machining calculations

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Homework

• Chapter 22– Review questions:

• 1,2,5,7,11,15,16,20– Multiple choice:

• 2,9– Problems:

• 1,2,5,12,13

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Cutting Parameters• We require relative motion between the cutter

and material to perform the machining operation

• 2 Motions: Speed and Feed– Speed: How fast the material moves past the

cutting edge– Feed: How fast the cutting edge moves

across(into) the material• For example:

– How much you squeeze the trigger on a hand drill will change the SPEED

– How fast you push the drill bit into your material will change the FEED

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Cutting Parameters for Turning

• f: FEED, in turning is distance per revolution (in/rev) or (m/rev)• v: Linear cutting SPEED, given in distance per minute (in/min) or

(m/min)• N : Rotational speed (rev/min) or RPM

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Cutting Parameters for Turning

• L : The total length (along the axis of rotation) that we are cutting• Do : The original Diameter• Df : The final Diameter• d : The depth of the cut (measured radially) = (Do-Df)/2

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Turning Calculations

• Speeds and Feeds are material and operation specific and can be found in a Machinist’s Handbook

• We need to calculate the settings for our machine, how long it will take to machine the piece, and how fast we will remove material

• So, Rotational Speed:

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Turning Calculations

• fr : Feed Rate is the linear travel rate (along the axis)

fr = N * fFeed Rate is in (in/min) or (mm/min)

• The time to turn a part from Do to Df is simply the time to travel across the length

L…so,Tm: Time to machine = L / fr

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Turning Calculations• Material Removal Rate (MRR):

volumetric amount of material being cut away per unit time– In Turning

MRR ~ v * f * d (approximation)

NOTE: units of feed in this calculation is simply distance not (in/rev)

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Turning Calculations (example)• We wish to turn a piece of 1” steel round stock down to 0.8” in

one pass. The total length of the cut is to be 4”. We want to calculate the feedrate and rotational speed for our lathe, material removal rate, and the time it will take to machine.

1. Look up feed and speed in handbook.2. We need: depth of cut, material, tool3. Depth of cut (Do-Df) / 2 = (1.0-0.8) / 2 = 0.1”4. From handbook, f = 0.03125 (inch/rev) v = 240

(feet/min)

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Turning Calculations (example)• We wish to turn a piece of 1” steel round stock down to 0.8” in

one pass. The total length of the cut is to be 4”. We want to calculate the feedrate and rotational speed for our lathe, material removal rate, and the time it will take to machine.

5. N = v / (pi*Do) = (240 * 12) / (pi * 1.0) = 916 rpm6. Feedrate: fr = N * f = 916 * 0.03125 = 28

inches/min7. MRR ~ v * f * d = (240 * 12) * 0.03125 * 0.1 =

9in3/min8. Tm = L /fr = 4 / 28 = 0.143min (8.5seconds)

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Milling Calculations

• f = feed (chip load): inch/tooth (mm/tooth)

• fr = feed rate = inch/min = N * nt * f (SET ON THE MACHINE)

• nt = number of cutter teeth

• v = cutting speed (feet/min) (m/min)

v

w

N

N

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Milling Calculations

• N = rotational speed (RPM) = v / (pi * D ) (SET ON THE MACHINE)• MRR = w * d * fr• d = depth of cut• w = width of cut

v

w

N

N

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Milling Calculations: Approach and Overtravel

• Time for machining: includes approach distance

• For slab milling: Tm = (L + A) / fr

Peripheral or “slab” milling

• D = diameter of cutter• d = depth of cut• A = approach length)( dDd −• Where: A =

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Milling Calculations: Approach and Overtravel

• Time for machining: includes approach and overtravel distance

• For centered face milling: – Tm = (L + 2A) / fr

FACE MILLING (CENTERED)

• Where: A = O = D / 2• D = diameter of cutter• A = approach length, O = overtravel

length

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Milling Calculations: Approach and Overtravel

• Time for machining: includes approach and overtravel distance

• For face milling: Tm = (L + 2A) / fr

FACE MILLING (OFFSET)

D = diameter of cutterw = width of cutA = approach length, O =

overtravel length)( wDw −• Where: A = O =

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Machining Calculations (example)

• We wish to face mill the top of a block of aluminum as shown, at a cutting depth of 0.1” We will use a 2” wide face mill with 5 cutting inserts.

• From a handbook:– Feed f = 0.010 (inch/tooth)

– Speed v = 350 feet/min

1.5”1.5”9.”

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Machining Calculations (example)

• N = v / (pi * D) = 350*12/ (pi*2) = 668 RPM• Feed rate = f * nt * N = 0.010 * 5 * 668 = 33inches/min• Time to machine = (L + 2A) / Feed rate =

(9 + 2(D/2)) / 33 = .33minutes1.5”1.5”

9.”

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Machining Calculations (example)

• Material removal rate MRR = feedrate * width of cut * depth of cut = 33 * 1.5 * 0.1 = 4.95in3/min

1.5”1.5”9.”