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Shear angle for given area of shear plane, width of cut and uncut chip thickness Formula

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

ϕ = a \sin (w c \cdot \frac{t 1}{A s})

ϕ - Shearing Angle?w_c - Cutting Width?t₁ - Uncut Chip Thickness in Machining?A_s - Area of Shear Plane?

Shear angle for given area of shear plane, width of cut and uncut chip thickness Example

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Here is how the Shear angle for given area of shear plane, width of cut and uncut chip thickness equation looks like with Values.

Here is how the Shear angle for given area of shear plane, width of cut and uncut chip thickness equation looks like with Units.

Here is how the Shear angle for given area of shear plane, width of cut and uncut chip thickness equation looks like.

5.257 = a \sin (9.6873 \cdot \frac{6.94}{733.764})

5.257° = a \sin (9.6873mm \cdot \frac{6.94mm}{733.764mm²})

5.257 = a \sin (9.6873 \cdot \frac{6.94}{733.764})

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Shear angle for given area of shear plane, width of cut and uncut chip thickness Solution

Follow our step by step solution on how to calculate Shear angle for given area of shear plane, width of cut and uncut chip thickness?

FIRST Step Consider the formula

ϕ = a \sin (w c \cdot \frac{t 1}{A s})

Next Step Substitute values of Variables

∴

ϕ = a \sin (9.6873mm \cdot \frac{6.94mm}{733.764mm²})

Next Step Convert Units

∴

ϕ = a \sin (0.0097m \cdot \frac{0.0069m}{0.0007m²})

Next Step Prepare to Evaluate

∴

ϕ = a \sin (0.0097 \cdot \frac{0.0069}{0.0007})

Next Step Evaluate

∴

ϕ = 0.0917519569605008rad

Next Step Convert to Output's Unit

∴

ϕ = 5.25699989590366°

LAST Step Rounding Answer

∴

ϕ = 5.257°

Shear angle for given area of shear plane, width of cut and uncut chip thickness Formula Elements

Variables

Functions

Shearing Angle

Shearing angle between 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 Shearing Angle

Cutting Width

Cutting Width can be defined as the width the tool cuts into the workpiece.

Symbol: w_c

Measurement: LengthUnit: mm

Note: Value can be positive or negative.

Formulas to find Cutting Width

Uncut Chip Thickness in Machining

Uncut chip thickness in machining can be referred as the thickness of the undeformed chip.

Symbol: t₁

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Uncut Chip Thickness in Machining

Area of Shear Plane

Area of shear plane is defined as the area of that plane along which the chip is formed by shear deformation as the tool is forced into the material.

Symbol: A_s

Measurement: AreaUnit: mm²

Note: Value should be greater than 0.

Formulas to find Area of Shear Plane

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)

asin

The inverse sine function, is a trigonometric function that takes a ratio of two sides of a right triangle and outputs the angle opposite the side with the given ratio.

Syntax: asin(Number)

Other formulas in Geometry and Dimensions category

Go Area of shear plane for given shear angle, width of cut and uncut chip thickness

A s = \frac{t 1 \cdot w c}{\sin (ϕ)}

Go Uncut chip thickness for given width of cut, shear angle and area of shear plane

t 1 = \frac{A s \cdot \sin (ϕ)}{w c}

Go Width of cut for given shear angle, uncut chip thickness and area of shear plane

w c = \frac{A s \cdot \sin (ϕ)}{t 1}

Go Side cutting edge angle for given width of cut

ψ = a \cos (\frac{d cut}{w c})

How to Evaluate Shear angle for given area of shear plane, width of cut and uncut chip thickness?

Shear angle for given area of shear plane, width of cut and uncut chip thickness evaluator uses Shearing Angle = asin(Cutting Width*Uncut Chip Thickness in Machining/Area of Shear Plane) to evaluate the Shearing Angle, Shear angle for given area of shear plane, width of cut and uncut chip thickness is defined as an angle between the shear plane and the horizontal plane. Shearing Angle is denoted by ϕ symbol.

How to evaluate Shear angle for given area of shear plane, width of cut and uncut chip thickness using this online evaluator? To use this online evaluator for Shear angle for given area of shear plane, width of cut and uncut chip thickness, enter Cutting Width (w_c), Uncut Chip Thickness in Machining (t₁) & Area of Shear Plane (A_s) and hit the calculate button.

FAQs on Shear angle for given area of shear plane, width of cut and uncut chip thickness

What is the formula to find Shear angle for given area of shear plane, width of cut and uncut chip thickness?

The formula of Shear angle for given area of shear plane, width of cut and uncut chip thickness is expressed as Shearing Angle = asin(Cutting Width*Uncut Chip Thickness in Machining/Area of Shear Plane). Here is an example- 288.3506 = asin(0.0096873*0.00694/0.000733764).

How to calculate Shear angle for given area of shear plane, width of cut and uncut chip thickness?

With Cutting Width (w_c), Uncut Chip Thickness in Machining (t₁) & Area of Shear Plane (A_s) we can find Shear angle for given area of shear plane, width of cut and uncut chip thickness using the formula - Shearing Angle = asin(Cutting Width*Uncut Chip Thickness in Machining/Area of Shear Plane). This formula also uses Sine (sin), Inverse Sine (asin) function(s).

Can the Shear angle for given area of shear plane, width of cut and uncut chip thickness be negative?

No, the Shear angle for given area of shear plane, width of cut and uncut chip thickness, measured in Angle cannot be negative.

Which unit is used to measure Shear angle for given area of shear plane, width of cut and uncut chip thickness?

Shear angle for given area of shear plane, width of cut and uncut chip thickness is usually measured using the Degree[°] for Angle. Radian[°], Minute[°], Second[°] are the few other units in which Shear angle for given area of shear plane, width of cut and uncut chip thickness can be measured.

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Shear angle for given area of shear plane, width of cut and uncut chip thickness Formula

Shear angle for given area of shear plane, width of cut and uncut chip thickness Example

Shear angle for given area of shear plane, width of cut and uncut chip thickness Solution

Shear angle for given area of shear plane, width of cut and uncut chip thickness Formula Elements

Other formulas in Geometry and Dimensions category

How to Evaluate Shear angle for given area of shear plane, width of cut and uncut chip thickness?

FAQs on Shear angle for given area of shear plane, width of cut and uncut chip thickness

Variable Name