GATE ME 2022 Set 1 — Question 54
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Manufacturing Processes → Machining & Machine Tools → Merchant's Circle & Forces
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Question
Under orthogonal cutting condition, a turning operation is carried out on a metallic workpiece at a cutting speed of . The orthogonal rake angle of the cutting tool is . The uncut chip thickness and width of cut are and , respectively. In this turning operation, the resulting friction angle and shear angle are and , respectively. If the dynamic yield shear strength of the workpiece material under this cutting condition is , then the cutting force is ______________ (round off to one decimal place).
Correct answer
2570 to 2576
Solution
Given parameters:
The shear area () is calculated as:The shear force is:Step 2: Calculate the cutting force () using Merchant's circle relationships.
The relationship between shear force and cutting force is given by:Alternatively, using the resultant force :Combining these, we get:Substituting the given values:Rounding off to one decimal place, the cutting force is .
- Cutting speed
- Rake angle
- Uncut chip thickness
- Width of cut
- Friction angle
- Shear angle
- Dynamic yield shear strength
The shear area () is calculated as:The shear force is:Step 2: Calculate the cutting force () using Merchant's circle relationships.
The relationship between shear force and cutting force is given by:Alternatively, using the resultant force :Combining these, we get:Substituting the given values:Rounding off to one decimal place, the cutting force is .
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