Shear angle for given Resultant force, force along shear force, friction, and normal rake angles Solution

STEP 0: Pre-Calculation Summary
Formula Used
Shear angle = Rake Angle-Friction Angle+(arccos(Resultant Force/Force along shear plane))
ϕ = α-β+(arccos(R/Fs))
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
Shear angle - (Measured in Radian) - Shear angle is the inclination of the shear plane with the horizontal axis at machining point.
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.
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.
STEP 1: Convert Input(s) to Base Unit
Rake Angle: 8.56 Degree --> 0.149400183970687 Radian (Check conversion here)
Friction Angle: 15 Degree --> 0.2617993877991 Radian (Check conversion here)
Resultant Force: 8 Newton --> 8 Newton No Conversion Required
Force along shear plane: 26 Newton --> 26 Newton No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
ϕ = α-β+(arccos(R/Fs)) --> 0.149400183970687-0.2617993877991+(arccos(8/26))
Evaluating ... ...
ϕ = 1.14563040102494
STEP 3: Convert Result to Output's Unit
1.14563040102494 Radian -->65.6397868606213 Degree (Check conversion here)
FINAL ANSWER
65.6397868606213 65.63979 Degree <-- Shear angle
(Calculation completed in 00.004 seconds)

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!

4 Force Normal to Shear Calculators

Force normal to shear force for given cutting force, thrust force, and shear angle
Go Normal Force = (Cutting Force*(sin(Shear angle)))+(Axial Thrust*(cos(Shear angle)))
Shear angle for given Resultant force, force along shear force, friction, and normal rake angles
Go Shear angle = Rake Angle-Friction Angle+(arccos(Resultant Force/Force along shear plane))
Cutting Shear Force given Uncut Chip Thickness and Shear Angle
Go Shear Force = (Shear Stress in Bolt*Width of cut*Uncut Chip Thickness)/sin(Shear angle)
Force normal to shear force for given mean normal shear stress and area of shear plane
Go Normal Force = Shear Stress*Shear Area

Shear angle for given Resultant force, force along shear force, friction, and normal rake angles Formula

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

What is Shear angle

Shear angle is the angle formed between shear force acting on shear plane and the longitudinal plane of the work piece

How to Calculate Shear angle for given Resultant force, force along shear force, friction, and normal rake angles?

Shear angle for given Resultant force, force along shear force, friction, and normal rake angles calculator uses Shear angle = Rake Angle-Friction Angle+(arccos(Resultant Force/Force along shear plane)) to calculate the Shear angle, Shear angle for given Resultant force, force along shear force, friction, and normal rake angles is inclination between the shear plane and longitudinal plane. Shear angle is denoted by ϕ symbol.

How to calculate Shear angle for given Resultant force, force along shear force, friction, and normal rake angles using this online calculator? To use this online calculator for Shear angle for given Resultant force, force along shear force, friction, and normal rake angles, enter Rake Angle (α), Friction Angle (β), Resultant Force (R) & Force along shear plane (Fs) and hit the calculate button. Here is how the Shear angle for given Resultant force, force along shear force, friction, and normal rake angles calculation can be explained with given input values -> 3760.883 = 0.149400183970687-0.2617993877991+(arccos(8/26)).

FAQ

What is Shear angle for given Resultant force, force along shear force, friction, and normal rake angles?
Shear angle for given Resultant force, force along shear force, friction, and normal rake angles is inclination between the shear plane and longitudinal plane and is represented as ϕ = α-β+(arccos(R/Fs)) or Shear angle = Rake Angle-Friction Angle+(arccos(Resultant Force/Force along shear plane)). Rake Angle is the angle of orientation of tool’s rake surface from the reference plane and measured on machine longitudinal plane, 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 is the vector sum of cutting force and thrust force & Force along shear plane is the shear force along the shear plane.
How to calculate Shear angle for given Resultant force, force along shear force, friction, and normal rake angles?
Shear angle for given Resultant force, force along shear force, friction, and normal rake angles is inclination between the shear plane and longitudinal plane is calculated using Shear angle = Rake Angle-Friction Angle+(arccos(Resultant Force/Force along shear plane)). To calculate Shear angle for given Resultant force, force along shear force, friction, and normal rake angles, you need Rake Angle (α), Friction Angle (β), Resultant Force (R) & Force along shear plane (Fs). With our tool, you need to enter the respective value for Rake Angle, Friction Angle, Resultant Force & Force along shear plane and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
Let Others Know
Facebook
Twitter
Reddit
LinkedIn
Email
WhatsApp
Copied!