1. A cylindrical stainless steel rod with length L=150 mm, diameter D0 = 12 mm is being reduced in
diameter to Df =11 mm by turning on a lathe. The spindle rotates at N = 400 rpm, and the tool is
travelling at an axial speed of υ=200 mm/min
Calculate:
a. The cutting speed V (maximum and minimum)
b. The material removal rate MRR
c. The cutting time t
d. The power required if the unit power is estimated to 4 w.s/mm3
SOLUTION:
a. The maximum cutting speed is at the outer diameter D0, and is obtained from the expression
V = π D0 N
Thus,
Vmax = (π) (12) (400) = 15072 mm/min
The cutting speed at the inner diameter Df is
Vmin = (π) (11) (400) = 13816 mm/min
b. From the information given, the depth of cut is
d = (12 – 11) / 2 = 0,5 mm
and the feed is
f = υ / Ν
f = 200 / 400 = 0,5 mm/rev
thus the material removal rate is calculated as
MRR = (π) (Davg) (d) (f) (N) = (π) (11,5) (0,5) (0,5) (400) = 3611 mm3/min = 60,2 mm3/s
c. The cutting time is
t = l / (f. N) = (150) / (0,5) (400) = 0,75 min
d. The power required is
Power = (4) (60,2) = 240,8 W
2. The part shown below will be turned in two machining steps. In the first step a length of (50 + 50) = 100 mm will be
reduced from Ø100 mm to Ø80 mm and in the second step a length of 50 mm will be reduced from Ø80 mm to Ø60
mm. Calculate the required total machining time T with the following cutting conditions:
Cutting speed V=80 m/min,
Feed is f=0.8 mm/rev,
Depth of cut = 3 mm per pass.
SOLUTION:
V=80 m/min
f=0.8 mm/rev
The turning will be done in 2 steps. In first step a length of (50 + 50) = 100 mm will be reduced from
Ø100 mm to Ø80 mm and in second step a length of 50 mm will be reduced from Ø80 mm to Ø60 mm.
3. The shaft shown in the figure below is to be machined on a lathe from a Ø 25mm bar. Calculate the
machining time if speed V is 60 m/min., turning feed is 0.2mm/rev, drilling feed is 0.08 mm/rev and knurling
feed is 0.3 mm/rev.
Turning, drilling, knurling
SOLUTION:
4. A batch of 800 workpieces is to be produced on a turning machine. Each workpiece with length L=120mm
and diameter D=10mm is to be machined from a raw material of L=120mm and D=12mm using a cutting
speed V=32 m/min and a feedrate f=0.8 mm/rev. How many times we have to resharpen or regrind the
cutting tool?
In the Taylor’s expression, use constants as n=1.25 and C=175.
