Calculating Shear Plane Angle & Strain in Orthogonal Cutting Operation

[GameReaper88]

In an orthogonal cutting operation, the 0.250 in wide tool has a rake angle of 6 degrees. The lathe is set so the chip thickness before the cut is 0.011 in. After the cut,t he deformed chip thickness is measured to be 0.027 in. Calculate (a) the shear plane angle and (b) the shear strain for the operation.

I really don't know where to begin other then to say I am now neck deep in a class that had no math prerequisite.
I don't have much math knowledge beyond minor algebra. Even with the help of the tutoring center here in my university and living with the book in front of my face I really don't understand what I am supposed to be doing here.

 

[Navin A S]

A. Shear Plane Angle = The shear plane angle is the angle between the cutting tool and the workpiece surface. It can be calculated using the following equation:Shear Plane Angle = tan-1 (rake angle / chip thickness ratio)Therefore, the shear plane angle for this operation is:Shear Plane Angle = tan-1(6 degrees / (0.027 in/ 0.011 in)) = 60.4 degrees B. Shear Strain = The shear strain is the ratio of the change in the chip thickness to the original chip thickness. It can be calculated using the following equation:Shear Strain = (deformed chip thickness - original chip thickness) / original chip thicknessTherefore, the shear strain for this operation is:Shear Strain = (0.027 in - 0.011 in) / 0.011 in = 1.45

 

[oswaler]

I understand your frustration with being thrown into a class without the necessary mathematical background. However, let's break down the problem step by step and see if we can make sense of it.

First, let's define some terms. In an orthogonal cutting operation, the tool is cutting at a 90 degree angle to the workpiece. The rake angle is the angle between the tool face and the workpiece surface. The chip thickness is the thickness of the material being removed by the cutting tool.

Now, let's look at the given information. The tool has a rake angle of 6 degrees and a width of 0.250 inches. The chip thickness before the cut is 0.011 inches and after the cut, it is 0.027 inches.

To calculate the shear plane angle, we need to use the following formula:

Shear Plane Angle = arctan (Chip Thickness / Tool Width)

Substituting the given values, we get:

Shear Plane Angle = arctan (0.011 / 0.250) = 2.52 degrees

This means that the shear plane angle for this operation is 2.52 degrees.

Next, let's calculate the shear strain. Shear strain is a measure of the deformation of a material due to shear stress. It is given by the following formula:

Shear Strain = (Final Chip Thickness - Initial Chip Thickness) / Initial Chip Thickness

Substituting the given values, we get:

Shear Strain = (0.027 - 0.011) / 0.011 = 1.45

This means that the shear strain for this operation is 1.45.

I hope this helps to clarify the problem for you. If you need further assistance, I would recommend seeking help from your professor or a tutor who can explain the concepts in a way that is more familiar to you. Mathematics can be challenging, but with practice and guidance, you can become more comfortable with it. Best of luck in your studies.