Open Access
Efficient geometric parametrization of blades cross-sections by means of B-splines
(IOP Publishing, 2024) Llamazares, G.; San Miguel, Unai; Plaza Puértolas, Aitor; Ingeniería; Ingeniaritza
Optimization and enhancement of rotor blade design are critical to improving the productivity of the wind energy industry. Airfoil geometry is a key factor that makes airfoil design and optimization a common task for aerodynamicists. Ensuring proper airfoil parametrization is essential. It serves as the first step in aerodynamic optimization, where the efficiency is directly related to the geometric complexity. This research presents a cost-effective and robust method for fitting airfoils using B-splines. We take into account factors such as computational cost, resource requirements, and accuracy. In this work, we present a method for minimizing the geometric distances between target points and a B-spline curve. We streamline the fitting process, create a computational Python package, and explore different approaches, objective functions, algorithms, and error tolerance settings. The work concludes that it is highly recommended to use an iterative fitting process, to adequately represent common airfoils with B-splines. Moreover, the accuracy and the computational cost can be managed subject to the minimization algorithm used, and the technique utilized for the objective cost calculation. The fitting procedure we develop in this study gives the smallest number of variables capable of accurately representing a desired airfoil.
Open Access
Trayectorias de máxima rigidez de un robot redundante actuando como soporte en el mecanizado de paredes delgadas
(Universitat Politècnica de València, 2023) Aginaga García, Jokin; García Cuesta, Iván; Iriarte Goñi, Xabier; Plaza Puértolas, Aitor; Ingeniería; Ingeniaritza; Institute of Smart Cities - ISC
La precisión de un robot está ligada a su rigidez. En comparación con la máquina herramienta tradicional, los robots industriales tienen un gran espacio de trabajo como ventaja, pero una rigidez reducida como desventaja. Además, la rigidez tiene una gran dependencia y variabilidad con la postura o configuración del robot. De ahí que resulte necesario un análisis de rigidez de los robots, que se evalúa mediante la matriz de rigidez. En este trabajo se presenta un análisis de rigidez de un robot serie. Ante la diversidad de índices representativos extraídos a partir de la matriz de rigidez, se ha propuesto el uso de un índice que tenga en cuenta la dirección de las cargas que soporta el robot y la dirección en que se desea que el robot aporte rigidez en la aplicación específica. Asimismo, se ha utilizado el índice de rigidez para llevar el robot a configuraciones que mejoren la rigidez, hecho que resulta posible en aplicaciones en las que el robot tiene al menos un grado de libertad (GDL) redundante. La metodología se ha aplicado a un robot de 7 GDL utilizado como robot de soporte en el mecanizado de paredes delgadas. Dado que para definir la trayectoria únicamente son necesarios 5 GDL, se utilizan 2 GDL reduntantes para mejorar la rigidez.
Open Access
Mode-displacement method for structural dynamic analysis of bio-inspired structures: a palm-tree stem subject to wind effects
(Taylor & Francis, 2022) Plaza Puértolas, Aitor; Vargas Silva, Gustavo Adolfo; Iriarte Goñi, Xabier; Ros Ganuza, Javier; Ingeniería; Ingeniaritza
Biological materials (orthotropic materials), like wood, can offer good mechanical properties with a minimum amount of material, making their internal structure the suitable one to be applied on bio-inspired structures. The knowledge of the exceptional structural performance of palm trees, and specially its response to different loading conditions, provides useful information when lightweight structures with high slenderness ratio are desired. Recent researches focused on the analysis of palm trees subject to static loading conditions, ignoring the fluctuating nature of the wind speed. The purpose of this study is to simulate in a computational efficient way the effect of dynamic loading conditions applied on palm trees. Using the mode displacement method, the number of degrees of freedom of a dynamic finite element analysis can be drastically reduced with a minimal loss of accuracy. It was applied to simulate the behavior of structures comprised of an orthotropic material subject to a stochastic dynamic load. The influence of the number of selected degrees of freedom has also been studied. In addition, an exponential integration method is proposed to perform the time integration procedure. The results obtained show that a properly reduced model suitably represents the full finite element model without any appreciable loss of accuracy; it is also shown that computational cost can be drastically reduced. This method could give an appropriate computational representation of the behavior of orthotropic structures, and it could be used for studying more complex bio-inspired structures.
Open Access
Ultra-low frequency multidirectional harvester for wind turbines
(Elsevier, 2023) Castellano Aldave, Jesús Carlos; Carlosena García, Alfonso; Iriarte Goñi, Xabier; Plaza Puértolas, Aitor; Ingeniería; Ingeniería Eléctrica, Electrónica y de Comunicación; Institute of Smart Cities - ISC; Ingeniaritza; Ingeniaritza Elektrikoa, Elektronikoaren eta Telekomunikazio Ingeniaritzaren; Universidad Pública de Navarra / Nafarroako Unibertsitate Publikoa
In this paper we propose, and demonstrate through a prototype, a completely novel device able to harvest mechanical energy from the multidirectional vibrations in a wind turbine, and convert it into electrical, to power autonomous sensors. The application is very challenging since vibrations are of ultra-low frequency, well below 1 Hz, with accelerations of tenths of cm/s2 (0.01 g), and the device must capture energy from the movement in any direction. According to our experiments, the device is capable to generate average powers around the milliwatt in the operation conditions of a wind turbine, which are enough for some very-low power sensor nodes, or at least to considerably extend the life-time of batteries. The device is based on the principle of moving (inertial) masses comprised of magnets in Hallbach arrays interacting with coils, and can work for movements on any direction of a plane. To the best of our knowledge, this is the first device specifically proposed for wind turbines and one of the few that work in such low frequencies, and capture energy from movements on any direction on a plane. Only three harvesters proposed in the literature, intended for distinct applications, can work at such low frequencies, and our device exhibits a better efficiency. Though comparisons with harvesters working in different contexts and, even using different conversion principles, is not completely fair, we make in this paper a comparison to the closest ones, resorting to two different figures of merit.
Open Access
Hybrid modelling and identification of mechanical systems using Physics-Enhanced Machine Learning
(Elsevier, 2025-11-15) Merino Olagüe, Mikel; Iriarte Goñi, Xabier; Castellano Aldave, Jesús Carlos; Plaza Puértolas, Aitor; Ingeniería; Ingeniaritza; Institute of Smart Cities - ISC; Ingeniería Eléctrica, Electrónica y de Comunicación; Ingeniaritza Elektrikoa, Elektronikoa eta Telekomunikazio Ingeniaritza; Universidad Pública de Navarra / Nafarroako Unibertsitate Publikoa
Obtaining mathematical models for mechanical systems is a key subject in engineering. These models are essential for calculation, simulation and design tasks, and they are usually obtained from physical principles or by fitting a black-box parametric input-output model to experimental data. However, both methodologies have some limitations: physics based models may not take some phenomena into account and black-box models are complicated to interpretate. In this work, we develop a novel methodology based on discrepancy modelling, which combines physical principles with neural networks to model mechanical systems with partially unknown or unmodelled physics. Two different mechanical systems with partially unknown dynamics are successfully modelled and the values of their physical parameters are obtained. Furthermore, the obtained models enable numerical integration for future state prediction, linearization and the possibility of varying the values of the physical parameters. The results show how a hybrid methodology provides accurate and interpretable models for mechanical systems when some physical information is missing. In essence, the presented methodology is a tool to obtain better mathematical models, which could be used for analysis, simulation and design tasks.
Open Access
Triaxial accelerometer based azimuth estimator for horizontal axis wind turbines
(Elsevier, 2023) Plaza Puértolas, Aitor; Ros Ganuza, Javier; Gainza González, Gorka; Fuentes Lárez, José David; Ingeniería; Ingeniaritza; Institute of Smart Cities - ISC; Universidad Pública de Navarra / Nafarroako Unibertsitate Publikoa
One of the elements that receives the greatest stresses is the main shaft. Its damage is directly related to the cyclical nature of its rotational motion. However, the vast majority of horizontal axis wind turbines (HAWT) do not have sensors to measure the main-shaft angular position (azimuth), or they are not always easily accessible. Using a main-shaft placed single triaxial accelerometer for the estimation of the azimuth is proposed as a low intrusion approach that can be easily deployed in machines already in use. An approach using a tandem of two extended Kalman filters (calibration/prediction), aiming for a precise and robust estimation, is presented. The estimator is able to calibrate for accelerometer positional and orientation errors, as well as for bias drift. To simplify the burden of deployment, a simple procedure is proposed to determine the covariance matrices for a particular HAWT from those determined in a synthetic case. The proposed approach is analyzed using synthetic data, OpenFAST simulation of NREL-5MW HAWT. It outperforms the ATAN naive approach by an order of magnitude, showing errors smaller than 0.4o. The filter shows a good behavior, coherent with that of the synthetic setup, when tested on experimental data obtained from a 3MW HAWT.
Open Access
Dynamic considerations of heel-strike impact in human gait
(Springer, 2015) Ros Ganuza, Javier; Font-Llagunes, Josep M.; Plaza Puértolas, Aitor; Kövecses, József; Ingeniería Mecánica, Energética y de Materiales; Mekanika, Energetika eta Materialen Ingeniaritza
Based on the impulsive-dynamics formulation, this article presents the analysis of different strategies to regulate the energy dissipation at the heel-strike event in the context of human locomotion. For this purpose, a seven-link 2D human-like multibody model based on anthropometric data is used. The model captures the most relevant dynamic and energetic aspects of the heel-strike event in the sagittal plane. The pre-impact mechanical state of the system, around which the analysis of the heel impact contribution to energy dissipation is performed, is defined based on published data. In the context of the proposed impulsive-dynamics framework, different realistic strategies that the subject can apply to modify the impact dynamics are proposed and analyzed, namely, the trailing ankle push-off, the torso configuration and the degree of joint blocking in the colliding leg. Detailed numerical analysis and discussions are presented to quantify the effects of the mentioned strategies.
Open Access
A directivity correction for accurate semi-empirical wind turbine noise prediction
(IOP Publishing, 2024) Saldaña Barroso, Oier; Rautmann, C.; Plaza Puértolas, Aitor; Ingeniería; Ingeniaritza
Public acceptance of wind farms is a significant challenge in the development of wind energy. The acoustic impact generated by wind turbines is a common concern among local residents. The primary noise source in wind turbines is generated by aerodynamics. Atmospheric turbulence reaching the blade leading edge or turbulent boundary layer passing the trailing edge produce the main aeroacoustic sources. The noise generated by these mechanisms is commonly predicted by means of semi-empirical models, which do not demonstrate great reliability when compared to acoustic measurements. This paper presents a correction to the directivity of airfoil noise radiation, resulting in improved sound pressure levels on the ground plane surrounding a wind turbine. This improvement is achieved without requiring any additional computational effort. The sound pressure levels perceived on the ground plane are known to have asymmetrical shape. Maximum noise levels correspond to observers directly in the upwind and downwind locations, whereas the minimum levels belong to the positions close to the rotor plane. Said asymmetrical shape is not represented in the semi-empirical models. The proposed correction takes into consideration the airfoil thickness in the radiation directivity equations, resulting in the expected asymmetrical shape of noise footprints on the ground plane around a wind turbine. The correction was found to not affect the accuracy of the spectrum predicted by the semi-empirical models when compared to dedicated field measurements under the standard IEC 61400-11 procedure. When implementing the proposed correction, the virtual NREL 5 MW wind turbine's published noise footprints, which were originally calculated using computationally expensive methods, are accurately reproduced.
Open Access
A unified analytical disk cam profile generation methodology using the Instantaneous Center of Rotation for educational purpose
(Elsevier, 2024) Iriarte Goñi, Xabier; Bacaicoa Díaz, Julen; Plaza Puértolas, Aitor; Aginaga García, Jokin; Ingeniería; Ingeniaritza; Institute of Smart Cities - ISC; Universidad Pública de Navarra / Nafarroako Unibertsitate Publikoa
Cam design is a fundamental part of the Mechanism and Machine Theory (MMT) and is included in the vast majority of MMT books. Cam profile design is usually determined with graphical and analytical methods. Graphical methods are didactically very successful to introduce the theory of cam profile generation in a simple way. In turn, analytical methods allow computer implementations of cam profile generation in order to reproduce it accurately. Most modern MMT books describe analytical methods using geometric equations and envelope theory. However, the analytical profile definition depends on the specific type of follower and there is a lack of a general formulation. This work presents a unified and general analytical formulation for the disk cam profile determination. Based on the Instantaneous Center of Rotation and the kinematic inversion, the formulation provides analytical expressions of the cam profile and is applicable to any type of follower. Thus, the unified formulation can be used in forthcoming books on this discipline.
Open Access
4P operational harmonic and blade vibration in wind turbines: a real case study of an active yaw system and a concrete tower
(Elsevier, 2024) Torres Elizondo, Antonio; Gil Soto, Javier; Plaza Puértolas, Aitor; Aginaga García, Jokin; Ingeniería; Ingeniaritza; Institute of Smart Cities - ISC; Universidad Pública de Navarra / Nafarroako Unibertsitate Publikoa
This study aims to comprehensively investigate the impact of mechanical loads on the performance and lifetime of wind turbines, with particular emphasis on blade vibration at the 4P operational harmonic. Experiments and advanced aeroelastic simulations are combined to assess how active yaw systems and concrete towers affect this specific vibration. Contrary to previous assumptions, field tests have shown that there is a resonance phenomenon in the blade. Specifically, the first edgewise mode of the blade resonates at the 4P frequency, which did not happen in the aeroelastic simulations. Remarkably, thorough aeroelastic simulations show that this resonance is triggered by the excitation of the Edgewise Backward Whirling mode of the rotor, which occurs at the 3P operating harmonic. This study highlights the need for accurate and precise modelling using aeroelastic simulations to reproduce the resonance phenomenon and analyse the contributing factors. A major breakthrough is the discovery that stiffening the active yaw system significantly reduces the 3P hub fixed motions, resulting in reduced blade vibration at the 4P frequency. Furthermore, the simulations show the sensitivity of the 4P vibration to different wind characteristics, providing valuable insights for the design of wind turbines in different environmental conditions.