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Shear Angle Formula

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

ϕ - Shear Angle Metal?w - Width?θ - Theta?

Shear Angle Example

With values

With units

Only example

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

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

Here is how the Shear Angle equation looks like.

14.2037 = a \tan (255 \cdot \frac{\cos (30)}{1 - 255 \cdot \sin (30)})

14.2037° = a \tan (255mm \cdot \frac{\cos (30°)}{1 - 255mm \cdot \sin (30°)})

14.2037 = a \tan (255 \cdot \frac{\cos (30)}{1 - 255 \cdot \sin (30)})

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Shear Angle Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

ϕ = a \tan (255mm \cdot \frac{\cos (30°)}{1 - 255mm \cdot \sin (30°)})

Next Step Convert Units

∴

ϕ = a \tan (0.255m \cdot \frac{\cos (0.5236rad)}{1 - 0.255m \cdot \sin (0.5236rad)})

Next Step Prepare to Evaluate

∴

ϕ = a \tan (0.255 \cdot \frac{\cos (0.5236)}{1 - 0.255 \cdot \sin (0.5236)})

Next Step Evaluate

∴

ϕ = 0.247901422197684rad

Next Step Convert to Output's Unit

∴

ϕ = 14.2037052272207°

LAST Step Rounding Answer

∴

ϕ = 14.2037°

Shear 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

Width

Width is the measurement or extent of something from side to side.

Symbol: w

Measurement: LengthUnit: mm

Note: Value can be positive or negative.

Formulas to find Width

Theta

Theta is an angle that can be defined as the figure formed by two rays meeting at a common endpoint.

Symbol: θ

Measurement: AngleUnit: °

Note: Value can be positive or negative.

Formulas to find Theta

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)

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.

Syntax: atan(Number)

Other Formulas to find Shear Angle Metal

Go Shear Plane Angle

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

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 Angle?

Shear Angle evaluator uses Shear Angle Metal = atan(Width*cos(Theta)/(1-Width*sin(Theta))) to evaluate the Shear Angle Metal, Shear Angle is the angle between shear plane and the cutting velocity. Shear Angle Metal is denoted by ϕ symbol.

How to evaluate Shear Angle using this online evaluator? To use this online evaluator for Shear Angle, enter Width (w) & Theta (θ) and hit the calculate button.

FAQs on Shear Angle

What is the formula to find Shear Angle?

The formula of Shear Angle is expressed as Shear Angle Metal = atan(Width*cos(Theta)/(1-Width*sin(Theta))). Here is an example- -3856.335845 = atan(0.255*cos(0.5235987755982)/(1-0.255*sin(0.5235987755982))).

How to calculate Shear Angle?

With Width (w) & Theta (θ) we can find Shear Angle using the formula - Shear Angle Metal = atan(Width*cos(Theta)/(1-Width*sin(Theta))). This formula also uses Sine (sin)Cosine (cos)Tangent (tan), Inverse Tan (atan) 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=arctan((Chip Ratio*cos(Rake Angle))/(1-Chip Ratio*sin(Rake Angle)))

Can the Shear Angle be negative?

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

Which unit is used to measure Shear Angle?

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

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