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

✖Resultant Force in Metal Cutting is the vector sum of cutting force and thrust force.ⓘ Resultant Force in Metal Cutting [R_f]			+10% -10%
✖Shear Angle in Metal Cutting is the inclination of the shear plane with the horizontal axis at machining point.ⓘ Shear Angle in Metal Cutting [φ_shr]			+10% -10%
✖Friction Angle in Metal Cutting is termed as the angle between the tool and chip, which resists the flow of the chip along the rake face of the tool is friction force.ⓘ Friction Angle in Metal Cutting [β_fr]			+10% -10%
✖Rake Angle in Metal Cutting is the angle of orientation of tool’s rake surface from the reference plane and measured on machine longitudinal plane.ⓘ Rake Angle in Metal Cutting [α_rk]			+10% -10%

✖Force alongside Shear Plane is the shear force along the shear plane.ⓘ Force along shear force for given R of merchant circle, shear, friction, and normal rake angles [F_sp]

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

Formula

`"F"_{"sp"} = ("R"_{"f"})*(cos("φ"_{"shr"}+"β"_{"fr"}-"α"_{"rk"}))`

Example

`"7.424621N"=("10.5N")*(cos("43°"+"11°"-"9°"))`

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

STEP 0: Pre-Calculation Summary

Formula Used

Force Alongside Shear Plane = (Resultant Force in Metal Cutting)*(cos(Shear Angle in Metal Cutting+Friction Angle in Metal Cutting-Rake Angle in Metal Cutting))
F_sp = (R_f)*(cos(φ_shr+β_fr-α_rk))
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

Force Alongside Shear Plane - (Measured in Newton) - Force alongside Shear Plane is the shear force along the shear plane.
Resultant Force in Metal Cutting - (Measured in Newton) - Resultant Force in Metal Cutting is the vector sum of cutting force and thrust force.
Shear Angle in Metal Cutting - (Measured in Radian) - Shear Angle in Metal Cutting is the inclination of the shear plane with the horizontal axis at machining point.
Friction Angle in Metal Cutting - (Measured in Radian) - Friction Angle in Metal Cutting is termed as the angle between the tool and chip, which resists the flow of the chip along the rake face of the tool is friction force.
Rake Angle in Metal Cutting - (Measured in Radian) - Rake Angle in Metal Cutting 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

Resultant Force in Metal Cutting: 10.5 Newton --> 10.5 Newton No Conversion Required
Shear Angle in Metal Cutting: 43 Degree --> 0.750491578357421 Radian (Check conversion here)
Friction Angle in Metal Cutting: 11 Degree --> 0.19198621771934 Radian (Check conversion here)
Rake Angle in Metal Cutting: 9 Degree --> 0.15707963267946 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

F_sp = (R_f)*(cos(φ_shr+β_fr-α_rk)) --> (10.5)*(cos(0.750491578357421+0.19198621771934-0.15707963267946))

Evaluating ... ...

F_sp = 7.42462120245984

STEP 3: Convert Result to Output's Unit

7.42462120245984 Newton --> No Conversion Required

FINAL ANSWER

7.42462120245984 ≈ 7.424621 Newton <-- Force Alongside Shear Plane

(Calculation completed in 00.004 seconds)

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Home » Engineering » Production Engineering » Metal Cutting » Merchant Force Circle » Force Along Shear » Force along shear force for given R of merchant circle, 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!

< 3 Force Along Shear Calculators

Force along Shear Force given Cutting Force and Thrust Force

Go Force Along Shear Force in Metal Cutting = (Force During Cutting*cos(Shear Angle in Metal Cutting))-(Axial Thrust on Job*sin(Shear Angle in Metal Cutting))

Force along shear force for given force normal to shear force, shear, friction and normal rake angle

Go Force Along Shear Force in Metal Cutting = (Normal Force)/(tan(Shear Angle in Metal Cutting+Friction Angle in Metal Cutting-Normal Rake Angle in Metal Cutting))

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

Go Force Alongside Shear Plane = (Resultant Force in Metal Cutting)*(cos(Shear Angle in Metal Cutting+Friction Angle in Metal Cutting-Rake Angle in Metal Cutting))

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

Force Alongside Shear Plane = (Resultant Force in Metal Cutting)*(cos(Shear Angle in Metal Cutting+Friction Angle in Metal Cutting-Rake Angle in Metal Cutting))
F_sp = (R_f)*(cos(φ_shr+β_fr-α_rk))

What is the force along shear plane?

Force along shear plane is the shear force which causes shear deformation to occur in the shear plane

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

Force along shear force for given R of merchant circle, shear, friction, and normal rake angles calculator uses Force Alongside Shear Plane = (Resultant Force in Metal Cutting)*(cos(Shear Angle in Metal Cutting+Friction Angle in Metal Cutting-Rake Angle in Metal Cutting)) to calculate the Force Alongside Shear Plane, The Force along shear force for given R of merchant circle, shear, friction, and normal rake angles formula is defined as the cosine of the resultant force on the tool. Force Alongside Shear Plane is denoted by F_sp symbol.

How to calculate Force along shear force for given R of merchant circle, shear, friction, and normal rake angles using this online calculator? To use this online calculator for Force along shear force for given R of merchant circle, shear, friction, and normal rake angles, enter Resultant Force in Metal Cutting (R_f), Shear Angle in Metal Cutting (φ_shr), Friction Angle in Metal Cutting (β_fr) & Rake Angle in Metal Cutting (α_rk) and hit the calculate button. Here is how the Force along shear force for given R of merchant circle, shear, friction, and normal rake angles calculation can be explained with given input values -> 7.160983 = (10.5)*(cos(0.750491578357421+0.19198621771934-0.15707963267946)).

FAQ

What is Force along shear force for given R of merchant circle, shear, friction, and normal rake angles?

The Force along shear force for given R of merchant circle, shear, friction, and normal rake angles formula is defined as the cosine of the resultant force on the tool and is represented as F_sp = (R_f)*(cos(φ_shr+β_fr-α_rk)) or Force Alongside Shear Plane = (Resultant Force in Metal Cutting)*(cos(Shear Angle in Metal Cutting+Friction Angle in Metal Cutting-Rake Angle in Metal Cutting)). Resultant Force in Metal Cutting is the vector sum of cutting force and thrust force, Shear Angle in Metal Cutting is the inclination of the shear plane with the horizontal axis at machining point, Friction Angle in Metal Cutting is termed as the angle between the tool and chip, which resists the flow of the chip along the rake face of the tool is friction force & Rake Angle in Metal Cutting is the angle of orientation of tool’s rake surface from the reference plane and measured on machine longitudinal plane.

How to calculate Force along shear force for given R of merchant circle, shear, friction, and normal rake angles?

The Force along shear force for given R of merchant circle, shear, friction, and normal rake angles formula is defined as the cosine of the resultant force on the tool is calculated using Force Alongside Shear Plane = (Resultant Force in Metal Cutting)*(cos(Shear Angle in Metal Cutting+Friction Angle in Metal Cutting-Rake Angle in Metal Cutting)). To calculate Force along shear force for given R of merchant circle, shear, friction, and normal rake angles, you need Resultant Force in Metal Cutting (R_f), Shear Angle in Metal Cutting (φ_shr), Friction Angle in Metal Cutting (β_fr) & Rake Angle in Metal Cutting (α_rk). With our tool, you need to enter the respective value for Resultant Force in Metal Cutting, Shear Angle in Metal Cutting, Friction Angle in Metal Cutting & Rake Angle in Metal Cutting and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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