Friction angle for given R of merchant circle, force along shear, shear, and normal rake angle Calculator

✖Force along shear plane is the shear force along the shear plane.ⓘ Force along shear plane [Fs]			+10% -10%
✖Resultant Force on Job is the vector sum of cutting force and thrust force.ⓘ Resultant Force on Job [R_frc]			+10% -10%
✖Tool rake angle is the angle of orientation of tool’s rake surface from the reference plane and measured on machine longitudinal plane.ⓘ Tool Rake Angle [α_tool]			+10% -10%
✖Shearing angle in machining is the inclination of the shear plane with the horizontal axis at machining point.ⓘ Shearing Angle in Machining [ϕ_shr]			+10% -10%

✖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.ⓘ Friction angle for given R of merchant circle, force along shear, shear, and normal rake angle [β_frc]

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Friction angle for given R of merchant circle, force along shear, shear, and normal rake angle

Formula

`"β"_{"frc"} = (arccos("Fs"/"R"_{"frc"}))+"α"_{"tool"}-"ϕ"_{"shr"}`

Example

`"23.99938°"=(arccos("7.78N"/"13.46N"))+"8.56°"-"39.25°"`

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Friction angle for given R of merchant circle, force along shear, shear, and normal rake angle Solution

STEP 0: Pre-Calculation Summary

Formula Used

Friction Angle = (arccos(Force along shear plane/Resultant Force on Job))+Tool Rake Angle-Shearing Angle in Machining
β_frc = (arccos(Fs/R_frc))+α_tool-ϕ_shr
This formula uses 2 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)
arccos - Arccosine function, is the inverse function of the cosine function.It is the function that takes a ratio as an input and returns the angle whose cosine is equal to that ratio., arccos(Number)

Variables Used

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.
Force along shear plane - (Measured in Newton) - Force along shear plane is the shear force along the shear plane.
Resultant Force on Job - (Measured in Newton) - Resultant Force on Job is the vector sum of cutting force and thrust force.
Tool Rake Angle - (Measured in Radian) - Tool rake angle is the angle of orientation of tool’s rake surface from the reference plane and measured on machine longitudinal plane.
Shearing Angle in Machining - (Measured in Radian) - Shearing angle in machining 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: 7.78 Newton --> 7.78 Newton No Conversion Required
Resultant Force on Job: 13.46 Newton --> 13.46 Newton No Conversion Required
Tool Rake Angle: 8.56 Degree --> 0.149400183970687 Radian (Check conversion here)
Shearing Angle in Machining: 39.25 Degree --> 0.685041731407646 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

β_frc = (arccos(Fs/R_frc))+α_tool-ϕ_shr --> (arccos(7.78/13.46))+0.149400183970687-0.685041731407646

Evaluating ... ...

β_frc = 0.418868166952254

STEP 3: Convert Result to Output's Unit

0.418868166952254 Radian -->23.9993781387498 Degree (Check conversion here)

FINAL ANSWER

23.9993781387498 ≈ 23.99938 Degree <-- Friction Angle

(Calculation completed in 00.004 seconds)

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Home » Engineering » Production Engineering » Metal Cutting » Merchant Force Circle » Forces and Friction » Friction angle for given R of merchant circle, force along shear, shear, and normal rake angle

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

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< 6 Forces and Friction Calculators

Coefficient of friction for given thrust force, cutting force and normal rake angle

Go Coefficient of Friction = (Thrust Force on Workpiece+Cutting Force*tan(Normal Rake Angle of Tool))/(Cutting Force-Thrust Force on Workpiece*tan(Normal Rake Angle of Tool))

Frictional force along tool rake face for given cutting and thrust forces, normal rake angle

Go Frictional Force on Sleeve = (Cutting Force*(sin(Normal Rake Angle of Tool)))+(Force Normal on Workpiece*(cos(Normal Rake Angle of Tool)))

Friction angle for given R of merchant circle, force along shear, shear, and normal rake angle

Go Friction Angle = (arccos(Force along shear plane/Resultant Force on Job))+Tool Rake Angle-Shearing Angle in Machining

Shear force acting on shear plane for given shear stress and area of shear plane

Go Shear Force on Job = Shear Stress on Workpiece*Area of the Shear Plane

Coefficient of Friction given Forces Normal and along Tool Rake Face

Go Coefficient of Friction = Force of Friction/Normal Force on Workpiece

Coefficient of friction for given friction angle

Go Coefficient of Friction = tan(Angle of Friction)

Friction angle for given R of merchant circle, force along shear, shear, and normal rake angle Formula

Friction Angle = (arccos(Force along shear plane/Resultant Force on Job))+Tool Rake Angle-Shearing Angle in Machining
β_frc = (arccos(Fs/R_frc))+α_tool-ϕ_shr

What is Friction angle?

friction angle is the tan inverse of the ratio of the friction force and the normal force on the rake surface

How to Calculate Friction angle for given R of merchant circle, force along shear, shear, and normal rake angle?

Friction angle for given R of merchant circle, force along shear, shear, and normal rake angle calculator uses Friction Angle = (arccos(Force along shear plane/Resultant Force on Job))+Tool Rake Angle-Shearing Angle in Machining to calculate the Friction Angle, The Friction angle for given R of merchant circle, force along shear, shear, and normal rake angle formula is defined as the tan inverse of the coefficient of friction. Friction Angle is denoted by β_frc symbol.

How to calculate Friction angle for given R of merchant circle, force along shear, shear, and normal rake angle using this online calculator? To use this online calculator for Friction angle for given R of merchant circle, force along shear, shear, and normal rake angle, enter Force along shear plane (Fs), Resultant Force on Job (R_frc), Tool Rake Angle (α_tool) & Shearing Angle in Machining (ϕ_shr) and hit the calculate button. Here is how the Friction angle for given R of merchant circle, force along shear, shear, and normal rake angle calculation can be explained with given input values -> 1375.063 = (arccos(7.78/13.46))+0.149400183970687-0.685041731407646.

FAQ

What is Friction angle for given R of merchant circle, force along shear, shear, and normal rake angle?

The Friction angle for given R of merchant circle, force along shear, shear, and normal rake angle formula is defined as the tan inverse of the coefficient of friction and is represented as β_frc = (arccos(Fs/R_frc))+α_tool-ϕ_shr or Friction Angle = (arccos(Force along shear plane/Resultant Force on Job))+Tool Rake Angle-Shearing Angle in Machining. Force along shear plane is the shear force along the shear plane, Resultant Force on Job is the vector sum of cutting force and thrust force, Tool rake angle is the angle of orientation of tool’s rake surface from the reference plane and measured on machine longitudinal plane & Shearing angle in machining is the inclination of the shear plane with the horizontal axis at machining point.

How to calculate Friction angle for given R of merchant circle, force along shear, shear, and normal rake angle?

The Friction angle for given R of merchant circle, force along shear, shear, and normal rake angle formula is defined as the tan inverse of the coefficient of friction is calculated using Friction Angle = (arccos(Force along shear plane/Resultant Force on Job))+Tool Rake Angle-Shearing Angle in Machining. To calculate Friction angle for given R of merchant circle, force along shear, shear, and normal rake angle, you need Force along shear plane (Fs), Resultant Force on Job (R_frc), Tool Rake Angle (α_tool) & Shearing Angle in Machining (ϕ_shr). With our tool, you need to enter the respective value for Force along shear plane, Resultant Force on Job, Tool Rake Angle & Shearing Angle in Machining 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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