R in merchant circle for given force along shear force, shear, friction and normal rake angles Solution

STEP 0: Pre-Calculation Summary
Formula Used
Resultant Force = (Force along shear plane)*(sec(Shear angle+Friction Angle-Rake Angle))
R = (Fs)*(sec(ϕ+β-α))
This formula uses 1 Functions, 5 Variables
Functions Used
sec - Secant is a trigonometric function that is defined ratio of the hypotenuse to the shorter side adjacent to an acute angle (in a right-angled triangle); the reciprocal of a cosine., sec(Angle)
Variables Used
Resultant Force - (Measured in Newton) - Resultant force is the vector sum of cutting force and thrust force.
Force along shear plane - (Measured in Newton) - Force along shear plane is the shear force along the shear plane.
Shear angle - (Measured in Radian) - Shear angle is the inclination of the shear plane with the horizontal axis at machining point.
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.
STEP 1: Convert Input(s) to Base Unit
Force along shear plane: 26 Newton --> 26 Newton No Conversion Required
Shear angle: 45 Degree --> 0.785398163397301 Radian (Check conversion here)
Friction Angle: 15 Degree --> 0.2617993877991 Radian (Check conversion here)
Rake Angle: 8.56 Degree --> 0.149400183970687 Radian (Check conversion here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
R = (Fs)*(sec(ϕ+β-α)) --> (26)*(sec(0.785398163397301+0.2617993877991-0.149400183970687))
Evaluating ... ...
R = 41.7111960086743
STEP 3: Convert Result to Output's Unit
41.7111960086743 Newton --> No Conversion Required
FINAL ANSWER
41.7111960086743 41.7112 Newton <-- Resultant Force
(Calculation completed in 00.004 seconds)

Credits

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Indian Institute of Technology (IIT), Bombay
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6 Resultants and Stress Calculators

Shear stress given cutting force, cut size, uncut chip thickness, friction, rake and shear angles
Go Average Shear Stress on Shear Plane = Cutting Force*(cos(Shear angle+Friction Angle-Rake Angle))/((Width of cut*Uncut Chip Thickness)*cos(Friction Angle-Rake Angle))
Force acting Normal to Rake Face given Cutting Force and Thrust Force
Go Normal Force = (Cutting Force*cos(Normal Rake Angle))-(Thrust force*sin(Normal Rake Angle))
Normal rake angle for given Resultant force, force along shear, shear, and friction angle
Go Rake Angle = Shear angle+Friction Angle-(arccos(Resultant Force/Force along shear plane))
R in merchant circle for given force along shear force, shear, friction and normal rake angles
Go Resultant Force = (Force along shear plane)*(sec(Shear angle+Friction Angle-Rake Angle))
Resultant force in merchant circle for given cutting force, friction and normal rake angles
Go Resultant Force = Cutting Force*(sec(Friction Angle-Rake Angle))
Mean normal stress in shear plane for given normal force and shear area
Go Normal Stress = Normal Force/Shear Area

R in merchant circle for given force along shear force, shear, friction and normal rake angles Formula

Resultant Force = (Force along shear plane)*(sec(Shear angle+Friction Angle-Rake Angle))
R = (Fs)*(sec(ϕ+β-α))

What is resultant force in merchant circle

The resultant force in the merchant circle diagram is the vector sum of the cutting force and thrust force. It can also be obtained as the vector sum of shear force acting on the shear plane and force normal to the shear plane

How to Calculate R in merchant circle for given force along shear force, shear, friction and normal rake angles?

R in merchant circle for given force along shear force, shear, friction and normal rake angles calculator uses Resultant Force = (Force along shear plane)*(sec(Shear angle+Friction Angle-Rake Angle)) to calculate the Resultant Force, R in merchant circle for given force along shear force, shear, friction and normal rake angles is the resultant of shear force and normal force on shear plane. Resultant Force is denoted by R symbol.

How to calculate R in merchant circle for given force along shear force, shear, friction and normal rake angles using this online calculator? To use this online calculator for R in merchant circle for given force along shear force, shear, friction and normal rake angles, enter Force along shear plane (Fs), Shear angle (ϕ), Friction Angle (β) & Rake Angle (α) and hit the calculate button. Here is how the R in merchant circle for given force along shear force, shear, friction and normal rake angles calculation can be explained with given input values -> 41.7112 = (26)*(sec(0.785398163397301+0.2617993877991-0.149400183970687)).

FAQ

What is R in merchant circle for given force along shear force, shear, friction and normal rake angles?
R in merchant circle for given force along shear force, shear, friction and normal rake angles is the resultant of shear force and normal force on shear plane and is represented as R = (Fs)*(sec(ϕ+β-α)) or Resultant Force = (Force along shear plane)*(sec(Shear angle+Friction Angle-Rake Angle)). Force along shear plane is the shear force along the shear plane, Shear angle is the inclination of the shear plane with the horizontal axis at machining point, 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.
How to calculate R in merchant circle for given force along shear force, shear, friction and normal rake angles?
R in merchant circle for given force along shear force, shear, friction and normal rake angles is the resultant of shear force and normal force on shear plane is calculated using Resultant Force = (Force along shear plane)*(sec(Shear angle+Friction Angle-Rake Angle)). To calculate R in merchant circle for given force along shear force, shear, friction and normal rake angles, you need Force along shear plane (Fs), Shear angle (ϕ), Friction Angle (β) & Rake Angle (α). With our tool, you need to enter the respective value for Force along shear plane, Shear angle, Friction Angle & 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 Resultant Force?
In this formula, Resultant Force uses Force along shear plane, Shear angle, Friction Angle & Rake Angle. We can use 1 other way(s) to calculate the same, which is/are as follows -
  • Resultant Force = Cutting Force*(sec(Friction Angle-Rake Angle))
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