Question

As the cutting speed increases, how do the machining cost and tooling cost behave?

• A. Machining cost decreases while tooling cost increases
• B. Both machining cost and tooling cost both increases
• C. Both machining cost and tooling cost both decreases
• D. Machining cost increases while tooling cost decreases

Hint:

- High cutting speeds $\rightarrow$ Shorter machining times $\rightarrow$ Machining cost drops. - High cutting speeds $\rightarrow$ Accelerated tool wear rate $\rightarrow$ Tooling cost rises. The minimum point of the combined cost curve defines the economic cutting speed.

Answer 1

The Correct Option is A

Concept: In the economics of machining operations, the total cost per component is composed of several factors that vary with cutting speed (\( V \)): \[ \text{Total Cost} = \text{Machining Cost} + \text{Tooling Cost} + \text{Handling/Setup Cost} \]

Step 1: Analyze the behavior of Machining Cost with respect to speed. Machining cost is directly proportional to the time required to cut the feature: \[ \text{Machining Cost} \propto \text{Machining Time} (t_m) \] As the cutting speed \( V \) increases, the material removal rate (MRR) increases, which shortens the time required to complete the operation (\( t_m \)). Because less time is spent on the machine tool per part, the direct machining cost decreases.

Step 2: Analyze the behavior of Tooling Cost with respect to speed. According to Taylor's tool life equation (\( V T^n = C \)), raising the cutting speed exponentially shortens the tool life (\( T \)). As a result, the tool wears out faster, requiring more frequent tool changes, insert indexing, and higher replacement tool expenditures. Consequently, the tooling cost increases.