Journal o KONES Powertrain and Transport, Vol. 18, No. 4 011 DEPENDENCE OF PISTON RING PARAMETERS DETERMINATION ACCURACY ON THE METHOD OF CALCULATION Wojciech Serdecki, Piotr Krzyie Pozna University o Technology Institute o Cobustion Engines and Transport Piotrowo Street, 60-965 Pozna tel.:+48 665 4, +48 665 9 e-ail: wojciech.serdecki@put.poznan.pl, piotr.krzyien@put.poznan.pl Abstract Matheatical odels are coonly used at the stage o piston ring design and during exaination o ring collaboration with liner surace. Both analytical and nuerical ethods are used or developent o such odels. In the case o odels based on analytical ethods the range o their application is usually liited only to selected cases while the use o nuerical ethods allow to widen the range o their applications but their accuracy depends on increent used. The paper presents a procedure o veriication o the piston ring atheatical odel constructed by the authors using nuerical ethods. Conority between the results obtained using this progra and the results o analytical calculations concerning the displaceent o ring ree ends brought about by the acting loads was the ai o the analysis. Exeplary coputations were carried out or three copression rings o dierent geoetry. Regarding the conority o achieved results as satisactory or practical use probable causes o observed discrepancies were pointed out. Relations between energy accuulated in curved bar and loading orce (according to the Castiliano s theore) were used in a course o calculations. Exeplary calculations were carried out or copression rings o three types engine, i.e. autootive, bulldozer and arine ones. A probable cause o dierences between results o calculations carried out according to various analytical ethods have been pointed out assuing their accuracy as satisactory or practical purposes. Keywords: cobustion engine, piston ring, ring geoetry, ring pressure, siulation 1. Role o copression ring in operation o piston-cylinder set In spite o apparently siple construction piston copression rings peror a good nuber o tasks during engine operation aong which tightness o cobustion chaber sees to be the ost iportant one. In correctly designed piston-cylinder assebly the ring should adjoin cylinder liner with its entire circuerence. However, due to the presence o a nuber o unavorable phenoena like liner itting deorations, cylinder wear etc. the circuerential contact o ring and liner deteriorates, which to liited extension is copensated by ring elasticity and pressure caused by gas orces. Due to the lack o contact, so called light tightness worsens (see Fig. 1) which eventually leads to the increased blow-by resulting in all o engine power and intensive wear o liner surace. Another daaging result o this phenoenon is an increased oil consuption caused by oil scraping towards cobustion chaber (an increase in exhaust toxic copounds is a secondary eect o this phenoenon). Lack o proper contact between ring and liner causes worsening o another vital task o ring, i.e. heat transer ro piston crown to cylinder liner. Because o presented reasons requireents concerning quality o ring to liner contact are very rigorous. For exaple, slit should not excess 0 (and at ost expand over 10% o entire ring circuerence) on arine engines o large cylinder diaeter [4]. A correct design o piston ring and subsequent thorough onitoring o its operation during engine run is being considered very iportant or liitation o light tightness loss. However, a direct observation o ring operation, especially evaluation o the contact between ring and liner.
W. Serdecki, P. Krzyie This results ro unavorable conditions in the neighborhood o running rings (high teperature and pressure) and presence o so called oil il. Indirect investigations using the easureent o distance between ring and liner or blow-by are highly inaccurate. Fig. 1. Schee o new ring contact with worn liner; 1 cylinder liner, piston, piston ring, l z clearance o ring ree gap, s 1, s, s - axiu gap size [9] Beside investigations carried out on real objects the odel ones are possible as well. A nuber o ore or less coplicated atheatical odels have been developed that are used or evaluation o ring and liner collaboration [6-8]. Soe o the concern a selection o copression rings but unortunately or a ew o the it is diicult to deine a precise range o application. Because o that the authors decided to develop a coputational odel o their own using or its construction relations obtained in a course o theoretical analyses and practical tests as well. Further part o this study presents a basic relations used or developent o piston ring atheatical odel and eventual exaples o its application to veriication o this odel.. Dependences used or design o copression rings For years specialists o piston-cylinder assebly have been trying to establish dependences between ring shape and orces loading the ring, especially on deinition o so called ring ree shape. First studies on this subject were published in the irst hal o XXth century. These studies presented trials on relations between selected quantities while the range o their applications was liited to soe cases o their variability. For instance, a constant circuerential load or ring radial thickness were assued constant ore inoration one can ind in [1, ]. Basic characteristic paraeters o copression ring are as ollows: external ring diaeter d (equal to the liner diaeter), radial thickness g p, axial height h p, distance between ends o ring ree shape and ring gap when in cylinder l z (Fig. a). On the other hand tangential and radial orce, F t and Q respectively (Fig. b) and circuerential pressure p (Fig. c) as well which are related to the odulus o elasticity E are used or evaluation o ring elastic properties. Values o Ft and Q orces are deined as those which ake ring ends close with the gap o lz. The schee o ring itted into liner and pressing continuously on its surace (as shown in Fig. c) was used or calculation o relations between ring geoetry and actual loads (Fig. shows only a hal o ring or siplicity). Results o analyses and calculations presented urther are related to so called ring neutral axis distant ro the center o claped ring o r (perect ring circularity is assued). 46
Dependence o Piston Ring Paraeters Deterination Accuracy on the Method o Calculation a) b) c) Fig.. Sketch o a copression ring: ree and tighten or (a), loaded with orce F t or Q (b) and exeplary picture o unior wall pressure distribution (c) Fig.. Sketch o a loaded ring or derivation according to [1] According to the presented schee dm() dierential o ring bending oent at point i equals: dm ( ) p( ) hp s ds, (1) where: p() - local value o ring to wall speciic pressure at point j, h p - ring axial height, s - distance between point i and the radius o orce P( ) p( ) h ds operation, ds - ring section within angle d. Ater necessary transorations an equation has been obtained that allows to carry out calculations o bending oent M() at the point deined by angle M ( ) r hp ) p( )sin( d. () Ring circuerential load resulting ro its installation in liner oten diers ro the even one. This could be a result o designer s intentional eort or cylinder deoration. Because the variability o circuerential load akes diicult or even prevents the deterination o relevant analytical relations the assuption o load peranence should be adopted, i.e. p() = p o = const which akes that the Eq. () takes the ollowing or M ( ) p r h (1 cos). () o One o the ring characteristic eatures is so called tangential orce F t acting in the vicinity o ring ree gap which causes the ring tightening up to the oent when the gap reaches the value o l z (equal to the gap o ring itted into cylinder liner). For evaluation o ring elastic properties and especially the tangential orce easureent as well as displaceent o ring ree ends caused by this orce special devices are used presented or instance in [8] (one o the is presented in Fig. 4). p p 47
W. Serdecki, P. Krzyie Fig. 4. Scheatic o device purposed or ring tangential orce easureent: 1 bea hold, elastic bea, sensor hold, 4 icroeter, 5 steel band, 6 lever handle, 7 liit screw, 8 screw, 9 band hold, 10 rotating dru, 11 tightening dru [1] Using a sketch shown in Fig. the dependency was established allowing to deine the value o bending oent or arbitrary angle as: M ( ) F r h (1 cos). (4) t Coparing values o oents deined by equations () and (4) one can ind a relation between circuerential load (corresponding to the constant wall pressure o ring p o ) and the tangential orce F t : Ft po. (5) r h Presented relation is precise only in a case when the tangential orce does not cause a ring deoration o a perect circle (actually such phenoenon occurs). a) b) p p Fig. 5. Sketch o ring loaded by orce P at the end (a) and in the iddle o circuerence (b) Displaceent o individual points o ring could be calculated analytically. The ring should be treated as bent bar o suiciently large radius o neutral axis r (relatively to its radial thickness g p ). Vertical displaceent o the ring ree end y (Fig. 5) is deined as the derivative o bar potential energy V relative to the orce P (according to the Castigliano s theore []): V y. (6) P The increase o potential energy dv caused by bending oent M() along the increase o angle d equals (other orces and oents are oitted as negligible ones) 48
Dependence o Piston Ring Paraeters Deterination Accuracy on the Method o Calculation M ( ) r d dv. (7) E I It could be proved that the potential energy accuulated in ring within the section deined by the angle (0 1 ) equals: P r 1 V (1 cos) d, (8) E I 0 a nd total displaceent o ring at the place where the orce acts (ring ree end): P r y ( 1 cos) d. (9) E I 0 Siilarly the horizontal displaceents x o ring points are being deterined. Changing the range o ring section subjected to load up to the ring hal (Fig. 5b) dependences allowing to calculate the displaceent resulting ro radial orce Q (ring part on the right hand side o the orce Q is unloaded and does not deor) could be deined. The developed equations are suarized in Tab. 1. The last row shows how any ties the displaceent caused by the orce acting at the ring ree ga p is higher than the displaceent relative to orce o the sae agnitude but applied at the iddle o circuerence. Point o orce location* (Fig. ) Middle o ring circuerence Tab. 1. Displaceents o ring points c aused by the P orce Displaceent along the x axis x Q r E I Displaceent along the y axis y Q r 4 E I Resultant displaceent Q r E I 1 Ring ree gap x Ft r E I y Ft r E I Ft r 1 E I 4 Relation o displaceents or equal orces Q and F t 4 6 5.5 *Usually, the P orce at ring ree gap is called tangential orce and is designated F t, while the P orce at the iddle o ring is called radial orce and designated Q.. Application o analytical relations to veriication o copression ring atheatical odel As entioned earlier, the ost signiicant studies on ring shape deterination were published already in the irst hal o last century. Because o obvious reasons the analytical dependences presented in these studies were developed using ar going liitations, which brought about the ring calculations to the conditions ar dierent ro those o ring actual operation. Aong other the assuptions were as ollows: the ring is located in perectly circular liner and with its entire circuerence contacts the cylinder, and the wall pressure is evenly distributed along the ull circuerence (as shown in Fig. c). The sipliications were introduced because variability o soe paraeters o ring geoetry and aterial were too diicult to describe with analytical unctions. Fortunately, nuerical ethods are ree o such restrictions. Nowadays, the piston rings can be designed with arbitral accuracy according to the atheatical odels presented in literature, also the Polish one. One o the ethods concerning the distribution o ring elastic wall pressure presented Iskra [1]. This ethod was used or the developent o atheatical odel applied by the Authors to their coputations described in [6, 7]. However, the useul application o any new 49
W. Serdecki, P. Krzyie odel should be preceded by the veriication which ean the coparison o obtained results with results achieved using other ethods. Following study presents results o odel calculations and their coparison with results got using analytical ethods concerning piston copression rings. Technical data o analyzed rings was necessary to begin the coparative calculations. These data, suarized in Table are taken ro anuacturers catalogues [5] or were easured directly. Their diensions and objects o application were dierent, i.e. autootive engine 170A.000, bulldozer DTI-817C and arine engine L48/60CR. Beside dierent diaeter other characteristic eatures are dierent including tangential orce which allowed to veriy correctness o odel applied or various ring design. The unknown value o the radial orce Q which cause the sae displaceent along the y axis as the tangential orce F t was deterined according to the orula Q =,69 F t ( this orula, presented in [4] or exaple will be veriied in another study). Tab.. Technical data o exeplary copression rings o cobustion engines Quantity Ring No 1 (autootive engine) Ring No (engine o a bulldozer) Ring No (arine engine) Ring neutral radius r [] 0.08 0.0655 0. Axial height h p [] 0.0014 0.00 0.015 Radial thickness g p [] 0.004 0.005 0.016 Modulus o elas ticity E [Pa] 115 10 9 11 10 9 9 105 10 Tangential orce F t [N] 9.60 18.6 19 Radial orce Q [N] 5. 49.1 578 Conority o calculations o ring point displaceents under load o orces F t and Q calculated with the use o data presented in Tab. 1 and own atheatical progra was analyzed during veriication studies. Calculations according to atheatical odel were carried out or 70 sections o ring circuerence. As it can be seen ro the data presented in Tab. considerable dierences occur between displaceents x and y calculated using orulas ro the Tab. 1 and authors progra, nevert heless their speciic value does not exceed 5%. Tab.. Results suary o ring points displaceent calculation carried out with ana lytical (A) and nuerical (N) ethods or load brought about by F t or Q orce Ring No 1 Ring No Ring No Method Metho Method Metho Method Method Displaceent A d N [%] A d [%] A N [%] N x [] (F t).0 1.96.45.98.84 4.69 10. 9.71 4.80 y [] (F t) 4.78 4.9.9 7.04 7.0.7 4.0 4.5.08 x [] (Q) 1.4 1.40 4.47 1.97.05 4.06 6.71 6.99 4.17 y [] (Q).10.11 0.47.09.1 1.9 10.5 10.6 0.10 Aong basic reasons o the noticed discrepancies one should point out that analytical calculations were carried out or deored ring, i.e. o the shape not circular. This conclusion is corroborated by the courses presented in Fig. 5 obtained during odel investigation carried out or 440
Dependence o Piston Ring Paraeters Deterination Accuracy on the Method o Calculation ring nuber. This course shows that or the analyzed ring distance o points r i ro ring center is constant only or evenly distributed load (line 1). The greatest variation o this distance occurs or the point nuber 1 (ring ree end) when ring is loaded with the radial orce Q. Fig. 5. Variations o calculation point distances r i situated on circuerence o loaded ring: 1 evenly, by the orce Ft, by the orce Q; results or the ring No ro Table (n=60) Suarizing one should ention that or the group o quite dierent rings dierences between results o analytical and odel investigations do not exceed 5% (dierences could be higher or rings o other construction or dierent load distribution). Taking this into account it was acknowledge that accordance o the results is quite satisactory or next step o veriication that will consist in coparison o accuracy o ring ree or deinition. Results will be presented in the next paper. Reerences [1] Iskra, A., Studiu konstrukcji i unkcjonalnoci piercieni w grupie tokowo-cylindrowej, Wydawnictwo PP, Pozna 1996. [] Kozaczewski, W., Konstrukcja grupy tokowo-cylindrowej silników spalinowych, WK, Warszawa 004. [] Kurowski, R., Niezgodziski, M., Wytrzyao ateriaów, PWN, Warszawa 1968. [4] Piaseczny, L., Technologia naprawy okrtowych silników spalinowych, Wydawnictwo Morskie, Gdask 199. [5] Piston Ring Manual. Published by Goetze. [6] Serdecki, W., Badania wspópracy eleentów ukadu tokowo-cylindrowego silnika spalinowego, Wydawnictwo Politechniki Poznaskiej, Pozna 00. [7] Serdecki, W., Krzyie, P., Model investigation o piston ring-cylinder liner collaboration on high power engine, Journal o KONES Powetrain and Transport, Vol. 16, No. 4, Warsaw 009. [8] Serdecki, W., Deterination o Copression Ring Wall Pressure Distribution, Journal o POLISH CIMAC, Energetic aspects, Vol. 5, No. 1, Gdask 010. [9] Wodarski, J., Podstawy eksploatacji aszyn okrtowych. Tarcie i zuycie, Akadeia Morska w Gdyni, Gdynia 006. 441