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

STEP 0: Pre-Calculation Summary
Formula Used
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))
w = Fc*(cos(ϕ+β-α))/(τ s*t1*cos(β-α))
This formula uses 1 Functions, 7 Variables
Functions Used
cos - Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle., cos(Angle)
Variables Used
Width of cut - (Measured in Meter) - The width of cut is defined as the width the tool cuts into the workpiece.
Cutting Force - (Measured in Newton) - Cutting Force is the force in the direction of cutting, the same direction as the cutting speed.
Shear angle - (Measured in Radian) - Shear angle is the inclination of the shear plane with the horizontal axis at machining point.
Friction Angle - (Measured in Radian) - The Friction angle is termed as the force between the tool and chip, which resists the flow of the chip along the rake face of the tool is friction force and having a friction angle β.
Rake Angle - (Measured in Radian) - Rake Angle is the angle of orientation of tool’s rake surface from the reference plane and measured on machine longitudinal plane.
Average Shear Stress on Shear Plane - (Measured in Pascal) - Average Shear Stress on Shear Plane is the ratio of shear force on the shear plane to the area of shear plane.
Uncut Chip Thickness - (Measured in Meter) - Uncut Chip Thickness is the thickness of the undeformed chip.
STEP 1: Convert Input(s) to Base Unit
Cutting Force: 647.55 Newton --> 647.55 Newton No Conversion Required
Shear angle: 45 Degree --> 0.785398163397301 Radian (Check conversion here)
Friction Angle: 15 Degree --> 0.2617993877991 Radian (Check conversion here)
Rake Angle: 8.56 Degree --> 0.149400183970687 Radian (Check conversion here)
Average Shear Stress on Shear Plane: 2 Newton per Square Meter --> 2 Pascal (Check conversion here)
Uncut Chip Thickness: 1.2 Millimeter --> 0.0012 Meter (Check conversion here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
w = Fc*(cos(ϕ+β-α))/(τ s*t1*cos(β-α)) --> 647.55*(cos(0.785398163397301+0.2617993877991-0.149400183970687))/(2*0.0012*cos(0.2617993877991-0.149400183970687))
Evaluating ... ...
w = 169251.26150394
STEP 3: Convert Result to Output's Unit
169251.26150394 Meter -->169251261.50394 Millimeter (Check conversion here)
FINAL ANSWER
169251261.50394 1.7E+8 Millimeter <-- Width of cut
(Calculation completed in 00.020 seconds)

Credits

Created by Shikha Maurya
Indian Institute of Technology (IIT), Bombay
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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)

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

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))
w = Fc*(cos(ϕ+β-α))/(τ s*t1*cos(β-α))

Significance of width of cut

Width of cut is required to calculate the depth of cut and this width is provided for the safety and tolerance, so as the object have required strength and ductility

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

Width of cut given cutting force, shear stress, uncut chip, friction, normal rake and shear angles calculator uses 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)) to calculate the Width of cut, The Width of cut given cutting force, shear stress, uncut chip, friction, normal rake and shear angles formula is defined as cutting force multiplied by the cosine of summation of shear angle to the difference of friction and rake angles divided by the product of the uncut chip thickness, shear stress and cosine of difference of friction and rake angles. Width of cut is denoted by w symbol.

How to calculate Width of cut given cutting force, shear stress, uncut chip, friction, normal rake and shear angles using this online calculator? To use this online calculator for Width of cut given cutting force, shear stress, uncut chip, friction, normal rake and shear angles, enter Cutting Force (Fc), Shear angle (ϕ), Friction Angle (β), Rake Angle (α), Average Shear Stress on Shear Plane s) & Uncut Chip Thickness (t1) and hit the calculate button. Here is how the Width of cut given cutting force, shear stress, uncut chip, friction, normal rake and shear angles calculation can be explained with given input values -> 1.7E+11 = 647.55*(cos(0.785398163397301+0.2617993877991-0.149400183970687))/(2*0.0012*cos(0.2617993877991-0.149400183970687)).

FAQ

What is Width of cut given cutting force, shear stress, uncut chip, friction, normal rake and shear angles?
The Width of cut given cutting force, shear stress, uncut chip, friction, normal rake and shear angles formula is defined as cutting force multiplied by the cosine of summation of shear angle to the difference of friction and rake angles divided by the product of the uncut chip thickness, shear stress and cosine of difference of friction and rake angles and is represented as w = Fc*(cos(ϕ+β-α))/(τ s*t1*cos(β-α)) or 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)). Cutting Force is the force in the direction of cutting, the same direction as the cutting speed, Shear angle is the inclination of the shear plane with the horizontal axis at machining point, The Friction angle is termed as the force between the tool and chip, which resists the flow of the chip along the rake face of the tool is friction force and having a friction angle β, Rake Angle is the angle of orientation of tool’s rake surface from the reference plane and measured on machine longitudinal plane, Average Shear Stress on Shear Plane is the ratio of shear force on the shear plane to the area of shear plane & Uncut Chip Thickness is the thickness of the undeformed chip.
How to calculate Width of cut given cutting force, shear stress, uncut chip, friction, normal rake and shear angles?
The Width of cut given cutting force, shear stress, uncut chip, friction, normal rake and shear angles formula is defined as cutting force multiplied by the cosine of summation of shear angle to the difference of friction and rake angles divided by the product of the uncut chip thickness, shear stress and cosine of difference of friction and rake angles is calculated using 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)). To calculate Width of cut given cutting force, shear stress, uncut chip, friction, normal rake and shear angles, you need Cutting Force (Fc), Shear angle (ϕ), Friction Angle (β), Rake Angle (α), Average Shear Stress on Shear Plane s) & Uncut Chip Thickness (t1). With our tool, you need to enter the respective value for Cutting Force, Shear angle, Friction Angle, Rake Angle, Average Shear Stress on Shear Plane & Uncut Chip Thickness 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 Width of cut?
In this formula, Width of cut uses Cutting Force, Shear angle, Friction Angle, Rake Angle, Average Shear Stress on Shear Plane & Uncut Chip Thickness. We can use 2 other way(s) to calculate the same, which is/are as follows -
  • Width of cut = (Area of Shear Plane*sin(Shear angle))/Uncut Chip Thickness
  • Width of cut = Depth of Cut/cos(Side Cutting Edge Angle)
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