Engineering

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

Last Updated on March 4, 2021

The image above represents shear angle.

To compute for shear angle, two essential parameters are needed and these parameters are Cutting Ratio (r) and Rake Angle (α).

The formula for calculating for shear angle:

φ = tan-1[rcosα / 1 – rsinα]

Where:

φ = Shear Angle
r = Cutting Ratio
α = Rake Angle

Let’s solve an example;
Find the shear angle when the cutting ratio is 24 and the rake angle is 8.

This implies that;

r = Cutting Ratio = 24
α = Rake Angle = 8

φ = tan-1[rcosα / 1 – rsinα]
φ = tan-1[24 x cos8° / 1 – 24 x sin8°]
φ = tan-1[24 x 0.99 / 1 – 24 x 0.139]
φ = tan-1[23.766 / 1 – 3.34]
φ = tan-1[23.766 / -2.34]
φ = tan-1[-10.155]
φ = -84.37

Therefore, the  shear angle is -84.37°.

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 Mechanics of Chips Formation under Metal Forming Processes

Now, Click on Shear Angle under Mechanics of Chips Formation

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 Cutting Ratio (r) and Rake Angle (α).

Now, enter the values appropriately and accordingly for the parameters as required by the Cutting Ratio (r) is 24 and Rake Angle (α) is 8.

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.

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