Simulation and Experimental Study on Improving Electrochemical Machining Stability of Highly Convex Structures on Casing Surfaces Using Backwater Pressure

Casing parts are regarded as key components of aero-engines.Most casing parts are attached to convex structures of diferent shapes,whose heights range from hundreds of microns to tens of millimeters.Using profling blocky electrodes for electrochemical machining(ECM)of casing parts is a commonly adopted method,especially when highly convex structures.However,with an increase in the convex structure height,the fow felds of the machining areas become more complex,and short circuits may occur at any time.In this study,a method to improve the fow feld characteristics within a machining area by adjusting the backwater pressure is proposed and validated through simulation and experiment analyses.The simulation results demonstrated that the back-pressure method can signifcantly improve the uniformity of the fow feld around the convex structure compared with the extraction and open outlet modes.Subsequently,the back-pressure value was optimized at 0.5 MPa according to the simulation results.The experimental results showed that using the optimized back-pressure parameters,the cathode feed-rate increased from 0.6 to 0.7 mm/min,and a 16.1 mm tall convex structure was successfully machined.This indicates that the back-pressure method is suitable and efective for electrochemical machining of highly convex structures with blocky electrodes.In this study,we propose a method to improve the electrochemical machining stability of a convex structure on a casing surface using backwater pressure,which has achieved remarkable results.

Investigation of anode shaping process during co-rotating electrochemical machining of convex structure on inner surface

A novel co-rotating electrochemical machining method is proposed for fabricating convex structures on the inner surface of a revolving part.The electrodes motion and material removal method of co-rotating electrochemical machining are different from traditional electrochemical machining.An equivalent kinematic model is established to analyze the novel electrodes motion,since the anode and cathode rotate in the same direction while the cathode simultaneously feeds along the line of centres.According to the kinematic equations of the electrodes and Faraday’s law,a material removal model is established to simulate the evolution of the anode profile in co-rotating electrochemical machining.The simulation results indicate that the machining accuracy of the convex structure is strongly affected by the angular velocity ratio and the radius of the cathode tool.An increase of the angular velocity ratio can improve the machining accuracy of a convex structure.A small difference in the radius of the cathode tool will cause changes in the shape of the sidewalls of the convex structure.The width of the cathode window affects only the width of the convex structure and the inclination a of the sidewall.A relation between the width of the cathode window and the width of the convex structure was obtained.The formation process for a convex structure under electrochemical dissolution was revealed.Based on the simulation results,the optimal angular velocity ratio and cathode radius were selected for an experimental verification,and 12 convex structures were simultaneously fabricated on the inner surface of a thin-walled revolving part.The experimental results are in good agreement with the simulation results,which verifies the correctness of the theoretical analysis.Therefore,inner surface co-rotating electrochemical machining is an effective method for fabricating convex structures on the inner surface of a revolving part.

Evolution of convex structure during counter-rotating electrochemical machining based on kinematic modeling

Counter-rotating electrochemical machining(CRECM)is a novel electrochemical machining(ECM)method,which can be used to machine convex structures with complex shapes on the outer surface of casings.In this study,the evolution of the convex structure during CRECM is studied.The complex motion form of CRECM is replaced by an equivalent kinematic model,in which the movement of the cathode tool is realized by matrix equations.The trajectory of the cathode tool center satisfies the Archimedes spiral equation,and the feed depth in adjacent cycles is a constant.The simulation results show that the variations of five quality indexes for the convex structure:as machining time increases,the height increases linearly,and the width reduces linearly,the fillets at the top and root fit the rational function,and the inclination angle of the convex satisfies the exponential function.The current density distributions with different rotation angles is investigated.Owing to the differential distribution of current density on workpiece surface,the convex is manufactured with the cathode window transferring into and out of the processing area.Experimental results agree very well with the simulation,which indicates that the proposed model is effective for prediction the evolution of the convex structure in CRECM.

COINCIDENCE POINT THEOREMS iN PROBABILISTIC METRIC SPACES WITH A CONVEX STRUCTURES

In lhis paper we draw some coincidence and common fixed point theorems fornonlinear hybrid contraction mappings on probabilistic metric spaces with a convexstructure.

Continuous selections for pseudo-lower semicontinuous set-valued mappings on convex structure spaces and hyperspace contractibility

SINCE 1956, Michael’s continuous selection theory has been applied to functional analysis,topology, approximation theory and other mathematical fields. In this letter, the concept ofthe pseudo-lower semicontinuity is introduced, and a convex structure of metric space is de-fined. A continuous selection theorem for pseudo-lower semicontinuity is given. This

Electrochemical machining of a convex strips structure on a revolving part by using site directed power interruption

Revolving parts with complex surface structures are widely used in machinery and mechanical equipment. The ECM process provides its adequacy to cut hard materials with different shapes, and its applications are widely increased, due to its outstanding advantages. In this paper, a new method for machining a convex strips structure on a cylinder by using site directed power interruption（SDPI） in the ECM process is presented. A variable correction value of the power-off time was defined and optimized to obtain the ideal interval for better machining accuracy and stability.The electric field distribution and the simulated convex profiles show that the stray current density can be reduced effectively by using the proposed method. The correction value has an important influence on the machining accuracy. A suitable correction value in the range of 0.6–1.2 s can effectively improve the machining accuracy of the convex strips structure. Experiments were also conducted to verify the proposed method. Results have confirmed that the stray corrosion on the convex strips surface is significantly reduced and the machining accuracy of convex strips structure is remarkably improved by using the proposed method with a suitable correction value in the ECM process. Finally, a convex strip with a height of 2 mm on a thin-wall revolving part was also produced successfully using a correction value of 0.9.

Proximal-Based Pre-correction Decomposition Methods for Structured Convex Minimization Problems

This paper presents two proximal-based pre-correction decomposition methods for convex minimization problems with separable structures.The methods,derived from Chen and Teboulle’s proximal-based decomposition method and He’s parallel splitting augmented Lagrangian method,remain the nice convergence property of the proximal point method and could compute variables in parallel like He’s method under the prediction-correction framework.Convergence results are established without additional assumptions.And the efficiency of the proposed methods is illustrated by some preliminary numerical experiments.