Studies of Electrochemical Machining : 1st Report, Theoretical Analysis for the Work Shape Processed by ECM

Kawafune, Kazuyoshi

doi:10.1299/jsme1958.11.554

Cited by 2 publications

(2 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The direct free boundary problem for the Laplace equation has been solved through conformal mapping (assuming constant conductivity) for a few special cases by Collett, Hewson-Browne, and Windle [1] and by Dietz, Gunther, and Otto [2], whereas Tipton [15] describes a finite difference procedure, and Kawafune, Mikoshiba, and Noto [8] suggest constructing an analogue model. The socalled cosine law of machining which appears extensively in the literature is a first order approximation for the inverse free boundary problem which has been solved exactly by Krylov for some mathematically tractable geometries.…”

Section: Formulation Of the Inverse Problem Of Ecmmentioning

confidence: 99%

“…Assuming for the moment that the electrolyte conductivity is uniform, the potential function is harmonic and must satisfy both of the conditions er 05 = 0 and ~-= cos fl on Fo (8) and the problem consists in finding the location of the equipotential lines F 4 which comprise the admissable tool family. It is noted that the following functions are also available from the prescribed data (7) and (8):…”

Section: Koa~ Go-vypamentioning

confidence: 99%

See 1 more Smart Citation

Inverted Cauchy problem for the Laplace equation in engineering design

Nilson

Tsuei

1974

J Eng Math

View full text Add to dashboard Cite

SUMMARYA Cauchy problem for the Laplace equation is solved by analytic continuation of the space variables on the plane of the complex potential, thereby obtaining an explicit expression for the geometry of physical boundaries of interest. In an illustrative application to the inverse free boundary problem of electrochemical machining, the general solution comprises a closed-form description of a tool family which can be used to machine a prescribed workpiece. The method is extended to include the effects of variable electrolyte conductivity, and a general tool design procedure is suggested in which an analytic series with correct asymptotic behavior is used to represent the given workpiece geometry. Applications in other fields such as heat conduction and hydrodynamics are discussed. The inverted formulation described herein affords considerable advantage and generality in solving Cauchy problems which are encountered in engineering design.

show abstract

Section: Formulation Of the Inverse Problem Of Ecmmentioning

confidence: 99%

Section: Koa~ Go-vypamentioning

confidence: 99%