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Force Exerted During Cutting is the force on workpiece in the direction of cutting, the same direction as the cutting speed. Check FAQs
Fc=R⋅cos(β-α)
Fc - Force Exerted During Cutting?R - Resultant Force?β - Friction Angle?α - Rake Angle?

Cutting force for given resultant force in merchant circle, friction angle and normal rake angle Example

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With units
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Here is how the Cutting force for given resultant force in merchant circle, friction angle and normal rake angle equation looks like with Values.

Here is how the Cutting force for given resultant force in merchant circle, friction angle and normal rake angle equation looks like with Units.

Here is how the Cutting force for given resultant force in merchant circle, friction angle and normal rake angle equation looks like.

11.3402Edit=12.398Edit⋅cos(25.79Edit-1.95Edit)
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Cutting force for given resultant force in merchant circle, friction angle and normal rake angle Solution

Follow our step by step solution on how to calculate Cutting force for given resultant force in merchant circle, friction angle and normal rake angle?

FIRST Step Consider the formula
Fc=R⋅cos(β-α)
Next Step Substitute values of Variables
∴ Fc=12.398N⋅cos(25.79°-1.95°)
Next Step Convert Units
∴ Fc=12.398N⋅cos(0.4501rad-0.034rad)
Next Step Prepare to Evaluate
∴ Fc=12.398⋅cos(0.4501-0.034)
Next Step Evaluate
∴Fc=11.3401743370836N
LAST Step Rounding Answer
∴Fc=11.3402N

Cutting force for given resultant force in merchant circle, friction angle and normal rake angle Formula Elements

Variables
Functions
Force Exerted During Cutting
Force Exerted During Cutting is the force on workpiece in the direction of cutting, the same direction as the cutting speed.
Symbol: Fc
Measurement: ForceUnit: N
Note: Value should be greater than 0.
Formulas to find Force Exerted During CuttingOpen Variable
Resultant Force
Resultant force is the vector sum of cutting force and thrust force.
Symbol: R
Measurement: ForceUnit: N
Note: Value can be positive or negative.
Formulas to find Resultant ForceOpen Variable
Friction Angle
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.
Symbol: β
Measurement: AngleUnit: °
Note: Value can be positive or negative.
Formulas to find Friction AngleOpen Variable
Rake Angle
Rake Angle 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 AngleOpen 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 Force Exerted During Cutting

​Go Cutting Force given Shear Force and Thrust Force
Fc=Fs+(FT⋅sin(Φ))cos(Φ)
​Go Cutting Force for Frictional Force along Tool Rake Face and Thrust Force
Fc=F-(FT⋅(cos(αo)))sin(αo)
​Go Cutting Force given Thrust Force and Normal Rake Angle
Fc=FN+FT⋅sin(αo)cos(αo)
​Go Cutting force for given force along shear force, shear, friction and normal rake angles
Fc=Fs⋅cos(β-α)cos(Φ+β-α)

How to Evaluate Cutting force for given resultant force in merchant circle, friction angle and normal rake angle?

Cutting force for given resultant force in merchant circle, friction angle and normal rake angle evaluator uses Force Exerted During Cutting = Resultant Force*cos(Friction Angle-Rake Angle) to evaluate the Force Exerted During Cutting, Cutting force for given resultant force in merchant circle, friction angle and normal rake angle is defined as the component of the resultant force responsible for cutting action. Force Exerted During Cutting is denoted by Fc symbol.

How to evaluate Cutting force for given resultant force in merchant circle, friction angle and normal rake angle using this online evaluator? To use this online evaluator for Cutting force for given resultant force in merchant circle, friction angle and normal rake angle, enter Resultant Force (R), Friction Angle (β) & Rake Angle (α) and hit the calculate button.

FAQs on Cutting force for given resultant force in merchant circle, friction angle and normal rake angle

What is the formula to find Cutting force for given resultant force in merchant circle, friction angle and normal rake angle?
The formula of Cutting force for given resultant force in merchant circle, friction angle and normal rake angle is expressed as Force Exerted During Cutting = Resultant Force*cos(Friction Angle-Rake Angle). Here is an example- 11.34017 = 12.398*cos(0.450120414089253-0.034033920413883).
How to calculate Cutting force for given resultant force in merchant circle, friction angle and normal rake angle?
With Resultant Force (R), Friction Angle (β) & Rake Angle (α) we can find Cutting force for given resultant force in merchant circle, friction angle and normal rake angle using the formula - Force Exerted During Cutting = Resultant Force*cos(Friction Angle-Rake Angle). This formula also uses Cosine (cos) function(s).
What are the other ways to Calculate Force Exerted During Cutting?
Here are the different ways to Calculate Force Exerted During Cutting-
  • Force Exerted During Cutting=(Force Along Shear Force+(Thrust force in Machining*sin(Shear Angle)))/(cos(Shear Angle))OpenImg
  • Force Exerted During Cutting=(Frictional Force in Machining-(Thrust force in Machining*(cos(Orthogonal Rake Angle))))/(sin(Orthogonal Rake Angle))OpenImg
  • Force Exerted During Cutting=(Force Normal to Shear Force+Thrust force in Machining*sin(Orthogonal Rake Angle))/cos(Orthogonal Rake Angle)OpenImg
Can the Cutting force for given resultant force in merchant circle, friction angle and normal rake angle be negative?
No, the Cutting force for given resultant force in merchant circle, friction angle and normal rake angle, measured in Force cannot be negative.
Which unit is used to measure Cutting force for given resultant force in merchant circle, friction angle and normal rake angle?
Cutting force for given resultant force in merchant circle, friction angle and normal rake angle is usually measured using the Newton[N] for Force. Exanewton[N], Meganewton[N], Kilonewton[N] are the few other units in which Cutting force for given resultant force in merchant circle, friction angle and normal rake angle can be measured.
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