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

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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. Check FAQs

A s = \frac{t 1 \cdot w c}{\sin (ϕ)}

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

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

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

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

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

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

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

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

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

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

FIRST Step Consider the formula

A s = \frac{t 1 \cdot w c}{\sin (ϕ)}

Next Step Substitute values of Variables

∴

A s = \frac{6.94mm \cdot 9.6873mm}{\sin (5.257°)}

Next Step Convert Units

∴

A s = \frac{0.0069m \cdot 0.0097m}{\sin (0.0918rad)}

Next Step Prepare to Evaluate

∴

A s = \frac{0.0069 \cdot 0.0097}{\sin (0.0918)}

Next Step Evaluate

∴

A s = 0.000733763985511188m²

Next Step Convert to Output's Unit

∴

A s = 733.763985511188mm²

LAST Step Rounding Answer

∴

A s = 733.764mm²

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

Variables

Functions

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

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

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

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

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)

Other formulas in Geometry and Dimensions category

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

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

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

Area of shear plane for given shear angle, width of cut and uncut chip thickness evaluator uses Area of Shear Plane = (Uncut Chip Thickness in Machining*Cutting Width)/sin(Shearing Angle) to evaluate the Area of Shear Plane, The Area of shear plane for given shear angle, width of cut and uncut chip thickness formula is defined as the ratio of product of uncut chip thickness and width of cut to the shear angle. Area of Shear Plane is denoted by A_s symbol.

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

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

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

The formula of Area of shear plane for given shear angle, width of cut and uncut chip thickness is expressed as Area of Shear Plane = (Uncut Chip Thickness in Machining*Cutting Width)/sin(Shearing Angle). Here is an example- 7E+8 = (0.00694*0.0096873)/sin(0.0917519587773246).

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

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

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

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

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

Area of shear plane for given shear angle, width of cut and uncut chip thickness is usually measured using the Square Millimeter[mm²] for Area. Square Meter[mm²], Square Kilometer[mm²], Square Centimeter[mm²] are the few other units in which Area of shear plane for given shear angle, width of cut and uncut chip thickness can be measured.

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

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

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

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

Other formulas in Geometry and Dimensions category

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

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

Variable Name