MACHINE OPERATION CALCULATIONS I.
Turning
A. Machine Speed: To achieve achieve a specific specific cutting speed:
N =
k*V *
N = machine machine speed in revolutions/mi revolutions/minute nute (RPM) k is a constant to “correct” speed (V) and part diameter (Di ) units V is desired cutting speed, a Handbook Value D1 is largest part diameter (initial size) V given in surface feet per minute (SFPM), D 1 in inches: k = 12 V given in meters per second (MPS), D1 in mm: k = 60000 V given in meters per minute (MPM), D1 in mm: k = 1000 If Cutting Speed for a given RPM rate is desired, solve above equation for V: V = π ND/k B. Cutting Time: minutes per operation CT is cutting time per “pass” L is length cut A is “allowance” or starting offset f r r is machine feed rate units/revolution, a Handbook Value
C. Material Removal Rate (MRR or Q): Volume Removed
(L + A)
CT =
f r * N
cutting time
MRR =
π
2
2
* L (D1 - D2 ) 4L f r N
D2 is Finished Diameter
D1 - D2 D1 + D 2 ] * [ ] 2 2 D1 D1 - D2 [ ] t 2 D1 + D2 [ ] 1 2 D1
MRR = k f r V [
≈
≈
Substituting for N from above:
and:
t is Depth of cut (inch or mm)
MRR Therefore:
≈
k V f r t
II. Boring
A. Machine Speed: as above except D1 is the finished (larger) diameter B. Cutting Time: same as above C: Material Removal Rate: as above except D1 is finished diameter while D2 is Initial (smaller) diameter. III. Facing, Slot Cutting or Cut Off
In facing, slot (plunge) cutting and cut off, the cutting speed for a given RPM decreases as the tool progresses toward the center of the piece being cut. This follows since most (manual) lathes cannot increase spindle speed (N) during cutting operations. Thus, the required N is calculated as above using the outside (largest) diameter of the part for a given V. A. Machine Speed
N =
k* V π
* D1
If Cutting Speed for a given RPM rate is desired, solve above equation for V: V = π ND/k
B. Cutting Time
(L + A)
CT =
f r * N
C. Material Removal Rate (here D1 is Outside Diameter)
MRR =
Vol.Removed CT
where: L is
D1 2
for solids;
π
=
D1 - Di 2
2
D1 f r tN 4*L for tubes
Di is inside diameter t is width of cut (tool) Substituting for N and L: MRR
≈
k 2
f r tV
IV. Slab (Horizontal) Milling (be careful with units!!)
Terms Used: N: RPM of Cutter n: Number of Teeth on Cutter W: Width of cut (may be full cutter or partial cutter) t: depth of cut V: cutting speed -- a Handbook value L: Length of pass or cut f m: Table (machine) Feed f t: feed/tooth of cutter -- a Handbook value D: Cutter Diameter A. Cutting Speed:
N =
kV π
D
If Cutting Speed for a given RPM rate is desired, solve above equation for V: V = π ND/k B. Table Feed Rate:
f m = f t *N*n C. Cutting Time:
CT =
L + LA f m
LA is Length of Approach of Tool to Work LA = t(D - t)
D. Material Removal Rate: MRR =
Vol. Removed CT
=
L*W*t CT
= W*t* f m
Remember that the length of approach calculated here puts the cutter against the work at the start, we will add a small additional air gap to spin the tool to speed and allow the table to achieve target feed rate before chip making begins. When determining cutting time and MRR, care must be exercised. Ask yourself if total cutting time or time to make one pass across the part is being requested, ie. is a single or multiple pass operation to be studied. Also, note that in the MRR equation the “cutting time” term does not include the time of partial engagement (LA). Again, if a multi-pass operation is being employed, the appropriate width term should be used in the MRR equation.
V. Face (Vertical) Milling
Terms Used: N: RPM of Cutter n: Number of Teeth on Cutter W: Width of cut (may be full cutter or partial cutter) t: depth of cutter engagement V: cutting speed -- a Handbook value L: Length of pass or cut f m: Table (machine) Feed f t: feed/tooth of cutter -- a Handbook value D: Cutter Diameter LA: Approach Length LO: Length of “OverTravel”
A. Cutting Speed: N =
kV π
D
If Cutting Speed for a given RPM rate is desired, solve above equation for V: V = π ND/k B. Table Feed:
f m = f t *N*n
C. Cutting Time. Here several situation must be considered, these include: 1. Tool Not Fully Engaged with W D/2 3. Tool Fully Engaged, Roughing Pass -- Doesn’t require “Full Wipe” 4. Tool Fully Engaged, Finishing Pass -- requires “Full Wiping Action”
CT =
(L+ LA + LO ) f m
1. LA = LO =
W(D - W)
2. LA = LO =
3. LA =
D 2
D 2
2 2 LO = - 0.5* D - W
4. LA = LO =
D 2
D: Metal Removal Rate:
MRR =
Vol. Removed CT
=
L*W*t CT
= W*t* f m
Again, the cautions on single vs. multiple pass CT and MRR apply as with Slab Milling. Remember too, that the length of approach here puts the cutter against the work at the start, we will add a small additional air gap to spin the tool to speed and allow the table to achieve target feed rate before chip making begins. Also, care should be exercised with regards to units.
VI. Drilling
N =
kV π
D
A. Drill Speed, RPM
k is a “Units Constant” D is Drill Diameter V is cutting speed, a Handbook Value, if Cutting Speed for a given RPM rate is desired, solve above equation for V: V = π ND/k B. Cutting Time (min)
CT =
(L + A) f r * N
A is allowance; usually
D 2
f r is drill feedrate L is length of Hole
MRR =
Vol.Removed
=
π
2 D Lf r N
=
π
2 D f r N
C. MRR is (again) Material Removal Rate And note, no material is removed while the Drill travels through the “Allowance Zone” Use caution with units!!
