Torsional analysis of the engine computational model

© JVE INTERNATIONAL LTD. VIBROENGINEERING PROCEDIA. DEC 2017, VOL. 16. ISSN 2345-0533 25 To sional analysis o he engine compu a ional model Pa el Kuče a1, Václa Píš ěk2 B no Uni e si y o Technology, Technicka 2896/2, 616 69, B no, Czech Republic 1Co esponding au ho E-mail: 1kuce a@ me. u b .cz, 2pis ek. @ me. u b .cz R ecei ed 22 No embe 2017; accep ed 3 Decembe 2017 D OI h p s://doi.o g /10.21595/ p .2017.19499 Abs ac . The pape deals wi h basic beha iou and o sional analysis o he engine compu a ional model. This compu a ional model is assembled om own blocks which a e c ea ed using he basic elemen s o Simulink so wa e. The pape desc ibes indi idual blocks and whole assembly o he engine compu a ional model. The simula ion o his diesel model was done o e i y i s unc ion. In conclusion, o sional analysis was ca ied ou . Keywo ds: compu a ional model, engine, Simulink, o sional ib a ion. 1. In oduc ion Di e en so wa e is used o de elopmen o engine compu a ional model and i is i s s ep o he engine p o o ype de elopmen . Howe e , some pa s o in e nal s uc u e o he p epa ed compu a ional model canno be ully modi ied. The e o e, i is necessa y o c ea e a cus om engine compu a ion model. This pape is ocused on de elopmen o own lib a y wi h blocks. They desc ibe indi idual pa s o he engine and a e c ea ed in Simulink so wa e. Then he use can assemble di e en ypes o engine cons uc ion. Fo he ep esen o he eal engine, indica ed p essu e measu emen we e used. F om his da a, he o que map is assembled and implemen o he engine compu a ional model. The model includes lexible elemen s; he e o e, o sional ib a ions can be simula ed. The pape also desc ibes an example o a compu a ional model o he eigh -cylinde diesel engine. I s simula ion o maximum load was compa ed wi h measu emen o he engine o que and engine powe cu es. O he simula ion desc ibes he o sional ib a ions which we e e alua ed by FFT analysis. The aim was o c ea e a compu a ional engine model wi h possibili y o eal ime simula ion. In he u u e, his will allow using o hese models o de eloping and es ing o ECU p o o ypes. 2. Inpu alue o he compu a ional model Fo ge ing inpu alues o he engine compu a ional model, engine o que and o ces ac ing on he c ank mechanism mus be calcula ed. The e o e, inpu alues o he engine compu a ional model a e cu es o indica ed p essu e in he engine cylinde . The ange o he engine speed, ep esen ing p essu e cu e, is om 800 pm o 2000 pm. The cylinde diame e o 120 mm, he engine s oke o 140 mm and he leng h o he connec ing od o 260 mm we e also used o he calcula ion and he equa ions a e desc ibed in [1]. To ob ain he whole engine o que map, he indi idual cu es o p essu e we e ecalcula ed o he o que and we e placed o he h ee-dimensional ma ices wi h he dimensions o 13×720×2 o each cylinde . Some dimensions o he ma ices could be di e en because i depends on he measu ed da a which a e a ailable. He e a e example ma ices used o simula ion. Fi s dimension has alue o 2, i ep esen s wo-dimensional a ays o maximum and minimum uel supply. The 13 ma ix ows con ain he engine speed ange om 800 pm o 2000 pm and he 720 ma ix columns ep esen he c ank angle. The ma ices o indi idual cylinde we e shi ed acco ding o cylinde igni ions. Fig. 1 shows he o que map o a maximum and a minimum uel supply. Be ween hese s a uses, he e is ange o engine o que which can be used o a d i e o powe ain. In he new e sion o blocks, he e is also a possibili y o using s aigh away indica ed p essu e, because blocks con ain equa ion o calcula ion o he o que. TORSIONAL ANALYSIS OF THE ENGINE COMPUTATIONAL MODEL. PAV EL KUČERA, VÁCLAV PÍŠTĚK 26 © JVE INTERNATIONAL LTD. VIBROENGINEERING PROCEDIA. DEC 2017, VOL. 16. ISSN 2345-0533 Fig. 1. To que map 3. Compu a ional model o he engine The compu a ional engine model is c ea ed in Simulink so wa e and uses own lib a y wi h blocks. Fo he c ea ion o compu a ional models, he li e a u e [2, 3, 4] was used. This lib a y includes blocks desc ibing he indi idual pa s o engine. Basic p inciple o blocks is based on lexible elemen s; he e o e, use can simula e o sional ib a ions. The engine compu a ional model is ep esen ed by a o sional model. The assembly o he compu a ional engine model includes blocks o pis on, sha , lywheel, o sion dampe , o name bu a ew. The compu a ional model is shown in Fig. 2. The e is o sional model wi h se en educed ine ia alues and six s i ness blocks be ween discs. In gene al, o sional sys em is desc ibed by using Lag angian me hod [5]:  󰇘 +󰇗+=(), (1) whe e  is mass ma ix,  – damping ma ix,  – s i ness ma ix,  – ec o o engine o que,  – ec o o gene alised coo dina es (󰇘 is he angula accele a ion, 󰇗 – angula eloci y,  – angle o de o ma ion) and  – ime. Fig. 2. In e n blocks o he engine compu a ional model Du ing he simula ion, he compu a ional model gene a es c anksha angle and engine speed. And he use con ols he engine model by an inpu signal o a h o le pedal. I s alue has he ange o 0-100 %. These h ee alues de e mine he alue o ac ual engine o que om o que map. The acqui ed engine o que is applied on he indi idual ine ia block o he o sional model. These pis on blocks a e connec ed oge he using by lexible blocks, he e o e, hey a ec each o he . Then o sional ib a ion can be simula ed. The compu a ional model o he dynamome e is also assembled as a o sional model. I s block is shown in Fig. 3. This dynamome e block gene a es a o que which coun e ac s he engine o que o achie e he desi ed engine speed. TORSIONAL ANALYSIS OF THE ENGINE COMPUTATIONAL MODEL. PAV EL KUČERA, VÁCLAV PÍŠTĚK © JVE INTERNATIONAL LTD. VIBROENGINEERING PROCEDIA. DEC 2017, VOL. 16. ISSN 2345-0533 27 Fig. 3. Compu a ional model o engine and dynamome e 4. Simula ion In he simula ion, he compu a ional model simula ed maximum load o diesel engine. The simula ion was di ided in o se e al s eps. In each s ep o engine speed, he mean o que was ob ained. F om hese alues we e c ea ed cu es o he engine o que and powe . Then hey we e compa ed wi h he speed cha ac e is ics o he eal engine. The esul s a e shown in Fig. 4. The esul s show ha he cu es o o que and powe a e simila in main ange o engine speed. In his engine load s a e, he compu a ional model can be conside ed wo king p ope ly. In he u u e, o he simula ions will be ca ied ou o e i y o o he condi ions. a ) b) Fig. 4. Resul o he engine speed cha ac e is ics 5. To sional ib a ion I is an eigh -cylinde engine and igni ion occu a e 90° o he c anksha . The e o e, i can be assumed ha he 4 h and 8 h ha monics o he engine speed a e e lec ed in o sional ib a ions. This equency  can be calcula ed using he ollowing equa ion:  = 60 ,  = 1, 2, 3 … , (2) whe e n is he engine speed wi h he uni pm and  – ha monic o de o engine speed. The equency co esponding o he 4 h and 8 h ha monic o de o he engine speed is calcula ed a 800 pm and esul s a e 53.33 Hz and 106.66 Hz. Fo he analysis o o sional ib a ions, he simula ions om he p e ious chap e we e used. Thei o al o que om each engine cycle was used o e alua e he FFT analysis [6] o he engine speed ange om 800 o 2000 pm. In his FFT spec um in Fig. 5, he 4 h and 8 h ha monic o de o he engine speed a e clea ly isible. I co esponds o he calcula ions in Eq. (2). These ha monic o de s can exci e o sional sys em o he engine o he ehicle powe ain. This occu s when he ac ual o sional equency is equal o he ha monic o de o he engine speed. In he g aph in Fig. 5, he e is e y li le isible ansi ion o e he 2nd own engine equency (282.73 Hz) because he TORSIONAL ANALYSIS OF THE ENGINE COMPUTATIONAL MODEL. PAV EL KUČERA, VÁCLAV PÍŠTĚK 28 © JVE INTERNATIONAL LTD. VIBROENGINEERING PROCEDIA. DEC 2017, VOL. 16. ISSN 2345-0533 o sional ib a ion is damped. Resul s o o sional ib a ion analyses shows ha he model wo ks p ope ly and can be used o analyses o o he engines o exci a ion o he whole i ual ehicle powe ain. Fig. 5. FFT spec um o he engine compu a ional model 6. Conclusions The aim was o assemble he compu a ional engine model which desc ibes he unc ions o he eal engine, can be simula ed in he eal ime and can be used o analyse o he o sional ib a ion. The compu a ional model was assembled om own lib a y wi h blocks. They ep esen indi idual pa s o he engine. The esul s o engine speed cha ac e is ics in he i s simula ion we e compa ed o he eal engine and he i ual engine can be used o a simula ion wi h maximum load o an engine. Howe e , o he simula ions mus be done o e i y o he ope a ing modes o he engine. The esul s o he o sional ib a ion analysis show gene a ed ha monic o de o he engine speed and i co espond wi h heo e ical assump ions. In he u u e, measu emen o o sional ib a ion mus be done o e i y o esul s. This engine compu a ional model can be also used o eal- ime simula ions in he Ha dwa e in he Loop sys ems. I is impo an o u u e de elopmen and es ing o ECU p o o ypes. Acknowledgemen s This wo k is an ou pu o he in e nal BUT Resea ch P ojec Reg. No. FSI-S-17-4104. Re e ences [1] Heisle H. Ad anced Engine Technology. 1s Edi ion. A nold, Ox o d, 2002. [2] Gillespie T.D. Fundamen als o Vehicle Dynamics. Socie y o Au omo i e Enginee s, Wa endale 1992. [3] Budynas R. G. Shigley’s Mechanical Enginee ing Design. McG aw-Hill, New Yo k, 2006. [4] Kuče a P. Mecha onic App oach o Vehicle Dynamics. Doc o al Thesis, BUT B no. 2015 [5] Nes o ides E. J. A Handbook on To sional Vib a ion. Camb idge Uni e si y P ess¸ Camb idge, 1958. [6] Tůma J. Vehicle Gea box Noise and Vib a ion. Wiley, Chiches e , 2014.