Machine Tool Wear

The Worcester Tool Grinding Company, a major machine fabrication firm, is looking to cut their machining costs. They are asking you to find the most economical cutting speed, V, for their top-of-the line widget. That is, they want you to find the cutting speed V that minimizes their cost per part. The cost factors they want you to consider are:

• Overhead and wages per part for the time actually spent machining;
• Overhead and wages per part for the time spent changing the cutting tool;
• Tool cost per part.

To help you in your task, WTG has provided the following data.

• Overhead and wages run approximately $45 per hour.
• Changing a tool takes approximately 5 minutes.
• The tools presently in use cost $3 each.

where L is the length of the ribbon of material removed during the process. The time for a tool bit to wear out enough that it must be replaced also depends on the cutting speed V. The engineers at WTG obtained the following data.