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

✖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.ⓘ Area of Shear Plane [A_s]			+10% -10%
✖Shearing angle between is the inclination of the shear plane with the horizontal axis at machining point.ⓘ Shearing Angle [ϕ_.]			+10% -10%
✖Uncut chip thickness in machining can be referred as the thickness of the undeformed chip.ⓘ Uncut Chip Thickness in Machining [t₁]			+10% -10%

✖Cutting Width can be defined as the width the tool cuts into the workpiece.ⓘ Width of cut for given shear angle, uncut chip thickness and area of shear plane [w_c]

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Formula

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

Formula

`"w"_{"c"} = ("A"_{"s"}*sin("ϕ"_{"."}))/"t"_{"1"}`

Example

`"9.6873mm"=("733.764mm²"*sin("5.257°"))/"6.94mm"`

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

STEP 0: Pre-Calculation Summary

Formula Used

Cutting Width = (Area of Shear Plane*sin(Shearing Angle))/Uncut Chip Thickness in Machining
w_c = (A_s*sin(ϕ_.))/t₁
This formula uses 1 Functions, 4 Variables

Functions Used

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., sin(Angle)

Variables Used

Cutting Width - (Measured in Meter) - Cutting Width can be defined as the width the tool cuts into the workpiece.
Area of Shear Plane - (Measured in Square Meter) - 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.
Shearing Angle - (Measured in Radian) - Shearing angle between is the inclination of the shear plane with the horizontal axis at machining point.
Uncut Chip Thickness in Machining - (Measured in Meter) - Uncut chip thickness in machining can be referred as the thickness of the undeformed chip.

STEP 1: Convert Input(s) to Base Unit

Area of Shear Plane: 733.764 Square Millimeter --> 0.000733764 Square Meter (Check conversion here)
Shearing Angle: 5.257 Degree --> 0.0917519587773246 Radian (Check conversion here)
Uncut Chip Thickness in Machining: 6.94 Millimeter --> 0.00694 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

w_c = (A_s*sin(ϕ_.))/t₁ --> (0.000733764*sin(0.0917519587773246))/0.00694

Evaluating ... ...

w_c = 0.00968730019128422

STEP 3: Convert Result to Output's Unit

0.00968730019128422 Meter -->9.68730019128422 Millimeter (Check conversion here)

FINAL ANSWER

9.68730019128422 ≈ 9.6873 Millimeter <-- Cutting Width

(Calculation completed in 00.004 seconds)

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Created by Vinay Mishra

Indian Institute for Aeronautical Engineering and Information Technology (IIAEIT), Pune

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Verified by Rushi Shah

K J Somaiya College of Engineering (K J Somaiya), Mumbai

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< 8 Geometry and Dimensions Calculators

Uncut chip thickness given cutting force, shear stress, cut, friction, normal rake and shear angles

Go Uncut Chip Thickness in Machining = Cutting Force in Metal Cutting*(cos(Shearing Angle+Cutting Friction Angle-Rake Angle of Cutting Tool))/(Cutting Width*Average Shear Stress Produced on Shear Plane*cos(Cutting Friction Angle-Rake Angle of Cutting Tool))

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

Go 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))

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

Go Area of Shear Plane = (Uncut Chip Thickness in Machining*Cutting Width)/sin(Shearing Angle)

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

Go Uncut Chip Thickness in Machining = (Area of Shear Plane*sin(Shearing Angle))/Cutting Width

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

Go Cutting Width = (Area of Shear Plane*sin(Shearing Angle))/Uncut Chip Thickness in Machining

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

Go Shearing Angle = asin(Cutting Width*Uncut Chip Thickness in Machining/Area of Shear Plane)

Side cutting edge angle for given width of cut

Go Side Cutting Edge Angle for Metal Cutting = acos(Depth of Cut Provided by Tool/Cutting Width)

Width of cut for given side cutting edge angle

Go Cutting Width = Depth of Cut Provided by Tool/cos(Side Cutting Edge Angle for Metal Cutting)

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

Cutting Width = (Area of Shear Plane*sin(Shearing Angle))/Uncut Chip Thickness in Machining
w_c = (A_s*sin(ϕ_.))/t₁

What is the metal cutting?

Metal cutting is the process of removing unwanted material in the form of chips, from a block of metal, using the cutting tool.

How to Calculate 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 calculator uses Cutting Width = (Area of Shear Plane*sin(Shearing Angle))/Uncut Chip Thickness in Machining to calculate 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 calculate Width of cut for given shear angle, uncut chip thickness and area of shear plane using this online calculator? To use this online calculator 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. Here is how the Width of cut for given shear angle, uncut chip thickness and area of shear plane calculation can be explained with given input values -> 9687.3 = (0.000733764*sin(0.0917519587773246))/0.00694.

FAQ

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

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 and is represented as w_c = (A_s*sin(ϕ_.))/t₁ or Cutting Width = (Area of Shear Plane*sin(Shearing Angle))/Uncut Chip Thickness in Machining. 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, Shearing angle between is the inclination of the shear plane with the horizontal axis at machining point & Uncut chip thickness in machining can be referred as the thickness of the undeformed chip.

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

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 is calculated using Cutting Width = (Area of Shear Plane*sin(Shearing Angle))/Uncut Chip Thickness in Machining. To calculate Width of cut for given shear angle, uncut chip thickness and area of shear plane, you need Area of Shear Plane (A_s), Shearing Angle (ϕ_.) & Uncut Chip Thickness in Machining (t₁). With our tool, you need to enter the respective value for Area of Shear Plane, Shearing Angle & Uncut Chip Thickness in Machining and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Cutting Width?

In this formula, Cutting Width uses Area of Shear Plane, Shearing Angle & Uncut Chip Thickness in Machining. We can use 2 other way(s) to calculate the same, which is/are as follows -

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))

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