Talk:Cylindrical Grinding machine

Project development - Comparative study between grinding and turning processes - Calculations -- Inddigital (talk) 20:06, 01 February 2023 (CET)

Below are the deductions that were made to obtain the results shown on the main page

• Initial data

D1p = 38 mm

;

D2p = 25 mm

;

Lp = 100 mm

;

D1p + D2p Dmp = ───────── = 31.5 mm 2

;

D1p - D2p prt = ───────── = 6.5 mm 2

Where: D1p: Initial diameter of the piece, D2p: Final diameter of the piece, Lp: Piece length, Dmp: Average diameter of the piece, prt: Total depth removed from the piece

• Material to be processed: Steel C45

kc11 = 2220 N/mm2

;

z = 0.14

;

ηm = 0.7

Where: kc11: Specific cutting force, z: material constant, ηm: machine efficiency

These values are obtained from the following sources^[1]:

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• Grinding process
  • Characteristics of the tool used

Cd = 11 USD

;

Ded = 152.4 mm

;

Did = 50 mm

;

Lr = 25 mm

;

Ded + Did Dmr = ───────── = 101.2 mm 2

Where: Cd: Cost of an abrasive wheel, Ded: Abrasive wheel outside diameter, Did: Internal diameter of abrasive wheel (useful), Abrasive wheel thickness, Dmr: Median diameter of abrasive wheel. For these measurements, a commercial wheel was taken as a reference.

• • Machining parameters

vr = 30 m/s

;

vpr = 0.22 m/s

;

q = vr / vpr = 136

;

fr = 17.5 mm/rev

;

dr = 0.03 mm

2 ⋅ vr nr = ────── = 5662 rpm Dmr

;

2 ⋅ vpr npzr = ─────── = 133 rpm Dmp

Where: vr: Abrasive wheel speed, vpr: Speed of the piece in grinding, q: velocity ratio; fr: Feed in grinding, dr: Depth of pass in grinding, nr: Rotational speed of abrasive wheel, npzr: Rotational speed of the piece in grinding

Sources^[1]:

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• 
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• • Performance

2 ⋅ (Lp + Lr) t1pr = ───────────── = 6.4 s fr ⋅ npzr

;

Npr = prt / dr = 23 min

;

tppr = t1pr ⋅ Npr = 23 min

;

Npsr = 1 week / tppr = 434 pieces/week

Where: t1pr: Time of one pass in grinding, Npr: Number of passes in grinding, tppr: Time per piece in grinding, Npsr: Weekly production in grinding.

• • Tooling cost

GR = 100

;

2 2 Ded - Did Lr Npd = GR ⋅ ─────────── ⋅ ── = 632 pieces/wheel 2 2 Lp D1p - D2p

;

1000 Cmpr = ──── ⋅ Cd = 17 USD Npd

Where: GR: Grinding volume ratio, Npd: Quantity of pieces per abrasive wheel, Cmpr: Cost of abrasive wheels to make 1000 pieces

Sources^[2]:

• 

• • Mechanical load

λke = 9.66 mm

;

λke ___________________ hm = ─── ⋅ ╲╱dr ⋅ (1/Dmr + 1/Dmp) = 0.0025mm q

;

K = 3.8691

z kc = (1mm/hm) ⋅ kc11 ⋅ K = 19869 N-mm2

;

b = 0.7 ⋅ Lr = 17.5 mm

;

Ftr = b ⋅ hm ⋅ kc = 870 N

Where: λke: Effective grain distance, hm: Mean thickness of cut, K: Correction factor for grain size, kc: Sspecific cutting force, b: Effective grinding width, Ftr: Cutting force for grinding

Sources^[1]:

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___________________ 360° ╱ dr φ = ──── ⋅ ╱ ─────────────────── = 0.96° π ╲╱ Dmr ⋅ (1 + Dmr/Dmp)

;

Dmr ⋅ π ⋅ φ ze = ─────────── = 0.0879 λke ⋅ 360°

;

Ftr ⋅ ze ⋅ vr Potr = ───────────── = 4.39hp ηm

Potr Tr = ──── = 5.53 N-m nr

;

Ftr ⋅ Dmp Ttr = ───────── = 13.7 N-m 2

;

Pottr = Ttr ⋅ npzr = 0.25 hp

Where: φ: Angle of approach, ze: Number of cutting edges in contact, Potr: Absorbed power in grinding, Tr: Grinding torque, Ttr: Piece torque, Potr: Absorbed power in piece

• Turning process
  • Characteristics of the tool used

Cc = 25 USD

;

Naf = 10

;

vuc = 50 min

Where: Cc Cost of a cutting tool, Naf: Number of sharps per tool, vuc: Lifespan of a sharp tool. For these data, a commercial cutting tool was taken as a reference.

• • Machining parameters

vt = 16 m/min

;

ft = 0.5 mm/rev

;

dt = 1 mm

;

2 ⋅ vt nt = ────── = 134 rpm D1p

Where: vt: Cutting speed in turning, ft: Feed in turning, dt: Depth of pass in turning, nt: Rotational speed in turning

Sources^[3]:

• 

• • Performance

Lp t1pt = ─────── = 89 s ft ⋅ nt

;

Npt = prt / dt = 7

;

tppt = t1pt ⋅ Npt = 10 min

;

Npst = 1 week / tppt = 1039 pieces/week

Where: t1pt: Time of one pass in turning, Npt: Number of passes in turning, tppt: Time per piece in turning, Npst: Weekly production in turning.

• • Tooling cost

vuc Npc = ──── ⋅ Naf = 51 tppt

;

1000 Cmpt = ──── ⋅ Cc = 485 USD Npc

Where: Npc: Number of pieces per curring tool, Cmpt: Cost of tools to make 1000 pieces

• • Mechanical load

κ = 70°

;

γ = 12°

;

α = 6°

;

h = ft ⋅ sin(κ) = 0.0748 mm

;

Ac = dt ⋅ ft ⋅ rev = 0.5 mm2

;

γ - α kγ = 1 - ───── = 0.999 100

Kv = 1.15

;

Kst = 1

;

Kver = 1.3

;

z kc = (1mm / h) ⋅ kc11 ⋅ kγ ⋅ Kv ⋅ Kst ⋅ Kver = 4767 N/mm2

;

Ftt = Ac ⋅ kc = 2383 N

nt2 = 140 rpm

;

vt2 = nt2 ⋅ D1p = 33.4 m/min

;

Ftt ⋅ vt2 Pott = ───────── = 2.54 hp ηm

;

Pott Tt = ──── = 129 N-m nt2

Where: κ: cutting-edge angle, γ: Rake angle, α: Basic rake angle, h: Thickness of cut, Ac: Sectional area of chip, kγ: Rake coefficient, Kv: Speed coefficient, Kst: compression factor, Kver: wear factor, kc: Specific cutting force, Ftt: Cutting force, nt2: Standard speed, vt2: Real cutting speed, Pott: Input power in turning, Tt: Turning torque

Sources^[1]:

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Notes

1. Applied Machining Technology, Eighth Edition, Springer, 2008.
2. Fundamentals of Modern Manufacturing: Materials, Processes, and Systems, Fourth Edition, JOHN WILEY & SONS, INC., 2010.
3. CUTTING SPEED, FEED, DEPTH OF CUT, MACHINING TIME IN LATHE MACHINE Retrieved February 01, 2023.
4. You can see a spreadsheet at this link