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(Resultant Force/Force along shear plane))+Rake Angle-Shear angle
β = (arccos(R/Fs))+α-ϕ
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.
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.
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
Resultant Force: 8 Newton --> 8 Newton No Conversion Required
Force along shear plane: 26 Newton --> 26 Newton No Conversion Required
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
β = (arccos(R/Fs))+α-ϕ --> (arccos(8/26))+0.149400183970687-0.785398163397301
Evaluating ... ...
β = 0.622031625426738
STEP 3: Convert Result to Output's Unit
0.622031625426738 Radian -->35.6397868606213 Degree (Check conversion here)
FINAL ANSWER
35.6397868606213 35.63979 Degree <-- Friction Angle
(Calculation completed in 00.004 seconds)

Credits

Created by Shikha Maurya
Indian Institute of Technology (IIT), Bombay
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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+Cutting Force*tan(Normal Rake Angle))/(Cutting Force-Thrust force*tan(Normal Rake Angle))
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)))+(Axial Thrust*(cos(Normal Rake Angle)))
Friction angle for given R of merchant circle, force along shear, shear, and normal rake angle
Go Friction Angle = (arccos(Resultant Force/Force along shear plane))+Rake Angle-Shear angle
Coefficient of Friction given Forces Normal and along Tool Rake Face
Go Coefficient of Friction = Force of Friction/Normal Force
Coefficient of friction for given friction angle
Go Coefficient of Friction = tan(Angle of Friction)
Shear force acting on shear plane for given shear stress and area of shear plane
Go Shear Force = Shear Stress*Area of Shear Plane

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

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

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(Resultant Force/Force along shear plane))+Rake Angle-Shear angle 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 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 Resultant Force (R), Force along shear plane (Fs), Rake Angle (α) & Shear angle (ϕ) 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 -> 2042.009 = (arccos(8/26))+0.149400183970687-0.785398163397301.

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 = (arccos(R/Fs))+α-ϕ or Friction Angle = (arccos(Resultant Force/Force along shear plane))+Rake Angle-Shear angle. Resultant force is the vector sum of cutting force and thrust force, Force along shear plane is the shear force along the shear plane, 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 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(Resultant Force/Force along shear plane))+Rake Angle-Shear angle. To calculate Friction angle for given R of merchant circle, force along shear, shear, and normal rake angle, you need Resultant Force (R), Force along shear plane (Fs), Rake Angle (α) & Shear angle (ϕ). With our tool, you need to enter the respective value for Resultant Force, Force along shear plane, 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.
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