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Cutting Width can be defined as the width the tool cuts into the workpiece. Check FAQs
wc=Fcut⋅cos(ϕ+β-α)τshear⋅t1⋅cos(β-α)
wc - Cutting Width?Fcut - Cutting Force in Metal Cutting?ϕ - Shearing Angle?β - Cutting Friction Angle?α - Rake Angle of Cutting Tool?τshear - Average Shear Stress Produced on Shear Plane?t1 - Uncut Chip Thickness in Machining?

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

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Here is how the Width of cut given cutting force, shear stress, uncut chip, friction, normal rake and shear angles equation looks like with Values.

Here is how the Width of cut given cutting force, shear stress, uncut chip, friction, normal rake and shear angles equation looks like with Units.

Here is how the Width of cut given cutting force, shear stress, uncut chip, friction, normal rake and shear angles equation looks like.

9.6873Edit=314.677Edit⋅cos(5.257Edit+67.48Edit-8.58Edit)3.95Edit⋅6.94Edit⋅cos(67.48Edit-8.58Edit)
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Width of cut given cutting force, shear stress, uncut chip, friction, normal rake and shear angles Solution

Follow our step by step solution on how to calculate Width of cut given cutting force, shear stress, uncut chip, friction, normal rake and shear angles?

FIRST Step Consider the formula
wc=Fcut⋅cos(ϕ+β-α)τshear⋅t1⋅cos(β-α)
Next Step Substitute values of Variables
∴ wc=314.677N⋅cos(5.257°+67.48°-8.58°)3.95MPa⋅6.94mm⋅cos(67.48°-8.58°)
Next Step Convert Units
∴ wc=314.677N⋅cos(0.0918rad+1.1777rad-0.1497rad)4E+6Pa⋅0.0069m⋅cos(1.1777rad-0.1497rad)
Next Step Prepare to Evaluate
∴ wc=314.677⋅cos(0.0918+1.1777-0.1497)4E+6⋅0.0069⋅cos(1.1777-0.1497)
Next Step Evaluate
∴wc=0.00968731872157385m
Next Step Convert to Output's Unit
∴wc=9.68731872157385mm
LAST Step Rounding Answer
∴wc=9.6873mm

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

Variables
Functions
Cutting Width
Cutting Width can be defined as the width the tool cuts into the workpiece.
Symbol: wc
Measurement: LengthUnit: mm
Note: Value can be positive or negative.
Formulas to find Cutting WidthOpen Variable
Cutting Force in Metal Cutting
Cutting force in metal cutting is the force in the direction of cutting, the same direction as the cutting speed.
Symbol: Fcut
Measurement: ForceUnit: N
Note: Value should be greater than 0.
Formulas to find Cutting Force in Metal CuttingOpen Variable
Shearing Angle
Shearing angle between is the inclination of the shear plane with the horizontal axis at machining point.
Symbol: ϕ
Measurement: AngleUnit: °
Note: Value should be greater than 0.
Formulas to find Shearing AngleOpen Variable
Cutting Friction Angle
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.
Symbol: β
Measurement: AngleUnit: °
Note: Value should be greater than 0.
Formulas to find Cutting Friction AngleOpen Variable
Rake Angle of Cutting 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.
Symbol: α
Measurement: AngleUnit: °
Note: Value can be positive or negative.
Formulas to find Rake Angle of Cutting ToolOpen Variable
Average Shear Stress Produced on Shear Plane
Average shear stress produced on shear plane is the reaction of workpiece when applied to different cutting forces on an imaginary shear plane.
Symbol: τshear
Measurement: StressUnit: MPa
Note: Value can be positive or negative.
Formulas to find Average Shear Stress Produced on Shear PlaneOpen Variable
Uncut Chip Thickness in Machining
Uncut chip thickness in machining can be referred as the thickness of the undeformed chip.
Symbol: t1
Measurement: LengthUnit: mm
Note: Value should be greater than 0.
Formulas to find Uncut Chip Thickness in MachiningOpen Variable
cos
Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle.
Syntax: cos(Angle)

Other Formulas to find Cutting Width

​Go Width of cut for given shear angle, uncut chip thickness and area of shear plane
wc=As⋅sin(ϕ)t1
​Go Width of cut for given side cutting edge angle
wc=dcutcos(ψ)

Other formulas in Geometry and Dimensions category

​Go Area of shear plane for given shear angle, width of cut and uncut chip thickness
As=t1⋅wcsin(ϕ)
​Go Shear angle for given area of shear plane, width of cut and uncut chip thickness
ϕ=asin(wc⋅t1As)

How to Evaluate 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 evaluator 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 evaluate 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 wc symbol.

How to evaluate Width of cut given cutting force, shear stress, uncut chip, friction, normal rake and shear angles using this online evaluator? To use this online evaluator for Width of cut given cutting force, shear stress, uncut chip, friction, normal rake and shear angles, enter Cutting Force in Metal Cutting (Fcut), Shearing Angle (ϕ), Cutting Friction Angle (β), Rake Angle of Cutting Tool (α), Average Shear Stress Produced on Shear Plane (τshear) & Uncut Chip Thickness in Machining (t1) and hit the calculate button.

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

What is the formula to find Width of cut given cutting force, shear stress, uncut chip, friction, normal rake and shear angles?
The formula of Width of cut given cutting force, shear stress, uncut chip, friction, normal rake and shear angles is expressed as 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)). Here is an example- 9687.319 = 314.677*(cos(0.0917519587773246+1.17774817924555-0.149749249821085))/(3950000*0.00694*cos(1.17774817924555-0.149749249821085)).
How to calculate Width of cut given cutting force, shear stress, uncut chip, friction, normal rake and shear angles?
With Cutting Force in Metal Cutting (Fcut), Shearing Angle (ϕ), Cutting Friction Angle (β), Rake Angle of Cutting Tool (α), Average Shear Stress Produced on Shear Plane (τshear) & Uncut Chip Thickness in Machining (t1) we can find Width of cut given cutting force, shear stress, uncut chip, friction, normal rake and shear angles using the formula - 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)). This formula also uses Cosine (cos) function(s).
What are the other ways to Calculate Cutting Width?
Here are the different ways to Calculate Cutting Width-
  • Cutting Width=(Area of Shear Plane*sin(Shearing Angle))/Uncut Chip Thickness in MachiningOpenImg
  • Cutting Width=Depth of Cut Provided by Tool/cos(Side Cutting Edge Angle for Metal Cutting)OpenImg
Can the Width of cut given cutting force, shear stress, uncut chip, friction, normal rake and shear angles be negative?
Yes, the Width of cut given cutting force, shear stress, uncut chip, friction, normal rake and shear angles, measured in Length can be negative.
Which unit is used to measure 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 is usually measured using the Millimeter[mm] for Length. Meter[mm], Kilometer[mm], Decimeter[mm] are the few other units in which Width of cut given cutting force, shear stress, uncut chip, friction, normal rake and shear angles can be measured.
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