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Mathematical and Economic Models for Material Removal Processes

  • Vijay A. Tipnis
Chapter
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Part of the Sagamore Army Materials Research Conference Proceedings book series (SAMC, volume 25)

Abstract

Since current phenomenological models of material removal processes do not provide predictive relationships, empirical models (deterministic, statistical, probabilistic and stochastic) have been developed and applied to material removal operations. A methodology for the development and application of these models is presented. Such models are vitally needed for the selection of economic machining conditions within the given constraints of the cutting tool, the machine tool and the workpiece.

Economic models are needed for the creation of cost-effective process plans, especially with the computer-aided process planning systems. Based on a rigorous generalized economic model for material removal process introduced earlier, macro- and micro-economic models have been developed. The macro-economic model is applicable to cost estimation and pre-planning; the micro-economic model is essential to the selection and optimization of operating parameters. The overall organization of the data generation, collection, analysis and implementation of the process and economic models is presented.

Keywords

Machine Tool Material Removal Tool Life Work Center Metal Removal Rate 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Nomenclature

AD, RD

axial and radial depths (in.), respectively

Hc, Ht

productivity functions

I, c, t

generalized economie function; cost function ($/piece); and time function (min./piece), respectively

R

process rate function, e.g., cutting rate or cutting rate function for material removal operations (cu.in./min.)

T

process interruption function, e.g., tool life or tool life function for material removal operations (min.)

td

duration of interruption, e.g., tool change time (min.)

n

batch size

ts

setup time for the batch

tL

load/unload time per piece

lr

rapid traverse distance

lc

length of cut

e

extra travel (air feed)

r

rapid traverse rate

V

cutting speed (fpm)

v

volume of air cut at feed (cu.in.)

va

volume of air cut at feed (cu.in.)

M

work center rate ($/min.)

Y

tool cost/usage (purchase cost + regrinding cost/no. of regrinds + 1), ($/usage)

z

number of flutes on milling cutter

λ0, m0, k0

generalized constant coefficients; (setup time/piece + load/unload time + rapid traverse time); (m0M), respectively

λ1, m1, k1

generalized process coefficient, (v + va) and (m1M), respectively

λ2, m2, k2

generalized auxiliary coefficient; (v x td) and (m2M + Y) , respectively

λ3, m3, k3

generalized material expenditures, expenditure of time for material preparation and material cost, respectively

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References

  1. 1.
    “Development of Mathematical Models for Process Planning of Machining Operations,” R.E. DeVor, W.J. Zdeblick, V.A. Tipnis, and S. Buescher, Proc. of Sixth NAMRC, April 1978.Google Scholar
  2. 2.
    “Economic Models for Process Planning,” V.A. Tipnis, S. Vogel, and H.L. Gegel, Proc. of Sixth NAMRC, April 1978.Google Scholar
  3. 3.
    “An Experimental Strategy for Designing Tool Life Experiments,” W.J. Zdeblick and R.E. DeVor, Journal of Engrg. for Industry, Trans. ASME, Series 3, 77-WA, Prod-24, 1977.Google Scholar
  4. 4.
    “Cutting Rate-Tool Life Function (R-T-F): General Theory and Applications,” G.L. Ravignani, V.A. Tipnis, and M.Y. Friedman, CIRP General Assembly, August 1977, New Delhi, India.Google Scholar

Copyright information

© Plenum Press, New York 1981

Authors and Affiliations

  • Vijay A. Tipnis
    • 1
  1. 1.Metcut Research Associates, Inc.CincinnatiUSA

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