plane using Shear Strength

F s = τ \cdot \frac{A c}{\sin (ϕ)}

Go Shear Strength given Coefficient of Friction in Metal Cutting

τ = μ \cdot σ y

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

Cutting Ratio for given Shear Angle of Continuous chip evaluator uses Cutting Ratio = tan(Shear Angle)/(cos(Working Normal Rake)+(tan(Shear Angle)*sin(Working Normal Rake))) to evaluate 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 evaluate Cutting Ratio for given Shear Angle of Continuous chip using this online evaluator? To use this online evaluator for Cutting Ratio for given Shear Angle of Continuous chip, enter Shear Angle (ϕ) & Working Normal Rake (γ_ne) and hit the calculate button.

FAQs on Cutting Ratio for given Shear Angle of Continuous chip

What is the formula to find Cutting Ratio for given Shear Angle of Continuous chip?

The formula of Cutting Ratio for given Shear Angle of Continuous chip is expressed as Cutting Ratio = tan(Shear Angle)/(cos(Working Normal Rake)+(tan(Shear Angle)*sin(Working Normal Rake))). Here is an example- 0.200006 = tan(0.199072254482436)/(cos(0.3490658503988)+(tan(0.199072254482436)*sin(0.3490658503988))).

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

With Shear Angle (ϕ) & Working Normal Rake (γ_ne) we can find Cutting Ratio for given Shear Angle of Continuous chip using the formula - Cutting Ratio = tan(Shear Angle)/(cos(Working Normal Rake)+(tan(Shear Angle)*sin(Working Normal Rake))). This formula also uses Sine (sin)Cosine (cos), Tangent (tan) function(s).

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