Question

A 150-mm-long, 75-mm-diameter titanium alloy rod is being reduced in diameter to 65 mm by turning on a lathe in one pass. The spindle rotates at 400 rpm and the tool is traveling at arn axial velocity of 200 mm/min. The unit power required for cutting titanium alloy is 3.5 a) Calculate the cutting speed. (1 points) b) Calculate the material removal rate. (2 points) c) Calculate the time of cut. (1 points) d) Calculate the power required. (2 points) e) Calculate the cutting force. (1 points)

Answer 1

The cutting speed can be calculated by finding the circumference of the rod and multiplying it by the spindle speed. The material removal rate can be determined by finding the volume difference between the original and reduced cylinders and dividing it by the time of cut. The time of cut can be calculated by dividing the length of the rod by the axial velocity. The power required can be found by multiplying the cutting force by the cutting speed. The cutting force can be calculated using the formula Cutting Force = Power / Cutting Speed.

Step-by-step explanation:

To calculate the cutting speed, we need to find the circumference of the rod and then multiply it by the spindle speed. The circumference is 2πr, where r is the radius of the rod. In this case, the radius is half the diameter, so r = 75 mm / 2 = 37.5 mm. Converting to meters, the radius is 0.0375 m. The cutting speed is then 2π(0.0375 m)(400 rpm).

To calculate the material removal rate, we need to find the volume of material being removed in one pass. Since the rod is being reduced in diameter, we can consider it as a cylinder with the volume of the removed material as the difference between the volumes of the two cylinders. The volume of the original cylinder is π(0.075 m)^2(0.150 m), and the volume of the reduced cylinder is π(0.065 m)^2(0.150 m). The material removal rate is then the volume difference divided by the time of cut, which is 200 mm/min.

To calculate the time of cut, we can use the axial velocity and the length of the rod. The time of cut is the length of the rod divided by the axial velocity, which is 150 mm / 200 mm/min.

To calculate the power required, we can use the formula Power = Force x Velocity. The force in this case is the cutting force and the velocity is the cutting speed. The power required is then the cutting force multiplied by the cutting speed.

To calculate the cutting force, we can use the formula Cutting Force = Power / Cutting Speed. Substituting the values we have, the cutting force is 3.5 / (2π(0.0375 m)(400 rpm)).