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Delegates are invited to meet and discuss with the poster presenters in this topic directly after the session 'Aerodynamics and rotor design' taking place on Wednesday, 12 March 2014 at 09:00-10:30. The meet-the-authors will take place in the poster area.

Federico Belloni University of Padua, Italy
Federico Belloni (1) F P Gabriele Bedon (1) Uwe Schmidt Paulsen (2) Marco Raciti Castelli (1) Ernesto Benini (1)
(1) University of Padua, Padova, Italy (2) Danmarks Tekniske Universitet, Kgs. Lyngby, Denmark

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Presenter's biography

Biographies are supplied directly by presenters at EWEA 2014 and are published here unedited

Mr. Federico Belloni is a Master’s student on the last semester of M. Sc. in Mechanical Engineering; he took the Bachelor Degree at Universtità degli studi di Padova in Italy in the same major. He started to work on wind turbines on his last year of Master of Science and decided to develop his Master’s Thesis on this topic at DTU Wind Energy, where he worked on a 1kW Darrieus turbine. He is dealing with structural and aerodynamic issues, modal analysis and turbine testing.


Structural analysis of a 1 KW Darrieus turbine spoke


A structural study of a 1 kW VAWT spoke was carried out in order to investigate the stress distribution on such component and make it lighter. The VAWT turbine, originally intended for urban operation, is provided with 3 blades and 6 spokes. Since during the testing procedure the turbine was found to have relevant balancing problems, the main analysis target was to reduce the rotor weight.


A finite element approach was adopted to simplify the structure composed by one blade and two spokes. Thanks to the symmetrical troposkien blade shape, only half of this model was analysed, using Strand7 finite element software.
A careful analysis of the involved forces (both inertial and aerodynamic) was performed in order to evaluate the most significant loads affecting the structure. The most critical case was taken as reference: maximum rotational speed (300 rpm) and maximum wind velocity (25 m/s). Centrifugal forces were discovered to be two order of magnitude higher than aerodynamic ones; hence, only the former were applied to the simplified structure. Self-weight forces were much lower than centrifugal ones, so they were neglected as well.
The spoke and the blade were both split in four beam elements. As a material and geometrical properties definition is required for each beam, the spoke was easily defined as formed by four steel beams with constant thickness and step varying width, while, as it concerns the blade, each element was characterized by different geometrical features and mechanical properties. This is due to the fact that the blade chord is varying along the span, and so in this model it had to be discretized in beams with various rectangular shape section; moreover, the blade was built in rapid prototyping material, with a steel frame, so mechanical properties were estimated as a weighted average between the ones of the two materials involved.
A Matlab model was then employed to evaluate centrifugal forces to be applied to each beam center of mass and these values were applied inside the finite element model as distributed loads.
This finite element approach was required since the structure is, structurally speaking, indeterminate.
The static solution of the model produced as results moments and stress distribution, and moreover showed beam reactions at spoke tip.
These reactions were the main target of this finite element model and were then used in a second step, with a second more refined model (FEM), representing only one spoke in order to evaluate stress distribution more precisely.

Main body of abstract

The second more refined FEM model was developed in ANSYS Mechanical and represented only one spoke.
Since, as previously described, centrifugal forces were observed to be much more remarkable than other loads, the spoke was considered rotating at the maximum admitted rotational speed (300 rpm). The model was integrated with particular boundary conditions which included a fixed support at the hub, as it is in real working condition, and force reactions applied at the spoke tip. Reaction consisted of a force parallel to the turbine shaft axis, a force perpendicular to the shaft axis and a moment which is opposite to spoke bending due to centrifugal forces.
After an accurate mesh sensitivity study, a structural mesh was chosen for the model, with a 2 mm element size for the whole piece, without size functions or element size variation. This mesh size was observed to be the one that guaranteed convergence on simulation results.
In order to validate the ANSYS model, several structural tests were performed on the original steel spoke. After analyzing the force system affecting the structure, an extremely simplified force model was developed in a horizontal coordinate system different from the real coordinate system of the spoke during operation. The force system affecting the spoke in its working configuration, i.e. with a slope angle of 28°, was rotated as the spoke was working in a horizontal position. Since vertical components were the ones who produce bending moment (which is the most critical as it concerns stress distribution) only these ones were considered in the simplified experimental model and converted in terms of weights to apply to the structure.
In the first two tests, which were performed as simple trials to evaluate model operation, two different masses were placed on a plate hung to spoke tip. On the other hand, the following three tests were representative of the real working behaviour of the spoke; thus a weight pushing down was applied at the half length spoke point, while a weight pulling up was applied at the tip. During experimental tests, the vertical displacement was chosen as the parameter to be measured.
The comparison between ANSYS simulation and experimental results revealed a partial accordance; ANSYS model is found to underestimate vertical displacement values.
After checking ANSYS model reliability, real spoke behavior was simulated with the focus on stress distribution, especially at hub section, which is the most critical for bending moment.
In the original spoke configuration, stress at hub was found to exceed steel yield stress, and therefore a different spoke design was required in order to reduce weight, and so centrifugal forces, and with them stress value at the hub.
Several spokes were designed with different hole shape and distribution along the span; the most suitable hole shape was found to be the triangular one and the space between next holes was made to vary in the different tested configurations.
These new spoke configurations managed to save between 20 and 30% of the original weight, which actually implied a relevant stress reduction at the hub. On the other hand, unfortunately, stress concentration phenomena were discovered at triangular hole corners. A few attempts were made by increasing fillet radius, but normal steel yield stress was always exceeded.
Finally, aluminum spoke was simulated and was found to be the most convincing configuration. In facts, using aluminum implied a gain in weight of about 66%, which is much more than the maximum weight gain achievable with a steel configuration. Moreover, this was obtainable avoiding holes and, therefore, stress concentration phenomena.


The proposed study has proved that, in a small Darrieus Turbine, spoke is one of the mostly stressed component during turbine operation. Therefore, an accurate study of its working behavior is definitely important within a structural study of the turbine.
Summarizing the results of the structural study, the following observations can be done:
The comparison between the forces involved in a working VAWT had proved how aerodynamic forces and self-weight forces are doubtless negligible in respect to centrifugal forces. Thus, component weight is found to be a very important aspect to consider for this typology of wind turbines.
ANSYS simulation results were made much more reliable thanks to the experimental tests conducted to validate the FEM model. This was definitely important within the analysis, since these results were taken as reference while changing spoke design. However, it must be underlined that both the Strand7 model and the ANSYS one are simplified models and that they had been statically studied. Therefore, dynamic loads in this analysis are not taken into account and could have a further impact on the component behavior.
Through the FEM model, the original steel configuration and different architectures with various-shape holes made along the span were simulated. Stress concentrations were found to exceed normal steel yield stress, even after increasing fillet radius at hole corners. Therefore, a final aluminum spoke was designed, obtaining a 66% weight reduction for each spoke, corresponding to 25% of the whole turbine weight.
This weight reduction was definitely significant and allowed to reduce turbine unbalance issues.

Learning objectives
This work has analyzed the force system affecting a VAWT spoke and through a finite element model has studied the mechanical behavior of different spoke configurations, ending that aluminum was much more suitable than steel as spoke material.

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