© Strojni{ki vestnik 48(2002)7,404-413 © Journal of Mechanical Engineering 48(2002)7,404-413 ISSN 0039-2480 ISSN 0039-2480 UDK 62-272.82:62-242:620.172 UDC 62-272.82:62-242:620.172 Strokovni ~lanek (1.04) Speciality paper (1.04) Rekonstrukcija odvaljnega bata zra~ne vzmeti Reconstruction of an Air-Spring Piston Toma` Be{ter Odvaljni bat, ki ga izdeluje Goodyear EPE (Engineered Products Europe), prenese vse obremenitve, ki jih zahtevajo evropski tehnični standardi , v primeru, ko je podprt po celotni spodnji površini. Če je odvaljni bat podprt samo po delu površine, ne prenese vseh zahtevanih obremenitev. Za rešitev problema je bila najprej narejena trdnostna analiza odvaljnega bata, nato pa je bil bat spremenjen, tako da je zdržal vse zahtevane obremenive. © 2002 Strojniški vestnik. Vse pravice pridržane. (Ključne besede: vzmeti zračne, bati odvaljni, analize trdnostne, modifikacije) An air-spring piston, produced by Goodyear EPE (Engineered Products Europe), is able to withstand all the loads that are required by European Engineering Standards when it is supported on its entire lower surface. When the piston was only supported on a part of the lower surface it was not able to withstand all the loads. To solve this problem we made a strength analysis of the existing piston. The piston was then modified so that it was able to withstand all the required loads. © 2002 Journal of Mechanical Engineering. All rights reserved. (Keywords: air springs, pistons, strength analysis, modifications) 0 OBREMENITVE ODVALJNEGA BATA Zračna vzmet [7] je sestavljena iz odvaljnega bata, meha, blažilnika in zgornje plošče (sl. 1). Evropski tehnični standardi [6] za zračne vzmeti predpisujejo, da mora vzmet prestati dinamični preskus, preskus na utrujanje in preskus na razpočni tlak. zgornja (upper plošča plate) 0 LOADS ON AN AIR-SPRING PISTON An air-spring [7] is made of an air-spring pis-ton, a skin, a rubber damper and an upper plate. Ac-cording to European Engineering Standards [6] an air-spring piston has to pass a dynamic test, a static test and a pressure test (Fig. 1). gumijast blažilnik (rubber damper) spodnja plošča (bowl) meh (skin) Odvaljni bat (air-spring piston) Sl. 1. Odvaljni bat zračne vzmeti Fig. 1. An air-spring piston VH^tTPsDDIK stran 404 Be{ter T.: Rekonstrukcija odvaljnega bata - Reconstruction of an Air-Spring Piston Pri dinamičnem preskusu mora zračna vzmet prestati tri milijone ponovitev pri spremembi višine vzmeti 50 mm, tlaku v mehu 6 bar in frekvenci 1,25 Hz. Vpetje vzmeti je prikazano na sliki 2. Izkušnje kažejo, da v tem preskusu odvaljni bat običajno ni kritično obremenjen, ampak se poškodbe zaradi utrujanja navadno pojavijo na mehu, kjer pride do spuščanja zraka. Preskus na razpočni tlak zahteva, da se meh zračne vzmeti pri višini vzmeti 300 mm napolni z vodo pod tlakom 18,2 bar. Pri tem tlaku ne sme priti do poškodbe meha ali odvaljnega bata. During the dynamic test the air spring has to withstand three million cycles at an amplitude of 50mm, a pressure of 6 bar and a frequency of 1.25 Hz. The suspension of the spring is shown in Fig. 2. Our experiences show that in this case the piston is usu-ally not critically loaded, while the damage usually occurs to the skin, which causes air to leak from the spring. The pressure test (Fig. 3) requires that the air spring is filled with water at a pressure of 18.2 bar while the spring is 300mm high. This pressure must not cause any damage to the air spring. Sl. 2. Dinamični preskus Fig. 2. Dynamic test Statični preskus zahteva, da morata odvaljni bat in blažilnik zdržati obremenitev s silo 180 kN. Pri tem preskusu se preskušata samo odvaljni bat in blažilnik vzmeti. Vpetje odvaljnega bata je odvisno od izdelovalca podvozja, tako je lahko podprt po celotni spodnji površini, ali pa je previsno podprt, kakor prikazuje slika 4. Odvaljni bati, ki jih izdeluje Goodyear EPE, so izdelani iz umetnih mas ali jekla. Za plastične bate, ki jih izdeluje Goodyear EPE, se je pri preskusih izkazalo, da prenesejo vse obremenitve, ki jih terjajo evropski tehnični standardi, razen statičnega preskusa s Sl. 3. Preskus na razpočni tlak Fig. 3. Pressure test The static test requires that an air-spring piston and damper withstand a loading of 180 kN. In this way only the piston and damper are tested. The suspension of the piston depends on the undercarriage. The undercarriage manufacturers use two ways of supporting the piston, some support it on the whole lower surface, and others only on a part of the lower surface, as shown in Fig. 4. The air-spring pistons manufactured by Goodyear EPE are made of plastic materials or steel. Tests of the plastic pistons have shown that they pass all the tests except the static ones, when only a Sl. 4. Statični preskus s previsnim vpetjem bata Fig. 4. Static test | IgfinHŽslbJlIMlIgiCšD I stran 405 glTMDDC Be{ter T.: Rekonstrukcija odvaljnega bata - Reconstruction of an Air-Spring Piston previsnim vpetjem. Za rešitev problema je bila najprej narejena trdnostna analiza sedanje konstrukcije, pri obremenitvi, kakršno predpisuje statični preskus, in previsnem vpetju. 1 TRDNOSTNA ANALIZA SEDANJE KONSTRUKCIJE Trdnostna analiza sedanje konstrukcije (sl. 5) je bila narejena z uporabo metode končnih elementov v programskem paketu Ideas [3]. V analizi se ni upoštevalo, da zaradi prevelike obremenitve pride do plastifikacije in porušitve, zato s to analizo nismo dobili natančnih napetosti na batu, ampak ta analiza razkrije mesta, na katerih se pojavijo največje napetosti, in da kriterij za primerjavo različnih variant. V modelu končnih elementov ([2] in [4]) so bili uporabljeni desetvozliščni piramidni elementi. Ker je odvaljni bat simetričen, je bilo mogoče modelirati samo polovico bata. part of the lower surface is supported. To solve this problem a strength analysis of the existing piston for a static test was carried out for an overhanging support. 1 STRENGTH ANALYSIS OF THE EXISTING PISTON A strength analysis of the existing piston (Fig. 5) was made using the finite-element method and the Ideas computer program [3]. The analysis did not consider that plastification and perhaps even destruc-tion might occur due to overload; therefore, this analy-sis does not provide the exact stresses on the piston, but only the location of the maximum stress, and this gives the criterion for a comparison of the different designs. In the finite-element model, ten-node tetrahedron elements were used ([2] and [4]). Since the piston is symmetrical, we only need to model half of it. Sl. 5. Sedanja konstrukcija Fig. 5. Existing air-spring piston Bat je na obeso v primeru previsnega vpetja pritrjen samo z dvema vijakoma in na spodnji ploskvi podprt na manj ko polovici površine. Matica vijaka je jeklena in je vstavljena v bat med brizganjem umetne mase. Zaradi svoje oblike matica preprečuje pomikanje bata v navpični smeri na spodnjem robu matice, pa tudi v vodoravni smeri. Ker bi modeliranje matice terjalo lokalno zgostitev mreže in s tem povezano podaljšanje že tako dolgega računanja, v modelu končnih elementov ta matica ni bila modelirana, ampak so bile na površini, kjer matica preprečuje pomik v navpični smeri, postavljene podpore v tej smeri. Na sliki 6 so prikazane podpore na mestu, kjer je v bat iz umetne mase vstavljena matica (v smereh, kjer so omejitve pomika, so puščice). Takšen model ne upošteva elastičnosti vijaka in matice, vendar je modul elastičnosti vijaka in matice bistveno večji od modula elastičnosti umetne mase, ki obdaja matico, zato je takšna poenostavitev dovoljena. Bat je podprt z jeklenim kvadrom na enako veliki površini kakor v primeru previsnega vpetja. Jeklen kvader je po vsej svoji spodnji površini podprt v navpični smeri. Takšno vpetje je zelo podobno In the case of the overhanging support the piston is screwed down with only two bolts and supported on less than half the lower surface. The nut is made of steel and is inserted into the piston. Because of its shape the nut does not allow move-ments in the vertical and horizontal directions. Modelling of the nut would require condensation of the mesh around the nut; this would result in a considerable increase in the calculation time. There-fore, in the finite-element model the nut was not modelled; however, restraints were set in the verti-cal direction in the place where the nut restrains the piston. Fig. 6 illustrates this particular case (the arrows show the directions in which the displacements are restrained). Such a model does not consider the elasticity of the bolt and of the nut, but because the bolt and the nut have a much greater module of elasticity such a simplification is admissible. The piston is supported with a steel block on the same surface as shown in Fig. 4. The steel block is supported in the vertical direction over its entire lower surface. Such a suspension is very similar to grin^SfcflMISDSD ^BSfiTTMlliC | stran 406 Be{ter T.: Rekonstrukcija odvaljnega bata - Reconstruction of an Air-Spring Piston Obremenitev 24,2 MPa Fiksiranje pomikov v x smeri Translational restrains in x direction Fiksiranje pomikov v y smeri 'Translational restrains in y direction Fiksiranje pomikov v x, y in z smeri y Translational restrains I f in x, y and z direction = 1,36 g/cm3 Poissonov količnik n = 0,3 Meja plastičnosti ni podana, vendar lahko rečemo, da je enaka natezni trdnosti, ker ima material skoraj povsem linearno karakteristiko v diagramu s -e. Rezultati linearne analize z metodo končnih elementov so smiselni samo v primeru, da napetosti ne presežejo meje plastičnosti. V obravnavanem problemu so rezultati (sl. 8) analize močno presegli mejo plastičnosti, zato napetosti, ki so prikazane na slikah, niso stvarne, saj prej pride do plastifikacije in porušitve. Lahko pa iz teh slik ugotovimo, kje so mesta, kjer se pojavijo največje napetosti. Na sliki 8 se vidi, da se pojavi največja primerjalna napetost na robu površine, kjer je bat podprt s kvadrom, hkrati pa je to tudi mesto, kjer je rebro povezano z notranjim valjem. 2 SPREMINJANJE OBLIKE VALJA, DA BI ZADOSTILI ZAHTEVAM STANDARDA Zunanja oblika valja se ne sme spreminjati, saj bi to pomenilo spremembo karakteristike vzmeti zato lahko na batu spreminjamo samo lego in debelino reber. Prav tako ne smemo spreminjati lege pritrdilnih matic. Najprej se je spremenila lega reber, tako da so ležala pravokotno na previsni rob (sl. 9), da se je obremenitev porazdelila na več reber. Poleg geometrijske oblike so se na modelu končnih elementov spremenili tudi elementi v dotiku. Namesto tako imenovanih elementov špranje so se med obe dotikalni površini na mesta, kjer pričakujemo dotik med površinama, postavili togi elementi. Uporaba togih elementov bistveno skrajša čas računanja. Razlike v rezultatu med modelom s togimi elementi in modelom z elementi špranje so minimalne, če pravilno napovemo mesto, kjer pride do dotika površin. Zato so se v trdnostnih analizah vseh različic uporabljali _____02 7 SnnBjtgleJUpillOlflifrSO | ^BSfiTTMlliC | stran 408 acteristic in the s-e diagram. Consideration of all these phenomena would require too much time for the com-putations, so a simplified model was made, where the prescribed force was uniformly distributed over the lower surface of the damper. Because we have a rela-tively concentrated transferance of the force, this simplification does not significantly influence the ten-sions in the piston. The air-spring piston is made of a plastic material called AG3 (H)(K), which has 30% of glass fi-bres that are uniformly distributed over the entire volume, so that the material can be considered iso-tropic. The material is produced by General Electric, and its properties, reproduced from the General Electric [1] catalogue and Machinery’s handbook, are as follows [5]: Tensile strength: sM = 170 MPa Modulus of elasticity: E = 9800 MPa Density: r = 1.36 g/cm3 Poisson’s ratio: n = 0.3 The yield stress is not given, but since the material has an almost linear characteristic we can assume that it equals the tensile strength. The linear finite-element method gives us rea-sonable results only when the tensions do not ex-ceed the yield stress. In our case the yield stress was exceeded. Therefore the stresses that are shown in Fig. 8 are not the true ones – because destruction would occur first. However, we can locate the most critical places where the maximum stresses occur. We can see in Fig. 8 that the maximum equivalent stress occurs on the edge of the surface, where the piston is supported with a solid block. At the same time this is the place where the rib is connected to the inner cylinder. 2 MODIFYING THE SHAPE OF THE PISTON TO SATISFY THE NEEDS OF THE STANDARD The external shape of the piston should not be changed, as this would change the characteristic of the air-spring piston; therefore, we can only change the position and thickness of the ribs. The position of the nuts should also not be changed. Firstly, the position of the ribs was changed so that they were perpendicular to the edge of the block. Secondly, the type of finite elements in the contact was changed. Instead of gap elements rigid elements were placed on the nodes where we anticipated contact between the surfaces. The use of rigid elements significantly reduced the computation time. The difference be-tween the model with a gap and the model with rigid elements is minimal, that is if the nodes where the contact of the two surfaces occurs are correctly pre-dicted. That is why in strength calculations of all the variants rigid elements were used, except for the last Be{ter T.: Rekonstrukcija odvaljnega bata - Reconstruction of an Air-Spring Piston togi elementi, razen pri zadnji varianti, ki se je preverila tudi z modelom z elementi špranje. Rezultati trdnostne analize (sl. 10) kažejo, da so se napetosti bistveno zmanjšale, še vedno pa so večje od natezne trdnosti, zato bi se ta izvedba bata na preskusu porušila. Še vedno je najbolj problematična zgostitev napetosti na mestu, kjer je rebro povezano z notranjim valjem. Sl. 9. Varianta 1 Fig. 9. Variant 1 V naslednji varianti sta bili rebrom iz prve variante simetrično dodani še dve, tako da eno od teh reber leži na robu podpornega kvadra (sl. 11). S tem se bistveno zmanjša površinski pritisk na robu kvadra. Rezultati analize (sl. 12) so pokazali, da so sedaj napetosti že blizu dovoljenim, zanimivo pa je tudi to, da največja napetost ni več na srednjem rebru, ampak na obeh rebrih ob njem. Sl. 11. Varianta 2 Fig. 11. Variant 2 V tretji varianti so se zgolj dodale zaokrožitve s polmerom 5 mm na mesta, kjer se križajo rebra (sl. 13). Rezultati trdnostne analize so pokazali, da so se napetosti na previsnem robu zmanjšale, vendar še niso manjše od natezne trdnosti. Pokazalo se je tudi, da so napetosti na mestu, kjer je matica vstavljena v bat, sedaj večje od tistih na previsnem robu (sl. 14 in 15). variant, which was checked with gap elements. The results of the strength analysis (Fig. 10) show that the stresses were substantially reduced, but they are still much greater than the tensile strength, so this variant would still break during the static test. The concentration of stress is still the most problematic area in connection with the ribs and the inner cylin-der. Sl. 10. Največja primerjalna napetost Fig. 10. Maximum equivalent stress In the next variant, two new ribs were symmetrically added to the existing ribs, so that one of these ribs lies on the edge of the steel block (Fig. 11). This significantly reduces the surface pressure near the edge of the block. The results of this analysis have shown that the stress is now near to the permitted stress. It is interesting that the maximum stress is no longer in the middle rib, but on the ribs beside it. Sl. 12. Največja primerjalna napetost Fig. 12. Maximum equivalent stress In the third variant, rounds with a radius of 5 mm were added to the rib joints (Fig. 13). The strength analysis results (Fig. 14 and Fig. 15) showed that the stress was reduced near the edge of the block, although it is still greater than the permitted stress. It was also shown that the stresses near the nut are now greater than the stresses near the edge of the block. | lgfinHi(s)bJ][M]lfi[j;?n 02-7______ stran 409 I^BSSIfTMlGC Be{ter T.: Rekonstrukcija odvaljnega bata - Reconstruction of an Air-Spring Piston Največja napetost ;.»:-)( Sl. 13. Varianta 3 Fig. 13. Variant 3 Sl. 14. Največja primerjalna napetost na dotiku Fig. 14. Maximum equivalent stress in the contact Sl. 15. Največja primerjalna napetost Fig. 15. Maximum equivalent stress V četrti varianti (sl. 16) so bila vsa rebra nekoliko debelejša kakor v tretji varianti, medtem ko se matica vijaka ni spreminjala. Rezultati trdnostne analize (sl. 17 in 18) so pokazali, da so napetosti na previsnem robu manjše od natezne trdnosti, medtem ko so napetosti ob matici vijaka še vedno prevelike. In the fourth variant, all the ribs were slightly thicker than in the third, while the nut was not changed. The results of the stress analysis showed that the stresses on the edge were now lower than the tensile strength while the stresses near the nut were still too high. I 4 V. Največja napetost Sl. 16. Varianta 4 Fig. 16. Variant 4 Sl. 17. Največja napetost v dotiku Fig. 17. Maximum equivalent stress in the contact VH^tTPsDDIK stran 410 Be{ter T.: Rekonstrukcija odvaljnega bata - Reconstruction of an Air-Spring Piston Največja napetost Maximum stress 200 MPa Sl. 18. Največja napetost ob matici Fig. 18. Maximum equivalent stress V peti varianti (sl. 19) se je znižala debelina matice vijaka zato, da je prišlo več materiala nad njo, poleg tega pa se je bat odebelil tudi ob straneh matice. V modelu končnih elementov so se med dotikalnima površinama zopet uporabili elementi špranje, da ne bi bilo nobenih dvomov o pravilnosti rezultata. Iz rezultatov (sl. 20, 21) je razvidno, da so napetosti v tej varianti povsod manjše od natezne trdnosti, tako da bi ta varianta zdržala obremenitve, ki jih zahtevajo evropski tehnični standardi. In the fifth variant, the thickness of the nut was lowered so that more plastic material was above it. In the finite-element model we used gap elements in order to avoid possible errors in the calculation. From the results (Fig. 20 and Fig. 21) it is clear that all the stresses in this variant are less than the tensile stress, which means that this variant would with-stand the loads that are anticipated by European Engineering Standards. Sl. 19. Varianta 5 Fig. 19. Variant 5 Sl. 20. Največja primerjalna napetost v dotiku Fig. 20. Maximum equivalent stress in the contact Največja napetost Maximum stress 159 MPa Sl. 21. Največja primerjalna napetost Fig. 21. Maximum equivalent stress stran 411 glTMDDC Be{ter T.: Rekonstrukcija odvaljnega bata - Reconstruction of an Air-Spring Piston 3 SKLEP 3 CONCLUSION Če primerjamo mase in napetosti različnih If we compare the masses and stresses of differ- variant odvaljnih batov (sl. 22 in 23), vidimo, da proti ent variants of air-spring pistons (Fig. 22 and Fig. 23), we sedanjemu izdelku napetosti bistveno bolj padejo, see that the stresses drop much more than the mass is kakor pa se poveča masa pri izboljšanih variantah, increased which is why we can say that the reduction in zato lahko rečemo, da zmanjšanje napetosti ni toliko the stresses is not the consequence of adding the mate- posledica dodajanja materiala, kakor je posledica rial as much as it is the consequence of an adjustment of prilagoditve konstrukcije načinu vpetja. Analize so the design to the suspension. Our analyses showed that pokazale, da je mogoče izdelati odvaljni bat, ki bo it is possible to produce a plastic air-spring piston that prenesel obremenitve, kakršne terja statični preskus would withstand the loads that are anticipated by Euro- po evropski tehnični standardi, vendar bi tako pean Engineering Standards, but such a piston would oblikovan bat prenesel obremenitve samo, če je vpet withstand all the loads only if it were supported exactly natančno tako kakor načrtuje standard. Če bi bil rob as it is predicted in the standard. If the edge were to be podstavka postavljen drugje kakor pod rebrom bata, placed anywhere else, for example, under the rib of the ta skoraj gotovo ne bi prenesel zahtevane piston, this piston would almost certainly not withstand obremenitve. Ker imajo nekateri izdelovalci podvozja the required loads. Because some manufacturers have nekoliko drugačna vpetja, ta bat zanje ne bi bil slightly different supports this piston would not be ap- primeren. Druga težava je v tem, da mora biti bat pri propriate for them. The other problem is that during as- montaži pravilno usmerjen, torej da rebro, za katero je sembly the piston should be adequately oriented, so that načrtovano, da leži na previsnem robu, dejansko leži the rib that is supposed to be on the edge of the block is tam in ne pravokotno na rob. really there and not perpendicular to it. Sl. 22. Primerjava največjih napetosti Sl. 23. Primerjava teže Fig. 22. Comparison of maximum stresses Fig. 23. Comparison of weights Analiza za primer vpetja po vsej spodnji površini An analysis of the fifth variant for support on za varianto 5 ni bila narejena. Ker je takšno vpetje the whole lower surface of the piston was not made. bistveno bolj ugodno, bi peta varianta zanesljivo zdržala Since such a support is much more favourable, the statični preskus tudi za tak način vpetja, vendar se fifth variant would certainly withstand all the loads pojavlja vprašanje, ali je primerno uporabljati peto of the static test for that kind of support. However, varianto odvaljnega bata za vpetje po celotni spodnji there is a question: is it reasonable to use the fifth površini bata, ker je težja od sedanjega izdelka in s tem variant of the piston for the suspension on the whole tudi dražja. Po drugi strani je zopet vprašanje, ali je lower surface, because this variant is heavier, and primerno izdelovati za različne izdelovalce podvozij thus more expensive than the current product? A različne odvaljne bate. Rešitev problema je, da se pod possible solution to this problem is to put a steel celotno spodnjo površino sedanjega odvaljnega bata plate under the lower surface of the existing piston postavi jeklena plošča (sl. 24), ki omili zgostitve (Fig. 24). This plate would diminish the stress napetosti ob previsnem robu. Tudi ta varianta ni idealna, concentration near the edge of the block. This is also saj smo dobili nov element v sestavi zračne vzmeti, not an ideal solution, but it has been shown in practice vendar se je v praksi izkazala kot najcenejša rešitev. that it is the cheapest solution so far. An analysis of Analize takšnega načina vpetja niso bile narejene, ker je such a support was not made because it was simpler bilo bolj preprosto narediti preskus, ki ga je bat uspešno to make a test, which the piston passed. To solve this prestal. Z računalniki, ki so bili na voljo, bi ta način problem with finite-element analysis would be very vpetja zelo težko trdnostno analizirali, saj je računanje difficult, because computing time, which was several že sedaj trajalo nekaj ur, če pa bi v model končnih hours, would have had to be prolonged if we were to ______02 7 SnnBjtgleJUpillOlflifrSO | ^BSfiTTMlliC | stran 412 i Be{ter T.: Rekonstrukcija odvaljnega bata - Reconstruction of an Air-Spring Piston elementov dodali še eno dodatno ploščo pod valjem, bi s tem dobili še nekaj dodatnih elementov in še eno dodatno dotikalno povreino, na kateri bi morali uporabiti elemente špranje. To bi vse skupaj bistveno podaljšalo čas računanja. Ker pa razvoj računalnikov zelo hitro napreduje, se bodo podobne analize v praksi vse bolj uveljavljale. add the additional plate to the model because it would not only increase the number of elements, but it would also mean a new contact surface with gap elements. Since development in the computer industry is very rapid, this type of analysis will become increasingly common. Sl. 24. Drugačna rešitev Fig. 24. Alternative solution 4 LITERATURA 4 REFERENCES [1] (1998) Catalog 1998, General Electric [2] Spyrakos, C, Finite element modeling, West Virginia University Press [3] Lawry, M.H., I - deas Master Series student guide, Structural Dynamics Research Corporation [4] Zienkiewicz, O.C. (1991) The finite element method, Mc Graw-Hill Publishing Company, London. [5] Oberg, E., Jones, F.D., Horton, H.L., Ryffel, H.H. (1996) Machinery’s handbook, Industrial Press Inc., New York. [6] Göbel, E. F (1974) Rubber springs design, London. [7] (1985) Procedure de reception de ressort a` air, European Engineering Standards 810. Naslov atvorjev: Tomaž Bester Fakulteta za strojništvo Univerza v Ljubljani Aškerčeva 6 1000 Ljubljana tomaz.bester@fs.uni-lj.si Authors’ Address: Tomaž Bester Faculty of Mechanical Eng. University of Ljubljana Aškerčeva 6 1000 Ljubljana, Slovenia tomaz.bester@fs.uni-lj.si Prejeto: Received: 12.4.2002 Sprejeto: Accepted: 20.9.2002 | IgfinHŽslbJlIMlIgiCšD I stran 413 glTMDDC