Talk:Cylindrical Grinding machine

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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: Unitary specific cutting force, z: material constant, ηm: machine efficiency

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

  • Oho trd k c 1 1-z.jpg
  • Oho trd eta.jpg
  • 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 = 0.01 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]:

  • Oho trd vc-vw-q.jpg
  • Oho trd f.jpg
  • Oho trd e-or-a e.jpg


    • Performance
       2 ⋅ (Lp + Lr)
t1pr = ───────────── = 6.4 s
         fr ⋅ npzr  
;
Npr = prt / dr = 23 min
;
tppr = t1pr ⋅ Npr = 69 min
;
Npsr = 1 week / tppr = 144 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]:

  • Oho trd GR.jpg


    • Mechanical load
λke = 27 mm
;
     λke     ___________________           
hm = ─── ⋅ ╲╱dr ⋅ (1/Dmr + 1/Dmp) = 0.0041mm
      q                                     
;
K = 3.43
             z                       
kc = (1mm/hm)  ⋅ kc11 ⋅ K = 16500 N-mm2
;
b = 0.7 ⋅ Lr = 17.5 mm
;
Ftr = b ⋅ hm ⋅ kc = 1174 N

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

Sources[1]:

  • Oho trd wheel2.jpg
  • Oho trd lambda ke.jpg
  • Oho trd K.jpg
               ___________________        
    360°      ╱        dr                
φ = ──── ⋅   ╱ ─────────────────── = 0.55°
      π    ╲╱  Dmr ⋅ (1 + Dmr/Dmp)        
;
     Dmr ⋅ π ⋅ φ         
ze = ─────────── = 0.018
     λke ⋅ 360°          
;
       Ftr ⋅ ze ⋅ vr         
Potr = ───────────── = 1.217 hp
            ηm               
     Potr         
Tr = ──── = 1.53 N-m
      nr          
;
      Ftr ⋅ Dmp         
Ttr = ───────── = 18.5 N-m
          2             
;
Pottr = Ttr ⋅ npzr = 0.34 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]:

  • Oho trd v-f-d.jpg
    • 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]:

  • Oho trd kappa.jpg
  • Oho trd alpha-gamma.jpg
  • Oho trd coeffs.jpg
  • Oho trd n.jpg


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
OPEN HARDWARE OBSERVATORY 2020
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