| Abstract | Cilj ovog zadatka je izvršiti statičku analizu ruke bagera na način da se izračunaju maksimalne sile u kritičnim spojevima. Za dodatno pojašnjenje unutarnjih sila u kritičnom elementu, izrađen je grafički prikaz raspodijele aksijalnih i poprečnih sila te momenta oko Z osi.
Koristeći se „MSC Adams“ softverom izrađen je trodimenzionalni model bagera. Kako bi se mogli simulirati pokreti koje bager izvodi pri kopanju tla, dijelovi grane bagera povezani su odgovarajućim zglobovima. Na spojevima klipova i cilindara korišteni su translacijski zglobovi a na spoju nosača grane sa kabinom korišten je fiksni zglob. Na svim mjestima u kojim se koristi poveznica zglobnim klinom poput spoja grane sa rukom ili ruke sa nastavkom i na svim hvatištima cilindara i klipova upotrijebljen je revolucijski zglob.
Kako bi program mogao izračunati sile koje se javljaju u modelu potrebno je odabrati vrstu materijala za sve dijelove modela. Koristeći volumene dijelova koje program izračunava iz trodimenzionalnog modela i svojstvima odabranih materijala poput gustoće, program izračunava masu dijelova i sve ostale podatke koji su potrebni za izračun sila.
Unosom matematičkih funkcija kao kodove za upravljanje izvlačenja klipa iz cilindra stvorena je simulacija tipičnih pokreta bagera. Simulacijom pokreta bagera koji se javljaju pri kopanju tla, program izračunava sile koje se javljaju u modelu koristeći se dinamikom složenih tijela.
Grafičkim prikazom uspješno su prikazane funkcije promjenjivih sila u zglobovima koje nastaju pri radu. Iz grafova funkcija za X i Y os očitani su maksimalni iznosi sila u glavnim spojevima. Poznavanje ovih podataka nužan je korak pri daljnjim izračunima s obzirom da se koriste pri odabiru veličine zglobova ili za odabir tipa profila i debljine stijenke profila.
Kako bi se detaljnije objasnilo ponašanje unutarnjih sila u grani bagera izrađuje se pojednostavljeni prikaz koristeći običnu gredu sa dva aksijalna ležaja. Dobivene maksimalne vrijednosti za zglob na poveznici grane sa nosačem grane i masa grane koriste se kao poznanice sustava.
Vrijednosti nepoznatih sila i momenta u zglobu na spoju ruke i grane bagera izračunate su pomoću sustava triju nepoznanica sa tri jednadžbe. Izračunata je pozicija ekstrema funkcije momenta savijanja koristeći nul-točku prve derivacije te funkcije. Dodatno se računaju iznosi momenta savijanja za različite udaljenosti po X osi od zgloba na poveznici grane sa rukom.
Koristeći poznate i izračunate vrijednosti u zglobovima te dodatno izračunate iznose momenta savijanja izrađuju se grafički prikazi raspodjele unutrašnjih sila za aksijalne i poprečne sile te za moment oko Z osi. Na ovaj način izvršena je statična analiza bagera te je prikazan smjer, način i iznos sila koje se javljaju u zglobovima pri njegovom radu. |
| Abstract (english) | The goal of this task is to perform a static analysis of the excavator arm in such a way as to calculate the maximum forces in the critical joints. For additional clarification of the internal forces in the critical element, a graphic representation of the distribution of axial and transverse forces and moments around the Z axis was created.
Using "MSC Adams" software, a three-dimensional model of the excavator was created. In order to simulate the movements that the excavator performs when digging the ground, the parts of the excavator are connected with appropriate joints. Translational joints were used as the connection between pistons and the cylinders, and a fixed joint was used at the joint connecting the boom carrier with the cabin. A revolutionary joint is used in all places where a hinged pin link is used, such as the connection between boom and arm or between arm and excavator attachments, revolutionary joint is also used on all grips of cylinders and pistons.
For the program to be able to calculate the forces occurring in the model, it is necessary to select the type of material for all parts of the model. Using the volumes of the parts that the program calculates from the three-dimensional model and the properties of the selected materials, such as density, the program calculates the mass of the parts and all other data that is necessary for the calculation of forces.
A simulation of typical excavator movements was created by entering mathematical functions as codes for managing the piston extraction from the cylinder. By simulating the movements of the excavator that occur when digging the soil, the program calculates the forces that occur in the model using multibody dynamics.
On the graphic display, functions of variable forces in the joints that arise during work are successfully shown. Maximum forces in the main joints were read from the function graphs for the X and Y axes. Knowing these data is a necessary step in further calculations, considering that they are used when selecting the size of joints or for choosing the type of profile and the thickness of the profile wall.
To explain in more detail, the behavior of internal forces in the excavator boom, a simplified scheme representation is made using a beam with two axial bearings. The obtained maximum values for the joint on the connection between boom and the boom carrier and the mass of the boom are used as acquaintances of the system.
The values of the unknown forces and moments in the joint between the arm and the boom of the excavator were calculated using a system with three variables three equations. The position of the extremum for function of the bending moment was calculated using the zero-point of the first derivative of that function. In addition, the amounts of the bending moment are calculated for different distances along the X axis from the joint connecting excavator boom with the arm.
Using the known and the calculated values in the joints and the additionally calculated values of the bending moment, graphic representations for the distribution of internal forces for axial and transverse forces including the bending moment around the Z axis were created. The graphic representation of the distribution of internal forces further explains the behavior of internal forces in the critical element of the excavator arm. In this way, a static analysis of the excavator was performed and the direction, manner and amount of the forces that occur in the joints during its operation were shown. |
