Final answer:
Using Taylor's tool life equation and given parameters, the cutting speed for maximum production rate and minimum cost are computed by considering machining time, handling time, tool change time, operational costs, and tooling costs.
Step-by-step explanation:
To find the cutting speed for maximum production rate (a) and the cutting speed for minimum cost (b), the student must apply Taylor's tool life equation. This can also be related to determining the hourly production rate and the cost per piece for the cutting speeds computed.
Taylor's tool life equation is given by:
VT^n × T = C
where VT is the cutting speed, T is the tool life, n is the exponent dependent on the tool and work material, and C is the cutting speed for a tool life of one minute.
The cutting speed for maximum production rate is calculated by maximizing the number of parts produced in a given time, considering both machining time and non-machining time (handling and tool change). Whereas the cutting speed for minimum cost considers the total cost including the cost of machining, tooling, and hourly rates.
Let's look at an example using provided parameters:
- n = 0.125
- C = 70 m/min
- Work part length = 500 mm
- Diameter = 100 mm
- Feed = 0.25 mm/rev
- Handling time per piece = 5.0 min
- Tool change time = 2.0 min
- Cost of machine and operator = $30/hr
- Tooling cost = $3 per cutting edge
A more thorough mathematical approach would then be used to solve (a) and (b) based on these parameters.