Final answer:
The feed rate must be reduced by a specific factor calculated from Taylor's tool life equation using the exponents n=0.5 and y=0.6 to maintain constant tool life after increasing the cutting speed by 50% for a ceramic cutting tool.
Step-by-step explanation:
The correct answer is that the feed rate must be reduced to compensate for the increased speed in order to maintain a constant tool life when using a ceramic cutting tool. According to the Taylor's tool life equation, which can be represented as VT^{n} = C, where V is the cutting speed, T is the tool life, n is the Taylor's exponent, and C is a constant specific to the cutting conditions, increasing the cutting speed (V) by 50% means that you multiply V by 1.5. After increasing the speed, to maintain the same tool life (T), we can rearrange the equation to find the new feed rate by using the relationship with the constant y, as specified by the tool life equation for feed and speed, which states that (feed)^{y} * (speed)^{n} = constant, where y is the exponent for feed rate. With n being 0.5 and y being 0.6 in the original state, we calculate the new feed rate factor accordingly.
By inserting the values into the equation, we solve it step-by-step to find out by what factor the feed rate must be modified:
Calculate the new constant for the increased speed: C' = (1.5V)^{n} * T
Find the ratio of the new constant to the old one: ratio = C' / C
Adjust feed rate: (new feed)^{y} = (old feed)^{y} / ratio, and hence find the new feed rate.