Feasibility of the tower crane jib made of composite material

The main purpose of this research is to design a jib of a tower crane using composite material and to compare the effects/performance on the whole machine due to this lightweight process. The research starts by sizing the jib with steel material. Many different load conditions were involved and different criteria were assumed; those are: stress safety factor, stiffness, dynamic performance (modal) and buckling phenomenon which is the most important parameter. Then other non-standard load conditions were applied to the tower crane: moving load and jib (rotation and elevating) and adopting wind variable in time. The results of these load conditions were assumed to design a new jib made of pultruded composite material. The next step involves the design of additional elements of the crane: ropes, counter boom, counterweight, electric motor, etc. The last step concerns the economic feasibility of the new solution. The results show that the weight of the jib made by composite material is about 25% of the one made by steel and the economic payout for making the composite arm can be equalized in about a year and a half of machine operation, making the proposed solution very worthwhile.


Introduction
Nowadays energy efficiency is one of the most important issue, at which many efforts are oriented.In the mechanical field, and in particular in the machine design sector, this topic can be studied in almost two aspects.The first one is by increasing the motor efficiency and the second one is by lightweighting the components.For example, this problem and its approach to study can be seen in the automotive sectors [1,2,3].The materials choice for lightweighting the structures can be done by adopting some criteria, for example through the Asby diagram [4,5,6].These maps correlate the mechanical properties of different materials: strength, Young modulus, density, and so on, to help the designers choose the best solution.The lightweight of the structural component is already affronted in different fields, such as the excavator [7], pressure vessel [8,9,10], hydraulic cylinder [11], etc.The present research is part of this issue i.e. the structural lightweihting of the machines and components correlated to the lifting and transport industry.In particular, the present research aims to evaluate the feasibility study inherent the implementation of a boom in composite material to a very big tower crane to assess the implications of this application on the entire machine and to estimate, including an economic point of view, the convenience of this innovative application.

Description of the tower crane
The tower crane adopted for this research is a classical tower crane with the jib that can be raised.In the horizontal position, the angle concerning the horizontal plane is 14,5° while in the vertical position is 85°.The length of the jib is 46,5 m and the tower height is 29 m.The maximum height below the hook is 75,5 m.These dimensions were acquired by a similar tower crane built by Liebherr company.The working load limit adopted is 11000 N. Figure 1 shows the crane and the jib.

Jib design in steel material
Three are the main criteria adopted to design the jib.The first one considers the stiffness of the jib, i.e. the displacement.This value can be imposed by adopting the ratio between the length of the jib and the displacement greater than 200.The second criterion considers the safety factor with respect to the yield of the materials.The value adopted is 3,5 to include the dynamic effect due to the moving load and the fatigue phenomena (that must be verified after the jib design).The last criterion imposed regards the safety factor concerning the buckling phenomena evaluated through the classical Euler equations.[12,13].By a very simplified schematization, it is possible to estimate the action in the jib (in two different configurations i.e. 14,5° and 85°) and then the action on each element (truss) that composes the reticular structure.These forces can be estimated through two different methods.The first one is the method of joints, and the second one is the sections method or Ritter method.The joints method is based on the equilibrium of each node that compose the structure while the Ritter method considers the equilibrium of the portion of the section.The material adopted is the classical structural steel S355 JR (UNI EN 10025) the main mechanical properties are: ultimate strength σR= 510 MPa, yield strength σY =355 MPa, Young modulus E=210000 MPa and the density equal to ρ=7810 kg/m 3 .After the preliminary design, the subsequent phase concerns making the solid model and carrying out the fem analyses, which confirm the hypothesis and boundary assumed to size the jib.It is very important to underline that the geometry of the jib is not double symmetric and the length of free bending defined in Euler's equation is not the same in two planes.In the lateral plane, the free length is equal to the jib length (the schematization is hinge and the roller); while in the front plane, the free length in the Euler's equation is a double of the jib length because the schematization is fixed (ad base) and free at jib end.
Table 1 shows the critical buckling load and the safety factor.Table 2 reports the first natural frequencies of the jib and the mass participation factors.The structure is characterized by low values of natural frequencies (as in the other crane types) and high values of the participation factor within the first frequencies.

New load conditions.
Over the previous load conditions, many others were involved in the design process to deeper characterise the mechanical behaviour of the jib.These actions are moving arm (rotation and rise) and wind adopting changing in time.
To carry out these analyses (time-varying) one of the most important parameters is the damping value.For this structure type (reticular /lattice) the damping values change from 0,5 to 12 % of critical damping [14,15].In this study, the value adopted is 3%.The numerical analyses were carried out through Solid Works ® software and the methodology adopted is the superpositions modal method; the damping value applied is the Rayleigh, which is characterized by two values (α and β), reported in the equation ( 1) These values depend on the natural frequencies and the values adopted are: : α=0,49 e β=6.6e-4 the values are the same for 14,5° and 85° configurations. (1)

Moving jib.
The moving of the jib can be done by many different motion laws.The parameters adopted are acquired from the brochure of the tower crane and concern the maximum velocity and the power installed on the machine; with these parameters, the classical three segments law of motion was applied to the model.Figure 3 shows the law of motion while figure 4 shows the displacement at the end of the jib.The trend is a classical motion of the damping system.The displacement is very low; when the jib is in vertical configuration i.e. 85° the displacement is minimum because the jib's barycentre is near the vertical axis of rotation.The trend in the vertical motion (lift or lower) is very similar even if the displacement magnitude is strictly correlated to the rope stiffness for moving the jib.
Where:  is the air density;   ;   are the aerodynamic coefficients (Drag and Lift); A is the relative area.
The constants CD and d CL are the aerodynamic coefficients and can be estimated by bibliography, numerical analysis (CFD) or experimental analyses (Wind tunnel) in this case the values adopted are: CD=1,65 and CL=0,3.
The wind model adopted for this research is stochastic stationary i.e. the wind velocity is a sum of two terms.The first one corresponds to the constant velocity correlated only to the height (Z) of the point in the exam, while the second term is variable in time and correlates to the point position (equation 3).
(, , , ) =   () + (, , ) The standards for crane design and lifting equipment (EN 13001 series) consider only the constant contribution which is correlated to the height and the environment (near the sea, hill, mountain, close to the buildings, etc.).The variable component in the wind velocity can be estimated through the power spectral density function.In the literature, there are many different formulations (also in Eurocode).These formulations are characterized by the magnitude of the peek values and its frequency value.[16,17,18,19].
In this research, the model adopted is the Kimal [17,18].Through a specific program developed by Mathcad software, it is possible to determine the wind speed in each zone into which the arm has been divided, and then determine the forces (by the equation 2) to be included in the fem model.Figure 5 shows the trend velocity in the wo zone near the base (29 m) ant at the end of the jib (75,5 m). Figure 6 shows the displacement trend at the end of the crane.It is very important to point out some issues.Assuming a wind velocity variable in time induces the displacement (and the stresses) variable in time.It is possible, therefore, to estimate the dynamic effect made by the wind and observe that the wind induces fatigue phenomena in the jib structure.It is very important to underline that the dynamic effect generated by assuming a calculation scheme with time-varying speed can cause overturning or buckling phenomena which are the main technical reasons why the crane collapses during an extreme event, like, for example hurricane.

Jib design in composite material
The material used to design the jib with composite material is a commercial product, it is the pultruded composite material with carbon fiber (65% in volume) and epoxy resin (35% in volume).The main mechanical properties are ultimate strength σR≈ 1000 MPa, Young modulus E=135000 MPa and a density equal to ρ=1900 kg/m3.The principal criteria assumed to design the jib with this material are as follows.First of all, the new jib must have a similar mechanical behaviour to the one made by steel i.e. the same performance with respect to the stiffness and buckling parameters.To do this, the product of the Young modulus with the inertia must be very similar for the two solutions, obviously in the two planes, the lateral and frontal plane (equation 4).
Other boundary regards the transportability of the solution and the use of already commercially available geometries.With these assumptions, figure 7 shows the final section of the jib.In particular the section changes from (bxh) 1500x1500 mm to 1800x1800 mm, current from 150x150 with thickness 5 mm to 100x100 thickness 8 mm and diagonal/upright from Øe=80 mm and Øi=74 mm to Øe=45 mm and Øi=35 mm for composite solution.The numerical results are reported in the tables 3 and 4. It can be seen from the reported results that the two solutions are absolutely comparable.Figure 8 shows the jib displacement due to the wind variable in time; for the solution made of composite material the magnitude is a bit larger but totally acceptable.The lattice structure was composted by commercial pultruded composite material (currents, diagonals and uprights).These elements must be assembled.The solutions proposed are reported in figure 9.The current must be joined by a plate in aluminium alloy bolted together and fixed to the pultruded composite material by glue.The same methodology was adopted to join the diagonals and uprights with the current.At the end of the jib was positioned a triangular structure (made of aluminium alloy) to increase the stiffness of the jib and fix the pulleys to move the jib and the payload.At the base of the jib a similar structure also made of aluminium alloy to make a cylindrical hinge to allow rotation of the jib in the lateral plane.

Results
The whole weight of the jib made of composite material is 12,17 kN, while in the steel solution the value is 49,37 kN, i.e. the weight in composite is about 25% of the one made by steel.With this performance it is possible to study and lightweight others tower elements.Figure 10 reports the main crane elements (black, in steel solution, while in pink the new solution).Due to the heavy lightweight of the jib it is possible to reduce the pawer to move the jib (obviously with the same performance) both for rotation and lift movements.The total power to move the jib changes from 185 kW to 92 kW.The nominal values change from 60,3 kW to 30,3 for lifting and 98 kw to 32 kW for rotation; the power installed is correlated do the power of commercially available motors.

Economic feasibility
Following the previous results this chapter reports a preliminary analysis in term of the economic point of view.Table 5 reposts the estimate cost to build the composite solution and the operating cost.This value was evaluated considering 5h per day and 255 days per year the electricity price and a classic load cycle: lifting, rotating and downloading the jib.

Conclusions
This research reports the feasibility study of the implementation of an innovative jib made of composite material instead of classical steel.The design was carried out considering different loading conditions in addition to those defined by the standards.
The research shows the preliminary solution to build the component in the composite material and the research was extended to the implications of the lightweight on the other mechanical components of the tower crane.The lightweight of the jib (the final weight is about 25% of the one made of steel) induces the weight reduction of many crane parts, particularly for the counterweight.Another important issue is the reduction of the installed power on the crane.Using a new jib, it is possible to adopt half power to move it with the same performance.This aspect cuts the operating cost.The jib made of composite material is more expensive than the one made of steel (5 times).Involving also the operating cost (5 h per 255 days per year) the composite material solution shows a high economic advantage considering 20 years as the useful life of this machine type.Based on the excellent results achieved, research is being developed in at least two aspects.The first one is to evaluate the environmental effects on the structural behaviour of the composite material (temperature, humidity, etc.); on the market there are protective films and their effects must be investigated.The second one is to estimate more precisely the real operations performed with this crane type (work cycle, assembly, transportation, maintenance, etc.) for which the lightening of the machine increases the economic benefits for the solution developed by adopting the composite material.

Figure 1 .
Figure 1.Tower crane size and the two different positions of the jib: horizontal and vertical.

Figure 2 .
Figure 2. Size and solid model of the jib made by steel.

Figure 3 .
Figure 3. Law of motions applied to the jib.

Figure 5 .
Figure 5. Wind velocity trend in two different jib zones (upper at 29 m; down at 75 m).

Figure 6 .
Figure 6.Displacement at the end of the jib due to the wind actions.

Figure 7 .
Figure 7. Geometry sections of the jib.

Figure 9 .
Figure 9. Solutions to join the elements of the jib.

Figure 10 .
Figure 10.Comparison of the two solutions developed.

Figure 11 .
Figure 11.Upper: determination of the equilibrium point; down economic advantage estimate after 20 years.Red for composite solution while blue for steel solution.

Table 1 .
Critical buckling load and safety factor.

Table 2 .
Natural frequencies and participation factor for the jib.

Table 4 .
Critical buckling load [kN] and safety factor.

Table 5 .
Cost estimate for the purchase and implementation of the arm [k€].