Cutting Force for Frictional Force along Tool Rake Face and Thrust Force Solution

STEP 0: Pre-Calculation Summary
Formula Used
Cutting Force = (Frictional Force on Sleeve-(Axial Thrust*(cos(Normal Rake Angle))))/(sin(Normal Rake Angle))
Fc = (Fsleeve-(Paxial*(cos(αnormal))))/(sin(αnormal))
This formula uses 2 Functions, 4 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.
Frictional Force on Sleeve - (Measured in Newton) - Frictional Force on Sleeve refers to the force generated by two surfaces that contacts and slide against each other.
Axial Thrust - (Measured in Newton) - The Axial Thrust is the resultant force of all the axial forces (F) acting on the object or material.
Normal Rake Angle - (Measured in Radian) - The Normal Rake Angle is the angle of orientation of the tool's rake surface from the reference plane and measured on a normal plane.
STEP 1: Convert Input(s) to Base Unit
Frictional Force on Sleeve: 1557 Newton --> 1557 Newton No Conversion Required
Axial Thrust: 1500 Newton --> 1500 Newton No Conversion Required
Normal Rake Angle: 2.01 Degree --> 0.0350811179650794 Radian (Check conversion here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
Fc = (Fsleeve-(Paxial*(cos(αnormal))))/(sin(αnormal)) --> (1557-(1500*(cos(0.0350811179650794))))/(sin(0.0350811179650794))
Evaluating ... ...
Fc = 1651.452543331
STEP 3: Convert Result to Output's Unit
1651.452543331 Newton --> No Conversion Required
FINAL ANSWER
1651.452543331 1651.453 Newton <-- Cutting Force
(Calculation completed in 00.020 seconds)

Credits

Created by Maiarutselvan V
PSG College of Technology (PSGCT), Coimbatore
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National Institute Of Technology (NIT), Hamirpur
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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 = (Normal Force+Thrust force*sin(Normal Rake Angle))/cos(Normal Rake Angle)
Cutting Force given Shear Force and Thrust Force
Go Cutting Force = (Shear Force+(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 Frictional Force along Tool Rake Face and Thrust Force Formula

Cutting Force = (Frictional Force on Sleeve-(Axial Thrust*(cos(Normal Rake Angle))))/(sin(Normal Rake Angle))
Fc = (Fsleeve-(Paxial*(cos(αnormal))))/(sin(αnormal))

What is Force Relationship in Orthogonal Cutting?

Merchant's Circle Diagram is constructed to ease the analysis of cutting forces acting during orthogonal (Two Dimensional) cutting of workpiece. Please refer to the topic for force relationship in orthogonal cutting.

What is cutting force for this relation?

It is the force in the direction of cutting, the same direction as the cutting speed. The horizontal component is the cutting force Fc and the vertical component is the thrust force Ft.

How to Calculate Cutting Force for Frictional Force along Tool Rake Face and Thrust Force?

Cutting Force for Frictional Force along Tool Rake Face and Thrust Force calculator uses Cutting Force = (Frictional Force on Sleeve-(Axial Thrust*(cos(Normal Rake Angle))))/(sin(Normal Rake Angle)) to calculate the Cutting Force, The Cutting Force for Frictional Force along Tool Rake Face and Thrust Force formula is defined using these relations. Please refer to the Merchant theory. Cutting Force is denoted by Fc symbol.

How to calculate Cutting Force for Frictional Force along Tool Rake Face and Thrust Force using this online calculator? To use this online calculator for Cutting Force for Frictional Force along Tool Rake Face and Thrust Force, enter Frictional Force on Sleeve (Fsleeve), Axial Thrust (Paxial) & Normal Rake Angle normal) and hit the calculate button. Here is how the Cutting Force for Frictional Force along Tool Rake Face and Thrust Force calculation can be explained with given input values -> 459.4829 = (1557-(1500*(cos(0.0350811179650794))))/(sin(0.0350811179650794)).

FAQ

What is Cutting Force for Frictional Force along Tool Rake Face and Thrust Force?
The Cutting Force for Frictional Force along Tool Rake Face and Thrust Force formula is defined using these relations. Please refer to the Merchant theory and is represented as Fc = (Fsleeve-(Paxial*(cos(αnormal))))/(sin(αnormal)) or Cutting Force = (Frictional Force on Sleeve-(Axial Thrust*(cos(Normal Rake Angle))))/(sin(Normal Rake Angle)). Frictional Force on Sleeve refers to the force generated by two surfaces that contacts and slide against each other, The Axial Thrust is the resultant force of all the axial forces (F) acting on the object or material & The Normal Rake Angle is the angle of orientation of the tool's rake surface from the reference plane and measured on a normal plane.
How to calculate Cutting Force for Frictional Force along Tool Rake Face and Thrust Force?
The Cutting Force for Frictional Force along Tool Rake Face and Thrust Force formula is defined using these relations. Please refer to the Merchant theory is calculated using Cutting Force = (Frictional Force on Sleeve-(Axial Thrust*(cos(Normal Rake Angle))))/(sin(Normal Rake Angle)). To calculate Cutting Force for Frictional Force along Tool Rake Face and Thrust Force, you need Frictional Force on Sleeve (Fsleeve), Axial Thrust (Paxial) & Normal Rake Angle normal). With our tool, you need to enter the respective value for Frictional Force on Sleeve, Axial Thrust & Normal Rake 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 Frictional Force on Sleeve, Axial Thrust & Normal Rake Angle. We can use 5 other way(s) to calculate the same, which is/are as follows -
  • Cutting Force = (Shear Force+(Axial Thrust*(sin(Shear angle))))/(cos(Shear angle))
  • Cutting Force = (Normal 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)
  • 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))
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