Cutting force for given force along shear force, shear, friction and normal rake angles Solution

STEP 0: Pre-Calculation Summary
Formula Used
Cutting Force = Force along shear plane*cos(Friction Angle-Rake Angle)/cos(Shear angle+Friction Angle-Rake Angle)
Fc = Fs*cos(β-α)/cos(ϕ+β-α)
This formula uses 1 Functions, 5 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.
Force along shear plane - (Measured in Newton) - Force along shear plane is the shear force along the shear plane.
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
Force along shear plane: 26 Newton --> 26 Newton No Conversion Required
Friction Angle: 15 Degree --> 0.2617993877991 Radian (Check conversion here)
Rake Angle: 8.56 Degree --> 0.149400183970687 Radian (Check conversion here)
Shear angle: 45 Degree --> 0.785398163397301 Radian (Check conversion here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
Fc = Fs*cos(β-α)/cos(ϕ+β-α) --> 26*cos(0.2617993877991-0.149400183970687)/cos(0.785398163397301+0.2617993877991-0.149400183970687)
Evaluating ... ...
Fc = 41.4479923970121
STEP 3: Convert Result to Output's Unit
41.4479923970121 Newton --> No Conversion Required
FINAL ANSWER
41.4479923970121 41.44799 Newton <-- Cutting Force
(Calculation completed in 00.004 seconds)

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)*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 given force along shear force, shear, friction and normal rake angles Formula

Cutting Force = Force along shear plane*cos(Friction Angle-Rake Angle)/cos(Shear angle+Friction Angle-Rake Angle)
Fc = Fs*cos(β-α)/cos(ϕ+β-α)

Significance of cutting force

The single point cutting tools being used for turning, shaping, planing, slotting, boring etc. are
characterized by having only one cutting force during machining. 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 given force along shear force, shear, friction and normal rake angles?

Cutting force for given force along shear force, shear, friction and normal rake angles calculator uses Cutting Force = Force along shear plane*cos(Friction Angle-Rake Angle)/cos(Shear angle+Friction Angle-Rake Angle) to calculate the Cutting Force, The Cutting force for given force along shear force, shear, friction and normal rake angles formula is defined as the product of force along the shear plane to the ratio of the cosine of difference of friction and rake angles to the cosine of summation of shear angle to difference of friction and rake angles. Cutting Force is denoted by Fc symbol.

How to calculate Cutting force for given force along shear force, shear, friction and normal rake angles using this online calculator? To use this online calculator for Cutting force for given force along shear force, shear, friction and normal rake angles, enter Force along shear plane (Fs), Friction Angle (β), Rake Angle (α) & Shear angle (ϕ) and hit the calculate button. Here is how the Cutting force for given force along shear force, shear, friction and normal rake angles calculation can be explained with given input values -> 41.44799 = 26*cos(0.2617993877991-0.149400183970687)/cos(0.785398163397301+0.2617993877991-0.149400183970687).

FAQ

What is Cutting force for given force along shear force, shear, friction and normal rake angles?
The Cutting force for given force along shear force, shear, friction and normal rake angles formula is defined as the product of force along the shear plane to the ratio of the cosine of difference of friction and rake angles to the cosine of summation of shear angle to difference of friction and rake angles and is represented as Fc = Fs*cos(β-α)/cos(ϕ+β-α) or Cutting Force = Force along shear plane*cos(Friction Angle-Rake Angle)/cos(Shear angle+Friction Angle-Rake Angle). Force along shear plane is the shear force along the shear plane, 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 given force along shear force, shear, friction and normal rake angles?
The Cutting force for given force along shear force, shear, friction and normal rake angles formula is defined as the product of force along the shear plane to the ratio of the cosine of difference of friction and rake angles to the cosine of summation of shear angle to difference of friction and rake angles is calculated using Cutting Force = Force along shear plane*cos(Friction Angle-Rake Angle)/cos(Shear angle+Friction Angle-Rake Angle). To calculate Cutting force for given force along shear force, shear, friction and normal rake angles, you need Force along shear plane (Fs), Friction Angle (β), Rake Angle (α) & Shear angle (ϕ). With our tool, you need to enter the respective value for Force along shear plane, 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 Force along shear plane, Friction Angle, Rake Angle & Shear 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 = (Frictional Force on Sleeve-(Axial Thrust*(cos(Normal Rake Angle))))/(sin(Normal Rake 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 = ((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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