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*Width of cut)/sin(Shear angle)
AS = (t1*w)/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 - (Measured in Meter) - Uncut Chip Thickness is the thickness of the undeformed chip.
Width of cut - (Measured in Meter) - The width of cut is defined as the width the tool cuts into the workpiece.
Shear angle - (Measured in Radian) - Shear angle 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: 1.2 Millimeter --> 0.0012 Meter (Check conversion here)
Width of cut: 4 Millimeter --> 0.004 Meter (Check conversion here)
Shear angle: 45 Degree --> 0.785398163397301 Radian (Check conversion here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
AS = (t1*w)/sin(ϕ) --> (0.0012*0.004)/sin(0.785398163397301)
Evaluating ... ...
AS = 6.78822509939186E-06
STEP 3: Convert Result to Output's Unit
6.78822509939186E-06 Square Meter --> No Conversion Required
FINAL ANSWER
6.78822509939186E-06 6.8E-6 Square Meter <-- Area of Shear Plane
(Calculation completed in 00.004 seconds)

Credits

Created by Sanjay Krishna
Amrita School of Engineering (ASE), Vallikavu
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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 = Cutting Force*(cos(Shear angle+Friction Angle-Rake Angle))/(Width of cut*Average Shear Stress on Shear Plane*cos(Friction Angle-Rake Angle))
Width of cut given cutting force, shear stress, uncut chip, friction, normal rake and shear angles
Go Width of cut = Cutting Force*(cos(Shear angle+Friction Angle-Rake Angle))/(Average Shear Stress on Shear Plane*Uncut Chip Thickness*cos(Friction Angle-Rake Angle))
Area of shear plane for given shear angle, width of cut and uncut chip thickness
Go Area of Shear Plane = (Uncut Chip Thickness*Width of cut)/sin(Shear angle)
Uncut chip thickness for given width of cut, shear angle and area of shear plane
Go Uncut Chip Thickness = (Area of Shear Plane*sin(Shear angle))/Width of cut
Width of cut for given shear angle, uncut chip thickness and area of shear plane
Go Width of cut = (Area of Shear Plane*sin(Shear angle))/Uncut Chip Thickness
Shear angle for given area of shear plane, width of cut and uncut chip thickness
Go Shear angle = asin(Width of cut*Uncut Chip Thickness/Area of Shear Plane)
Side cutting edge angle for given width of cut
Go Side Cutting Edge Angle = acos(Width of cut/Depth of Cut)
Width of cut for given side cutting edge angle
Go Width of cut = Depth of Cut/cos(Side Cutting Edge Angle)

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

Area of Shear Plane = (Uncut Chip Thickness*Width of cut)/sin(Shear angle)
AS = (t1*w)/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*Width of cut)/sin(Shear 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 AS 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 (t1), Width of cut (w) & Shear 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 -> 6.8E-6 = (0.0012*0.004)/sin(0.785398163397301).

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 AS = (t1*w)/sin(ϕ) or Area of Shear Plane = (Uncut Chip Thickness*Width of cut)/sin(Shear angle). Uncut Chip Thickness is the thickness of the undeformed chip, The width of cut is defined as the width the tool cuts into the workpiece & Shear angle 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*Width of cut)/sin(Shear angle). To calculate Area of shear plane for given shear angle, width of cut and uncut chip thickness, you need Uncut Chip Thickness (t1), Width of cut (w) & Shear angle (ϕ). With our tool, you need to enter the respective value for Uncut Chip Thickness, Width of cut & Shear 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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