Dynamic interaction between the structure and the trolley of high performance gantry cranes

U radu se analizira dinamičko ponašanje noseće konstrukcije portalne dizalice usled dejstva kolica kao pokretnog opterećenja. Dat je prikaz klasifikacije portalnih dizalica pri čemu su izdvojene portalne dizalice za kontejnerske terminale sa svojim visokih performansama koje imaju stalnu tendenciju poboljšanja. Prvo je dat koncept primene analitičkog pristupa za modeliranje noseće konstrukcije preko sistema elastičnih tela tipa prizmatične grede i razmatranje slobodnih poprečnih oscilacija. Kao savremen i pre svega neophodan, usvojen je kombinovani pristup za istraživanje naslovnog problema, tj. konačnoelementni pristup je iskorišćen za modeliranje noseće konstrukcije portalne dizalice a principi analitičke mehanike su iskorišćeni za modeliranje kolica. Razmatraju se dva najčešća konstrukciona tipa portalne dizalice za formiranje modela strukture. Kolica su obuhvaćena kroz model pokretne mase, model pokretnog oscilatora i kroz model pokretnog oscilatora sa klatnom koji predstavlja originalan model pokretnog opterećenja. Za svaki od modela je utvrđena dinamička interakcija između ovih sistema i postavljeni su matematički modeli koji predstavljaju sistem diferencijalnih jednačina drugog reda sa promenljivim koeficijentima. Rešenja su dobijena pomoću originalnih programa, na bazi metode direktne integracije‐ Njumarkove metode. Identifikacija i analize odziva su izvršene za dva realna primera portalnih dizalica. Istražen je uticaj brzine, ubrzanja/usporenja i težine kolica, kao i uticaj klaćenja tereta i elastične opruge u sistemu kolica. Dobijeni rezultati se mogu iskoristiti u početnim fazama konstruisanja portalnih dizalica koje imaju tendenciju da ostvare veoma visoke performanse, u smislu ostvarivanja boljeg uvida u dinamičko ponašanje.The dynamics of a two‐dimensional gantry crane structure subjected to various types of moving load is examined in this work. First, the classification of gantry cranes is suggested and group of gantry cranes at container terminals are distinguished because of high performances which have tendency to become even better in near future. The analytical approach is introduced in modeling the gantry structure as continuous system with transverse vibrations. However, modern approach, i.e. combined finite element and analytical method is adopted to solve the title problem. Two types of structure of gantry cranes are considered. Three types of trolleys are implemented in calculation, i.e. moving mass, moving oscillator and moving oscillator with swinging payload as original model are considered as moving loads acting upon the structure of the gantry cranes. The interaction between the structure and each moving load model is derived and the governing equations for MDOF systems are obtained. The postulated equations, which are second order differential equations with time dependent coefficients, are solved with direct integration method‐Newmark method. The analysis is applied to two types of gantry cranes and dynamic responses are obtained for both the structure and the trolley. There are studied factors of moving loads such as magnitude, speed, acceleration, deceleration and factors within the trolley structure such as swinging of the payload and spring stiffness. Numerical results reveal that used approach is useful and can draw conclusions for structural design purposes of gantry cranes

Considerations of various moving load models in structural dynamics of large gantry cranes

Rad se bavi problematikom pokretnog opterećenja kod portalnih dizalica visokih performansi. Usvojen je kombinovani pristup, koji podrazumeva primenu metode konačnih elemenata u kombinaciji sa jednačinama analitičke mehanike, za formiranje matematičkih modela portalne dizalice. Model kolica je razmatran kroz nekoliko modela: pokretna sila, pokretna masa, pokretni oscilator i pokretni oscilator sa klatnom. Svaki od modela ima svoje dinamičke karakteristike koje profilišu dinamički odziv strukture dizalice. Rešenja su dobijena numerički, metodom direktne integracije, razmatranjem ravanskog ramovskog konačno elementnog modela strukture pod dejstvom ekvivalentnog pokretnog opterećenja na osnovu postavljenog sistema diferencijalnih jednačina drugog reda sa promenljivim koeficijentima. Prikazana je problematika koja nastaje pri povećanju broja parametara pri formiranju dinamičkog modela-postavci matematičkog modela. Na realnom primeru dizalice su dati dinamički odzivi različitih modela koji mogu poslužiti kao preporuka za izbor modela u zavisnosti od važnosti željenih dinamičkih parametara u fazi projektovanja kontejnerskih dizalica.The paper deals with the moving load problems within the structural dynamic analysis of a large gantry crane as high-performance machine. The emphasis is placed on combined method approach, i.e. finite element method and analytical postulations, to obtain the mathematical model of crane. Moving trolley is considered throughout several models: moving force, moving mass, moving oscillator and moving oscillator with swinging object. Each model has characteristics which determine the responses of the crane structure, along with its dynamic properties. The title problem is solved by calculating the forced vibration responses of the two-dimensional framework with time-dependent property matrices and subjected to an equivalent moving load. Improving the moving load models increases complexity as well for postulating as for obtaining the solutions from overall crane model. Comparative presentation of models is shown here with conclusion that leads to an appropriate way of model selection prior to crane problem postulation

Consideration of a moving mass effect on dynamic behaviour of a jib crane structure

U radu se razmatra dinamičko ponašanje ravninske konstrukcije stupne konzolne dizalice izložene djelovanju gibanja kolica elektromotornog vitla koje nosi teret. Dinamički odzivi konstrukcije, u vertikalnom i u horizontalnom pravcu, dobiveni su uporabom metode konačnih elemenata i metode direktne integracije. Umjesto konvencionalnog pristupa uporabe modela pokretne sile, u ovom su radu obuhvaćeni utjecaji inercije masa kolica, vitla i tereta. Radi toga, koncept matrice pokretne mase je implementiran u matrici masa cijelog sustava. Određene su prinudne oscilacije konstrukcije stupne konzolne dizalice zbog djelovanja ekvivalentnog pokretnog opterećenja pri čemu je matrica masa sustava promjenjiva u vremenu. Razmatran je utjecaj intenziteta, brzine i ubrzanja pokretnog opterećenja. Rezultati daju korisne zaključke za konstruiranje konzolnih dizalice.This work examines the dynamics of a two-dimensional jib crane structure subjected to a moving trolley with hoist and payload. Dynamic responses of the structure, both in the vertical (Y) and horizontal direction (X), are calculated using the finite element method and the direct integration method. Instead of the conventional moving force problem, this paper deals with the two-dimensional inertial effects due to the masses of trolley, hoist and payload. For this purpose, the moving mass matrix has been used to give contribution to the overall mass matrix of the entire system. The title problem was solved by calculating the forced vibration responses of the jib crane structure with time-dependent overall mass while subjected to an equivalent moving force. Factors as magnitude, speed and acceleration of the moving trolley were studied as well. Numerical results reveal that the approach used herein is usefull and can be used to draw conclusions for the structural design purposes of jib cranes

Experimental study on the stresses at the i-beam end-plate moment connection

The paper deals with experimental study of the stresses at the bolted end-plate moment connection. The design parameters are adopted to include prying effects in joint. A stress level is obtained in the elements where the highest values occur in the tension zone of the end-plate. The accompanied finite element analysis is performed for comparing purposes with experimental results. It is shown that end-plate thickness should be the unavoidable joint parameter in structural analysis of frame-like structures

Consideration of the horizontal inertial effects at cantilever beams with nonuniform open sections

U ovom radu se analizira uticaj horizontalnih inercijalnih sila na konzolne nosače sa promenljivim poprečnim presekom oblika I-profila. Razmatra se varijacija preseka koja uključuje promenu visine preseka, kao najpraktičnije varijante pri projektovanju nosača dizalica. Zbog složenosti postavljenog problema koji uključuje problem ograničenog uvijanja, statički odzivi su dobijeni numeričkim metodama. Modeli nosača su usvojeni prema poznatim konstrukcionom preporukama za varijaciju nosača, sa ciljem praktične primene kod konstrukcija konzolnih dizalica. Poređenje rezultata je izvršeno sa poznatim vrednostima efekata uvojnog savijanja kod nosača uniformnog poprečnog preseka. Sa aspekta postavljenog problema i izabranih modela nosača, prikazane su prednosti korišćenja nosača sa promenljivim poprečnim presekom.The problem of torsion due to horizontal inertial effects is considered at cantilever beam with variable I-section. Linear variation of height is concerned as most practical one for the design of cantilever beams. The solution for adopted cases of beams is obtained numerically, according to the complexity of the given ordinary differential equation which deals with pure torsion along with warping torsion. The models are based on known tailor-made beams with possibility for application in design of jib cranes, as practical aspect of this work. The comparison of results is done with uniform cantilever beam models which can be used as one way for verification of stress state of variable cantilever beams subjected to bending with torsion. The obtained results show corresponding advantages of usage of variable sections

Experimental study on the stresses at the i-beam end-plate moment connection

The paper deals with experimental study of the stresses at the bolted end-plate moment connection. The design parameters are adopted to include prying effects in joint. A stress level is obtained in the elements where the highest values occur in the tension zone of the end-plate. The accompanied finite element analysis is performed for comparing purposes with experimental results. It is shown that end-plate thickness should be the unavoidable joint parameter in structural analysis of frame-like structures

Fault tree analysis of most common rolling bearing tribological failures

Wear as a tribological process has a major influence on the reliability and life of rolling bearings. Field examinations of bearing failures due to wear indicate possible causes and point to the necessary measurements for wear reduction or elimination. Wear itself is a very complex process initiated by the action of different mechanisms, and can be manifested by different wear types which are often related. However, the dominant type of wear can be approximately determined. The paper presents the classification of most common bearing damages according to the dominant wear type, i.e. abrasive wear, adhesive wear, surface fatigue wear, erosive wear, fretting wear and corrosive wear. The wear types are correlated with the terms used in ISO 15243 standard. Each wear type is illustrated with an appropriate photograph, and for each wear type, appropriate description of causes and manifestations is presented. Possible causes of rolling bearing failure are used for the fault tree analysis (FTA). It was performed to determine the root causes for bearing failures. The constructed fault tree diagram for rolling bearing failure can be useful tool for maintenance engineers

Determination of resistances to coal reclaiming at bridge-type stacker-reclaimer with bucket chain booms

Jednu od osnovnih etapa projektovanja pretovarnih mostova sa elevatorima predstavlja identifikacija spoljašnjeg opterećenja izazvanog otporom kopanja. Ono je po svojoj prirodi dinamičkog, i pri tom, stohastičkog karaktera. U radu je izložen originalni postupak određivanja pomenutog opterećenja, koji, uz razvijenu softversku podršku, omogućava da se brzo, i dovoljno tačno, odrede njegove relevantne dinamičke i stohastičke karakteristike. Znatno veća tačnost, koja uz to, nije osetljiva na promenu konstrukcionih parametara i parametara režima rada, predstavlja osnovnu prednost izloženog postupka u odnosu na postupke koji se daju u literaturi. U radu je na konkretnom primeru analiziran uticaj nekih konstrukcionih i radnih parametara na karakter i intenzitet opterećenja izazvanog otporom zahvatanja uglja. Izvršena je i uporedna analiza rezultata koji se dobijaju izloženim postupkom i postupcima datim u literaturi. Konačno, na osnovu opterećenja definisanog na način izložen u ovom radu, moguće je izvršiti potpunu simulaciju statičkog i dinamičkog ponašanja strukture i mehanizama pretovarnog mosta sa elevatorima.One of the basic stages in design of bridge-type stacker-reclaimer with bucket chain booms is identification of external loads caused by resistances to reclaiming process. In its nature, it is both dynamic and stochastic. In this paper it an original model is presented for calculating such loads which, along with developed software's, enables fast and accurate identification of its dynamic and stochastic characteristics. High accuracy along with no sensibility for variation of constructive parameters and operating stages, presents main advantage of this model respected to other models in literature. This paper analyzes, on a real model, effects of some structural and operating parameters upon character and magnitude of loads caused by resistance to reclaiming process. It presents comparative analysis of output results obtained by this model and others that are given in literature. Finally, based on loads defined in this paper, it is possible to perform a static and dynamic behavior simulation of structure and mechanisms of bridge-type stacker-reclaimer with bucket chain booms

Determination of resistances to coal reclaiming at bridge-type stacker-reclaimer with bucket chain booms

Jednu od osnovnih etapa projektovanja pretovarnih mostova sa elevatorima predstavlja identifikacija spoljašnjeg opterećenja izazvanog otporom kopanja. Ono je po svojoj prirodi dinamičkog, i pri tom, stohastičkog karaktera. U radu je izložen originalni postupak određivanja pomenutog opterećenja, koji, uz razvijenu softversku podršku, omogućava da se brzo, i dovoljno tačno, odrede njegove relevantne dinamičke i stohastičke karakteristike. Znatno veća tačnost, koja uz to, nije osetljiva na promenu konstrukcionih parametara i parametara režima rada, predstavlja osnovnu prednost izloženog postupka u odnosu na postupke koji se daju u literaturi. U radu je na konkretnom primeru analiziran uticaj nekih konstrukcionih i radnih parametara na karakter i intenzitet opterećenja izazvanog otporom zahvatanja uglja. Izvršena je i uporedna analiza rezultata koji se dobijaju izloženim postupkom i postupcima datim u literaturi. Konačno, na osnovu opterećenja definisanog na način izložen u ovom radu, moguće je izvršiti potpunu simulaciju statičkog i dinamičkog ponašanja strukture i mehanizama pretovarnog mosta sa elevatorima.One of the basic stages in design of bridge-type stacker-reclaimer with bucket chain booms is identification of external loads caused by resistances to reclaiming process. In its nature, it is both dynamic and stochastic. In this paper it an original model is presented for calculating such loads which, along with developed software's, enables fast and accurate identification of its dynamic and stochastic characteristics. High accuracy along with no sensibility for variation of constructive parameters and operating stages, presents main advantage of this model respected to other models in literature. This paper analyzes, on a real model, effects of some structural and operating parameters upon character and magnitude of loads caused by resistance to reclaiming process. It presents comparative analysis of output results obtained by this model and others that are given in literature. Finally, based on loads defined in this paper, it is possible to perform a static and dynamic behavior simulation of structure and mechanisms of bridge-type stacker-reclaimer with bucket chain booms

Consideration of moving oscillator problem in dynamic responses of bridge cranes

U radu je razmatrano dinamičko ponašanje noseće konstrukcije mosne dizalice usled dejstva ovešenog tereta na kolicima koja se kreću determinisanom brzinom. Glavni nosač je modeliran kao greda podeljena na 10 elemenata, kolica kao pokretna masa i teret kao masa, koja je ovešena na kolica sistemom užadi modeliranim oprugom. Matrice inercije, prigušenja i krutosti se računaju za svaki vremenski interval, a ekvivalentno spoljašnje opterećenje grede je formulisano kroz konačnoelementni pristup problemu. Jednačine kretanja sistema sa konačnim brojem stepena slobode su prikazane za model pokretnog oscilatora koji se kreće determinisanom brzinom po grednom nosaču. Dinamički odziv (ugib, brzine, ubrzanja) za sve stepene slobode je dobijen rešavanjem jednačina numerički, metodom direktne integracije. Verifikacija celog algoritma je data kroz poređenje rešenja za dinamički ugib proste grede pod dejstvom pokretne sile koja se kreće konstantnom brzinom. U radu je razmatran uticaj brzine kretanja kolica i krutosti opruge na dinamičko ponašanje noseće konstrukcije dizalice.The dynamics of an overhead crane system with the suspended payload on the trolley moving at a specified constant speed is considered in this paper. The beam is discretizied by 10 elements, while the trolley is modeled as particle along with payload suspended with rope system modeled as spring. The overall mass, damping and stiffness matrix is calculated at each time interval, along with finite element formulation of equivalent force vector. Equations of motion of MDOF system are given for oscillator moving on beam structure. Dynamic responses in the vertical direction for all DOFS are obtained by solving the governing equations with direct integration method. For validation purposes, the technique is first applied to a simple beam subjected to a force moving along the beam with constant velocity. The influence of moving velocity and spring stiffness are investigated