Electrochemical Machining Tool Research Articles

Design and analysis of erosion in electrochemical machining tool

The electro chemical machining system is the type of system in which it is used in the machining operations. In our project we have analyse the erosion in the electro chemical machining tool. The main disadvantage of the electrochemical machining system is that, due to repeated use of electrochemical machining tool there may be occurance of erosion in the machining tool. This effect is due to the presence of oxygen content in the electrolyte. We compared different types of metal like beryllium copper, copper tungsten, copper and brass with the electrolyte combination of sodium chloride and sodium nitrate. Normally the electrolyte used in the electro chemical machining system is that the sodium chloride and sodium nitrate [5]. So that we have used to compare the metals and electrolytes and used to find the best among them. Finally we have concluded that the beryllium copper has the best results. So the use of berylliumcopperwiththeelectrolyteofsodiumchloridewill havethereductionintheerosion.

Multiphysics Modeling Prediction of Electrochemically Machined Workpiece Geometries

Electrochemical machining (ECM) is a manufacturing technology that allows metal to be precisely removed by electrochemical oxidation and dissolution into an electrolyte solution. ECM is suited for fabrication operations using “difficult to cut” materials and/or producing parts with complicated and intricate geometries. In ECM, an electrochemical cell is established wherein the workpiece is the anode and the tool is the cathode; by relative movement of the shaped tool into the workpiece while applying a suitable electrical potential, the mirror image of the tool is “copied” into the workpiece. Compared to mechanical or thermal machining processes, where metal is removed by cutting or electric discharge/laser machining, respectively, ECM does not suffer from tool wear or result in a thermally damaged surface layer on the workpiece. Consequently, ECM has strong utility as a manufacturing technology for fabrication of a wide variety of metallic parts and components, and encompasses machining, deburring, boring, radiusing and polishing processes, among others. As noted, ECM provides particular value when applied to high strength/tough and/or work-hardening materials such as high strength steel, chrome-copper alloy (C18200), nickel alloy (IN718), cobalt-chrome alloy (Stellite 25) and tantalum-tungsten alloy (Ta10W), since the material removal process involves no mechanical interaction between the tool and the part.One notable difficulty with ECM is an inability to predict a priori the tool and process parameters required in order to satisfy the final specifications of the fabricated part. Currently, most practical applications of ECM require an iterative prototyping process for tool development, where a succession of tools and parts are fabricated until the desired final form is achieved. In this talk, Faraday will present results from ongoing development work of a multiphysics-based design platform to predict optimal ECM tool shapes and processing parameters using commercial multiphysics simulation software. Simulation results for both an axisymmetric tubular tool and a non-axisymmetric tool fabricated by powder-bed additive manufacturing methods will be compared to experimental data gathered from ECM tests on various materials of commercial interest (alloy steel, nickel and titanium alloys). A notional non-axisymmetric tool, the electrochemically machined indentation obtained in an IN718 alloy plate, and the indentation predicted from multiphysics modeling are shown in the Figure. The effect of including selected physical phenomena in the simulations (kinetic polarization, surface occlusion by insoluble dissolution products, etc.) on the quality of the predicted machined forms will be discussed, and general guidelines for successful multiphysics modeling of ECM processes will be highlighted. Replacement of most or all of a costly experimental prototyping cycle with a more-rapid and less-expensive in silico multiphysics modeling like that described herein, along with enhanced ECM process performance [1-3] and simplified management of ECM electrolytes [4] through the application of pulse/pulse-reverse electrical waveforms, has the potential to significantly advance ECM as a mainstream manufacturing technology. Figure Caption Left to right: Non-axisymmetric tool fabricated by additive-manufacturing methods. Photograph and optical profilometry scan of indentation obtained by pulse-reverse waveform ECM. Indentation form predicted by multiphysics simulation.

Fabrication of micro-mixer on printed circuit board using electrochemical micromachining

Electrochemical micromachining (ECMM) has been mostly carried out in situations demanding precision, complexity in the shapes of final components and in case the surface integrity and performance are independent of the machining process. In this work, the following have been demonstrated:The first part of the work demonstrates the experimental setup for ECMM that is used to fabricate a micro-mixer on a printed circuit board (PCB) substrate by using a single point electrochemical machining tool with a tip diameter—150 µm. The method is able to show a promising route of fabrication where the circuit lines on a PCB substrate can be printed with high yield and processing speeds. The second part of the article points out that machining can be carried out on PCB substrates through electrochemical processes using a single point tool and a minimum feature size of 243 µm can be machined with a fine tolerance of 0.025 µm and roughness = 3.0459 µm~7.2404 µm. The third part of the article reports the geometrical parameters of a relatively complex geometry of a micro-mixer which is arrived at through a COMSOL based simulation platform that is fabricated using the mentioned manufacturing process. The process is further validated through the design of experiments, and fluid flow and mixing behaviour on the fabricated structure is evaluated through an epifluorescence microscope.The advantages that this technique may offer is in terms of achieving an overall low feature size in comparison to micro-milling and avoiding the complexities of lithography-driven processes to produce a process which has a much lower equipment dependency, is environmentally benign in comparison to the lithography driven techniques and is overall low in cost.

Multiphysics Modeling Prediction of Electrochemically Machined through-Hole Geometries

Electrochemical machining (ECM) is a manufacturing technology that allows metal to be precisely removed by electrochemical oxidation and dissolution into an electrolyte solution. ECM is suited for machining parts fabricated from “difficult to cut” materials and/or parts with complicated and intricate geometries. In ECM, the workpiece is the anode and the tool is the cathode in an electrochemical cell; by relative movement of the shaped tool into the workpiece, the mirror image of the tool is “copied” or machined into the workpiece. Figure 1 shows photographs of a shaped ECM tool (cathode, panel A) and the resulting part (anode) surface after machining (panel B). Compared to mechanical or thermal machining processes where metal is removed by cutting or electric discharge/laser machining, respectively, ECM does not suffer from tool wear or result in a thermally damaged surface layer on the workpiece. Consequently, ECM has strong utility as a manufacturing technology for fabrication of a wide variety of metallic parts and components, and includes machining, deburring, boring, radiusing and polishing processes. ECM provides particular value in that application is straightforward to high strength/tough and/or work-hardening materials such as high strength steel, chrome-copper alloy (C18200), nickel alloy (IN718), cobalt-chrome alloy (Stellite 25) and tantalum-tungsten alloy (Ta10W), since the material removal process involves no mechanical interaction between the tool and the part. A variety of production applications are envisioned as well suited for ECM techniques. One notable difficulty with ECM, common to a variety of manufacturing operations, is an inability to predict a priori the tool and process parameters required in order to satisfy the final specifications of the fabricated part. In this talk, Faraday will present results from ongoing development work of a physics-based design platform to predict optimal ECM tool shape using commercially available multiphysics simulation software. This predictive capability is anticipated to dramatically shorten the process/tooling development cycle, eliminating much or all of the iterative prototyping necessary in the absence of a predictive tool. The main focus of this talk will be a comparison of through-holes fabricated by CM in flat plate and/or tube geometries to those predicted by multiphysics simulation. The various physics included in the models to enable accurate simulations will be discussed, along with any (semi-)empirical simplifying assumptions made to accelerate execution of the simulations. The overarching objective of the current and future work, to demonstrate accurate modeling of ECM through-hole features of progressively increasing experimental complexity (e.g., the perpendicular and angled holes of panels C and D of Figure 1), will also be presented. Figure 1 Caption Photograph of shaped ECM tool (A), with resulting machined surface (B). Conceptual schematics of perpendicular (C) and angled (D) through-holes in a flat-plate part geometry. Figure 1

Multiphysics Modeling of Surface Finishing Performance in Pulsed-Waveform Electrochemical Machining

Electrochemical machining (ECM) is a manufacturing technology that allows metal to be precisely removed by electrochemical oxidation and dissolution into an electrolyte solution. ECM is suited for machining parts fabricated from “difficult to cut” materials and/or parts with complicated and intricate geometries. In ECM, the workpiece is the anode and the tool is the cathode in an electrochemical cell; by relative movement of the shaped tool into the workpiece, the mirror image of the tool is “copied” or machined into the workpiece. One notable difficulty with ECM is an inability to predict a priori the tool and process parameters required in order to satisfy the final specifications of the fabricated part [[1]]. Accordingly, there is potential value in development of a physical phenomenon-based design platform to predict optimal ECM tool shape. Such a capability is anticipated to dramatically shorten the process/tooling development cycle. A further goal of ECM is to simultaneously achieve a target surface finish on the machined part. It is thus of interest to develop the capability also to predict the distribution of local surface finish resulting from ECM processing. Modeling of the changes in local surface finish intrinsically operates on a different length scale from that of bulk material removal (μm, versus mm or cm), and thus is most easily treated separately. The physicochemical phenomena involved in the evolution of surface finish during ECM processing are strongly coupled, and include the electric field itself (primary current distribution), surface polarization and electrochemical kinetics (secondary current distribution), and fluid flow and mass transfer (tertiary current distribution). Of particular interest is modeling of pulsed-waveform ECM, for which significant practical advantages have been demonstrated [[2],[3],[4]]. While an extensive body of literature exists analyzing pulsed electrodeposition [[5],[6]], comparatively little work has been published to date on pulsed ECM [[7],[8]]. This talk will discuss recent modeling work seeking to develop a solid foundation for a predictive understanding of the surface finishing aspects of ECM processes. The work described herein encompasses time-dependent modeling of concentration profiles and other relevant physical quantities under the application of pulse(-reverse) current ECM waveforms, starting from simulations assuming a locally flat surface and working toward quantitative descriptions of the transient and steady-periodic behavior on structured substrates. Prior work (see, e.g., Ref. 3) has demonstrated the value in differential pulsed-ECM processing of surfaces with features of size comparable to or larger than the hydrodynamic boundary layer thickness (“macroprofiles”) versus surfaces with features much smaller than the boundary layer thickness (“microprofiles”). Figure 1 (left) plots a schematic of the pulsating concentration profiles at the end of the pulse on-time in forward-only pulsed ECM, assuming 100% current efficiency. Here, the pulse period (ton + toff) and the peak applied current density (jpeak) are assumed constant, with the curves corresponding to different values of ton. The saturation concentration of the dissolved metal is Cs, and the bulk metal concentration Cb equals zero. The quantity τ is the “transition time,” which is the value for ton for which the metal concentration at the surface rises exactly to Cs at the end of the forward pulse. As can be seen, for ton < τ, metal dissolution is not mass transfer limited, but for any ton > τ the rate of dissolution is constrained by the diffusion of the dissolved material, approaching the DC mass transfer rate for sufficiently high ton. Figure 1 (right) illustrates that preliminary simulations performed with COMSOL Multiphysics® exhibit behavior consistent with this qualitative concept.

Fabrication of an Electrode Insulated by Using Hot Dip Aluminizing and Micro-arc Oxidation Method for Electrochemical Microhole Machining

In this research, electrode insulation of the electrochemical machining tool has been produced by hot dip aluminized micro arc oxidation techniques. In order to form an effective layer on the tungsten carbide tool and achieve higher precision, the tool will then be micro-arc oxidizing, convert the aluminum-rich into aluminum oxide insulating layer. Withstanding Voltage of the tool is being tested afterward by sodium chloride electrolysis method, and the surface and the cross section is being observed. Eventually, the tools were examined and discussed for their machining performance by ECM drilling through stainless steel plate. We were expecting to produce a precise and better insulation. By reducing ECM stray effect, the precision can be achieved.The experimental result shows the optimum parameters are aluminum dipping for 4minutes, 450V of micro-arc voltage for 20minutes and 40minutes of boiling water sealing, reaching 10.2V of withstanding voltage. A further electrochemical drilling has been done to explore the effect of insulation. Two electrodes, with and without insulation had been compared. The difference between the entrance and the exit diameter of the hole of insulated tool reaches 17um, compare to the one without insulation, we have successfully reduced 81um. The result shows that the insulation has effectively reduced the stray effect, and achieve high precision machining.

Accelerated Electrochemical Machining Tool Design Via Multiphysics Modeling

Electrochemical machining (ECM) is a manufacturing technology that allows metal to be precisely removed by electrochemical oxidation and dissolution into an electrolyte solution. ECM is suited for machining parts fabricated from “difficult to cut” materials and/or parts with complicated and intricate geometries. In ECM, the workpiece is the anode and the tool is the cathode in an electrochemical cell; by relative movement of the shaped tool into the workpiece, the mirror image of the tool is “copied” or machined into the workpiece. Figure 1 shows a schematic and photograph of a shaped ECM tool (cathode) and the resulting part (anode) surface after machining. Compared to mechanical or thermal machining processes where metal is removed by cutting or electric discharge/laser machining, respectively, ECM does not suffer from tool wear or result in a thermally damaged surface layer on the workpiece. Consequently, ECM has strong utility as a manufacturing technology for fabrication of a wide variety of metallic parts and components, and includes machining, deburring, boring, radiusing and polishing processes. ECM provides particular value in that application is straightforward to high strength/tough and/or work-hardening materials such as high strength steel, chrome-copper alloy (C18200), nickel alloy (IN718), cobalt-chrome alloy (Stellite 25) and tantalum-tungsten alloy (Ta10W), since the material removal process involves no mechanical interaction between the tool and the part. A variety of commercial and military production applications are envisioned as well suited for ECM techniques. One notable difficulty with ECM, common to a variety of manufacturing operations, is an inability to predict a priori the tool and process parameters required in order to satisfy the final specifications of the fabricated part. In this talk, Faraday will present preliminary results from a Phase I SBIR program aiming to demonstrate the potential for a phenomena-based design platform to predict optimal ECM tool shape using commercially available multiphysics simulation software. This capability is anticipated to dramatically shorten the process/tooling development cycle, eliminating much or all of the iterative prototyping necessary in the absence of a predictive tool. The validation argument will be presented via comparison of simulation results with data from parallel ECM experiments. The initial validation work encompasses a small subset of experimental parameters: electrolyte salt (“active” NaCl vs “passive” NaNO3) and electrolyte flow/tool geometry (“cross flow” past a solid tool, and “through-flow” in a tubular tool). The initial feasibility demonstration of the tool design platform will include only ECM based on potentiostatic direct currents, constant tool advancement rates, and simulations including only primary current distributions. Reasonable agreement between the simulated and experimentally derived profiles is observed. Eventually, however, the goal is to extend the model to other modes of ECM processing, including: 1) pulse-current ECM (PECM), where the tool is withdrawn from the workpiece during pulse current off-times to flush the gap; and also 2) pulse/pulse-reverse ECM (P/PR ECM) in metal-solubilizing electrolytes, where the tool gap is maintained relatively constant. An approach to modeling the optimal inter electrode gap dimension during PECM has been reported by Rajurkar and collaborators [[1]]; to our knowledge no modeling has been performed on constant-gap pulse/pulse-reverse ECM in solubilizing electrolytes. Faraday has developed and patented novel approaches to ECM based on pulse reverse currents [[2],[3],[4]] that do not require complicated electrolytes and results in improved surface finishes and better process control; application of the predictive model to these approaches is anticipated to provide substantial gains in both manufacturing logistics and economics. The authors acknowledge the financial support of U.S. Army Contract No. W15QKN-16-C-0070. References [[1]] B. Wei, K.P. Rajurkar, S. Talpallikar. “Identification of Interelectrode Gap Sizes in Pulse Electrochemical Machining.” J. Electrochemical Society 144(11): 3913-19, 1997. [[2]] C. Zhou, E.J. Taylor, J. Sun, L. Gebhart, R. Renz. “Electrochemical Machining using Modulated Reverse Electric Fields.” U.S. Patent No. 6,402,931, issued 11 June 2002. [[3]] E.J. Taylor. “Sequential Electromachining and Electropolishing of Metals and the like using Modulated Electric Fields.” U.S. Patent No. 6,558,231, issued 6 May 2003. [[4]] E.J. Taylor, M. Inman. “Method and Apparatus for Pulsed Electrochemical Grinding.” U.S. Patent No. 9,403,228, issued 2 August 2016. Figure 1

Design of ECM tool electrode with controlled conductive area ratio for holes with complex internal features

The design method of electrochemical machining (ECM) tool electrode with controlled conductive area for the machining of holes with given complex internal features was presented in this paper. Such holes were difficult to machine with traditional mechanical machining methods. In authors’ previous work, it has been proved that electrochemical machining (ECM) using tool electrode with controlled conductive area ratio was effective to machine many kinds of complex holes. However, it is considered that the inverse problem, i.e., designing of suitable tool electrode for given internal feature is of great importance for practical application. Therefore, in this work, the proposed ECM process was modeled to investigate the electric potential and current distribution in the electrolyte and on the electrodes’ surface, and the evolution of inner hole profile. Then, the relationship between conductive area ratio and the machining depth was investigated by a set of fundamental simulation experiments. Simulation result showed that suitable tool electrode with specific helical conductive area can be designed for the machining of hole with given internal feature. A prototype tool electrode with non-uniform conductive area ratio from its tip to the root was fabricated and used in the verification experiment. The machining result showed that a free-formed hole was successfully shaped and the inner hole profile is in well accordance with the given internal feature.

Fabrication and Experimental Verification of Electrochemical Machining Tool for Complex-shaped Hole

The demand for processing of reverse-tapered holes and other complex-shaped holes made of difficult-to-cut materials has increased in recent years. The hole processing by the electrolysis processing is thought to be suitable because there are no heat affected layer and tool wear in electrochemical machining (ECM). It has been reported that, a tool with insulated side surface had been used to process reverse-tapered holes from straight pre-drilled holes by controlling the applied voltage as well as feeding speed. However, the processing efficiency is low because the anodic dissolution occurs only in the area nearing the electrode‘s end surface, also control of the power supplied or the electrode feed is necessary. To solve the problem of low processing efficiency, an ECM tool with changed conductive area ratio along the axial direction was proposed by our research group, and the effectiveness was confirmed through computer simulation. The purpose of this study is to experimentally confirm the processing possibility of the proposed ECM tool for complex-shaped holes. First, the ECM tool was fabricated by winding a copper wire over the cylindrical surface of a non-conductive shaft. The shaft with pitch-changed spiral groove was produced by a 3D printer. Then, machining experiments were carried out by inserting the fabricated tool into a pre-drilled straight hole. In order to investigate the influence of experimental conditions, the current value and processing time were changed in experiments. As the results, reverse-tapered and complex-shaped holes were shaped from a straight hole of 7mm in diameter and 45mm in depth. The experimental results showed that our proposed ECM tool is effective in processing complex-shaped holes. In addition, it was found that the processing quantity can be controlled through the current value and processing time.

Improving cylindricity and connectricity of hollow cylinder parts by electrochemical machining

Widely used in many mechanical systems, hollow cylinder-shaped parts should be accurately machined to ensure two critical specifications, i.e., cylindricity and concentricity. A dedicated electrochemical machining (ECM) system is designed to improve the cylindricity and concentricity of a small bearing. In order to optimise the ECM process, the commercial CAE software, COMSOL multi-physics, is utilised to analyse some key process parameters such as temperature, current density and flow distribution. From the analysis results, a suitable cathode, which is the ECM tool, could be designed. Temperature distribution, the cathode tool, current distribution, material removal rate (MRR) with the assistance of CAE software and the design of the ECM cathode tool are more efficient and accurate.

Variable Gap Amendment of Cathode for the Electrochemical Machining of Turbine Blade

For improving the accuracy of blade electrochemical machining(ECM),the variable gap amendment method of cathode is proposed and a mathematical model of this method is presented.The correction data of cathode are variable based on the value of interelectrode gap and are used to the cathode design.The approximate formula of cathode correction data which are calculated along the contours line is given and the experimental method of interpolation approximation is adopted.The experimental investigations are carried out by using a new self-designed blade ECM tool system.The results show that the accuracy of blade is improved to 0.05 mm by using the cathode amendment method three times.

Real-time parameterization of electrochemical machining by ultrasound measurement of the interelectrode gap

This paper discusses the development of an ultrasound technique that enables the continuous, uninterrupted collection of time-resolved data for dissolution valency, interelectrode gap, and overpotential during electrochemical machining (ECM). These parameters, in combination with the dissolution current, give insight into the ECM process. The accuracy and expediency of this approach has been established using results collected from the ECM of the stainless steel SS410. The enhanced accuracy and resolution offered by this approach has been demonstrated through comparison with established current-time and interelectrode gap-time analysis methods. This superiority has been explained both in terms of the relative accuracy of the analysis methods and the removal of the requirement for the approximation of constant-valency machining. The resulting current-overpotential relationships are sufficiently accurate to give insight into the ECM dissolution characteristics of the steel, as well as providing an improved parameter base essential for increasingly accurate simulation of the ECM process and tool design techniques.

Two-Dimensional Tool Design for Two-Dimensional Equilibrium Electrochemical Machining Die-Sinking Using a Numerical Method

Electrochemical machining (ECM) can be defined as controlled electrolytic anodic erosion. ECM can machine hard alloys and metals with tools of softer metals, without affecting either workpiece microstructure or surface properties. There is no tool wear owing to a lack of tool/workpiece contact. The ECM medium between the tool and workpiece is electrically conductive, causing the finished workpiece geometry to vary from the tool and not to become a direct inverse of the tool shape. The characteristics of the workpiece material can also affect shape transfer, increasing the difficulty of designing and simulating ECM tools. At present, ECM tool design in industry is a trial-and-error process that can be prohibitively time-consuming. Automated design and simulation procedures are, therefore, desirable. This paper describes a computational approach to ECM tool design for two-dimensional cases based on the solution of a set of ordinary differential equations in a basis function format that are based on the electric field during the ECM process. This method has a number of advantages. It allows for the use of geometric representations of the tool and workpiece, such as B-Splines and Bèzier curves. This enables easy integration with most current computer-aided design software. It is also possible more easily to design and simulate tools for non-ideal machining conditions, where parameters such as electrolyte conductivity vary with the ECM cell. Above all, this method can design tools directly for the ECM process, given a particular workpiece shape without iterative methods. Computational trials have been carried out and compared with the results of an experimentally validated model. These showed that the method was effective for tool design under ideal machining conditions and was easier to use for non-ideal condition modelling.

Electrochemical machining under orbital motion conditions

The range of practical applications of electrochemical machining (ECM) is limited by relatively low machining accuracy, specially in cases of complicated shapes. One of the major problems is the generation of spikes which delay the accuracy of the process. The problem is strongly exaggerated if the tool includes multi-electrolyte holes. Moreover, additional machining processes will be needed to remove the resultant spikes. In the present work, tool orbital motion has been proposed as a new technique to enhance the ECM accuracy and to eliminate the presence of the spikes. A special test rig has been constructed for the orbital motion process. A theoretical model has been derived to predict the shape of the frontal zone, the effective machining time and the effective feed rate. The obtained results are an endeavor to provide the ECM tool designer with useful information to enhance the process accuracy. Furthermore, the results facilitate the utilization of the ECM process in die sinking and mold industry. The effect of the applied voltage, feed rate, and tool eccentricity on the spike formation are also presented.

A direct analytical solution to the tool design problem in electrochemical machining under steady state conditions

A method for the direct computation of two-dimensional electrochemical machining tool designs is described. The required workpiece geometry is represented by a Fourier series. Conformal transformation is then used to express the tool shape in series form, each term being a direct analytical function of the corresponding workpiece harmonic. Tool designs are thus achieved without numerical iteration. The model has been experimentally validated for a required workpiece geometry consisting of two harmonics, for which a tool was designed and manufactured. An In 718–15 per cent NaC1 workpiece-electrolyte system was used to produce a machined surface, whose Fourier transform was obtained. The measured and predicted harmonic amplitudes agree closely. This harmonic design method is also shown to give insight into the relationship and limitations between tool design and achievable workpiece detail.

Some Aspects of ECM Performance and Control

This paper presents results of experimental investigation carried out to develop quantitative relationships for inter-electrode gap and surface characteristics in Electrochemical Machining (ECM). The effect of grain size on the machining gap and, therefore, on the ECM performance and tool design is discussed. The wavelength decomposition of surface profiles and current signals have been carried out with a view to develop a better understanding of surface generation and random occurrences of sparking in ECM respectively. The dynamics of ECM process is modeled in state space notation and the adequacy of the model has been verified by simulation.

Free Boundary Problem for the Laplace Equation With Application to ECM Tool Design

The tool design problem of electrochemical machining (ECM) is formulated by the inverted approach in which the spatial coordinates are treated as the dependent variables on the plane of the complex potential. A general solution of this free boundary problem by analytic continuation provides the basis for a series approximation with correct asymptotic behavior using the method of weighted residues. The procedure is used to determine the noninsulated or partially insulated tool shapes which can be used to machine a prescribed workpiece geometry. The method is generally applicable to inverse (design) problems of potential theory which involve a given equipotential (or streamline) boundary along which a Neumann boundary condition is also prescribed as occurs in heat conduction, ideal flow, and electrostatics. The inverted approach not only eliminates the need for trial-and-error design procedures but also provides the advantage of adjustment in geometry by superposition.