MODELLING STUDIES ON THE USE OF ALUMINIUM ALLOYS IN LIGHTWEIGHT LOAD-CARRYING CRANE STRUCTURES Summary

The article presents the results of numerical analysis whose aim was to compare the basic dynamic and strength parameters of lightweight load-carrying crane structures made of aluminium alloys and steel. The analysis covered the typical construction of workshop cranes with a span of 3 to 5 meters, girders in the form of an Ibeam and maximum load capacities amounting to 5 tons. The values of stresses, deflections and natural frequencies were compared and then matched with the masses of the various structures. In the simulation a girder model was used and computed by the finite element method.


INTRODUCTION
Light cranes produced today are used in industry as mobile cargo handling equipment.From a theoretical point of view, they are among the basic machines that are used in the transport of freight.The construction material mainly used for load-carrying structures is steel, but they are also increasingly built from aluminium alloys [1,2].
An important advantage of such structures is much less weight compared to steel structures.However, the negative consequence is the change of the strength and dynamic parameters.Mechanical vibrations caused by the intermittent work of enforcement mechanisms cause an induction of dynamic loads in each transshipment cycle, which affects both the construction of the device and its operation [3].
Such cranes are easy to transport and install-in most cases human muscle strength without specialized hardware is enough.Another difference from steel load-carrying structures is the method of manufacture.In the case of aluminium alloy, welded joints are avoided and replaced by screw joints -this increases mobility at the same time as facilitating quick assembly and disassembly.Unfortunately, the influence of welding significantly reduces the strength parameters in the heataffected zone [4,5].In addition, each load-carrying crane structure shall "inform" of any overloads, and cracks cannot propagate immediately [6 -8].The advantage of steel in this respect lies mainly in its higher impact strength relative to aluminium alloys; therefore, aluminium structures are used for low-intensity use (crane classes) [9 -11].
The structure of the analyzed cranes is made of aluminium alloy with magnesium and silicon.Such alloys have good mechanical properties and enhanced corrosion resistance, particularly in water and maritime atmospheres.They are mainly used for medium stressed parts of ships and cranes, as well as in the aerospace industry.

MATERIALS AND METHODS
In order to analyze the impact of using aluminium alloys for the construction of crane structures in terms of strength parameters, numerical models of the discussed structure were built.Both the dynamic and static behaviour of the supporting structure were analyzed using Matlab and Abaqus software [12,13], with particular emphasis on the stresses occurring in the lower flange of the I-beam girder.The stresses occurring there have a decisive influence on the strength of the structure due to the presence of the cumulative phenomenon of general bending and local bending of the lower flange [14].
In the numerical simulation, an I-beam crane girder with a span equal to 3, 4 or 5 m and a maximum capacity of 3 t was used.In the presented model, the construction of headstocks and other unnecessary elements of the crane were omitted.The model was loaded in the middle of its span.The girder had the same design and dimensions for each case, and only the material parameters were modified.
The load-carrying structure was made from ASTM A284 steel and aluminium 6061-T6.Standardized general purpose quadratic shell elements S8R and general purpose quadratic brick elements with reduced integration points C3D20R from Abaqus Software Documentation were used.
The boundary conditions were applied to the reference points, which are combined with the construction by using an MPC beam type connector.Construction of the girder was divided into three parts-two surface types and one as a solid type (in order to shorten the calculation time).These parts were combined with each other by using a shell-to-solid coupling, which connects the side surface of the solid model with the edge of the shell.The load was applied by adding masses to the wheel axles of the hoist by using kinematic coupling constraints.The load at the bottom flange of the girder was made by using node-to-surface type contact elements.Between the contact of the wheel and the surface of the lower flange of the girder, a friction coefficient was used, differing for aluminium alloy and steel (Table 1).In the simulation, gravity as an acceleration value of 9,81 m/s 2 was also applied.In the Matlab-Simulink environment, the dynamic model was formulated (Fig. 1) [3].The physical parameters describing the considered vibrating model were estimated on the basis of the technical documentation of the overhead travelling crane.Then the numerical experiments with the classical elastic-damping model (Kelvin-Voigt) for the wire rope were performed.c Lstiffness coefficient of steel wire rope, R 3radius of the cable drum, R 4radius of the pulley, i wgear ratio of pulley blocks, q 1 , q 2 , q 3 , q 4 , 3 , 4generalized displacements, b 1girder damping ratio, b pground damping ratio, b Lsteel wire rope damping ratio, M n (t) -drive torque of rope drum Rys. 1. Uproszczony model fenomenologicznyczny mechanizmu podnoszenia, zawierający w gałęzi linowej model Kelvina-Voigta, gdzie: m 1masa zredukowana ustroju nośnego wraz z masą wciągnika, m 2masa ładunku, m 3 -masa bębna, m 4 -masa wielokrążka, J 3masowy moment bezwładności bębna linowego, J 4masowy moment bezwładności wielokrążka, 1 , 2 , 3 , 4 , 3 , 4 -prędkości uogólnione, c 3 -sztywność łożysk osi bębna linowego, c 2 -sztywność haka, c p -sztywność podłoża, c 1 -sztywność ustroju nośnego (dźwigara), c L -sztywność liny, R 3 -promień bębna, , R 4 -promień krążka, i wprzełożenie wielokrążka, 1 , q 2 , q 3 , q 4 , 3 , 4 -uogólnione przemieszczenia, b 1 -tłumienie dźwigara, b p -tłumienie podłoża, b L -tłumienie liny, M n (t) -moment napędowy na bębnie The extortion signal is used as a constant driving torque, corresponding to fast start of the engine without the control system, i.e., the worst case.In accordance with the applicable standard [9], the hoist drive class HD1 for the lifting mechanisms without creep speed was examined.Simulations were carried out using algorithm ode4 with constant step of integration 0,0001 s.Simulations were performed for the load value of 30000 N. The rope stiffness and damping coefficients were defined by the relation that their value depends on the length of the rope [3] (fig 2).The values of simplified phenomenological model parameters of examined overhead travelling crane are shown in Table 2 [3].Variable damping coefficient of the wire rope strand is taken from the publications [3, 16]: (1) where: c Lstiffness coefficient of steel wire rope, b Lwire rope damping ratio,dimensionless coefficient according to [16], msum of load mass with current steel wire rope mass (depending of its length).

RESULTS AND DISCUSSION
Comparison of the results of the numerical analysis for the aluminium alloy and steel is shown in Tables 3 and 4. The natural frequencies are calculated with the use of the FEM model.The values are much lower for the aluminium alloy construction than for the steel one (Table 3, Table 4).This is due to the lower rigidity of the structure.These values are important for the interaction (two-way) with other structural elements of the road, mechanisms or possibly an operator working a crane.
The tables show the maximum value of stress occurring in the contact between the wheel and lower flange of the girder, while Fig. 3 shows the stress values along the lower flange.These values are similar for both the analysed materials and corresponding load capacities.For each of the six stress curves, there are three characteristic points at which, in particular, the stress values are analysed.for steel and aluminium alloy, where: Pforce, ndistance between force direction and edge of flange, 0, 1, 2, -characteristic points of the flange Rys. 3. Porównanie wartości naprężeń w dolnej półce dźwigara (lewa połowa) wraz z kołem wciągnika (dolna część) dla stali i stopów aluminium, gdzie: P -siła, n -odległość pomiędzy kierunkiem przyłożenia siły i krawędzią półki, 0, 1, 2,punkty charakterystyczne na dźwigarze As in the case o stress, a situation with dynamic coe icient ϕ 2 is presented [9] (Fig. 4, Table 3, Table 4).This value is mostly related to the characteristics of the hoisting mechanism drive rather than to the behaviour of the load-carrying structure.In the analyzed cases, the same characteristics of the mechanism were simulated for all models.A vast difference occurs in the case of the mass of the structures (about three times for each span).This may have important implications for the crane when mounted on a means of transport-sea, air or land.A negative consequence of the three times smaller modulus of elasticity of aluminium alloys compared to steel is the differences between the displacement of the girder centre point (Fig. 5, Table 3, Table 4), the values of the natural frequency, and the acceleration in the middle of the girder span (Fig. 6).The differences in the case of displacement in the middle of the girder span for the steel and aluminium alloy structures are three times to the benefit of the steel.In the case of load-carrying crane structures, this is very important due to the hoisting operations in each working cycle.In addition, the permissible deflections are standardized and, if they are exceeded, the structure has to be reinforced.

CONCLUSIONS
Selected aluminium alloys are very good construction materials and suitable for use in lightweight load-carrying crane structures.The main advantage of such structures is the reduced mass with retained strength parameters.Taking into account the dynamic parameters of the analyzed structures, it must be noted that those made of aluminium alloy show much less stiffness.Therefore, for larger bridge spans and larger load capacities, their use may be illegitimate because of the permitted deflection of the girder.Moreover, the structure of aluminium alloy is significantly less resistant to loss of local stability.In the case of A284 steel (Table 1), the difference between ultimate strength and yield tensile strength is 210 MPa.For analyzed aluminum alloy, it is only 34 MPa.Taking into account the fact that the load-carrying structure should "inform" about the overloads, in this case there will not be a lot of warning before the disaster.Another limitation may be economic considerations, which are not included in this Urrea, C. & uez, G. Jamett, M. Development of an expert system to select materials for the main structure of a transfer crane designed for disabled people.

Fig. 3 .
Fig. 3. Dynamic and static values of stress in the bottom flange of the girder (left half) and wheel (bottom half)for steel and aluminium alloy, where: Pforce, ndistance between force direction and edge of flange, 0, 1, 2, -characteristic points of the flange