How to Calculate and Solve for Shear Angle | Merchant Force Circle

The image above represents shear angle. To calculate shear angle, two essential parameters are needed and these parameters are Rake Angle (in Radians) (α) and Angle of Friction (in Radians)(β).

The formula for calculating shear angle:

φ = ^π / ₄ – (β – α)

Where:

φ = Shear Angle
α = Rake Angle
β = Angle of Friction

Let’s solve an example;
Find the shear angle when the rake angle is 24 and the angle of friction is 10.

This implies that;

α = Rake Angle = 24
β = Angle of Friction = 10

φ = ^π / ₄ – (β – α)
That is, φ = ^π / ₄ – (10 – 24)
φ = 0.78 – -14
φ = 14.78

Therefore, the shear angle is 14.78 radians.

Calculating the Rake Angle when the Shear Angle and the Angle of Friction are Given

α = β – (^π / ₄ + φ)

Where;

α = Rake Angle
φ = Shear Angle
β = Angle of Friction

Let’s solve an example;
Find the rake angle when the shear angle is 20 and the angle of friction is 52.

This implies that;

φ = Shear Angle = 20
β = Angle of Friction = 52

α = β – (^π / ₄ + φ)
Then, α = 52 – (^π / ₄ + 20)
α = 52 – 20.78
α = 31.22

Therefore, the rake angle is 31.22 radians.

Read more: How to Calculate and Solve for Shear Angle | Mechanics of Chip Formation

Calculating the Angle of Friction when the Shear Angle and the Rake Angle are Given

β = (^π / ₄ + φ) + α

Where;

β = Angle of Friction
φ = Shear Angle
α = Rake Angle

Let’s solve an example;
Find the angle of friction when the shear angle is 16 and the rake angle is 10.

This implies that;

φ = Shear Angle = 16
α = Rake Angle = 10

β = (^π / ₄ + φ) + α
β = (^π / ₄ + 16) + 10
That is, β = 16.79 + 10
β = 26.79

Therefore, the angle of friction is 26.79 radians.

How to Calculate Shear Angle Using Nickzom Calculator

Nickzom Calculator – The Calculator Encyclopedia is capable of calculating the shear angle.

To get the answer and workings of the shear angle using the Nickzom Calculator – The Calculator Encyclopedia. First, you need to obtain the app.

You can get this app via any of these means:

Web – https://www.nickzom.org/calculator-plus

To get access to the professional version via web, you need to register and subscribe for NGN 2,000 per annum to have utter access to all functionalities.
You can also try the demo version via https://www.nickzom.org/calculator

Android (Paid) – https://play.google.com/store/apps/details?id=org.nickzom.nickzomcalculator
Android (Free) – https://play.google.com/store/apps/details?id=com.nickzom.nickzomcalculator
Apple (Paid) – https://itunes.apple.com/us/app/nickzom-calculator/id1331162702?mt=8
Once, you have obtained the calculator encyclopedia app, proceed to the Calculator Map, then click on Materials and Metallurgical under Engineering.

Now, Click on Metal Forming Processes under Materials and Metallurgical

Now, Click on Merchant Force Circle under Metal Forming Processes

That is, Click on Shear Angle under Merchant Force Circle

The screenshot below displays the page or activity to enter your values, to get the answer for the shear angle according to the respective parameters which is the Rake Angle (in Radians) (α) and Angle of Friction (in Radians) (β).

Now, enter the value appropriately and accordingly for the parameter as required by the Rake Angle (in Radians) (α) is 24 and Angle of Friction (in Radians) (β) is 10.

Finally, Click on Calculate

As you can see from the screenshot above, Nickzom Calculator– The Calculator Encyclopedia solves for the shear angle and presents the formula, workings and steps too.