Journal cf Materials Processing Technology 66 (1997) 146- 1.52 Cathode shape prediction in electrochemical mat ining usin simulated cut-and-try procedure S. Bhattacharyya, A. Ghosh*, A.K. Mallik Department oj Mechanical Engineering, Indian Institute of Technology Kalapur, Post Oj$ce, 1.1.T. Kanpar -208016, hdia Received 14 September 1995 Abstract The paper presents a computer simulaiion of the cut-and-try procedure for designing tool shapes in the electrochemical machining of prescribed work geometry. The procedure is capable of tackling complex work geometries where other existing methods fail. The variation of electrolyte conductivity has also been taken into account. It has been shown that an optimum value of the feed-back factor for iterative modification of the tool shape exists, which results in the minimum number of iterations to achieve the final result. The optimum value of the parameter has been shown to depend on some particular geometrical features. A parameter has been identified which determines the unique tool shape for a prescribed complex work geometry. ,3 1997 Elsevier Science S.A. Keywords: Electrochemical machining; Cut-and-try procedure; Cathode shape; Computer simulation - - 1. Introduction Despite several advantages of using electrochemical machining (ECM) in industry persistent problems in process control due to the complex nature of the in- volved electrochemical, thermal and hydrodynamic phenomena have rendered the applicability of the pro- cess limited. One of the most serious problems is the lack of adequate accuracy with which the tool shapes can be predicted for a prescribed work geometry. The tooling problem is of great concern because it is usu- ally linked with high cost and long start-up time. In practice the trial-and-error method (i.e., cathode burbering) is relied upon with repeatative machining runs to obtain the required tool geometry. In the case of the small batch-type production of parts with com- plex shapes, the use of ECM becomes uneconomical because of the above-mentioned long and expensive pre-production activities. Among all the earlier attempts to solve the tool shape prediction problem, the perturbation technique [l] and complex variable approach [2] need special mention. Tipton [3] developed a very simple theory * Corresponding author. Fax: (0512) 250007. e-mail: amitabha@iitk.emet.in. 0924-0136/97/$17.000 1997 Elsevier Science S.A. All rights reserved PII SO924-0 136(96)02508-3 called the cos(8)-theory which could yield satisfactory results for jobs with gentle profiles. Beside these ana- lytical works, a practical approach, called the electric- tank analogue method [4] has been proposed for the determination of tool shape. However, accounting for various kind of job shapes and flow conditions is impossible with any analytical technique. Consequently the choice of numerical tech- nique was inevitable for the solution of the work-tool gap region. Lawrence [5] developed a finite-difference- based numerical technique for modelling the gap re- gion. This model was very simple but unsuitable for representing the boundaries accurately. Later, he de- veloped another technique called the continuity method [6]. Tsui and Nilson [7] used the inverted Cauchy problem to determine a solution which in- volved mapping of the work-tool gap zone onto a regular region in the potential-current density plane and solving it by the finite-difference method (FDM). This procedure could take into account only those jobs and tools which could be represented by straight- forward mathematical functions. Jain and Pandey [8] applied the finite-element method (FEM) to solve the equilibrium job shape for a given tool. Narayanan et al. [9] used FEM for the determination of job shapes under equilibrium conditions, discussing in detail dif- ferent methods of boundary translation, which