Cutting force for shear stress, width of cut, uncut chip thickness, friction, rake and shear angles Solution

STEP 0: Pre-Calculation Summary
Formula Used
Cutting Force = ((Average Shear Stress on Shear Plane*Width of cut*Uncut Chip Thickness)*sin(Friction Angle-Rake Angle))/(sin(Shear Angle)*cos(Shear Angle+Friction Angle-Rake Angle))
Fc = ((τ*w*t1)*sin(β-α))/(sin(Φ)*cos(Φ+β-α))
This formula uses 2 Functions, 7 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)
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
Cutting Force - (Measured in Newton) - Cutting Force is the force in the direction of cutting, the same direction as the cutting speed.
Average Shear Stress on Shear Plane - (Measured in Pascal) - Average Shear Stress on Shear Plane is the average shear stress induced at imaginary shear plane.
Width of cut - (Measured in Meter) - The width of cut is defined as the width the tool cuts into the workpiece.
Uncut Chip Thickness - (Measured in Meter) - Uncut Chip Thickness is the thickness of the undeformed chip.
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.
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
Average Shear Stress on Shear Plane: 2 Newton per Square Meter --> 2 Pascal (Check conversion here)
Width of cut: 4 Millimeter --> 0.004 Meter (Check conversion here)
Uncut Chip Thickness: 1.2 Millimeter --> 0.0012 Meter (Check conversion here)
Friction Angle: 15 Degree --> 0.2617993877991 Radian (Check conversion here)
Rake Angle: 8.56 Degree --> 0.149400183970687 Radian (Check conversion here)
Shear Angle: 45 Degree --> 0.785398163397301 Radian (Check conversion here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
Fc = ((τ*w*t1)*sin(β-α))/(sin(Φ)*cos(Φ+β-α)) --> ((2*0.004*0.0012)*sin(0.2617993877991-0.149400183970687))/(sin(0.785398163397301)*cos(0.785398163397301+0.2617993877991-0.149400183970687))
Evaluating ... ...
Fc = 2.44294633144688E-06
STEP 3: Convert Result to Output's Unit
2.44294633144688E-06 Newton --> No Conversion Required
FINAL ANSWER
2.44294633144688E-06 2.4E-6 Newton <-- Cutting Force
(Calculation completed in 00.004 seconds)

Credits

Created by Shikha Maurya
Indian Institute of Technology (IIT), Bombay
Shikha Maurya has created this Calculator and 100+ more calculators!
Verified by Rushi Shah
K J Somaiya College of Engineering (K J Somaiya), Mumbai
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6 Cutting Force Calculators

Cutting force for shear stress, width of cut, uncut chip thickness, friction, rake and shear angles
Go Cutting Force = ((Average Shear Stress on Shear Plane*Width of cut*Uncut Chip Thickness)*sin(Friction Angle-Rake Angle))/(sin(Shear Angle)*cos(Shear Angle+Friction Angle-Rake Angle))
Cutting force for given force along shear force, shear, friction and normal rake angles
Go Cutting Force = Force Along Shear Plane*cos(Friction Angle-Rake Angle)/cos(Shear Angle+Friction Angle-Rake Angle)
Cutting Force for Frictional Force along Tool Rake Face and Thrust Force
Go Cutting Force = (Frictional Force on Sleeve-(Axial Thrust*(cos(Normal Rake Angle))))/(sin(Normal Rake Angle))
Cutting Force given Thrust Force and Normal Rake Angle
Go Cutting Force = (Force Normal to Shear Force+Thrust force*sin(Normal Rake Angle))/cos(Normal Rake Angle)
Cutting Force given Shear Force and Thrust Force
Go Cutting Force = (Force Along Shear Plane+(Axial Thrust*(sin(Shear Angle))))/(cos(Shear Angle))
Cutting force for given resultant force in merchant circle, friction angle and normal rake angle
Go Cutting Force = Resultant Force*(cos(Friction Angle-Rake Angle))

Cutting force for shear stress, width of cut, uncut chip thickness, friction, rake and shear angles Formula

Cutting Force = ((Average Shear Stress on Shear Plane*Width of cut*Uncut Chip Thickness)*sin(Friction Angle-Rake Angle))/(sin(Shear Angle)*cos(Shear Angle+Friction Angle-Rake Angle))
Fc = ((τ*w*t1)*sin(β-α))/(sin(Φ)*cos(Φ+β-α))

Significance of cutting force

Cutting force is responsible for cutting and its largest in magnitude and acts in the direction of cutting velocity. It decides the cutting power consumption during machining

How to Calculate Cutting force for shear stress, width of cut, uncut chip thickness, friction, rake and shear angles?

Cutting force for shear stress, width of cut, uncut chip thickness, friction, rake and shear angles calculator uses Cutting Force = ((Average Shear Stress on Shear Plane*Width of cut*Uncut Chip Thickness)*sin(Friction Angle-Rake Angle))/(sin(Shear Angle)*cos(Shear Angle+Friction Angle-Rake Angle)) to calculate the Cutting Force, Cutting force for shear stress, width of cut, uncut chip thickness, friction, rake and shear angles is defined as the product of average shear stress along the shear planes, uncut chip thickness, and width of cut to the ratio of the cosine of difference of friction and rake angles to the cosine of shear angle added to difference of friction and rake angles. Cutting Force is denoted by Fc symbol.

How to calculate Cutting force for shear stress, width of cut, uncut chip thickness, friction, rake and shear angles using this online calculator? To use this online calculator for Cutting force for shear stress, width of cut, uncut chip thickness, friction, rake and shear angles, enter Average Shear Stress on Shear Plane (τ), Width of cut (w), Uncut Chip Thickness (t1), Friction Angle (β), Rake Angle (α) & Shear Angle (Φ) and hit the calculate button. Here is how the Cutting force for shear stress, width of cut, uncut chip thickness, friction, rake and shear angles calculation can be explained with given input values -> 2.4E-6 = ((2*0.004*0.0012)*sin(0.2617993877991-0.149400183970687))/(sin(0.785398163397301)*cos(0.785398163397301+0.2617993877991-0.149400183970687)).

FAQ

What is Cutting force for shear stress, width of cut, uncut chip thickness, friction, rake and shear angles?
Cutting force for shear stress, width of cut, uncut chip thickness, friction, rake and shear angles is defined as the product of average shear stress along the shear planes, uncut chip thickness, and width of cut to the ratio of the cosine of difference of friction and rake angles to the cosine of shear angle added to difference of friction and rake angles and is represented as Fc = ((τ*w*t1)*sin(β-α))/(sin(Φ)*cos(Φ+β-α)) or Cutting Force = ((Average Shear Stress on Shear Plane*Width of cut*Uncut Chip Thickness)*sin(Friction Angle-Rake Angle))/(sin(Shear Angle)*cos(Shear Angle+Friction Angle-Rake Angle)). Average Shear Stress on Shear Plane is the average shear stress induced at imaginary shear plane, The width of cut is defined as the width the tool cuts into the workpiece, Uncut Chip Thickness is the thickness of the undeformed chip, 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 & Shear angle is the inclination of the shear plane with the horizontal axis at machining point.
How to calculate Cutting force for shear stress, width of cut, uncut chip thickness, friction, rake and shear angles?
Cutting force for shear stress, width of cut, uncut chip thickness, friction, rake and shear angles is defined as the product of average shear stress along the shear planes, uncut chip thickness, and width of cut to the ratio of the cosine of difference of friction and rake angles to the cosine of shear angle added to difference of friction and rake angles is calculated using Cutting Force = ((Average Shear Stress on Shear Plane*Width of cut*Uncut Chip Thickness)*sin(Friction Angle-Rake Angle))/(sin(Shear Angle)*cos(Shear Angle+Friction Angle-Rake Angle)). To calculate Cutting force for shear stress, width of cut, uncut chip thickness, friction, rake and shear angles, you need Average Shear Stress on Shear Plane (τ), Width of cut (w), Uncut Chip Thickness (t1), Friction Angle (β), Rake Angle (α) & Shear Angle (Φ). With our tool, you need to enter the respective value for Average Shear Stress on Shear Plane, Width of cut, Uncut Chip Thickness, Friction Angle, Rake Angle & Shear Angle 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 Force?
In this formula, Cutting Force uses Average Shear Stress on Shear Plane, Width of cut, Uncut Chip Thickness, Friction Angle, Rake Angle & Shear Angle. We can use 5 other way(s) to calculate the same, which is/are as follows -
  • Cutting Force = (Force Along Shear Plane+(Axial Thrust*(sin(Shear Angle))))/(cos(Shear Angle))
  • Cutting Force = (Frictional Force on Sleeve-(Axial Thrust*(cos(Normal Rake Angle))))/(sin(Normal Rake Angle))
  • Cutting Force = (Force Normal to Shear Force+Thrust force*sin(Normal Rake Angle))/cos(Normal Rake Angle)
  • Cutting Force = Resultant Force*(cos(Friction Angle-Rake Angle))
  • Cutting Force = Force Along Shear Plane*cos(Friction Angle-Rake Angle)/cos(Shear Angle+Friction Angle-Rake Angle)
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