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

GoWidth of cut for given side cutting edge angle Formula

GoWidth of cut given cutting force, shear stress, uncut chip, friction, normal rake and shear angles Formula

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

w c = \frac{A s \cdot \sin (ϕ)}{t 1}

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

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

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

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

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

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

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

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

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

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

FIRST Step Consider the formula

w c = \frac{A s \cdot \sin (ϕ)}{t 1}

Next Step Substitute values of Variables

∴

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

Next Step Convert Units

∴

w c = \frac{0.0007m² \cdot \sin (0.0918rad)}{0.0069m}

Next Step Prepare to Evaluate

∴

w c = \frac{0.0007 \cdot \sin (0.0918)}{0.0069}

Next Step Evaluate

∴

w c = 0.00968730019128422m

Next Step Convert to Output's Unit

∴

w c = 9.68730019128422mm

LAST Step Rounding Answer

∴

w c = 9.6873mm

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

Variables

Functions

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

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

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

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

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 to find Cutting Width

Go Width of cut for given side cutting edge angle

w c = \frac{d cut}{\cos (ψ)}

Go Width of cut given cutting force, shear stress, uncut chip, friction, normal rake and shear angles

w c = F cut \cdot \frac{\cos (ϕ + β - α)}{τ shear \cdot t 1 \cdot \cos (β - α)}

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 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 Side cutting edge angle for given width of cut

ψ = a \cos (\frac{d cut}{w c})

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

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

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

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

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

The formula of Width of cut for given shear angle, uncut chip thickness and area of shear plane is expressed as Cutting Width = (Area of Shear Plane*sin(Shearing Angle))/Uncut Chip Thickness in Machining. Here is an example- 9687.3 = (0.000733764*sin(0.0917519587773246))/0.00694.

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

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

What are the other ways to Calculate Cutting Width?

Here are the different ways to Calculate Cutting Width-

Cutting Width=Depth of Cut Provided by Tool/cos(Side Cutting Edge Angle for Metal Cutting)
Cutting Width=Cutting Force in Metal Cutting*(cos(Shearing Angle+Cutting Friction Angle-Rake Angle of Cutting Tool))/(Average Shear Stress Produced on Shear Plane*Uncut Chip Thickness in Machining*cos(Cutting Friction Angle-Rake Angle of Cutting Tool))

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

Yes, the Width of cut for given shear angle, uncut chip thickness and area of shear plane, measured in Length can be negative.

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

Width of cut for given shear angle, uncut chip thickness and area of shear plane is usually measured using the Millimeter[mm] for Length. Meter[mm], Kilometer[mm], Decimeter[mm] are the few other units in which Width of cut for given shear angle, uncut chip thickness and area of shear plane can be measured.

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

​GoWidth of cut for given side cutting edge angle Formula

​GoWidth of cut given cutting force, shear stress, uncut chip, friction, normal rake and shear angles Formula

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

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

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

Other Formulas to find Cutting Width

Other formulas in Geometry and Dimensions category

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

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

Variable Name

GoWidth of cut for given side cutting edge angle Formula

GoWidth of cut given cutting force, shear stress, uncut chip, friction, normal rake and shear angles Formula