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

✖Average Shear Stress on Shear Plane is the average shear stress induced at imaginary shear plane.ⓘ Average Shear Stress on Shear Plane [τ]			+10% -10%
✖The width of cut is defined as the width the tool cuts into the workpiece.ⓘ Width of Cut [w]			+10% -10%
✖Uncut Chip Thickness is the thickness of the undeformed chip.ⓘ Uncut Chip Thickness [t]			+10% -10%
✖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.ⓘ Friction Angle [β]			+10% -10%
✖Rake Angle is the angle of orientation of tool’s rake surface from the reference plane and measured on machine longitudinal plane.ⓘ Rake Angle [α]			+10% -10%
✖Shear angle is the inclination of the shear plane with the horizontal axis at machining point.ⓘ Shear Angle [Φ]			+10% -10%

✖Cutting Force is the force in the direction of cutting, the same direction as the cutting speed.ⓘ Cutting force for shear stress, width of cut, uncut chip thickness, friction, rake and shear angles [F_c]

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

Formula

`"F"_{"c"} = (("τ"*"w"*"t")*cos("β"-"α"))/(cos("Φ"+"β"-"α"))`

Example

`"11.33918N"=(("0.5N/mm²"*"14mm"*"1.1656mm")*cos("25.79°"-"1.95°"))/(cos("25°"+"25.79°"-"1.95°"))`

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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)*cos(Friction Angle-Rake Angle))/(cos(Shear Angle+Friction Angle-Rake Angle))
F_c = ((τ*w*t)*cos(β-α))/(cos(Φ+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

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: 0.5 Newton per Square Millimeter --> 500000 Pascal (Check conversion here)
Width of Cut: 14 Millimeter --> 0.014 Meter (Check conversion here)
Uncut Chip Thickness: 1.1656 Millimeter --> 0.0011656 Meter (Check conversion here)
Friction Angle: 25.79 Degree --> 0.450120414089253 Radian (Check conversion here)
Rake Angle: 1.95 Degree --> 0.034033920413883 Radian (Check conversion here)
Shear Angle: 25 Degree --> 0.4363323129985 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

F_c = ((τ*w*t)*cos(β-α))/(cos(Φ+β-α)) --> ((500000*0.014*0.0011656)*cos(0.450120414089253-0.034033920413883))/(cos(0.4363323129985+0.450120414089253-0.034033920413883))

Evaluating ... ...

F_c = 11.3391772570935

STEP 3: Convert Result to Output's Unit

11.3391772570935 Newton --> No Conversion Required

FINAL ANSWER

11.3391772570935 ≈ 11.33918 Newton <-- Cutting Force

(Calculation completed in 00.004 seconds)

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Home » Engineering » Production Engineering » Metal Cutting » Merchant Force Circle » Cutting Force » Cutting force for shear stress, width of cut, uncut chip thickness, friction, rake and shear angles

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

Rushi Shah has verified this Calculator and 200+ more calculators!

< 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)*cos(Friction Angle-Rake 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 Force*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 in Machining-(Thrust force in Machining*(cos(Orthogonal Rake Angle))))/(sin(Orthogonal Rake Angle))

Cutting Force given Thrust Force and Normal Rake Angle

Go Cutting Force = (Force Normal to Shear Force+Thrust force in Machining*sin(Orthogonal Rake Angle))/cos(Orthogonal Rake Angle)

Cutting Force given Shear Force and Thrust Force

Go Cutting Force = (Force Along Shear Force+(Thrust force in Machining*(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

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)*cos(Friction Angle-Rake 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 F_c 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 (t), 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 -> 7.3E-6 = ((0.5*0.014*0.0011656)*cos(0.450120414089253-0.034033920413883))/(cos(0.4363323129985+0.450120414089253-0.034033920413883)).

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 F_c = ((τ*w*t)*cos(β-α))/(cos(Φ+β-α)) or Cutting Force = ((Average Shear Stress on Shear Plane*Width of Cut*Uncut Chip Thickness)*cos(Friction Angle-Rake 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)*cos(Friction Angle-Rake 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 (t), 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 Force+(Thrust force in Machining*(sin(Shear Angle))))/(cos(Shear Angle))
Cutting Force = (Frictional Force in Machining-(Thrust force in Machining*(cos(Orthogonal Rake Angle))))/(sin(Orthogonal Rake Angle))
Cutting Force = (Force Normal to Shear Force+Thrust force in Machining*sin(Orthogonal Rake Angle))/cos(Orthogonal Rake Angle)
Cutting Force = Resultant Force*(cos(Friction Angle-Rake Angle))
Cutting Force = Force Along Shear Force*cos(Friction Angle-Rake Angle)/cos(Shear Angle+Friction Angle-Rake Angle)

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