Question

The Taylorian tool life equation is provided by VTn = C, where n and C are constants, and is used to calculate tool life while cutting C-40 steel with an 18: 4: 1 H.S.S. cutting tool at a feed rate of 0.2 mm/min and a depth of cut of 2 mm. It has been recorded the following V and T observations. V1 m/min 22 40 T1 85 20 Calculate (i) n and C (ii) Consequently, suggest a 60-minute tool life at the recommended cutting speed.

Answer 1

By creating two equations from the provided V and T values using the Taylorian tool life equation, we can solve for the constants n and C. Once obtained, we can determine the cutting speed that allows a tool life of 60 minutes.

Step-by-step explanation:

Calculation of the Taylorian Tool Life Equation Constants

We have the Taylorian tool life equation VTn = C, where V is the cutting speed, T is the tool life, and n and C are constants. Given the data for two sets of V and T values, we can set up two equations based on the tool life equation.

• For V1 = 22 m/min and T1 = 85 minutes: (22)n * 85 = C
• For V2 = 40 m/min and T2 = 20 minutes: (40)n * 20 = C

By dividing the second equation by the first, we get:

(40/22)n = 85/20

We solve for n using logarithms, and then we can substitute back to find C.

Recommendation for 60-minute Tool Life

Once we have n and C, we can calculate the recommended cutting speed for a 60-minute tool life:

V(60)n = C

This equation can be solved for V to find the cutting speed that would allow for a tool life of 60 minutes.