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

✖Force produced along shear plane Force Produced Along Shear Plane.ⓘ Force Produced Along Shear Plane [F_s]			+10% -10%
✖Shear angle for metal cutting is the inclination of the shear plane with the horizontal axis at machining point.ⓘ Shear Angle for Metal Cutting [ϕ^']			+10% -10%
✖Machining 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.ⓘ Machining Friction Angle [β^']			+10% -10%
✖Cutting tool rake angle is the angle of orientation of tool’s rake surface from the reference plane and measured on machine longitudinal plane.ⓘ Cutting Tool Rake Angle [α^']			+10% -10%

✖Resultant force on workpiece is the vector sum of cutting force and thrust force.ⓘ R in merchant circle for given force along shear force, shear, friction and normal rake angles [R^']

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Formula

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

Formula

`"R"^{"'"} = ("F"_{"s"})*(sec("ϕ"^{"'"}+"β"^{"'"}-"α"^{"'"}))`

Example

`"170.0001N"=("96.5982N")*(sec("27.3°"+"36.695°"-"8.6215°"))`

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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 on Workpiece = (Force Produced Along Shear Plane)*(sec(Shear Angle for Metal Cutting+Machining Friction Angle-Cutting Tool Rake Angle))
R^' = (F_s)*(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 on Workpiece - (Measured in Newton) - Resultant force on workpiece is the vector sum of cutting force and thrust force.
Force Produced Along Shear Plane - (Measured in Newton) - Force produced along shear plane Force Produced Along Shear Plane.
Shear Angle for Metal Cutting - (Measured in Radian) - Shear angle for metal cutting is the inclination of the shear plane with the horizontal axis at machining point.
Machining Friction Angle - (Measured in Radian) - Machining 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.
Cutting Tool Rake Angle - (Measured in Radian) - Cutting tool 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 Produced Along Shear Plane: 96.5982 Newton --> 96.5982 Newton No Conversion Required
Shear Angle for Metal Cutting: 27.3 Degree --> 0.476474885794362 Radian (Check conversion here)
Machining Friction Angle: 36.695 Degree --> 0.640448569019199 Radian (Check conversion here)
Cutting Tool Rake Angle: 8.6215 Degree --> 0.150473561460663 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

R^' = (F_s)*(sec(ϕ^'+β^'-α^')) --> (96.5982)*(sec(0.476474885794362+0.640448569019199-0.150473561460663))

Evaluating ... ...

R^' = 170.000093021258

STEP 3: Convert Result to Output's Unit

170.000093021258 Newton --> No Conversion Required

FINAL ANSWER

170.000093021258 ≈ 170.0001 Newton <-- Resultant Force on Workpiece

(Calculation completed in 00.004 seconds)

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Home » Engineering » Production Engineering » Metal Cutting » Merchant Force Circle » Resultants and Stress » R in merchant circle for given force along shear force, shear, friction and normal rake angles

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 Resultants and Stress Calculators

Shear stress given cutting force, cut size, uncut chip thickness, friction, rake and shear angles

Go Average Shear Stress Induced on Shear Plane = Cutting Force on Workpiece*(cos(Shear Angle for Metal Cutting+Machining Friction Angle-Cutting Tool Rake Angle))/((Cutting Thickness*Uncut Chip Width)*cos(Machining Friction Angle-Cutting Tool Rake Angle))

Force acting Normal to Rake Face given Cutting Force and Thrust Force

Go Normal Force Induced on Workpiece = (Cutting Force on Workpiece*cos(Normal Rake Angle of Cutting Tool))-(Thrust Force in Metal Cutting*sin(Normal Rake Angle of Cutting Tool))

Normal rake angle for given Resultant force, force along shear, shear, and friction angle

Go Cutting Tool Rake Angle = Shear Angle for Metal Cutting+Machining Friction Angle-(arccos(Force Produced Along Shear Plane/Resultant Force on Workpiece))

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

Go Resultant Force on Workpiece = (Force Produced Along Shear Plane)*(sec(Shear Angle for Metal Cutting+Machining Friction Angle-Cutting Tool Rake Angle))

Resultant force in merchant circle for given cutting force, friction and normal rake angles

Go Resultant Force on Workpiece = Cutting Force on Workpiece*(sec(Machining Friction Angle-Cutting Tool Rake Angle))

Mean normal stress in shear plane for given normal force and shear area

Go Normal Stress on Workpiece = Normal Force Induced on Workpiece/Shear Area on Workpiece

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

Resultant Force on Workpiece = (Force Produced Along Shear Plane)*(sec(Shear Angle for Metal Cutting+Machining Friction Angle-Cutting Tool Rake Angle))
R^' = (F_s)*(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 on Workpiece = (Force Produced Along Shear Plane)*(sec(Shear Angle for Metal Cutting+Machining Friction Angle-Cutting Tool Rake Angle)) to calculate the Resultant Force on Workpiece, 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 on Workpiece 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 Produced Along Shear Plane (F_s), Shear Angle for Metal Cutting (ϕ^'), Machining Friction Angle (β^') & Cutting Tool 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 -> 170.0033 = (96.5982)*(sec(0.476474885794362+0.640448569019199-0.150473561460663)).

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^' = (F_s)*(sec(ϕ^'+β^'-α^')) or Resultant Force on Workpiece = (Force Produced Along Shear Plane)*(sec(Shear Angle for Metal Cutting+Machining Friction Angle-Cutting Tool Rake Angle)). Force produced along shear plane Force Produced Along Shear Plane, Shear angle for metal cutting is the inclination of the shear plane with the horizontal axis at machining point, Machining 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 & Cutting tool 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 on Workpiece = (Force Produced Along Shear Plane)*(sec(Shear Angle for Metal Cutting+Machining Friction Angle-Cutting Tool Rake Angle)). To calculate R in merchant circle for given force along shear force, shear, friction and normal rake angles, you need Force Produced Along Shear Plane (F_s), Shear Angle for Metal Cutting (ϕ^'), Machining Friction Angle (β^') & Cutting Tool Rake Angle (α^'). With our tool, you need to enter the respective value for Force Produced Along Shear Plane, Shear Angle for Metal Cutting, Machining Friction Angle & Cutting Tool 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 on Workpiece?

In this formula, Resultant Force on Workpiece uses Force Produced Along Shear Plane, Shear Angle for Metal Cutting, Machining Friction Angle & Cutting Tool Rake Angle. We can use 1 other way(s) to calculate the same, which is/are as follows -

Resultant Force on Workpiece = Cutting Force on Workpiece*(sec(Machining Friction Angle-Cutting Tool Rake Angle))

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