关 键 词：

数控 电解 机床 电解液 输送 装置 系统 设计

资源描述：

数控电解机床电解液输送装置系统设计,数控,电解,机床,电解液,输送,装置,系统,设计

内容简介：

南京理工大学紫金学院毕业设计说明书(论文)作 者:学 号：系：机械系专 业:机械工程及自动化题 目:数控电解机床电解液输送装置系统设计副教授指导者： (姓 名) (专业技术职务)评阅者： (姓 名) (专业技术职务) 2010年 5 月毕业设计说明书（论文）中文摘要本课题主要是为了推广电解加工技术，对现有数控电解机床及其电解液循环过滤系统进行改造。电解加工由于加工效率高、无工具损耗等显著优点，在难切削材料复杂型面、型腔加工方面获得了越来越广泛的应用，而多轴联动数控机床一般都是针对具体加工对象进行设计，且进口设备价格昂贵，因此，基于实验室现有设备进行改造设计，并对电解液输送系统在保证现有循环过滤的基础上，增加恒温及压力控制装置，使得加工过程中电解液参数易于精确控制，从而提高电解加工精度，对于电解加工工程应用具有重要意义。本课题中，设计了电解液槽的方案，电解液的过滤，搅拌，增加了温度控制系统，用电子程序对温度进行控制，选择了合适的泵，可以保证电解加工对电解液的要求。加入了搅拌系统可以控制电解液的浓度，以保证加工质量。关键词 电解加工 电解液 过滤 温度控制 电解液槽 毕业设计说明书（论文）外文摘要Title ：CNC machine tools electrolyte electrolysis system design transmission equipmentAbstractThis issue is mainly to promote the electrochemical machining technology to the existing NC machine tools and electrolyte electrolytic recycling system to reform. Since ECM high efficiency, no tool wear and other significant advantages, in hard cutting materials of complex surface cavity machining gained more and more widespread concerns applications other multi-axis NC machine tools are generally designed for specific processing of object and imported equipment is expensive, therefore, to renovate existing equipment based on laboratory design, and electrolyte delivery system in ensuring the existing, increased temperature and pressure control equipment, making process in the electrolyte parameters easy precise control, thereby enhancing the electrochemical machining precision engineering applications for ECM is important. The projects are in the trough of the program is designed electrolyte, electrolyte filtering, mixing, increasing the temperature control system, electronic temperature control program to select the appropriate pump, you can ensure the electrochemical machining of the electrolyte requirements. Joined the agitation system can control the concentration of electrolyte in order to ensure processing quality. Keywords ECM Electrolyte Filter Temperature Control Electrolyte tank 南 京 理 工 大 学 紫 金 学 院毕业设计(论文)开题报告学 生 姓 名： 吴文俊学 号：060104206专 业：机械工程及自动化设计(论文)题目：数控电解机床电解液输送装置系统设计指 导 教 师:赵建社 2010年 3 月 19 日 毕 业 设 计（论 文）开 题 报 告1结合毕业设计（论文）课题情况，根据所查阅的文献资料，每人撰写2000字左右的文献综述：文 献 综 述特种加工技术属于机械制造学科的科研前沿。电解加工是特种加工技术中应用最广泛的技术之一尤其适合于难加工材料、形状复杂或薄壁零件的加工。加工时，工件为阳极，接电源正极；工具为阴极，接电源负极，极间通以524V的直流电，同时保持一定的加工间隙，间隙内流过具有一定压力（0.52MPa）的电解液(一般为中性盐的水溶液，常用的为NaCl或NaNO3水溶液)，阳极逐渐溶解，电解产物被高速（550m/s）电解液带走。如果工件初始形状与工具阴极形状不同，则工件上各点距离工具阴极型面的距离不同，相应地，各点的电流密度（一般为10500A/cm2）也不同。距离近的位置，相应的电流密度相对较大，阳极溶解速度快；反之，距离远的位置，电流密度小，相应的电流密度相对较小，阳极溶解速度慢。经过一段时间的电化学溶解，工件表面形成与阴极工作面基本相似的形状2。电解加工以其加工速度快，表面质量好，不怕材料强、硬、韧，无宏观机械切削力，工具阴极无损耗，可用同一个成型阴极作单方向送进而成批加工复杂型腔、型面、型孔等优点15，20世纪60年代初，首先在炮管膛线和航空发动机涡轮叶片的加工中得到应用；其后又逐渐扩大应用于加工锻模型腔、深孔、小孔、长键槽、等截面叶片整体叶轮以及去毛刺等，取得了显著的技术经济效果5。70年代以后，虽然其应用范围有所减小，但应用要求更高且在某些新的领域又得到新的应用6。电解加工设备是一个完整的配套系统，由机床、电源、输液系统、以及控制系统四大部分组成1。在国内,南京航空学院、西北工业大学，航天航空工艺研究所和首都机械厂等单位相继开展了脉冲电流电解加工的研究。尤其是在1987年.合肥工业大学特种加工研究所研制出大功率脉冲、直流两用电源(脉冲电流峰值达5000安培).并应用于锻模生产12。近几年来华南理工大学等又开展了高振窄脉冲电解加工的研究，最小加工间隙0.05mm， 加工精度显著提高13。可以预见，高频窄脉冲加工将成为提高电解加工精度的最重要手段之一。近年来我国生产企业的数控机床拥有率率逐年上升，在大中型企业已有较多的使用，在中小企业甚至个体企业中也普遍开始使用14。在这些数控机床中，除少量机床以FMS模式集成使用外，大都处于单机运行状态，并且相当部分处于使用效率不高，管理方式落后的状态3。目前世界数控机床消费趋势已从初期以数控电加工机床、数控车床、数控铣床为主转向以加工中心、专用数控机床、成套设备为主4。电解液的研究和改进方面，七十年代初，除了传统的NaCl线性电解液之外，国际上也开展了以NaNO3,和NaClO3为代表的非线性电解液的应用研究。我国是较早研究非线性电解液的国家之一，在八十年代初，合肥工业大学通过对电流效率曲线的试验研究，证明低浓度NaNO3电解液具有良好的尺寸控制性能7。在此基础上，又对非线性复合电解液进行了深入研究，获得一系列适合不同加工材料的电解液配方，从而在满足提高加工精度要求的同时，又克服了低浓度非线性电解液的电流效率和电导率低的缺点，因而更适合于实际生产8。正确使用电解液是电解加工的重要条件电解液在电l解过程中要起到导电并形成电化学反应的作用，一般其反应能力对于铁、铬、镍等金属以卤素族作电解质能力最强，而以OH一为最差，电解液还要有利于避免正离子沉附于负极，以这点来说，Na、K为最好，电解液的溶剂要求有较高的导电率外，还要有较低的粘度，以利于离子的流动，以水溶液为佳12。常用的电解液有12 18的氯化钠溶液和14 20硝酸钠溶液，一般由于氯化钠溶液腐蚀速度比硝酸钠溶液快，所以常用于去除大量材料的加工，如电解针阀体盛油槽，泵体内孔去毛刺等。相反，硝酸钠溶液的加工精度比氯化钠溶液要高14。电解液的各种参数对电解加工过程有显著影响的是浓度和温度一般在其它条件相同时，电解液浓度低，表面粗糙度就好，加工精度就较高18。另外，实践证明，当电解液的温度高于4O 5O时，加工部位表而质量明显破坏，精度下降，为了不影响生产效率 温度下限也不宜过低，一般控制在3o 35 以保证加工尺寸的一致性16。电解液系统还必须有足够的流速，藉以清理正极表面，带走沉淀物，并冷却加工反应区，因此，电解液系统应实现较高的压力一般为5至15个大气压与较大的流速5 ms10 ms15。另外，电解液必须经过过滤，把腐蚀物和杂质过滤出，不但加工质量好，而且不容易短路。目前过滤的方法有沉淀过滤，离心过滤，陶瓷芯(纸芯)过滤三种17。本课题中，设计要求电解液输送系统在保证现有循环过滤的基础上，增加恒温及压力控制装置，使得加工过程中电解液参数易于精确控制，从而提高电解加工精度。即包括电解液输送装置设计和电解液温度控制系统设计两部分，其输送装置是为了满足电解加工过程中对电解液的过滤、输送、压力、流量控制等要求，其温度控制系统是为了满足对电解液温度实现智能控制的要求，这一设计可以提高电解加工机床的智能化、数字化程度，可以提高生产效率、减小工人劳动强度、提高经济效益。电解液的温度控制系统的设计是本次设计的关键，电解液的温度是影响电解加工的重要因素，为了精确的方便的对电解液温度进行控制，我将选用80C552单片机和热电耦等电器元件共同构成温度控制硬件系统，最后同过编制汇编程序以达到温度恒定控制的要求，这套系统可达到对电解液温度的精确智能控制。本课题还要求设计电解液液压控制系统，可以选用合理的液压元件和动力元件构成整个装置可满足方案要求，以达到对电解液的流速和压力的控制。参考文献：1 王建业, 徐家文. 电解加工原理及应用M. 北京: 国防工业出版社, 2001.12 刘晋春，赵家齐，赵万生. 特种加工M. 机械工业出版社，1998.8：833 北京市金属切削理论与实践编委会. 电解加工J. 北京: 北京出版社，19814 朱荻.电解加工阴极型面计算机辅助设计基础研究M. 南京航空学院博士论文, 19855 洛阳拖拉机厂等. 锻模混气电解加工总结(一)M. 电加工，1977(3)6 余承业等编著. 特种加工新技术M. 北京: 国防工业出版社，19957 朱树敏. 低浓度硝酸钠电解液的特性和应用电加工M. 1983(4).8 朱树敏, 陈淑芬, 张海岩. 低浓度复合电解液的性能及应用J. 电加工，1985(6)9 K .Kobayashi.The Present and Future Development of EDM and ECM. Proceeding of the 11th ISEM(1995).10 钱军. 精密电解加工及大功率脉冲斩波器的研究. 南京航空航天大学博士论文J，199611 金庆同, 余承业. 探讨赶上国际先进水平的途径. 全国电加工学术年会论文集M. 1993.12 朱树敏，沈光祖锻模的脉冲电流电解加工J. 电加工，1990(1).13 王建业电解加工技术的新发展 高版窄脉冲电流电解加工J. 电加工，1998(2)14 张永俊数控展成法电解加工扭曲叶片整体叶轮的研究南京航空航天大学博士论文J，1994.15 电解加工编译组编译电解加工一根据国外资料编译M. 北京: 国防工业出版社, 1977.16 朱荻. 国外电解加工的研究进展J. 电加工与棋具，2000(1).17 徐锦康机械设计M北京：机械工业出版社，200118 章成军. 电解加工原理及应用. 上海浦东依维燃油喷射有限公司J. 2003.19 丁苏赤, 陈远龙, 万胜美. 基于可编程控制器技术的新型数控电解加工机床J.机械工人，2004,(1)：29-31. 毕 业 设 计（论 文）开 题 报 告本课题要研究或解决的问题和拟采用的研究手段（途径）：一要求解决的问题：（1）根据电解加工机床的设计要求,设计电解液槽的结构。（2）电解液的恒温控制，系统要求对电解液的温度有精确的控制，以达到更高的电解加工精度。（3）电解液的液压输送系统，要求能精确控制电解液输送的流速和压力。二解决的方法：（1）学习电解加工的基本原理，要严格按照毕业设计任务书的要求及安排的进度，在综合运用机械工程及自动化专业知识的基础上，设计合理的符合任务要求的系统装置。（2）采用80C552单片机及相关硬件组成微机基本系统采用汇编语言进行单片机编程，以实现温度控制，并采用热电耦、键盘、显示管等硬件与上述硬件设备共同构成温度控制模块,安装加热和冷却装置，以调节温度。（3）液压输送系统选取液压泵，电动机，和溢流阀，节流阀，单向阀等液压元件来组成。（4）电解槽选用玻璃钢来制造，安装过虑网，采用4级逐级过虑方法，设计4个电解槽，使电解液流经自然沉淀。（5）使用AUTOCAD等二维工具，完成液压控制输送系统及电解槽的结构、零部件和总体设计等。 毕 业 设 计（论 文）开 题 报 告指导教师意见：1对“文献综述”的评语：从文献综述可看出已经查阅了较多资料，对电解加工原理、设备及电解液系统有了初步认识，对国内外研究情况进行了较详细的介绍。但有总体思维逻辑顺序有点混乱，希望更进一步阅读资料进行整理分析，以利于在后续设计工作中借鉴和参考。2对本课题的深度、广度及工作量的意见和对设计（论文）结果的预测：本课题是在研省部级研究项目中的一项重要研究内容，需要学生参与实质性的科研设计工作，对电解加工设备有个总体认识的基础上，设计电解液循环过滤系统，涉及知识面比较广泛，工作量较大，但已经有较好研究基础，开题报告表明学生对需解决的问题明确，拟采用的研究方法可行，通过学生的努力，能够完成预计工作，达到预期效果，同意开题。 指导教师： 年 月 日所在专业审查意见： 负责人： 年 月 日 本科毕业设计说明书（论文） 第 页 共 页目 次1 引言12电解液输送装置的总体设计思路32.1 电解液输送装置总体方案论证33 电解液槽总体结构设计63.1 设计基础及分析63.2 电解液槽材料的选择63.3 电解液槽结构设计634电解液过滤器的设计和选择74 电解液搅拌装置设计94.1 搅拌叶轮的选用104.2 搅拌系统传动方案设计124.3 搅拌支架的结构设计145 温度控制系统设计185.1 温度控制硬件电路的设计185.2 温度控制的算法215.3 温度控制程序设计22结论33致谢34参考文献35The mathematical modelling of electrochemical machiningwith flat ended universal electrodesAdam Ruszaj*, Maria Zybura-SkrabalakThe Institute of Metal Cutting, Cracow, PolandAbstractFormer investigations have proved that it is possible to reach significantly higher accuracy in comparison to classical electrochemicalsinking when universal electrodes are applied. When the ball ended universal electrodes are applied the majority sculptured surfaces can bemachined using 3D electrode displacement control system. When flat ended universal electrodes are applied for sculptured surfacesmachining usually the 5D electrode displacement control system must be applied. However, the last case gives the possibility to achieve thehigher metal removal rate. In this paper the primary investigations of machining with flat rectangular universal electrode are presented.# 2001 Elsevier Science B.V. All rights reserved.Keywords: Mathematical modelling; Universal electrodes; Machining1. Problem formulationInvestigations in the field of electrochemical machiningwith ball ended electrode proved that this way of machiningis very useful, especially in sculptured surfaces finishing.The main disadvantage of machining with ball ended elec-trode is small metal removal rate 13. In order to increasethe metal removal rate the investigations with flat endedelectrode have been undertaken. The scheme of sculpturedsurface machining with ball ended and flat rectangularelectrodes are presented in Fig. 1. The condition whichshould be fulfilled for flat ended electrode is: electrode axisof symmetry should be perpendicular to machined sculp-tured surface.In order to fulfil this condition the electrode displacementshould be controlled at least in 45 axes, while in the case ofmachining with ball ended electrode in three axis.In order to prove that it is right to build a test standequipped with 5 axes control unit the primary investigationsinthecaseofmachiningflatsurfacehavebeenundertaken.Atfirst the mathematical model has been built and then experi-ments have been carried out for the case presented in Fig. 2.2. The mathematical modelThe scheme of machining process, which is being ana-lysed is presented in Figs. 2 and 3. The rectangular universalelectrode is displaced over the machined surface. Theelectrochemical machining action takes place only in thearea below the electrode.Electrolyte is supplied into the machining area by aspecialnozzle insidewhichtheelectrodeismounted.Duringoneelectrodepassthematerialexcessaisremoved(Eq.(1):ai? s ? s0(1)Time of machining of an optional point on machined surfaceduring one electrode pass t can be calculated from Eq. (2):t ?bvp(2)Accordingly 1,4, the interelectrode gap thickness is givenby Eq. (3):s ?Bt ? s20q?(3)From Eqs. (2) and (3) result that thickness of interelectrodegap after oneelectrode pass decreases together with increaseof velocity of the electrode displacement and the same withdecrease of machining time.Taking into account the relationships (1)(3), Eq. (4) canbe obtainedai?Bt ? s20q? s0?(4)where B ? 2Zkvk?U ? E? is the constant of the machiningprocess, Z the current efficiency of electrochemical dissolu-Journal of Materials Processing Technology 109 (2001) 333338*Corresponding author.0924-0136/01/$ see front matter # 2001 Elsevier Science B.V. All rights reserved.PII: S0924-0136(00)00816-5tion process, kvthe electrochemical equivalent of machinedmaterial, k the electrolyte electrical conductivity, U themean interelectrode voltage, E the mean drops of potentialin the layers adjacent to the electrode and workpiece, aithethickness of material excess removed during one electrodepass, b the electrode length, s0the distance between elec-trode face and machined material initial interelectrodegap thickness in successive electrode pass, s the interelec-trodegapthicknessaftereachelectrodepassandtthetimeofmachining during successive electrode pass.From Fig. 2 it results that in the casewhen c b the samearea of machined surface can be machined during a fewelectrode passes. In this case the total material excessremoved can be calculated from the relationship:at?Xi?ni?1ai(5)where atis the total thickness of the material excessremoved, aithe thickness of material excess removed duringith electrode pass calculated from relationship (4), n thenumber of electrode passes over taken into account area.Material removal rate:Vw?Flt? at?vp;s0;U;c?cvp(6)where Vwis the metal removal rate, F the surface of materialexcess removed cross-section in a direction perpendicular toelectrode displacement.From the above presented relationships it results that:? together with velocity of electrode displacement increasethickness of material excess removed decreases becausetime of machining during one electrode pass alsodecreases;? metal removal rate increases with velocity of electrodedisplacement, however, at the same time, thickness ofmaterial excess removed decreases what is the reason ofmetalremovalratedecrease; inotherwordswhenvelocityof electrode displacement is higher than optimal value,Fig. 1. Scheme of sculptured surface machining with ball ended and flatrectangular electrode.Fig. 2. Scheme of electrochemical machining with universal rectangular electrode moving above the machined surface. E: electrode made of M1 copper, P:workpiece made of NC6 steel (hardness 64 HRC), E1and E2: position of electrode in the first pass (E1), second pass (E2), and so on 1,2.Fig. 3. Scheme of ECM machining with rectangular universal electrodedisplaced over machined surface. vp: velocity of electrode displacement; 1:workpiece; 2: electrode tool; 3: nozzle for electrolyte supplying intointerelectrode gap; s0: thickness of initial interelectrode gap; s: thickness ofinterelectrode gap after time t; b: electrode length.334A. Ruszaj, M. Zybura-Skrabalak/Journal of Materials Processing Technology 109 (2001) 333338metal removal rate decreases together with velocity ofelectrode displacement increase;? together with interelectrode voltage increase thickness ofmaterial excess removed and metal removal rate increasesbecausetheintensityofdissolutionprocessalsoincreases;? together with initial interelectrode thickness decrease thecurrent density and intensity of dissolution processincreases which is the reason of thickness of materialexcess removed and metal removal rate increase; how-ever, for small interelectrode thickness values the hydro-dynamic conditions become worse which can limit theintensity of dissolution process by increase of hydrogenconcentration and electrolyte temperature;? thickness of material excess removed and metal removalrate increase together with electrode dimensions increase;however, electrode dimensions are limited because ofworse and worse hydrodynamic conditions into themachining area;? together with electrode cross feed increase the time ofmachining decreases which is the reason of thickness ofmaterial excess removed decrease and metal removal rateincrease.From the above presented model it is difficult to deducesurface waviness (shape errors on the border line betweensuccessive electrode passes); taking into account formerinvestigations 2,3 with ball ended electrode it is possibleto state that waviness should increase together with elec-trode cross feed; electrode cross feed should be chosen so asthe total time of machining was constant for each area onmachined surface; waviness will be also dependent onelectrode edges reproduction in machined material; a moredetailed explanation will be possible after experimental testresults analysis.3. Experimental testsExperiments have been carried out for the case presentedin Figs. 2 and 3. In the result of analysis of phenomenaoccurring in interelectrode gap the following factors havebeen distinguished.Input factors:vpvelocity of electrode tool displacement,vp? 1?59mm=minUinterelectrode voltage, U ? 8?20Vs0initial interelectrode gap thickness, s0? 0:1?1:3mmccross feed per electrode pass, c ? 0?5mm=passOutput factors:attotal thickness of material excess removed duringmachiningDmachined surface waviness (shape error on theborder line between successive electrode passes)Vwmetal removal rateConstant factors:peinlet electrolyte pressure, pe? 1MPabdimensions of the electrode, b ? 5mm; electrodematerial, copper Cu; machined material, hardenedsteel NC6CeNaNO3water solution concentration, Ce? 15%For experimental test results presentation the neural netshave been applied. The neural nets give significantly lowererrors of approximation in comparison to equations ofregression. In the presented investigations the three-layerneural nets have been applied.1Using these nets it is veryeasy tofindoutquickly machiningprocessindicatorsforanycombinations of investigated parameter values. Main tech-nologicalindicatorsofthe process: a,Dand F(necessaryformetal removal rate calculations) have been taken fromprofilograms of machined surface cross-section in the direc-tion perpendicular to electrode displacement. Examples oftheseprofilogramsarepresented inFigs.4and5.Someotherresults of experiments obtained from neural nets are pre-sented in Figs. 68.From Figs. 4 and 5 result that primary explanation ofrelation between D and electrode cross feed c was right.In the case presented in Fig. 4, c was too high incomparison to electrode dimensions and because of thisfact in the machined surface there are areas with differenttotal times of machining. As a result waviness D is sig-nificant. In the case presented in Fig. 5 cross feed c wassmaller and total time of machining was for the wholemachined surface constant. Waviness D was in this casecreated mainly as a result of electrode edges reproductionin machined material and its value is significantly smallerthan in the case presented in Fig. 4. Process of electrodeedges reproduction depends significantly on interelectrodevoltage U and velocity of electrode displacement vp(seeFig. 6).From Fig. 6 results that electrode edge reproduction inmachined material depends on thickness of material excessremoved and waviness D increase with decrease of velocityof electrode displacement and increase of interelectrodevoltage U. However, there is an optimal value of U forwhich the waviness reaches minimum. Relationships pre-sented in Figs. 7 and 8 can be explained using a mathema-tical model (as it has been done above in analysis ofmathematical model).Below, the comparison between experimental test result-sand results of theoretical calculation will be presented(Figs. 912). The theoretical calculations have been carriedoutunderassumptionthatZkv? 1:7mm3=Amin,k ? 0:13O?1cm?1and E ? 0. In reality, above specifiedcoefficients, are not constant and change together withprocess parameters (especially current density: j ? f?U;vp?.1The neural nets have been built and taught by Dr. Inz . KrzysztofKarbowski from Cracow University of Technology.A. Ruszaj, M. Zybura-Skrabalak/Journal of Materials Processing Technology 109 (2001) 333338335From Figs. 911 result that generally the differencesbetween results of experiments and theoretical calculationare not significant, but there are some exceptions. Forinstance, for small values of interelectrode voltage (Fig. 9)and velocity of electrode displacement (Fig. 12). In this casebecause of high electrodes polarisation and passivationphenomena the real process is stopped for same values ofinterelectrode gap thickness while the theoretical processcarried out according to the above presented mathematicalmodel does not taken into account this fact.This is the reason for significant differences betweenexperimental tests and theoretical calculation results forsmall values of U and vp.Mathematical model can also be used for waviness cal-culation. But only waviness resulted from differences inmachining time for different areas of machined surface canFig. 4. Machined surface cross-section in the direction perpendicular to electrode displacement for process parameters: U ? 17V, vp? 15:5mm=min,s0? 0:4mm, c ? 3:75mm=pass, at? 0:371mm, D ? 0:109mm (from experimental tests); at? 0:403mm, D ? 0:169mm (from theoretical calculations).Fig. 5. Machined surface cross-section in the direction perpendicular to electrode displacement for process parameters: U ? 17V, vp? 44:5mm=min,s0? 0:4mm, c ? 1:25mm=pass, at? 0:299mm, D ? 0:008mm (from experimental tests); at? 0:304mm, D ? 0mm (from theoretical calculations).Fig. 6. Relationship D ? f?U;vp? for s0? 0:1mm and c ? 1:25mm=pass (according to the mathematical model, D ? 0).336A. Ruszaj, M. Zybura-Skrabalak/Journal of Materials Processing Technology 109 (2001) 333338be calculated (see Fig. 4). Using this model, it is impossibleto calculate the waviness resulting from electrode edgesreproduction in machined area. But this component ofwaviness is not significant in the analysed case (Figs. 5and 6) on condition that time of machining is constant foreach point of machined surface.4. RecapitulationTaking into account results of former investigations 13and above presented considerations it is right to state thatwhen machining with flat electrode it is possible to reachhigher metal removal rate and smaller machined surfacewaviness than in the case of machining with ball endedelectrode. This statement is true for the electrodes with theFig. 7. Relationship at? f?U;vp? for s0? 0:1mm and c ? 1:25mm=pass.Fig.8. RelationshipVw? f?U;vp?fors0? 0:1mmandc ? 1:25mm=pass.Fig. 9. Relationship at? f?U?. 1: experimental tests results, 2: results ofcalculations when using the above presented mathematical model, otherparameters: c ? 2:5mm=pass, U ? 14V, s0? 0:7mm, vp? 30mm=min.Fig. 10. Relationship at? f?s0?. 1: experimental tests results, 2: results ofcalculation when using the above presented mathematical model, otherparameters: c ? 2:5mm=pass, U ? 14V, vp? 30mm=min.Fig. 11. Relationship at? f?c?. 1: experimental tests results, 2: results ofcalculations when using the above presented mathematical model, otherparameters: U ? 14V, s0? 0:7mm, vp? 30mm=min.Fig. 12. Relationship at? f?vp?. 1: experimental tests results, 2: results ofcalculations when using the above presented mathematical model, otherparameters: c ? 2:5mm=pass, U ? 14V, s0? 0:7mm.A. Ruszaj, M. Zybura-Skrabalak/Journal of Materials Processing Technology 109 (2001) 333338337samemachiningsurface.Itmeansthattheconditionbelowisfulfilled:F1? ab ? F2? pR2(7)where F1is the surface of flat electrode, F2the surface of theball ended electrode main cross-section.The increase of metal removal rate in the case of machin-ing with flat electrode results from the fact that the meaninterelectrodegapthicknessishigherthanincaseofmachin-ing with ball ended one. But increase of the flat endedelectrode surface is limited by hydrodynamic conditionsinto interelectrode area and radius of machined surfacecurvature. For electrode surface higher than in the caseof presented