Resea ch A icle
Ad ances in Mechanical Enginee ing
2019, Vol. 11(12) 1–9
ÓThe Au ho (s) 2019
DOI: 10.1177/1687814019896927
jou nals.sagepub.com/home/ade
Modeling and expe imen al esea ch o
quay c ane ca go lowe ing p ocesses
To m a s E g l y n a s
1
, A unas Andziulis
1
, Ma ijonas Bogde ic
ˇius
2
, Jolan a
Janu _
enien_
e
3
, Se gej Jako le
1,3
, Valdas Jank
unas
1
, Aud ius Senulis
1
,
Mindaugas Jusis
1,4
, Paulius Bogde ic
ˇius
2
and Saulius Gudas
4
Abs ac
This a icle s udies an ope a ional p oblem a ising a a con aine e minal. Klaipeda ci y po ope a ions we e su eilled
up close and ele an ema ks we e made. The ime e iciency o he exis ing con aine -lowe ing p ocedu es using he
simula ion s udies wi h a es -bed and wi h a eal li e c ane ope a ion was examined. S a is ical analysis o he expe i-
men al esul s has showed ha non-au oma ed p ocesses ha e highe ime a iance o he lowe ing p ocess. The ope -
a ions o quay c ane o con aine handling ‘‘ship- o-sho e’’ we e analyzed, and lowe ing p ocedu es ime a ia ions
we e de e mined. Each con aine is anspo ed a ope a o s own isk and wi h p e-de ined ime e iciency; he e o e, i
is ha d o p edic he op imal ime o each con aine handling ope a ion, hus, e en ually, addi ional cos s a ise.
Ma hema ical model was de eloped, which desc ibed dynamical cha ac e is ics o he con aine mo emen du ing lowe -
ing p ocedu es. The lowe ing c ane ope a ion was modeled using known dynamic alues o each sepa a e case, and he
complexi y o he p oblem was p o en. The esul s o modeling and expe imen al esul s show ha i is possible o
achie e op imal alues wi h he exis ing p ocesses.
Keywo ds
Dynamics modeling, quay c ane, simula ion, expe imen al esea ch, con aine -lowe ing p ocess, s a is ical analysis
Da e ecei ed: 24 Sep embe 2019; accep ed: 27 No embe 2019
Handling Edi o : James Baldwin
In oduc ion
In e modal shipping con aine s a e widely adop ed in
he global anspo chain o deli e a ious goods o
end-use s. Despi e he ob ious ad an ages, he e is s ill
plen y o oom o imp o emen s when i comes o
ime e iciency and quali y inc ease. Global anspo
ma ke is a ne wo k o companies and end-use s, who
ely on well-managed s anda ds and sys ems. Recen
ends and numbe s sugges ha abou 90% o non-
bulk global ade is being managed by shipping con-
aine s wo ldwide.
1,2
Eu ope alone in 2016 managed
0.8 billion ons o ca go.
3
S a is ics shows ha du ing
he 10-yea pe iod be ween 2007 and 2017, shipping
quan i ies inc eased by 66% (up o 148 million TEUs),
aking in o accoun he global me chandise ade by
ma ine a ic.
4
Many enginee s and manage s wo ld-
wide o esaw such apid inc ease. Ye , hey could no
manage i in an op imal manne . Thus, e iciency is a
c i e ion which needs o be inc eased in o de o adop
new challenges o he u u e. Ca go loading ope a ions
ely on loading and unloading speeds, sa e y o
1
Klaipeda Uni e si y, Klaipeda, Li huania
2
Vilnius Gediminas Technical Uni e si y, Vilnius, Li huania
3
VSB-Technical Uni e si y o Os a a, Os a a-Po uba, Czech Republic
4
Cybe -Social Sys ems Enginee ing G oup, Vilnius Uni e si y, Vilnius,
Li huania
Co esponding au ho :
Tomas Eglynas, Klaipeda Uni e si y, He kaus Man o g. 84, LT-92294
Klaipeda, Li huania.
Email: [email protected]
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wi hou u he pe mission p o ided he o iginal wo k is a ibu ed as speci ied on he SAGE and Open Access pages
(h ps://us.sagepub.com/en-us/nam/open-access-a -sage).
ope a ion,
5
and ene gy consump ion in he icini y o
he po .
2
These ac o s end o make inal decisions
when adop ing new and un es ed echnologies in
p ac ice.
The mode niza ion o con aine e minals h ough
mode n ICT (in o ma ion and communica ion echnol-
ogy) solu ions pa ly sol es he p oblems conce ning
he ‘‘G een’’ e minal ini ia i e.
2
Au onomy o ope a-
ions is adop ed in many a eas o con ol s abili y o
con aine handling, anspo a ion using e minal
ucks, au onomous guided ehicle (AGV),
6
and so on.
E en now, newly buil c anes a e using ope a o on si e
o manage he loading p ocedu es.
7
Each new ope a o
sees he loading s anda ds as guidelines, bu no s ic
ules. The e o e, c ane au onomy
8
is necessa y, in o de
o inc ease he e iciency o adop ed s anda ds and eg-
ula ions, mechanical sys ems, and associa ed po
in es men s. An au onomous quay c ane is no an
inno a ion on i s own.
9
These complex sys ems al eady
exis .
10
They a e applied in many a eas o indus y
including po ope a ions.
11
Howe e , mode niza ion
o exis ing in as uc u e is a p io i y o mos compa-
nies, wo king wi h con aine handling. Mo e p ac ical
and eal solu ion is o mode nize exis ing sys ems,
a he han pu chase all new expensi e in as uc u e.
O e all, he e a e c ane s abiliza ion sys ems ha a e
al eady in use,
12
bu hey mos ly lack o quali y eed-
back and ope a o expe ience ha makes huge impac
on he e iciency o hese expensi e sys ems.
13
In p ac ice, he ealiza ion o complex con ol solu-
ions is limi ed by he luc ua ions o he sp eade wi h
load. I s mo emen s a e andom in na u e, due o
ex e nal impac s, such as wind o physical con ac wi h
o he objec s.
14
I is di icul o p edic such andom
de ia ions in p ac ice. The mos ad anced Eu opean
po s, such as Ro e dam o Hano e , he handling
p ocedu es and IT ope a ions a e mos ly au oma ed.
Howe e , he inclusion o he mode n au oma ed quay
c anes is s ill an inno a ion o smalle po s h ough-
ou he wo ld. In he ligh o he esea ch and p og ess
made in his a ea,
15–19
many po s in he wo ld lack he
applica ion o hese inno a ions.
Inc easing he ime e iciency o he ca go p ocess is
a opical issue add essed in he scien i ic wo k, o
which a ious solu ions a e p oposed, om manage-
men algo i hms o ca go planning solu ions.
2,6,20
The
quay c anes a e analyzed in he way o inc easing load-
ing ime,
2,21
damping he load swinging du ing he
loading–unloading p ocess
21
using addi ional eedbacks
in con ol sys em wi h he p opo ional–in eg al–de i-
a i e (PID) o p opo ional–in eg al (PI) con olle s
o using a i icial in elligence analysis.
22,23
The p oblem add essed in he po is he c ane and
he e minal uck synch oniza ion means. The c ane
ope a o has o wai o he e minal uck o he e mi-
nal uck has o wai o he ope a o o inish his
unloading ou ine. Due o cons an ope a o aul s,
he e is a delay in he end-o -shipmen p ocedu es.
Especially, he con aine loading on e minal uck is
managed di icul ly. Au ho s p opose o es analyze
he lowe ing end p ocedu e o he u u e con ol solu-
ion. The solu ion would use eal e minal uck and
sp eade senso y da a. Depending on he ac ual posi-
ion o he e minal uck o he c ane,
20
decisions a e
made sys ema ically o slow down he speed o mo e-
men so ha he a ge poin eached a he same ime
by all in ol ed bodies. This sa es bo h ene gy esou ces
and echnical esou ces,
6
and inc eases c ane and, con-
sequen ly, he en i e po e iciency.
Ma hema ical modeling o con aine -
lowe ing p ocedu e by quay c ane
The ma hema ical model o he quay c ane was de el-
oped. The quay c ane consis s o asynch onous elec i-
cal mo o , gea s, sha s, d um, cables, con aine , and
ehicle. Because he mos impo an pa was he end o
con aine loading, he sway o con aine was no aken
in o accoun . The sway o con aine will be included in
he u u e imp o ed model. The s uc u e o his model
is shown in Figu e 1.
In Figu e 1, I1,...,I9a e he mass momen s o ine -
ia; R2,...,R9a e he adii; u1,...,u10 a e he angles
( o a ion angles); Mmo o is he quay c ane sp eade low-
e ing mo o ; q1and q2a e he displacemen s; 12, 34, 56,
78 a e he sha s; 10 is he cable; and 11 is he ehicle
suspension.
In Figu e 2(a), His he ca go heigh , H
1
is he dis-
ance be ween oad su ace and d um axis, H
2
is he
dis ance be ween oad su ace and ehicle pla o m, L
is he cable leng h, and F
12
is he con ac o ce. In
Figu e 2(b), qiand qja e he gene alized displacemen s,
eis he numbe o elemen ; ke,ce, and Dea e he s i -
ness, damping coe icien s, and gap, espec i ely.
The mechanical sys em in ques ion (Figu e 2) con-
sis s o an elec ic mo o (1), gea s (2–9), cable, con-
aine , and e minal uck. Main pa ame e s o he
analyzed sys em in Figu es 1 and 2 a e 500 kW powe
Figu e 1. The o e all dynamic model o he d i e.
2Ad ances in Mechanical Enginee ing
in he main mo o used o lowe ing con aine ,
n= 995 /min, and equency o = 50 Hz. The main
ansmission pa ame e s a e gi en in Table 1.
The dynamics o he loading p ocess a e desc ibed
in he equa ions below. Ca go dis ance om he axis o
o a ion o he d um H( ), cable leng h L( ), dis ance
be ween he ca go and he e minal uck is H
12
( )a
any gi en ime is gi en in equa ion (1)
H ðÞ=L ðÞ+H0,L ðÞ=L0+q1 ðÞ,
H12 ðÞ=H1H ðÞH2+q2 ðÞ ð1Þ
He e, h
0
is he heigh o he ca go. The igidi y coe i-
cien o he cable is gi en in equa ion (2)
kLq1
ðÞ=ELAL
L0+q1 ðÞ ð2Þ
He e, ELand ALa e he cable elas ic modulus and
c oss-sec ional a ea, espec i ely. The momen o ine -
ia o he d um masses is gi en in equa ion (3)
I10 =I10,0 2
10mL0L ðÞ ð3Þ
He e, mL0is he mass pe uni leng h o cable. The equa-
ions o mo ion o he load d i e a e de i ed using he
second-o de Lag ange equa ion (4)
d
d
∂EK
∂qj

∂EK
∂qj

+∂EP
∂qj

+∂D
∂qj

=Qjð4Þ
He e, E
k
,E
P
, and Da e he kine ic ene gy o he d i e,
po en ial ene gy, and dissipa i e unc ion, espec i ely;
qjand Qja e he j h gene alized coo dina e and o ce,
espec i ely. The o que o asynch onous mo o MMo o
( he equa ion o a ia ion) is gi en in equa ion (5)
M
Mo o =c wM0_
1

d MMo o ð5Þ
He e, c and d a e he asynch onous mo o pa a-
me e s, and wM0is he mo o o o synch onic angula
eloci y. Asynch onous mo o o a ion (equa ion (6)) is
gi en as
I1€
1=MMo o ðÞMb ðÞk12 1 2
ðÞ
c12 _
1_
2

c1_
1
ð6Þ
He e, Mb( ) is he engine b aking o que; k12 and c12
a e he sha s i ness and esis ance coe icien s, espec-
i ely; and 1, 2,_
1,_
2a e he i s and second body
o a ion angles and angula eloci ies. Second- and
hi d-gea o a ions (equa ions (7) and (8)) a e
I2€
2=k12 2 1
ðÞc12 _
2_
1

k23R2u23 c2_
2
ð7Þ
I3€
3=k34 3 4
ðÞc34 _
3_
4

k23R3u23 c3_
3
ð8Þ
whe e
u23 =d23psign d23p

+d23msign d23m
ðÞð9Þ
d23p=R2 2+R3 3D23 ...D23 ð10Þ
He e, D23 is he gap be ween gea s 2 and 3
d23m=R2 2+R3 3+D23 ð11Þ
He e, R2and R3a e he adii o he main ci cles o he
gea s 2 and 3; sign(x)=1, when x.1and o he wise 0.
The ou h- o nin h-gea o a ions a e calcula ed
Figu e 2. Con aine loading sys em design diag am: (a)
dynamic model o sp eade and anspo , and cable (b) scheme
o nonlinea elemen .
Table 1. The main pa ame e s o ansmission.
Pa ame e Uni s Value
Dis ance, H
1
m 11.0
Dis ance, H
2
m 1.50
Ini ial leng h o cable, L
0
m 2.0
Mass momen o ine ia o
o o mo o , I
1
kg m
2
2.0
Mass momen o ine ia, I
2
kg m
2
0.0308
Mass momen o ine ia, I
3
kg m
2
0.368
Mass momen o ine ia, I
4
kg m
2
0.368
Mass momen o ine ia, I
5
kg m
2
0.445
Mass momen o ine ia, I
6
kg m
2
0.445
Mass momen o ine ia, I
7
kg m
2
0.710
Mass momen o ine ia, I
8
kg m
2
0.920
Mass momen o ine ia, I
9
kg m
2
0.920
Mass momen o ine ia, I
10
kg m
2
2.30
Mass o ca go and sp eade , m
1
kg 22,572.0
Mass o ehicle, m
2
kg 10,000.0
Mass o 1 m cable, mL0kg 1.0
Modulus o elas ici y o cable, ELGN/m
2
200.0
C oss sec ion a ea o cable, ALm
2
3.1415E24
S i ness coe icien o con ac , kcon ac MN/m 0.10E6
Damping coe icien o con ac , ccon ac MN s/m 0.010E6
In eg a ion ime s ep s 1.0E26
Eglynas e al. 3
simila ly as he second and hi d. Ten h gea o a ion
equa ion is as equa ion (12)
I10 €
10 =_
I10 _
10 +1
2
∂I10
∂ 10
_
10

2
k910 10  9
ðÞ
c910 _
10 _
9

c10 _
10 R10kLq1
ðÞR10 10 q1
ðÞ
R10c10 R10 _
10 _
q1

ð12Þ
Ca go and ehicle mo emen equa ions (13) and (14)
a e
m1€
q1=_
m1_
q1kLq1R10 10
ðÞ
cL_
q1R10 _
10

+m1gF12sign d12
ðÞ
+1
2R6 6q1
ðÞ
2ELAL
L2

cae 0_
q1
ðÞ
2sign _
q1
ðÞ
ð13Þ
m
2q2=F12sign d12
ðÞ+m2gk2q2c2_
q2ð14Þ
He e, q1,q2is he displacemen o masses m
1
and m
2
;
m1and _
m1a e he ca go, sp eade , and cable o al mass
and i s de i a i e o ime, espec i ely; cLis he cable
coe icien o esis ance; and cae 0is he ae odynamic
o ce coe icien o esis ance (equa ion (15))
d12 =H2q2
ðÞH1Hq
1
ðÞðÞð15Þ
He e, m
2
is he ehicle mass, and k2and c2is he coe i-
cien s o ehicle suspension s i ness and esis ance,
espec i ely.
Thus, he ma hema ical model o quay c ane was
cons uc ed and he esul s o con aine -lowe ing we e
examined o he compa ison wi h he expe imen al
da a and gi ing implica ion o he possible lowe ing
ime educ ion.
Expe imen al in es iga ion
The aim o esea ch was o es he eal wo king condi-
ions o he quay c ane, ope a o s wo k, he sp eade
e iciency, and unnecessa y o ces accumula ed du ing
con aine loading.
24
A simula ion model was de eloped
and es ed. In ecen yea s, esea che s wo k closely
wi h elec ically powe ed e minal ucks and c anes.
25
In o de o assess he need o synch oniza ion, au ho s
conduc ed expe imen al esea ch in Klaipeda po .
Du ing he expe imen al esea ch, he quay c ane ca -
ied ou loading ope a ions, du ing which he da a we e
collec ed. The p ac ical expe imen collec ed da a om
204 eal cycles o he loading p ocess om ship o he
quay and back again. MK2 da a logge ha dwa e was
used o hese expe imen al measu emen s (see
Figu e 3).
When de e mining he dynamic pa ame e s o he
objec unde in es iga ion (in his case, he con aine ),
da a abou i s accele a ion, speed, and posi ion in space
we e measu ed and eco ded. Fo his pu pose, a DL1-
MK2 da a logge (Race Technology, UK), a h ee-way
accele ome e (gua an eed 2 g minimum ull scale on
bo h axes; esolu ion o 0.005 g; op ional 6 g senso
a ailable as a ac o y op ion) ib a ion measu emen s
( ib a ion ac o y es ed a 25 g, 50 Hz sinusoid o
5 min), was used o eco d and s o e ehicle mo ion
dynamics pa ame e s. Fo posi ioning, he me e is
connec ed o a GPS an enna (GPS—ou pu s posi ion,
speed, posi ion accu acy, and speed accu acy e e y
200 ms wi h no in e pola ion; GPS acking loops op i-
mized o applica ions up o abou 4 g; acking o all
sa elli es in iew). Based on he ime cou se o he ehi-
cle and he accele a ion eadings, he de ice measu es
he speed o he es objec wi h an accu acy o 0.16 km/h,
wi h a measu emen e o o up o 1%. Longi udinal
and ans e se accele ome e s eco d accele a ions up
o 20 m/s
2
and measu emen e o up o 0.05 m/s
2
.
A e p ocessing he da a collec ed du ing he expe i-
men al measu emen s, he en i e loading p ocess was
di ided in o s ages o iden i y which echnological load-
ing p ocess akes he longes . The pu pose o his
expe imen was o iden i y p oblema ic ope a ions in
he loading p ocess when scheduling a synch oniza ion
ask, he eby jus i ying he need o synch oniza ion.
By synch onizing indi idual po acili ies (such as e -
minal ucks and quay c anes) and by planning ca go
ope a ions acco dingly, i is possible o minimize he
impac o hese p oblem a eas on he loading ime.
These s ages and summa ized expe imen al esul s a e
gi en in Table 2.
Expe imen al measu emen s we e implemen ed
when he ca go was shipped om he ship o he sho e.
Depending on he loading p ocess, he ope a ions a e
Figu e 3. DL1-MK2 da a logge (Race Technology, UK).
4Ad ances in Mechanical Enginee ing
di ided in o se en s ages: (1) s a o li ing (hooking),
(2) e ical li ing, (3) diagonal li ing, (4) ho izon al
anspo a ion, (5) diagonal lowe ing, (6) e ical low-
e ing, and (7) placing on e minal uck. The o e all
loading cycle in he ship- o-sho e p ocess was also e al-
ua ed. The summa ized esul s o expe imen al s udies
show ha he en i e du a ion o he ship- o-sho e cycle
o he loading p ocess du ing he ans e o ca go om
he ship o he sho e is in acco dance wi h s a is ical
log-no mal law.
The numbe o da a n= 102 was measu ed ( om
ship o sho e). The log-no mal law hypo hesis was
es ed by Pea son’s x
2
c i e ion. The his og am o he
expe imen al loading imes de e mined du ing expe i-
men al measu emen s is shown in Figu e 4.
A e analyzing he loading p ocess measu emen s in
s ages, s eps 6 and 7 we e chosen o u he analysis,
ha is, e ical lowe ing and posi ioning on he ehicle.
These s ages de e mine he c ane- o- ehicle alignmen
o op imize he loading p ocess and make i con inu-
ous. In Figu e 5, he dis ibu ion o he e ical lowe -
ing ime is p esen ed.
We can see ha he e ical lowe ing mean ime o
he con aine is equal o 7.3 s, and he e ical lowe ing
heigh mean alue is 8.8 m, conside ing he s anda d
de ia ion as 4.5 m. Hypo hesis o lowe ing ime dis ibu-
ion by No mal law was es ed by Pea son’s x
2
c i e ion.
Expe imen al esul s show ha he a e age weigh o he
con aine load du ing he expe imen al measu emen s is
22.2 on and he s anda d de ia ion is 10.2 on, and coe -
icien o a ia ion is 46%. In Figu e 6, he dis ibu ion
o he loading phase du a ion is p esen ed, when he
load is placed on he e minal uck and de ached.
As we can see sho e in e als p edomina e, hey
ep esen abou 50% o he o al (n= 102) measu e-
men esul . A e age is abou 5.43 s; howe e , con aine
placemen can ake up o 20 s. Du a ion o his s ep
could be op imized by au oma ion o loading p ocess,
and his p ocess could be abou 2 s, as show expe imen-
al esul s. The pu pose o he synch oniza ion ask is
o make he ehicle a i e when he load lowe ed du -
ing he loading p ocess. The e o e, expe imen al mea-
su emen s ca ied ou when he equipmen moun ed on
a con aine anspo . Expe imen al esea ch measu ed
Table 2. S a is ical da a o con aine loading ime.
S age o loading Mean Min Max S anda d de ia ion Va ia ion coe icien (%)
1. S a o li ing (hooking) 2.43 0.62 11.47 1.84 76.01
2. Ve ical li ing 4.68 1.04 13.47 3.32 70.89
3. Diagonal li ing 5.14 0.79 9.84 1.97 38.28
4. Ho izon al anspo a ion 6.34 2.05 19.03 3.46 54.68
5. Diagonal lowe ing 6.36 2.72 23.97 3.05 47.90
6. Ve ical lowe ing 7.25 1.66 19.13 2.86 39.42
7. Placing on ehicle 5.43 2.36 20.43 2.99 55.16
To al (Ship- o-sho e) 37.63 26.91 63.87 7.68 20.42
Figu e 4. His og am o expe imen al load om ship- o-ship on
he quay.
Figu e 5. His og am o expe imen al measu emen s o e ical
lowe ing o con aine owa d ehicle heigh .
Eglynas e al. 5

he ajec o y o he e minal uck in he po a ea and
i s wai ing ime a he c ane (see Figu e 7).
The esul s show ha he wai ing ime o he ehicle
a he con aine c ane a ies om 4 s o 34 min
(2096 s). The a e age wai ing ime is 229 s and s anda d
de ia ion 346 s. The p ocess is ex emely uns able wi h
a coe icien o a ia ion o mo e han 150%. Du ing
he expe imen al measu emen s, he ca go was also
e alua ed (when moun ing he equipmen on he
g ippe — he closes poin o he con aine ). Du ing
hese expe imen al measu emen s, he eloci ies and
accele a ions o he mo ing load we e measu ed. A e
p ocessing he esul s, we selec ed he bes esul — he
expe imen al esul o he as es lowe ing o he load
(see Figu e 8).
The esul s show ha in es iga ed case o load low-
e ing e ically was done in 1.9 s. The lowe ing speed o
his si ua ion is gi en in Figu e 8(a). As a esul , speed
alues a e nega i e because he load is lowe ed. We
also wa ched he luc ua ions o he load ha in luence
he ull au oma ion o he p ocess. The load luc ua-
ions in he ho izon al plane du ing lowe ing a e shown
in Figu e 8(b). As one can no ice, con aine sways in a
10 cm bounda y. This alue sugges s ha he ca go
lowe ed in a s able manne and no ou e o ces a ec
he sway (wind gus s o ope a o mis akes).
The expe imen al esul s show he need o mo e
sophis ica ed con ol o he c ane–con aine e minal
uck sys em, bu o wo k in eal si ua ion and o
imp o e he pe o mance a e di icul due o he in e -
en ion in o he po ope a ion. The e o e, he ma he-
ma ical model o lowe ing he con aine was de eloped
o make adequa e modeling and p oducing he ool o
con ol sys em de elopmen .
Resul s and discussion
Du ing he nume ical simula ion, he ca go lowe ing
p ocess was analyzed, which co esponds o he loading
s age 6 o he expe imen al in es iga ions. Simula ion
o he lowe ing p ocess was comple ed by e alua ing
he o ce du ing con ac placing he load on he ehicle.
The esul s o nume ical simula ion a e p esen ed in
Figu e 9.
Du ing nume ical simula ion, he load was lowe ed
e ically down (see in Figu e 9(a)). Due o he high
weigh o he load and he elas ici y o he cable, he
damping occu s. Figu e 10 shows he si ua ion when
he load is placed on a ehicle wi h a dynamic o ce
F12 o ;180 kN (see Figu e 9(b)).
Changes o o que momen o he gea wheels du ing
lowe ing p esen ed in Figu e 10.
Du ing he modeling phase, he gap be ween he
gea ee h was es ima ed. As we see du ing he lowe ing
o he load, i has a nega i e e ec ; i exci es he ib a-
ions o he gea s. This a ec s he lowe ing p ocess; he
ib a ions pass o he cable and consequen ly wo sen
he loading condi ions. Figu e 11 shows he accele a-
ion du ing ho izon al lowe ing, and in Figu e 11(a),
he nume ical simula ions show ha he accele a ion
alues inc ease signi ican ly when ca go has a con ac
wi h e minal uck. This is consis en wi h expe imen-
al measu emen s (Figu e 11(b) (poin 7)), wi h a signi -
ican inc ease in accele a ion alues and exci a ion o
he e minal uck when he load is applied. On com-
pa ison, he esul s wi h he bes expe imen al da a ha
was achie ed du ing he lowe ing (b) – was 2.4 s, bu
modeling esul s show ha i is – in ideal condi ions –
possible o make he ope a ion in 0.5 s (a). And, he
esul s a e compa able in ime and ampli ude, hus
Figu e 6. His og am o expe imen al measu emen con aine
placemen on e minal ehicle.
Figu e 7. His og am o expe imen al measu emen s o ehicle
wai ing ime.
6Ad ances in Mechanical Enginee ing
app o ing he model adequacy. So, he mean ime o
las s age o lowe ing o con aine could be mo ed
owa d he ange o 0.5–2.5 s.
Figu es abo e demons a e ha when he con aine
is placed on he e minal uck, addi ional dynamic
o ce is added, which a some imes can be wice as la ge
Figu e 8. Expe imen ally measu ed da a: (a) he speed o he ehicle in he z-di ec ion when he load lowe ed e ically and (b)
con aine sway in ho izon al plane du ing lowe ing.
Figu e 9. The esul o nume ical simula ion: (a) a ia ion o he e ical dis ance Ho he load o he ehicle and (b) a ia ion o
impac o ce du ing loading.
Figu e 10. Nume ical simula ion esul : o ques du ing load lowe ing.
Eglynas e al. 7
as he le e ing con aine weigh . This is a known
e ec in classical mechanics. Such egula i y is con-
i med by he esul s o nume ical simula ion and
expe imen al accele a ion measu emen s (see Figu e
11). Expe imen al measu emen s show a e y simila
endency du ing con aine loading p ocedu es.
Conclusion
In his a icle, as a esul , we demons a e he gene ali-
za ion o he measu emen s wi h eal quay c ane and
e minal ehicle and p opose a ma hema ical model
desc ibing he dynamic p ope ies o bo h.
Expe imen al measu emen s ‘‘in si u’’ o con aine -
lowe ing o e minal uck ha e been in es iga ed in
de ail and s a is ical analysis o he new expe imen al
esul s ca ied ou . Expe imen al measu emen s showed
ha a iance coe icien eached up o 150% on inal
handling ope a ion. These ope a ion du a ions a ied
be ween 2.36 and 20.43 s, wi h a mean alue o 5.43 s.
The en i e lowe ing cycle a ia ion coe icien eached
55.16%. Sho e ime bounda y shows ha he han-
dling p ocess is op imizable up o wo imes by schedul-
ing he ope a ions be ween quay c ane and e minal
uck ope a o s and using specialized algo i hms o
lowe ing p ocess con ol o each indi idual case. This
in ac could p o ide s abili y o po ope a ions and
make p ocesses and p ocedu es mo e agile o long-
e m planning. Acco ding o hese new expe imen al
da a and esea ch indings, u he plans will be p e-
pa ed o de elop a me hodology o c ane and e minal
uck, AGV synch oniza ion in eal ime and will be
used o b idge he scheduling mechanisms in o a single
eal- ime synch oniza ion sys em.
Acknowledgemen s
The au ho s hank o he p ojec (No. 01.2.2-LMT-K-718-01-
0081) membe s: D R Didziokas, D E Guseino iene, D M
Ku mis, D D D ugnilas, and Z Lukosius o aluable
insigh s and collec ion o da a on si e.
Decla a ion o con lic ing in e es s
The au ho (s) decla ed no po en ial con lic s o in e es wi h
espec o he esea ch, au ho ship, and/o publica ion o his
a icle.
Funding
The au ho (s) disclosed eceip o he ollowing inancial sup-
po o he esea ch, au ho ship, and/o publica ion o his
a icle: This esea ch was unded by he Eu opean Regional
De elopmen Fund acco ding o he suppo ed ac i i y
‘‘Resea ch P ojec s Implemen ed by Wo ld-class Resea che
G oups’’ unde Measu e No. 01.2.2-LMT-K-718-01-0081.
ORCID iD
Tomas Eglynas h ps://o cid.o g/0000-0002-9973-5896
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