Auto-dizalice imaju jednu od ključnih uloga tokom izgradnje i održavanja svih
vidova stambene, saobraćajne i industrijske infrastrukture. Česte promene lokacije
utovara i istovara, manipulacija raznovrsnim teretom u uslovima ograničenog
manevarskog prostora, povećanje nosivosti, visine dizanja i dohvata, operativna
bezbednost i stabilnost, ergonomsko i efikasno upravljanje, uz visok stepen
iskorišćenja energije formiraju kompleksan skup suprotstavljenih zahteva i
ograničenja pri njihovom projektovanju. U cilju dobijanja lakših, energetski
efikasnijih i ekonomičnijih rešenja, inženjeri su primorani da optimizuju noseću
strukturu strela auto-dizalica. Direktna posledica ove tendencije je povećanje
elastičnosti i pojava oscilacija, koje nepovoljno utiču na radni vek strele usled
pojave zamora i otežavaju upravljanje dizalicom. U radu je prezentovan kombinovani
pristup modeliranju dinamičkog ponašanja zglobno vezanih segmenata strele, pri
savojnim oscilacijama, na primeru jedne... realne konstrukcije, sastavljene od dva
segmenta i hidrocilindra sa vešajnim sklopovima. Segmenti strele su tretirani kao
Euler-Bernoulli-jeve grede sa distribuiranim inercijalnim i elastičnim parametrima,
dok je zbirni uticaj hidrocilindra i vešajnih podsklopova uzet u obzir preko
koncentrisanih masa u vešajnim tačkama. Takođe, pri definisanju modela uzeta je u
obzir aksijalna krutost samog hidrocilindra. Masa tereta je koncentrisana u krajnjoj
tački fleksibilnog manipulatora. S obzirom da šasija vučnog vozila nije apsolutno
kruta, elastičnost oslanjanja je ugrađena u model preko opruge u osloncu. Posebna
pažnja je posvećena konstruktivnoj specifičnosti strela auto-dizalica koja se tiče
ekscentričnosti vešajnih tačaka hidrocilindra u odnosu na neutralne linije
segmenata. Veza hidrocilindra i segmenata je modelirana specijalnim sistemom
lakih, aksijalno krutih štapova. Kao generalisane koordinate slobodnih savojnih
oscilacija usvojena su poprečna pomeranja ekvidistantnih tačaka duž neutralnih
linija. Uspostavljena je analitička zavisnost sile u hidrocilindru u funkciji
transverzalnih pomeranja karakterističnih tačaka na segmentima, čije su aksijalne
deformacije zanemarene. Cela zglobna struktura je izdeljena na sekcije tačkama u
kojima deluju transverzalne sile. Diferencijalni oblici dinamičkih elastičnih
linija sekcija i graničnih uslova su diskretizovani metodom centralnih konačnih
razlika. Granični problem je transformisan u sistem lineranih algebarskih
jednačina, pogodan za programiranje. Tačnost dobijenih zavisnosti elasto-dinamičkih
parametara strukture je potvrđena poređenjem prirodnih učestanosti predloženog
modela sa rezultatima iz modela izgrađenog na bazi metode konačnih elemenata, za sve
geometrijske konfiguracije zglobnog manipulatora. Problem promenljivosti
poprečnih preseka segmenata je obuhvaćen posebnim poglavljem. Korišćenjem istog
pristupa, izvršena je i frekventna analiza teleskopskog dela strele.
Truck cranes have one of key roles in construction and maintenance of all kinds of
residential, traffic and industrial infrastructure. Frequent changes in loading and unloading
locations, manipulation with different loads in conditions of restricted maneuver space,
capacity increase, lifting height and reach increase, operating safety and stability, ergonomic
and efficient control, with high degree of energy utilization, create a complex set of opposing
demands and restrictions in their design. In order to get the lightweight, energetically more
efficient and economical solutions, the engineers are forced to optimize the carrying structure
of truck crane booms. Direct effect of this tendency is the increase of elasticity and the
occurrence of vibrations which unfavorably affect the boom’s life due to fatigue and make the
crane control difficult. In this research, a combined approach to modeling of dynamic
behaviour of boom articulated segments in bending vibration is presente...d, in the case of a
real-life structure which consists of two segments, hydro cylinder and mounting
subassemblies. Segments of the boom are considered as Euler-Bernoulli’s beams with
distributed inertial and elastic parameters, while the total influence of hydro cylinders and
mounting subassemblies has been taken into account through lumped masses in mounting
points. Given that the towing vehicle’s chassis is not absolutely rigid, the boom support
elasticity has been built in the model through the spring in the support. Special attention has
been given to the constructive specificity of truck cranes’ booms which deals with the
eccentricity of hydro cylinders’ mounting points in relation to segments’ neutral lines. Bond
of hydro-cylinders and segments has been modeled by a special system of light, axially rigid
rods. As generalized coordinates of free bending vibrations there have been adopted the
transverse displacements of equidistant points along the neutral lines. There has been
established the analytic dependence of the force in hydro-cylinder in terms of transverse
displacements of characteristic points on segments, whose axial deformations are neglected.
Whole articulated structure is divided in sections by points where transverse forces act.
Differential forms of sections’ dynamic elastic lines and boundary conditions are discretized
by central finite difference method. Boundary problem is transformed into a system of linear
algebraic equations, suitable for programming. Accuracy of obtained dependencies of elasticdynamic
structure parameters is confirmed by comparing the natural frequencies of proposed
model with results from the model built on the base of finite element method, for all
geometrical configurations of articulated manipulator. The problem of segments’ crosssections
non-uniformity is covered in special chapter. By using the same approach, there has
been also carried out the frequency analysis of telescopic part of the boom.
Faculty:
University of Kragujevac, Faculty of Mechanical and Civil Engineering, Kraljevo
