Final answer:
The shear plane angle and shear strain in an orthogonal cutting operation can be calculated using the chip thickness ratio and the rake angle. The shear plane angle is derived from Merchant's Circle Diagram equations, and the shear strain can be estimated using the natural logarithm of the chip thickness ratio.
Step-by-step explanation:
The operation being described involves calculating the shear plane angle (φ) and the shear strain during an orthogonal machining process. To find the shear plane angle, one can use the Merchant's Circle Diagram and relevant equations, typically including the rake angle (α) and the ratio of chip thickness before and after the cut. As per Merchant's theory, the equation to find the shear plane angle is given by:
tan(φ) = α + tan(α) / (1 - r), where r is the chip thickness ratio (t1/t2).
For the provided values, rake angle α = 12°, initial chip thickness t1 = 0.25 mm and final chip thickness t2 = 0.70 mm, so the chip thickness ratio r = t1/t2 = 0.25/0.70. Plugging the values into the above equation allows calculation of φ.
To calculate the shear strain, you use the definition.
Shear strain γ = Ax/Lo, where Ax is the difference between the final and the initial length, and Lo is the original length. In cutting operations, shear strain can be estimated using chip thickness values, and is given by:
γ = ln(t2/t1).
Using the given chip thicknesses the shear strain can be calculated.