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

✖Cutting force in metal cutting is the force in the direction of cutting, the same direction as the cutting speed.ⓘ Cutting Force in Metal Cutting [F_cut]			+10% -10%
✖Shearing angle between is the inclination of the shear plane with the horizontal axis at machining point.ⓘ Shearing Angle [ϕ_.]			+10% -10%
✖Cutting Friction Angle is termed as the angle between the tool and chip, which resists the flow of the chip along the rake face of the tool.ⓘ Cutting Friction Angle [β_.]			+10% -10%
✖Rake Angle of Cutting Tool is the angle of orientation of tool’s rake surface from the reference plane and measured on machine longitudinal plane.ⓘ Rake Angle of Cutting Tool [α_.]			+10% -10%
✖Average shear stress produced on shear plane is the reaction of workpiece when applied to different cutting forces on an imaginary shear plane.ⓘ Average Shear Stress Produced on Shear Plane [τ_shear]			+10% -10%
✖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.ⓘ Width of cut given cutting force, shear stress, uncut chip, friction, normal rake and shear angles [w_c]

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Formula

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

Formula

`"w"_{"c"} = "F"_{"cut"}*(cos("ϕ"_{"."}+"β"_{"."}-"α"_{"."}))/("τ"_{"shear"}*"t"_{"1"}*cos("β"_{"."}-"α"_{"."}))`

Example

`"9.687319mm"="314.677N"*(cos("5.257°"+"67.48°"-"8.58°"))/("3.95MPa"*"6.94mm"*cos("67.48°"-"8.58°"))`

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

STEP 0: Pre-Calculation Summary

Formula Used

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))
w_c = F_cut*(cos(ϕ_.+β_.-α_.))/(τ_shear*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

Cutting Width - (Measured in Meter) - Cutting Width can be defined as the width the tool cuts into the workpiece.
Cutting Force in Metal Cutting - (Measured in Newton) - Cutting force in metal cutting is the force in the direction of cutting, the same direction as the cutting speed.
Shearing Angle - (Measured in Radian) - Shearing angle between is the inclination of the shear plane with the horizontal axis at machining point.
Cutting Friction Angle - (Measured in Radian) - Cutting Friction Angle is termed as the angle between the tool and chip, which resists the flow of the chip along the rake face of the tool.
Rake Angle of Cutting Tool - (Measured in Radian) - Rake Angle of Cutting Tool is the angle of orientation of tool’s rake surface from the reference plane and measured on machine longitudinal plane.
Average Shear Stress Produced on Shear Plane - (Measured in Pascal) - Average shear stress produced on shear plane is the reaction of workpiece when applied to different cutting forces on an imaginary shear plane.
Uncut Chip Thickness in Machining - (Measured in Meter) - Uncut chip thickness in machining can be referred as the thickness of the undeformed chip.

STEP 1: Convert Input(s) to Base Unit

Cutting Force in Metal Cutting: 314.677 Newton --> 314.677 Newton No Conversion Required
Shearing Angle: 5.257 Degree --> 0.0917519587773246 Radian (Check conversion here)
Cutting Friction Angle: 67.48 Degree --> 1.17774817924555 Radian (Check conversion here)
Rake Angle of Cutting Tool: 8.58 Degree --> 0.149749249821085 Radian (Check conversion here)
Average Shear Stress Produced on Shear Plane: 3.95 Megapascal --> 3950000 Pascal (Check conversion here)
Uncut Chip Thickness in Machining: 6.94 Millimeter --> 0.00694 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

w_c = F_cut*(cos(ϕ_.+β_.-α_.))/(τ_shear*t₁*cos(β_.-α_.)) --> 314.677*(cos(0.0917519587773246+1.17774817924555-0.149749249821085))/(3950000*0.00694*cos(1.17774817924555-0.149749249821085))

Evaluating ... ...

w_c = 0.00968731872157385

STEP 3: Convert Result to Output's Unit

0.00968731872157385 Meter -->9.68731872157385 Millimeter (Check conversion here)

FINAL ANSWER

9.68731872157385 ≈ 9.687319 Millimeter <-- Cutting Width

(Calculation completed in 00.004 seconds)

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Home » Engineering » Production Engineering » Metal Cutting » Merchant Force Circle » Geometry and Dimensions » Width of cut given cutting force, shear stress, uncut chip, friction, normal rake and shear angles

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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 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)

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

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 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)) to calculate the Cutting Width, 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. Cutting Width is denoted by w_c 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 in Metal Cutting (F_cut), Shearing Angle (ϕ_.), Cutting Friction Angle (β_.), Rake Angle of Cutting Tool (α_.), Average Shear Stress Produced on Shear Plane (τ_shear) & Uncut Chip Thickness in Machining (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 -> 9687.319 = 314.677*(cos(0.0917519587773246+1.17774817924555-0.149749249821085))/(3950000*0.00694*cos(1.17774817924555-0.149749249821085)).

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_c = F_cut*(cos(ϕ_.+β_.-α_.))/(τ_shear*t₁*cos(β_.-α_.)) or 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)). Cutting force in metal cutting is the force in the direction of cutting, the same direction as the cutting speed, Shearing angle between is the inclination of the shear plane with the horizontal axis at machining point, Cutting Friction Angle is termed as the angle between the tool and chip, which resists the flow of the chip along the rake face of the tool, Rake Angle of Cutting Tool is the angle of orientation of tool’s rake surface from the reference plane and measured on machine longitudinal plane, Average shear stress produced on shear plane is the reaction of workpiece when applied to different cutting forces on an imaginary shear plane & Uncut chip thickness in machining can be referred as 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 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)). To calculate Width of cut given cutting force, shear stress, uncut chip, friction, normal rake and shear angles, you need Cutting Force in Metal Cutting (F_cut), Shearing Angle (ϕ_.), Cutting Friction Angle (β_.), Rake Angle of Cutting Tool (α_.), Average Shear Stress Produced on Shear Plane (τ_shear) & Uncut Chip Thickness in Machining (t₁). With our tool, you need to enter the respective value for Cutting Force in Metal Cutting, Shearing Angle, Cutting Friction Angle, Rake Angle of Cutting Tool, Average Shear Stress Produced on Shear Plane & Uncut Chip Thickness in Machining 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 Width?

In this formula, Cutting Width uses Cutting Force in Metal Cutting, Shearing Angle, Cutting Friction Angle, Rake Angle of Cutting Tool, Average Shear Stress Produced on Shear Plane & Uncut Chip Thickness in Machining. We can use 2 other way(s) to calculate the same, which is/are as follows -

Cutting Width = (Area of Shear Plane*sin(Shearing Angle))/Uncut Chip Thickness in Machining
Cutting Width = Depth of Cut Provided by Tool/cos(Side Cutting Edge Angle for Metal Cutting)

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