Modeling of hydraulic axial piston pumps including specific signs of wear and tear

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1 Modeling of hydrulic xil piton pump including pecific ign of wer nd ter Chritin Byer Olf Enge-Roenltt Frunhofer Intitute for Integrted Circuit, Diviion Deign Automtion Zeunertre 38, Dreden, Germny {Chritin.Byer; e.ii.frunhofer.de Atrct Reliility of mchine nd fcilitie h plyed n importnt role ince mny yer. Nowdy, ttention i lo pid to mintennce time. Mintennce tndtill re to e reduced fr poile. On the other hnd, technicl ytem re uject to ign of wer nd ter which re in generl growing lowly nd imperceptily. The grdul rion of pplied tool my led to poor production tolernce or to component tndtill. Hence, condition-ed mintennce trtegy will e of increing importnce. Such trtegy require permnent condition monitoring during opertion. To thi end, ile high-performnce lgorithm for ignl proceing, feture extrction, nd clifiction re needed. Modeling the proce of wer nd ter my e ueful to find the prticulr tep of the condition monitoring ytem ignl proceing. Thi trtegy w invetigted y men of one very importnt device from utomtion engineering, hydrulic xil piton pump. The procedure of getting ignl y n pproprite Modelic model of the min prt of the pump i hown within the pper. Additionlly, the mnipultion proce for the ignl nd the tep of clifiction re hortly preented to give n overview to the poiilitie of model-ed ignl genertion ed on Modelic model. The dvntge of the multi-phyic modeling lnguge re emphized ecue the xil piton pump model comine the mechnicl nd the hydrulic domin in very efficient wy. Keyword condition monitoring; clifiction; ignl proceing 1 Introduction Long-lting correct opertion nd the highet level of vilility re importnt requirement concerning mchine nd fcilitie in tody indutry. While iility h plyed n importnt role ince mny yer, more nd more ttention h een pid to the time needed for mintennce procee in the lt decde. The numer of mintennce tndtill h to e reduced to decree the totl cot of ownerhip (TCO). Thi i enforced y the increing uine rivlry of tody economy. On the other hnd, technicl ytem re uject to proceeding deteriortion nd often to certin wer. But ign of wer nd ter re in generl growing lowly nd imperceptily. The grdul rion of pplied tool my led little y little to poor production tolernce or even to tndtill of component or complete production fcility. Hence, condition-ed mintennce trtegy will e of increing importnce. Such trtegy require permnent condition monitoring during opertion ed on efficient ehvior nlyi procedure. Condition monitoring ytem nlyze vriou meured ignl uing ppliction-pecific lgorithm. In thi context, ile highperformnce lgorithm for ignl proceing, feture extrction, nd clifiction re needed. Modeling the proce of wer nd ter my e ueful to find the prticulr tep of ignl proceing which re uitle for certin condition monitoring ytem. Thi trtegy w invetigted y men of hydrulic xil piton pump, which i very importnt device from utomtion engineering nd i till n intene uject of computer ided modeling [1, ]. In ection, two model of the tndrd pump re explined firt. Both model comine mechnicl nd hydrulic u-model. Phyiclly motivted inter-modulr connection re etlihed. In ection 3, prmeter optimiztion method i preented nd dicued. Thi method i pplied to fit unknown prmeter of the mechnicl u-model. Meured time ignl re ued for comprion. Afterwrd, ome ign of wer re implemented in the model. Thi i preented in ection 4. Two of the mot prolemtic ce leding to the min filure re hown. Chrcteritic feture deduced from Fourier trnform of virtion ignl re ued for clifiction of good pump nd pump hving filure.

2 Figure 1 Schemtic of the modeled xil piton pump with 9 cylinder. Only mechnicl prt re hown. Modelic model.1 The xil piton pump For demontrtion of the ove mentioned condition monitoring pproch we choe n xil piton pump. Thoe device iclly conit of certin numer of cylinder nd piton to pump hydrulic oil under high preure condition. The cylinder re evenly ligned round rotting xi, where the piton re ttched to tilted cm, which i clled wh plte. Due to rottion, the piton cn perform n xil motion nd thu pump the oil through inlet nd outlet port repectively. Figure 1 how rough chemtic of the pump, which i cptured from 3D Dymol nimtion [3]. The oil flow i controlled y ditriutor plte, which e.g. connect the outlet port to the cylinder with high oil preure. The plte i not hown in Figure 1 the flow control i implemented within the hydrulic model.. 3D model Modelic i cple of imulting multi-ody dynmic well model ed on uer-pecific differentil eqution. A good reference of the Modelic lnguge cn e found in [4]. Our initil model w ptil model (3D) exploiting the MultiBody pckge for mechnic nd uing further differentil eqution for hydrodynmic. Unfortuntely, lot of prmeter, for exmple certin friction coefficient or pring rte, re not known exctly, even not y the mnufcturer. Hence, the model mut e uited for prmeter optimiztion lgorithm in term of computtionl effort. Since the 3D model i very complex, we reduced the model Figure Comprion of xil nd rdil force cting on the houing. The reult re ed on the 3D model. to the very eentil prt nd developed 1D equivlent. To jutify thi pproch we evluted the force cting to the pump houing. The device rotted t contnt peed of 1500 revolution per minute. Figure how xil nd rdil force during ection of 1/9 of full revolution of the pump. Oviouly, the trnltionl motion of the piton i the min ource of virtion, which i the vlue we wnt to meure nd imulte. In n idel ce, the rottion itelf doe not contriute to virtion. Only the light tilt of the cylinder gint the rottionl xi cue rdil force, which i directly ted to the ine of the tilt ngle. Since thi ngle i mll, the rdil force cn e neglected. Therefore, the reduced model conider xil motion only nd thu ecome 1D repreenttion. Since we focued on the 1D model, the 3D implementtion will not e explined in detil here..3 1D model The reduced mechnicl model i depicted in Figure 3. Ech element of the chemtic te to dedicted Modelic u-model, which in turn i decried y certin differentil eqution nd n individul et of prmeter. Our 1D model complie with the convention of Modelic trnltionl mechnic lirry nd we lo ued few ic component thereof. The element re chined exctly hown in Figure 3 nd form line or prllel line repectively. The houing of the pump i modeled imple m, which emrce ll other prt of the model. It i therefore connected in prllel to oth ide of the pump interior element chin. The m i not fixed nd it movement give rie to the ccelertion vlue nd thu virtion. On the left ide of the chin

3 m with pring dmper ngle of rottion m with pring dmper follow the houing. It um up certin me inide the pump nd connect them to the houing y men of pring. Thi indeed pproximte the rel emly of the pump. The next element in the row i the tilted wh plte, repreented y the ine curve in Figure 3. It cue ll piton to follow inuoidl motion with individul phe offet. Thi effect i implemented y time dependent diplcement follow 0 F F ˆ 1 co N t 60 piton xil diplcement houing lipper pd with xil ply piton oil volume xil poition on wh plte Figure 3 Reduced 1D model of the xil piton pump. (1) F denote force t the u-model flnge nd i the ditnce etween flnge or the poition of them. φ i the olute revolution ngle of the pump. The wh plte model cn only drive one of the 9 piton with pecific phe offet. At thi point the model chin rek up into 9 individul line in prllel. Ech line conit of wh plte model followed y lipper pd, piton nd the cylinder oil volume. All 9 line finlly merge into the right hnd frme of the houing m. The connection etween piton nd wh plte i etlihed y lipper pd. They offer tight connection to the piton with mll ply, which extend reult of wer. The u-model llow mll ditnce of free motion until the piton hit one of the two limiting oundrie. Once in contct with the limittion, the model witche to dmped pring m ytem ehvior with pring rte D, cn e een in the eqution elow. F F F 0 F gp otherwie v 0 R1 otherwie v 0 R otherwie R1 t R t 0 0 R 0 R * 1 * D 1 D gp () R correpond to friction coefficient nd v to the velocity of the ted piton. It turned out, tht the imultion reult improve, if there i no friction when the piton pull prt from oundry. The eqution for R i therefore depend on the ign of v. The piton itelf i imple m of length L with friction nd inerti. Strieck friction i not ued in the model it would introduce too mny unknown prmeter. The piton eqution red F F m R t L t. (3) The u-model of oil volume V pproximte the condition within cylinder nd finlly link hydrulic quntitie to the mechnicl prt of the model. In [5] thi w done y incorporting two different oftwre pckge for hydrulic nd mechnic. We ued Modelic for oth phyicl domin to merge them into one model. Preure p inide cylinder cue fluid flow q through the port well force to piton flnge. The oil i conidered compreile fluid with ulk modulu K. It flow either through the inlet or the outlet port, which depend on the tive ngulr poition of cylinder lock nd ditriutor plte. Both port re modeled vlve with vrile cro ection nd, thu, hve time dependent hydrulic conductnce G. For ingle cylinder the vlve cro ection re hown in Figure 4. Other cylinder experience the me chrcteritic, ut with phe offet. The model ume turulent flow through vlve [6], which finlly led to the eqution

4 Figure 4 Repreenttive cro ection of inlet nd outlet vlve for ingle cylinder. The grph how condition for one revolution of the pump. V q G out G in A piton gn P gn P mx min p p Q q Apiton t Q p K t V F F F pa piton P P mx min p p. (4) The time dependent cro ection of inlet nd outlet re provided y the mnufcturer. They were implemented y uing Modelic look-up tle component. A cn e een from eqution (4), the oil volume u-model h two frme with vrile nd F. Hence, it cn e eily connected to our chin of other mechnicl trnltionl component. 3 Prmeter optimiztion 3.1 Method Figure 5 Comprion of imultion reult with optimized prmeter et nd verged meurement. The ignl correpond to the time reolved ccelertion of the houing in xil direction. The grph how one revolution of the pump. Ech u-model h n individul et of prmeter. Some of them re known, i typiclly true for geometric prmeter. Other hve to e etimted or cn e found y optimiztion. For thi purpoe, everl meurement with t let one undmged pump hve to e done. With thi reference dt, n optimiztion lgorithm w ued to find n pproprite prmeter et. Thi i common method nd w lo pplied in [7] for exmple. We ued MAT- LAB [8] for n utomted prmeter weep in Dymol. The gol function for minimiztion i imply the devition of the imultion reult from the verged meurement ignl. The meurnd equl in oth ce the ccelertion of the houing in xil direction. Unfortuntely, the numer of prmeter i quite high, which impede reonle optimiztion proce. Within our reduced 1D model we identified even prmeter, which ignificntly influence the reult nd were ued for optimiztion The imultion i very enitive to the interction of piton hed nd lipper pd. Alredy four prmeter cn e extrcted from thi knowledge, two for ech limiting oundry. When hitting oundry, the piton will penetrte into the mteril of the lipper pd, queeze the oil film etween pd nd wh plte or trin the pd. An ey ut efficient wy i to ume pringlike model with dmping for tht proce. Thi give two prmeter for ech oundry, nmely pring rte nd friction coefficient. Another importnt prmeter i the friction of the piton within the cylinder. The lt two prmeter elong to the pringm ytem, which i locted etween houing nd wh plte (ee Figure 3). One prolem of the optimiztion i tht there i no unique idel prmeter et. The reult differ with the initil prmeter. To ccount for thi, we lo implemented rndom weep of trting vlue. Once good prmeter et i found, the ctul optimiztion i performed. The lgorithm ued here w the implex erch method. 3. Reult In pite of the complicted optimiztion proce, we found et which fit the rel meurement quite well. Figure 5 how the reult. The ignl itelf h

5 Figure 6 Spectr of imultion reult with optimized prmeter et nd verged meurement. The pectr correpond to the Fourier trnform of the ccelertion of the houing in xil direction. ome cler chrcteritic. During one revolution of the pump, ech piton ccomplihe one period of it inuoidl movement. Thi led to 9 eqully hped pule in the time ignl. Both, imulted nd meured ignl, how thi chrcteritic nd re comprle. The xil piton pump i rotting device. For condition monitoring of thi pecil ppliction the pectrum nd evlution of hrmonic i fr more intereting thn the time ignl. Hence, the conitency of imulted nd meured ignl in the frequency domin i very importnt. Figure 6 compre the reult. Due to the 9 piton nd the rottionl frequency of 5 Hz, hrmonic with pcing of 5 Hz cn e oerved. Both pectr how imilr ditriution. However, within the meurement dt hrmonic 4 to 7 eem to e rther uppreed, which hold for ll meurement, even for different pump with vrying ign of wer. Thi effect might e cued y the experimentl etup. The pump i ttched to motor nd other mchinery which cn virte well. Our model doe not conider the exct environmentl condition nd i not le to reproduce the hrmonic uppreion. But it turned out, tht we cn imply ignore thee hrmonic for clifiction. 4 Modeling defect 4.1 Introducing defect The min purpoe of the imultion i the etimtion of meurement ignl for worn pump. Once the model prmeter re optimized for n undmged device, they cn e modified lightly to introduce Figure 7 Spectr of meurement ignl of worn pump with xil piton ply nd imultion reult. defect. A mtter of coure thi require the prmeter to e ted to certin ign of wer. We invetigted two type of defect. One of them i cvittion pitting, which influence the hydrulic conductnce of the cylinder vlve. Biclly, the cro ection of ech vlve chnge lightly with grdul rion. Worn pump give uitle informtion on the modified cro ection nd we imply exchnged the chrcteritic re function, hown in Figure 4. However, our reult ugget tht reonle chnge of the function h only minor effect to the xil virtion within the conidered frequency rnge. Thi i conitent with meured dt, where the difference i preent ut comprly mll. In the following we focu on more ignificnt defect. Ech piton i ttched to lipper pd with certin mount of ply. Thi mll gp incree with time nd led to defect referred to xil piton ply (pp). We introduced thi effect in the lipper pd u-model y increing the ply prmeter nd decreing one of the pring rte, which model the trin of the pd when pulled y the piton. Figure 7 compre meurement of worn pump with xil piton ply nd our imultion reult. Since the clifiction i done in the pectrl domin, only the Fourier trnform re hown. Ignoring hrmonic 4 to 7, we cn ee very imilr trend of chnge in oth the imultion nd meurement. The firt 3 hrmonic drop in mplitude, while other ner khz incree. Bed on uch effect unique feture for clifiction cn e found. 4. Clifiction The clifiction method ued here i ed on the firt 17 hrmonic of the ignl pectrum excluding hrmonic 4 to 7. Severl ttiticl prmeter, like

6 the experimentl effort during development of CMS. For demontrtion n xil piton pump with t let two ign of wer w modeled. The imultion reult gree comprtively well with experimentl dt. Modeling h everl dvntge compred to experimentl etup. The invetigtion of defect i much more flexile nd one i le to find cortion etween thoe defect nd detected ignl. Thi pproch lo fcilitte the development of improved ignl proceing technique nd the genertion of etter feture for clifiction. Figure 8 Clifiction reult for n undmged pump (good) nd xil piton ply (pp). Line denote the expected output of the NN for idel clifiction. Circle nd croe denote clifiction reult of meured dt. tndrd devition or kewne were defined nd pplied to pecific hrmonic rrnged in group of t let 7. If the group re thoroughly compoed, meningful feture cn e extrcted. With uject to complexity neurl network (NN) w employed to clify the condition of pump. A gret dvntge i the ility to trin uch network with imultion dt inted of experimentl dt, which would cue higher effort. However, in mot ce meurement dt of undmged device hould e ville. It i therefore reonle to trin the NN with thoe meurement nd in ddition with model dt of ll imulted defect nd condition. In our ce we modeled n undmged pump well one with xil piton ply nd preented oth imultion nd meurement (undmged) dt to the NN for trining. The NN ccepted 1 feture input nd hd 3 output neuron. Thu, 3 cle could e eprted, ut we ued only two of them for n undmged pump nd xil piton ply. The clifiction reult re preented in Figure 8. Only meurement dt w preented to the NN for teting. A vlue of 1 t n output neuron men tht ignl i trongly ted to the pecific cl. Smller vlue indicte lower proility of cl memerhip. The clifiction work well for our preented model nd i uitle for CMS. 5 Concluion In thi pper we preented model-ed method to upport the development of condition monitoring ytem (CMS). The ic ide i to replce n experimentl etup y imultion or t let to reduce Acknowledgement Thi project w funded in prt y the Germn Federl Minitry of Eduction nd Reerch (BMBF). Aocited prtner re GEMAC GmH (Chemnitz), Frunhofer Intitute IIS (EAS, Dreden) nd Lenord+Buer & Co. GmH (Oerhuen). Reference [1] Ming Liu, Dynmiche Verhlten hydrotticher Axilkolengetriee. Bochum, Germny PhD thei, Intitute Product nd Service Engineering, Ruhr-Univerität Bochum, 001 [] Ling Chen, Model-ed fult dignoi nd fult-tolernt control for nonliner electrohydrulic ytem, PhD thei, TU Kierlutern, 010. [3] Dymol 7.3, Dult Sytème [4] Fritzon P., Principle of Oject-Oriented Modeling nd Simultion with Modelic.1, IEEE Pre, 004 [5] A. Rocctello, S. Mncò nd N. Nervegn, Modelling Vrile Diplcement Axil Piton Pump in Multiody Simultion Environment, J. Dyn. Sy., Me., Control, 19(4)456, 007. [6] Zoel H., Kruchik J., Strömung durch Rohre und Ventile, Springer-Verlg Wien, Autri, 1978 [7] R. Petrovic, Mthemticl Modeling nd Experimentl Reerch of Chrcteritic Prmeter Hydrodynmic Procee of Piton Axil Pump, Journl of Mechnicl Engineering, 55(4)4-9, 009 [8] MATLAB 010, The MthWork, Inc.