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

✖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.ⓘ Cutting Width [w_c]			+10% -10%
✖Shearing angle between is the inclination of the shear plane with the horizontal axis at machining point.ⓘ Shearing Angle [ϕ_.]			+10% -10%

✖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 for given shear angle, width of cut and uncut chip thickness [A_s]

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Formula

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

Formula

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

Example

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

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

STEP 0: Pre-Calculation Summary

Formula Used

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

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

STEP 1: Convert Input(s) to Base Unit

Uncut Chip Thickness in Machining: 6.94 Millimeter --> 0.00694 Meter (Check conversion here)
Cutting Width: 9.6873 Millimeter --> 0.0096873 Meter (Check conversion here)
Shearing Angle: 5.257 Degree --> 0.0917519587773246 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

A_s = (t₁*w_c)/sin(ϕ_.) --> (0.00694*0.0096873)/sin(0.0917519587773246)

Evaluating ... ...

A_s = 0.000733763985511188

STEP 3: Convert Result to Output's Unit

0.000733763985511188 Square Meter -->733.763985511188 Square Millimeter (Check conversion here)

FINAL ANSWER

733.763985511188 ≈ 733.764 Square Millimeter <-- Area of Shear Plane

(Calculation completed in 00.004 seconds)

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Home » Engineering » Production Engineering » Metal Cutting » Merchant Force Circle » Geometry and Dimensions » Area of shear plane for given shear angle, width of cut and uncut chip thickness

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Created by Sanjay Krishna

Amrita School of Engineering (ASE), Vallikavu

Sanjay Krishna has created this Calculator and 300+ more calculators!

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)

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

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

Calculating the area of shear

the area of a plane or other surface along which rocks are ruptured by compressive stress, This area is used to study how much width of cut or uncut chip thickness should be there so as to reduce the shearing of plane

How to Calculate 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 calculator uses Area of Shear Plane = (Uncut Chip Thickness in Machining*Cutting Width)/sin(Shearing Angle) to calculate 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 calculate Area of shear plane for given shear angle, width of cut and uncut chip thickness using this online calculator? To use this online calculator 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. Here is how the Area of shear plane for given shear angle, width of cut and uncut chip thickness calculation can be explained with given input values -> 7E+8 = (0.00694*0.0096873)/sin(0.0917519587773246).

FAQ

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

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

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

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

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