Total cost per part: Cc = Co Th + Co Tm + Co Tt /np + Ct /np Substituting for Tm and np: Cc = Co Th + Co DL/fv + (CoTt + Ct )DLv(1/n -1)/( f C(1/n) ) Minimizing cost per part (dCc/dv = 0) gives cutting speed and tool life to minimize machining costs per part: vmin = C{n Co/[(1 – n)(Ct + CoTt)]}n Tmin = (1 – n) (Ct + CoTt)/(n Co) - Problem statement:
- Suppose a turning operation is to be performed with HSS tooling on mild steel (n = 0.125, C = 200 from text table). The workpart has length = 20.0 in. and diameter = 4.0 in· Feed = 0.010 in./rev. Handling time per piece = 5.0 min and tool change time = 2.0 min. Cost of machine and operator = $30.00/hr, and tooling cost = $3.00 per cutting edge. Find (a) cutting speed for maximum production rate and (b) cutting speed for minimum cost
- Minimum cost per unit - example
- Solution:
- Cutting speed for maximum production rate is
- vmax = C/[(1 - n) Tt/n]n = 200/[(.875) 2/0.125]0.125 = 144 ft/min
- Converting Co from $30/hr to $0.5/min, the cutting speed for minimum cost is given by
- vmin = C{n Co/[(1 – n)(Ct + CoTt)]}n = = 200{(0.125)(0.5)/[(0.875)(3.00 + (0.5)(2))]}0.125 = 121 ft/min
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