Time Estimation for Sinking EDM Operations

Transcription

1 Tme Estmaton for Snkng EDM Operatons W. Vanderauwera, B. Lauwers Department of Mechancal Engneerng, Dvson PMA, K.U.Leuven, Leuven, Belgum Abstract Although EDM s wdely used n ndustry, lttle research has been undertaken nto the complex problem of accurately estmatng the machnng tme. Often estmaton errors of 200% and more occur. Ths paper ntroduces a new concept for accurately estmatng the machnng tme for snkng EDM operatons. The concept s based on machne dependent reference values on whch a correcton factor s appled to take devatons from the reference, due to flushng and effcency, nto account. A valdaton of the proposed concept showed that for the machnng of prsmatc cavty shapes a huge reducton of the estmaton error s acheved compared to exstng methods. Keywords: Tme estmaton, Snkng EDM INTRODUCTION Electrcal dscharge machnng (EDM) s one of the most wdely used non-tradtonal machnng processes n the mould makng and precson sector. One of the varants of EDM s snkng EDM n whch a preshaped electrode moves nto the workpece. The result of such an operaton s a cavty whch has the negatve shape of the electrode. Unlke tradtonal processes the machnng speed of EDM operatons depends on the process condtons. Ths means that one needs to have an dea of the process condtons n order to make an estmaton of the EDM tme. Research has been carred out n whch especally the nfluence of electrcal parameters (e.g. dscharge current e, dscharge duraton t e) on the machnng speed has been nvestgated [,2]. Besdes the electrcal parameters also the flushng condtons affect the machnng speed [3]. Rather less attenton has been pad to the quantfcaton of the effect of flushng related parameters on machnng speed and EDM tme. Even by knowng the effect of all these parameters accurate EDM tme estmatons were not always possble n the past due to the often unpredctable behavour of the process. Tme estmatons were mostly based on rules of thumb or based on values for the materal removal rate (MRR) determned by the machne tool bulders. These values are determned wth smple electrodes under deal flushng condtons. As a result estmaton errors of 200% and more occurred even when estmated by experenced persons [4]. The recent development of automated flushng technques and optmsaton of machne controllers ncreased the relablty of the process and cleared the way for accurate EDM tme estmatons. However, lttle research has been conducted n developng a systematc approach for accurately estmatng the EDM tme. The most pronounced result that can be found n lterature s the development of an EDM tme estmaton software tool, named EDcam [4], but wth lmted results. Ths paper proposes a new concept for estmatng the machnng tme of snkng EDM operatons by takng the effect of flushng and effcency related parameters nto account. Ths study manly focused on tme estmatons for machnng cases havng a prsmatc geometry because these appear n most of the cases n practce. It s nvestgated whether more accurate results can be obtaned compared to exstng EDM tme estmaton methods. 2 CONCEPT OF EDM TIME ESTIMATION In ths study EDM tme estmatons are based on reference values for the EDM tme. For every generator settng of an EDM technology a reference value needs to be determned. In ths way the nfluence of electrcal parameters lke e and t e s already ncluded. These reference values are determned by a so called calbraton procedure whch conssts of machnng cylndrcal cavtes wth predefned dmensons and loggng the correspondng EDM tmes. The way n whch the calbraton s performed resembles more to the daly practce use of EDM compared to the way n whch EDM machne tool bulders determne ther characterstc values. By performng ths calbraton procedure for every EDM machne also the machne characterstcs (e.g. behavour of electrode pulsaton, protecton measures) are largely ncluded. A tme estmaton solely based on reference values wll not gve accurate results. Intal experments showed that devatons from the reference values occur when comparng dfferent machnng cases although machned wth dentcal generator settngs on the same EDM machne. These devatons are the result of a dfference n debrs densty n the sparkng gap. The debrs densty s manly nfluenced by two groups of parameters: flushng related parameters (e.g. actve area, machnng depth) and effcency related parameters (e.g. e, t e, t o, current densty). In the concept of ths study devatons are taken nto account by correctng the reference values. Ths correcton s dependent on the machnng case and s therefore functon of factors causng the devaton. Not only between machnng cases devatons from the reference values occur (e.g. devatons due to a dfferent cavty shape) but also wthn a machnng case the devaton can fluctuate (e.g. varaton of MRR caused by the machnng depth). A consequence of ths s that the 6th Internatonal Symposum on Electromachnng (ISEM XVI)

2 correcton on the reference values needs to be dependent on the varaton of nfluencng parameters durng an EDM operaton. Because of ths the EDM tme s estmated as a summaton of EDM tmes of small machnng steps. Equaton shows ths summaton for the case of an EDM operaton wth only one generator settng. n EDM Tme = C tme ref () = Wth: the th calculaton step; n the total number of calculaton steps; C the correcton on the reference tme; tme ref the reference EDM tme. In standard EDM operatons two knds of operatons can be dstngushed namely roughng and fnshng operatons. Roughng operatons refer to the part of an EDM operaton n whch hgh energetc generator settngs are used n combnaton wth a snkng electrode movement. These operatons remove the bulk of the materal n a relatvely fast way. On the other hand fnshng operatons refer to the part of an EDM operaton n whch low energetc generator settngs are used n combnaton wth ether a snkng or a planetary electrode movement. The purpose of these operatons s to obtan the desred end roughness. Intal experments showed that for both operaton types dfferent parameters nfluence the EDM tme. Consequently dfferent analytcal models have been developed both based on the general concept gven n Equaton (see secton 3 and 4). Followng the dstncton between roughng and fnshng operatons the total EDM tme s estmated as the summaton of the estmated roughng and fnshng tme. The next sectons dscuss the elaboraton of the concept for roughng and fnshng operatons. All experments n ths study have been performed on an EDM de snkng machne, type AgeCharmlles FO350γ, wth Total MS 7000 as delectrc. Copper was used as electrode materal and hardened steel (Sverker 2) as workpece materal. Durng these experments only the standard electrode pulsaton was used for flushng. 3 TIME ESTIMATION FOR ROUGHING OPERATIONS 3. Formulaton of EDM roughng tme Durng EDM roughng operatons the bulk of the cavty materal s removed. In fact, these operatons can be seen as volume removal operatons n whch the volume exerts a large nfluence on the EDM tme. To decouple the nfluence of the volume from the nfluence of other parameters affectng the EDM tme, the MRR [mm³/mn] has been chosen as the reference parameter (MRR ref). MRR ref s determned by the calbraton procedure. Ths procedure conssts of machnng cylndrcal cavtes wth a depth of 20mm n steps of mm for every generator settng wth a fxed current densty of 9A/cm². For each mllmeter MRR ref s calculated. As a result MRR ref s functon of the machnng depth. For roughng operatons the correcton on the reference values wll be splt up nto two correcton factors: a flushng factor (C flushng) and an effcency factor (C effcency). These factors are functon of parameters nfluencng the debrs densty n the sparkng gap and resultng n a devaton from the reference. C flushng corrects MRR ref for the effect of flushng related parameters (e.g. frontal electrode area, machnng depth) on the EDM roughng tme. On the other hand C effcency corrects MRR ref for the effect of effcency related parameters (e.g. current densty). Appled to the common case of an electrode wth multple dentcal protrusons (see Fgure ) C flushng takes the effect of the flushng condtons of one protruson nto account. Due to a dfference n current densty C effcency takes the addtonal effect of havng more than one of these protrusons nto account. Fgure : Electrode wth multple dentcal protrusons. Followng Equaton the EDM roughng tme s calculated as a summaton of EDM tmes, each representng the machnng of an ncremental volume along the snkng drecton (Fgure 2). Equaton 2 shows the formulaton of the EDM roughng tme for the case of usng only one generator settng durng the roughng operaton. n Volume EDM Tme = roughng (2) = Ceffcency Cflushng MRRref Wth: the th calculaton step; n the total number of calculatons steps; Volume the volume removed durng the th step; MRR ref the reference MRR for the th step. = 4, Vol 4, C flushng,4, C effcency,4 = 3, Vol 3, C flushng,3, C effcency,3 = 2, Vol 2, C flushng,2, C effcency,2 =, Vol, C flushng,, C effcency, Fgure 2: Incremental calculaton of EDM roughng tme. 3.2 Modellng of correcton on MRR ref A large number of parameters nfluence the EDM roughng tme. In ths study only the most mportant parameters were consdered n order to make an accurate EDM tme estmaton possble for rather smple machnng cases. These parameters were ether related to C flushng or C effcency by nvestgatng ther effect on the MRR. The relaton between MRR and the correcton factors s gven n Equaton 3. MRR(depth) = Ceffcency Cflushng MRRref (depth) (3) Modellng of C effcency The ntal purpose of C effcency was to nclude the effect of multple dentcal protrusons nto the tme estmaton (see Fgure ). The current densty [A/cm²], defned as the mean current dvded by the actve frontal electrode area, s a good parameter to characterze ths effect. The mean current s calculated based on parameters lke maxmal current, t e, t 0 and the servo parameter. To examne the effect of the current densty on the MRR machnng experments were performed n whch the current densty was vared by varyng both the frontal surface area and the mean current (see Table ). Each experment conssted of a machnng operaton untl a depth of mm was reached and determnng the resultng MRR. Each experment was performed 3 tmes. The determned MRR was compared to MRR ref(0-) resultng from the calbraton procedure for machnng between 0 and mm n depth. Accordng to Equaton 3 the total correcton was calculated. In order to determne C effcency, C flushng needs to be known. C flushng for these experments was

3 determned by performng an extra experment for each frontal area at a fxed current densty of 9A/cm². Because MRR ref s also determned at 9A/cm² C effcency equals for these experments. Consequently the total correcton s equal to C flushng. Frontal Area [mm²] Mean current [A] C flushng C effcency 39 9/3.4/ /0.62/ /3.4/ /0.75/ / / /9.2.2/ /6.7/9/ /.3/.4/.4 Table : Testng plan and results for C effcency. By usng a test setup smlar to the one shown n Fgure 3 the flushng condtons could be held constant durng each experment. In ths setup a cylndrcal workpece s machned wth a cylndrcal electrode of the same dameter so that the top of the workpece s removed layer-by-layer. The results of these experments are lsted n Table and shown graphcally n Fgure 4. Ths fgure clearly shows that C effcency decreases when hgher current denstes are used. Note that C flushng gven n Table s only vald for the test setup n Fgure 4. C effcency,6,4,2 0,8 0,6 0,4 0,2 0 Fgure 3: Test setup for C effcency Current densty [A/cm²] Fgure 4: Relaton between C effcency and current densty. Modellng of C flushng The flushng factor refers to the part of the devaton from the reference value caused by the flushng condtons. Ths factor was determned by correlatng flushng related parameters to t. In ths study only the machnng depth and the frontal surface area were consdered as nfluencng parameters. Machnng experments were performed n whch rectangular cavtes were machned wth machnng depths rangng from mm to 20mm wth steps of mm and wth varyng frontal surface area (see Table 2). Each experment was performed 3 tmes and as a result the MRR was determned. Wth the knowledge of MRR ref and C effcency (estmated by the trend from Fgure 4) C flushng was calculated accordng to Equaton 2. From these experments some conclusons can be drawn. Frstly these experments showed that the machnng depth strongly affects the MRR. Ths can be clearly seen n Fgure 5 whch shows the results of some experments together wth the MRR ref for the appled generator settng. Ths fgure shows that especally for small machnng depths the effect on the MRR s clear. Ths fgure also ndcates that the nfluence of the machnng depth s affected by the current densty. Ths can be explaned by consderng the debrs densty n the sparkng gap. In [5] t s stated that an optmal debrs densty exsts whch results n an optmal MRR. Experments showed that besdes the flushng condtons also the current densty affects the debrs densty (an ncrease of the current densty results n an ncrease of the debrs densty). Appled to Fgure 5, the combned effect of a low current densty and an ncreasng machnng depth results n a more optmal debrs densty (especally for small depths). As a result an ncrease of the MRR can be noted. In case of hgh current denstes ntally more debrs are generated but due to the varyng flushng condtons resultng from an ncrease of the machnng depth the debrs densty becomes larger than the optmal value. Ths results n a decrease of MRR. Mean Current [A] MRR [mm³/mn] Table 2: Experments for determnng C flushng Frontal Area [cm²] Number of Protrusons Current Densty [A/cm²] /0.5 / 9.6/ /0.5 / 3.8/ /0.5/0.75/ /// 26.9/3.4/9/ / / 8/ ///.5/.5/ 2/3 6//2//2/ / 4.5/3.4/6.7/9/4.5/ 6.7/ //2/2/3 /2//2/ 20/0/0/0/5/ ///.5/2/ 3/3/4/6 6//2/2// /// /32/6//6/ //8/ /4 2/ 22.76/.38 MRRref A B Depth [mm] Fgure 5: Influence of the machnng depth on the MRR (A: 20A, 2x2cm², 5A/cm²; B: 20A, cm², 20A/cm²). More mportant for the modellng of C flushng s to look at the relaton between C flushng and the machnng depth. In fgure 6 C flushng s shown for the same cases as shown n Fgure 5. Fgure 6 shows that C flushng s dependent on the machnng depth. Ths means that the machnng depth needs to be taken nto account n the modelng of C flushng. Secondly these experments showed that there exsts a relaton between the frontal surface area of the electrode and C flushng. Ths relaton s shown n Fgure 7 for two current denstes when comparng 3 frontal areas at a depth of 5mm. Smlar to the results of the nfluence of the machnng depth ths fgure shows that the relaton

4 between the frontal area and C flushng s affected by the current densty. In case of low current denstes C flushng ncreases wth ncreasng frontal surface area. Most probably the debrs densty wll ncrease towards the optmal value when the flushng condtons become worse (e.g. for large frontal areas) because ntally the debrs densty was low due to the low current densty. On the contrary n case of hgh current denstes the debrs densty s ntally hgh so that good flushng condtons are needed to obtan the optmal densty. Here most probably large frontal areas accumulate too much debrs n the sparkng gap leadng to a hgher than optmal debrs densty. C flushng 3,0 2,5 2,0,5,0 0,5 0,0 5A/cm² 20A/cm² Depth [mm] Fgure 6: Influence of the machnng depth on C flushng. C flushng,8,6,4,2 0,8 0, Frontal surface area [mm²] Fgure 7: Relaton between frontal area and C flushng. Due to the nteracton between the current densty on the one hand and the machnng depth and frontal area on the other hand t was necessary to also nclude the current densty nto the modelng of C flushng. As a result C flushng looses ts ntal meanng of a purely flushng related correcton factor. Nonetheless C flushng s especally a functon of flushng related parameters. Wth the determned nfluencng parameters (machnng depth, frontal area and current densty) a least squares approxmaton of second order was appled to all test results n order to develop a model for C flushng. 4 TIME ESTIMATION FOR FINISHING OPERATIONS 4. Formulaton of EDM fnshng tme 4,5A/cm² A/cm² Unlke roughng operatons where the focus s on the volume to be machned fnshng operatons machne the surface of a cavty n order to obtan the requred end roughness. Due to the large uncertanty about the volume to be removed durng these operatons a formulaton as n Equaton 2 wll not be used. Instead of usng the MRR the EDM fnshng tme s used as reference. These reference tmes (tme ref) are determned for every generator settng by fnshng a pre-machned cylndrcal cavty wth predefned dmensons by applyng a planetary electrode movement (= calbraton procedure). On these reference tmes a correcton s appled whch takes the devaton from tme ref nto account. A fnshng operaton usually conssts of several generator settngs, each of them reducng the surface roughness. The total EDM fnshng tme s then the sum of the machnng tmes of all generator settngs appled durng a fnshng operaton (Equaton 4). m EDM Tmefnshng = Cfnshng tme j ref (4) j j= Wth: j the jth fnshng generator settng; m the total number of generator settngs; C fnshng,j the correcton for generator settng j. 4.2 Modellng of correcton on tme ref Intal experments showed that n practce several parameters can explan the devaton from the reference tmes. The effects of these parameters have been nvestgated n ths research by performng a mxed full factoral desgn of experments (DOE). Table 3 lsts the selected DOE parameters. Machnng length (= machnng dstance n lateral and frontal drecton) and total area (frontal + lateral) were vared over 2 levels whle cavty shape and startng roughness were vared over 3 levels. Each experment conssted of fnshng a pre-machned cavty wth predefned dmensons (lsted n Table 4) wth one generator settng (E240: e = 6A, t e = 3.2µs, t 0 = 6.4µs). For each experment the machnng tme was logged and C fnshng was calculated wth the knowledge of tme ref. Each experment was executed 3 tmes and an ANOVA analyss was performed to determne the sgnfcant effects. Table 5 lsts the results of ths analyss for each cavty shape. In ths table SS effect refers to the sum of squares between dfferent experments where the varaton could be caused by the change of sgnfcant parameters. SS effect s expressed as the percentage of the total sum of squares. R² ndcates how well a model based on the lsted sgnfcant parameters matches realty. An R² value close to means that the most sgnfcant parameters are taken nto account to explan the most of the varaton. DOE level Machnng Length [µm] Total Area [mm²] Cavty Shape Startng Roughness [µm] Low Cylnder.78 Intermedate - - Rb.99 Hgh Square 2.24 Table 3: Selected DOE parameters. * Each depth corresponds to a level for the total area. Cylnder Rb Square Depth [mm].7/22.8* 3.84/8.54* 0.3/2.7* Dmensons Ø x x 3.84 [mm] Table 4: Dmensons of pre-machned cavtes. Fgure 8 shows the man effects of the selected DOE parameters on C fnshng. Both machnng length and total area strongly affect C fnshng. A doublng of the machnng length results n a doublng of the fnshng tme. However a doublng of the area results n a fnshng tme less than the double. The nfluence of the startng roughness s less pronounced but there s a slght decrease of C fnshng notceable when ncreasng the startng roughness.

5 These effects can be explaned by consderng the volume to be removed durng the fnshng operaton. An ncrease of the machnng length, the total area or a decrease of the startng roughness results n more volume to be removed resultng n a hgher machnng tme. SS effect Effect Cylnder Rb Square Machnng length Total area Mach. Length x Tot. Area Roughness R² Table 5: Sgnfcant effects on C fnshng for 3 shapes. When comparng the three cavty shapes dfferent trends of the nvestgated parameters are noted. The trends for cavty shapes wth corners (rb-lke and square cavtes) are smlar. A large dfference exsts between the former two cavty shapes and cylndrcal cavtes. The effects of the machnng length and the total area (slopes n Fgure 8) are lower for cylndrcal cavtes. Besdes ths also the level of C fnshng s lower for cylndrcal cavtes. Ths means that t takes less tme to fnsh a cylndrcal cavty wth dentcal settngs, machnng length, surface area and startng roughness compared to rb-lke and square cavtes. The reason for ths behavour can be found n the varaton of the energy concentraton durng one revoluton of the planetary electrode movement. In case of cavtes wth corners the energy s more concentrated n the corners than on the sde walls due to the small actve area n the corners. Because the electrode rotates at a constant speed less materal s removed at the sde walls. Hence more revolutons are needed compared to cylndrcal cavtes where a unform energy concentraton over the entre crcumference exsts. Because of the strong effect of the shape on the other nvestgated parameters the modellng of C fnshng has been splt up nto a model for cavtes wth corners and a model for cavtes wthout corners. C Machnng Total Area Roughness fnshng length [µm] [mm²] [µm] 0, Cylnder 5 VALIDATION OF DEVELOPED MODELS 5. Valdaton of EDM roughng tme model In order to check the valdty of the developed model for estmatng the EDM roughng tme addtonal machnng experments were performed. These experments concerned roughng operatons coverng the entre range of the developed model (prsmatc electrodes, no external flushng, frontal areas smaller than 000mm², machnng depths smaller than 20mm). The real EDM tme was compared to the estmated EDM tme. Fgure 9 shows the error dstrbuton when estmatng the EDM roughng tme wth the developed model. A mean error of 3.8% s noted. In some cases the error even exceeds 00% but ths only happens n a small amount of cases. In 9% of all tested cases (579 n total) the error s lower than 25%. Although large errors occur n some cases the developed concept s a large mprovement compared to the method whch makes use of reference values for the MRR determned by the machne tool bulder. Fgure 0 shows for the same cases the error dstrbuton when estmatng the EDM roughng tme by usng the former method. Here large errors (mean error: 68.9%) occur n all cases. Note that only postve errors occur.e. underestmatons of the EDM roughng tme. So by developng a model for estmatng the EDM roughng tme the mean estmaton error has been reduced wth 50%. 0,8 0,6 0,4 0,2 0,0 0,08 0,06 0,04 0, Procentual error Fgure 9: Hstogram of errors for EDM roughng tme estmaton by usng the developed model. Rb ,25 0,20 0,5 Square ,0 0,05 Fgure 8: DOE results for 3 cavty shapes. All these experments were performed by usng only one generator settng. Addtonal experments ponted out that the same trends occurred for other generator settngs. Ths means that C fnshng s ndependent of the generator settng. 0, Procentual error Fgure0: Hstogram of errors for EDM roughng tme estmaton by usng reference values from the machne tool bulder.

6 Roughng operatons Fnshng operatons Real Estmated tme [mn] Machne reference [mn] Real Estmated tme [mn] Machne reference [mn] Case Case Case Case Case Table 7: Results of valdaton for complex shapes. 5.2 Valdaton of EDM fnshng tme models Smlar to the valdaton of the EDM roughng tme model addtonal experments were performed to check the valdty of the EDM fnshng tme models. In these experments only smple prsmatc cavty shapes were consdered. The results of ths valdaton are shown n Table 6. The developed models gve very accurate results (mean error lower than 0% and maxmal error lower than 25%) for the consdered cases. A comparson wth the method of usng the reference values from the machne tool bulder showed that wth the development of the fnshng models the estmaton error has been reduced wth more than 65%. Fnshng model Machne reference Cylndrcal cavtes Cavtes wth corners Mean error Max. error Mean error Max. error Table 6: Valdaton results for the developed EDM fnshng tme models and comparson wth the tme estmaton method based on machne reference values. 5.3 Valdaton for complex machnng cases The valdty of the developed models was also checked for the machnng of 5 complex shaped cavtes. The results are shown n Table 7. As can be expected larger errors occur for these cases, especally for the fnshng tme. Ths can be explaned by the fact that external flushng was used n these cases whch results n a less predctable stuaton. Besdes ths, only the man nfluencng parameters have been taken nto account n the developed models. In order to obtan more accurate EDM tme estmatons also other parameters need to be taken nto account (e.g. curvature of bottom surface of the cavty). When compared to the method of EDM tme estmaton based on the reference values from the machne tool bulders Table 7 shows that more accurate results can be obtaned wth the developed models. 6 CONCLUSIONS Ths paper descrbed the development of tme estmaton models for snkng EDM operatons. A new concept based on reference values for ether materal removal rate or EDM tme has been proposed. On these reference values a correcton needs to be appled to compensate for devatons from the reference that occur n practce. Ths study focused on the development of analytcal models for ths correcton. Due to dfferent nfluencng parameters t was necessary to splt up the tme estmaton problem nto the development of a model for roughng operatons and a model for fnshng operatons. For both type of models the effects of the man nfluencng parameters were dentfed and ncluded nto the models. A valdaton of the models showed that accurate results can be obtaned for smple prsmatc electrode geometres. Compared to exstng EDM tme estmaton methods the developed models are able to reduce the estmaton error wth 50%. For more complex electrode geometres the developed models gve less accurate results. Further research s needed to enlarge the applcaton range of the models e.g. by quantfyng the nfluence of other parameters. Ths requres a large set of experments. To avod ths future research can shft to the use of self-learnng systems (e.g. neural networks) whch can be mplemented on the EDM machne. Wthn the frame of ths research a software tool has been developed for automated EDM tme calculatons. Based on a STL-representaton of the electrode and the approprate reference values the software automatcally calculates the EDM tme. 7 ACKNOWLEDGEMENTS Ths research has been carred out wthn the EU-FP6- COLL project KnowEDM (COLL-CT ) and the EU-FP7-NMP project Integ-µ (NMP ). 8 REFERENCES [] Che Haron, C.H., Deros, B., Gntng, A., Fauzah, M., 200, Investgaton on the Influence of Machnng Parameters when Machnng Tool Steel usng EDM, Journal of Materals Processng Technology, 6: [2] Wang, P., Tsa, K., 200, Sem-emprcal Model on Work Removal and Tool Wear n Electrcal Dscharge Machnng, Journal of Materals Processng Technology, 4: -7 [3] Lonardo, P.M., Bruzzone, A.A., 999, Effect of Flushng and Electrode Materal on De Snkng EDM, Annals of the CIRP, 48/: [4] Watanabe, Y., 2004, Estmatng Machnng Tme of Snker EDM by EDcam, Internatonal Journal of Electrcal Machnng, No. 9 [5] Fre, C., Hrt, C., 987, A New Approach for Contamnaton Measurements for EDM Delectrc, Annals of the CIRP, 36/: -3