Shear Angle Calculator

✖Width is the measurement or extent of something from side to side.ⓘ Width [w]			+10% -10%
✖Theta is an angle that can be defined as the figure formed by two rays meeting at a common endpoint.ⓘ Theta [θ]			+10% -10%

✖Shear angle metal is the inclination of the shear plane with the horizontal axis at machining point.ⓘ Shear Angle [ϕ]

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Shear Angle Solution

STEP 0: Pre-Calculation Summary

Formula Used

Shear Angle Metal = atan(Width*cos(Theta)/(1-Width*sin(Theta)))
ϕ = atan(w*cos(θ)/(1-w*sin(θ)))
This formula uses 4 Functions, 3 Variables

Functions Used

sin - Sine is a trigonometric function that describes the ratio of the length of the opposite side of a right triangle to the length of the hypotenuse., sin(Angle)
cos - Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle., cos(Angle)
tan - The tangent of an angle is a trigonometric ratio of the length of the side opposite an angle to the length of the side adjacent to an angle in a right triangle., tan(Angle)
atan - Inverse tan is used to calculate the angle by applying the tangent ratio of the angle, which is the opposite side divided by the adjacent side of the right triangle., atan(Number)

Variables Used

Shear Angle Metal - (Measured in Radian) - Shear angle metal is the inclination of the shear plane with the horizontal axis at machining point.
Width - (Measured in Meter) - Width is the measurement or extent of something from side to side.
Theta - (Measured in Radian) - Theta is an angle that can be defined as the figure formed by two rays meeting at a common endpoint.

STEP 1: Convert Input(s) to Base Unit

Width: 255 Millimeter --> 0.255 Meter (Check conversion here)
Theta: 30 Degree --> 0.5235987755982 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

ϕ = atan(w*cos(θ)/(1-w*sin(θ))) --> atan(0.255*cos(0.5235987755982)/(1-0.255*sin(0.5235987755982)))

Evaluating ... ...

ϕ = 0.247901422197684

STEP 3: Convert Result to Output's Unit

0.247901422197684 Radian -->14.2037052272207 Degree (Check conversion here)

FINAL ANSWER

14.2037052272207 ≈ 14.20371 Degree <-- Shear Angle Metal

(Calculation completed in 00.008 seconds)

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Created by Anirudh Singh

National Institute of Technology (NIT), Jamshedpur

Anirudh Singh has created this Calculator and 300+ more calculators!

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< Metal Cutting Calculators

Shear Plane Angle

LaTeX Go Shear Angle Metal = arctan((Chip Ratio*cos(Rake Angle))/(1-Chip Ratio*sin(Rake Angle)))

Shear Angle

LaTeX Go Shear Angle Metal = atan(Width*cos(Theta)/(1-Width*sin(Theta)))

Shear Force

LaTeX Go Shear Force = Centripetal Force*cos(Theta)-Tangential Force*sin(Theta)

Shear Strain

LaTeX Go Shear Strain = tan(Shear Angle Metal)+cot(Shear Angle Metal-Rake Angle)

Shear Angle Formula

LaTeX Go

Shear Angle Metal = atan(Width*cos(Theta)/(1-Width*sin(Theta)))
ϕ = atan(w*cos(θ)/(1-w*sin(θ)))

What is Shear Angle?

In orthogonal cutting, shear angle is the angle between
(a) shear plane and the cutting velocity. (b) shear plane and the rake plane. (c) shear plane and the vertical direction. (d) shear plane and the direction of elongation of crystals in the chip.

How to Calculate Shear Angle?

Shear Angle calculator uses Shear Angle Metal = atan(Width*cos(Theta)/(1-Width*sin(Theta))) to calculate the Shear Angle Metal, Shear Angle is the angle between shear plane and the cutting velocity. Shear Angle Metal is denoted by ϕ symbol.

How to calculate Shear Angle using this online calculator? To use this online calculator for Shear Angle, enter Width (w) & Theta (θ) and hit the calculate button. Here is how the Shear Angle calculation can be explained with given input values -> -3856.335845 = atan(0.255*cos(0.5235987755982)/(1-0.255*sin(0.5235987755982))).

FAQ

What is Shear Angle?

Shear Angle is the angle between shear plane and the cutting velocity and is represented as ϕ = atan(w*cos(θ)/(1-w*sin(θ))) or Shear Angle Metal = atan(Width*cos(Theta)/(1-Width*sin(Theta))). Width is the measurement or extent of something from side to side & Theta is an angle that can be defined as the figure formed by two rays meeting at a common endpoint.

How to calculate Shear Angle?

Shear Angle is the angle between shear plane and the cutting velocity is calculated using Shear Angle Metal = atan(Width*cos(Theta)/(1-Width*sin(Theta))). To calculate Shear Angle, you need Width (w) & Theta (θ). With our tool, you need to enter the respective value for Width & Theta 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 Shear Angle Metal?

In this formula, Shear Angle Metal uses Width & Theta. We can use 1 other way(s) to calculate the same, which is/are as follows -

Shear Angle Metal = arctan((Chip Ratio*cos(Rake Angle))/(1-Chip Ratio*sin(Rake Angle)))

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