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Shear Plane Angle Formula

GoShear Angle Formula

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Shear angle metal is the inclination of the shear plane with the horizontal axis at machining point. Check FAQs

ϕ = \arctan (\frac{r \cdot \cos (α)}{1 - r \cdot \sin (α)})

ϕ - Shear Angle Metal?r - Chip Ratio?α - Rake Angle?

Shear Plane Angle Example

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Here is how the Shear Plane Angle equation looks like with Values.

Here is how the Shear Plane Angle equation looks like with Units.

Here is how the Shear Plane Angle equation looks like.

22.8109 = \arctan (\frac{0.4 \cdot \cos (8.56)}{1 - 0.4 \cdot \sin (8.56)})

22.8109° = \arctan (\frac{0.4 \cdot \cos (8.56°)}{1 - 0.4 \cdot \sin (8.56°)})

22.8109 = \arctan (\frac{0.4 \cdot \cos (8.56)}{1 - 0.4 \cdot \sin (8.56)})

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Shear Plane Angle Solution

Follow our step by step solution on how to calculate Shear Plane Angle?

FIRST Step Consider the formula

ϕ = \arctan (\frac{r \cdot \cos (α)}{1 - r \cdot \sin (α)})

Next Step Substitute values of Variables

∴

ϕ = \arctan (\frac{0.4 \cdot \cos (8.56°)}{1 - 0.4 \cdot \sin (8.56°)})

Next Step Convert Units

∴

ϕ = \arctan (\frac{0.4 \cdot \cos (0.1494rad)}{1 - 0.4 \cdot \sin (0.1494rad)})

Next Step Prepare to Evaluate

∴

ϕ = \arctan (\frac{0.4 \cdot \cos (0.1494)}{1 - 0.4 \cdot \sin (0.1494)})

Next Step Evaluate

∴

ϕ = 0.398125174793451rad

Next Step Convert to Output's Unit

∴

ϕ = 22.8108922335772°

LAST Step Rounding Answer

∴

ϕ = 22.8109°

Shear Plane Angle Formula Elements

Variables

Functions

Shear Angle Metal

Shear angle metal 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 Metal

Chip Ratio

Chip Ratio is the thickness of metal before cutting to the thickness of metal after cutting.

Symbol: r

Measurement: NAUnit: Unitless

Note: Value should be less than 1.

Formulas to find Chip Ratio

Rake Angle

Rake Angle is the angle of orientation of tool’s rake surface from the reference plane and measured on machine longitudinal plane.

Symbol: α

Measurement: AngleUnit: °

Note: Value can be positive or negative.

Formulas to find Rake Angle

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)

ctan

Cotangent is a trigonometric function that is defined as the ratio of the adjacent side to the opposite side in a right triangle.

Syntax: ctan(Angle)

arctan

Inverse trigonometric functions are usually accompanied by the prefix - arc. Mathematically, we represent arctan or the inverse tangent function as tan-1 x or arctan(x).

Syntax: arctan(Number)

Other Formulas to find Shear Angle Metal

Go Shear Angle

ϕ = a \tan (w \cdot \frac{\cos (θ)}{1 - w \cdot \sin (θ)})

Other formulas in Metal Cutting category

Go Shear Force

F s = Fc \cdot \cos (θ) - P t \cdot \sin (θ)

Go Shear Strain

𝜂 = \tan (ϕ) + \cot (ϕ - α)

Go Shear Strain in Machining

γ = \tan (φ - α) + \cos (φ)

Go Shear Strain given Tangential Displacement and Original Length

𝜂 = \frac{t}{L 0}

How to Evaluate Shear Plane Angle?

Shear Plane Angle evaluator uses Shear Angle Metal = arctan((Chip Ratio*cos(Rake Angle))/(1-Chip Ratio*sin(Rake Angle))) to evaluate the Shear Angle Metal, The shear plane angle is the angle of inclination of the assumed shear plane from the cutting velocity vector, as measured on orthogonal plane. Shear Angle Metal is denoted by ϕ symbol.

How to evaluate Shear Plane Angle using this online evaluator? To use this online evaluator for Shear Plane Angle, enter Chip Ratio (r) & Rake Angle (α) and hit the calculate button.

FAQs on Shear Plane Angle

What is the formula to find Shear Plane Angle?

The formula of Shear Plane Angle is expressed as Shear Angle Metal = arctan((Chip Ratio*cos(Rake Angle))/(1-Chip Ratio*sin(Rake Angle))). Here is an example- 1306.968 = arctan((0.4*cos(0.149400183970687))/(1-0.4*sin(0.149400183970687))).

How to calculate Shear Plane Angle?

With Chip Ratio (r) & Rake Angle (α) we can find Shear Plane Angle using the formula - Shear Angle Metal = arctan((Chip Ratio*cos(Rake Angle))/(1-Chip Ratio*sin(Rake Angle))). This formula also uses Sine (sin)Cosine (cos)Tangent (tan)Cotangent (ctan), Inverse Tangent (arctan) function(s).

What are the other ways to Calculate Shear Angle Metal?

Here are the different ways to Calculate Shear Angle Metal-

Shear Angle Metal=atan(Width*cos(Theta)/(1-Width*sin(Theta)))

Can the Shear Plane Angle be negative?

No, the Shear Plane Angle, measured in Angle cannot be negative.

Which unit is used to measure Shear Plane Angle?

Shear Plane Angle is usually measured using the Degree[°] for Angle. Radian[°], Minute[°], Second[°] are the few other units in which Shear Plane Angle can be measured.

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