© JVE INTERNATIONAL LTD. VIBROENGINEERING PROCEDIA. DEC 2017, VOL. 16. ISSN 2345-0533
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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
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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
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[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.