Ayman A. Nada

A Continuum Based Three-Dimensional Modeling of Wind Turbine Blades

Accurate modeling of large wind turbine blades is an extremely challenging problem. This is due to their tremendous geometric complexity and the turbulent and unpredictable conditions in which they operate. In this paper, a continuum based three dimensional finite element model of an elastic wind turbine blade is derived using the absolute nodal coordinates formulation (ANCF). This formulation is very suitable for modeling of largedeformation, large-rotation structures like wind turbine blades. An efficient model of six thin plate elements is proposed for such blades with non-uniform, and twisted nature. Furthermore, a mapping procedure to construct the ANCF model of NACA (National Advisory Committee for Aeronautics) wind turbine blades airfoils is established to mesh the geometry of a real turbine blade. The complex shape of such blades is approximated using an absolute nodal coordinate thin plate element, to take the blades tapering and twist into account. Three numerical examples are presented to show the transient response of the wind turbine blades due to gravitational/aerodynamics forces. The simulation results are compared with those obtained using ANSYS code with a good agreement. [DOI: 10.1115/1.4007798]

Use of the floating frame of reference formulation in large deformation analysis: Experimental and numerical validation

Abstract The finite-element floating frame of reference (FFR) formulation is used, for the most part, in the small deformation analysis of flexible bodies that undergo large reference displacements. This formulation allows for filtering out systematically complex shapes associated with high frequencies that have no significant effect on the solution in the case of small deformations. The resulting low-order FFR models have been widely used to obtain efficient and accurate solutions for many engineering and physics applications. In this investigation, the use of the FFR formulation in the large deformation analysis is examined, and it is demonstrated that large deformation FFR models can be accurate in applications, where the deformation can be described using simple shapes as it is the case in robot system manipulators. In these cases, the standard finite-element FFR formulation must be used with non-linear strain—displacement relationships that account for the geometric non-linearities. The results obtained using the large deformation FFR models are compared with the results obtained using the large deformation absolute nodal coordinate formulation (ANCF), which does not allow for the use of linear modes. The ANCF models are developed using two different methods for formulating the elastic forces: the basic continuum mechanics approach (ANCF-BC) and the elastic line method (ANCF-EL). While the explicit Adams method can be used to obtain the numerical solution of the FFR model, two implicit integration methods are implemented in order to be able to obtain an efficient solution of the FFR and ANCF models. These implicit integration methods are the RADAU5 method and the Hilber—Hughes—Taylor (HHT) method. In the case of simple large deformation shapes, the simulation results obtained in this study show a good agreement between the FFR and the ANCF solutions. The results also show that, in the case of thin and stiff beams, the coupled deformation modes that result from the use of the ANCF-BC can be a source of numerical and locking problems, as reported in the literature. These ANCF-BC numerical problems can be circumvented using the implicit HHT integration method. Nonetheless, the HHT integrator does not capture high-frequency FFR axial modes which are necessary in order to obtain accurate solutions for high-speed rotating beams. In addition to the comparison with the ANCF solutions, experimental results of a forward dynamics model are used in this study to validate the large deformation FFR numerical solutions. The experimental set-up used in the validation of the numerical solutions is also described in this investigation.

Modeling Slope Discontinuity of Large Size Wind-Turbine Blade Using Absolute Nodal Coordinate Formulation

This paper describes the use of the Absolute Nodal Coordinate Formulation (ANCF) in modeling large-size wind turbine blades. An efficient procedure is developed for mapping NACA airfoil wind-turbine blades into ANCF thin plate models. The procedure concerns the wind turbine blade with non-uniform, twisted nature. As a result, the slope discontinuity problem arises and presents numerical errors in the dynamic simulation. This investigation illustrates a method for modeling slope discontinuity resulting from the variations of the cross sectional layouts across the blade. A method is developed and applied for the gradient-deficient thin plate element in order to account for structural discontinuity. The numerical results show a numerical convergence and satisfy the principle of work and energy in dynamics. The simulation results are compared with those obtained using ANSYS code with a good agreement.Copyright

Methods of modeling slope discontinuities in large size wind turbine blades using absolute nodal coordinate formulation

This paper describes and evaluates the use of the Absolute Nodal Coordinate Formulation (ANCF) in modeling large size wind turbine blades. Modern blade model can be divided into two regions classified by aerodynamic and structural function. The aerodynamic region, blade-span, is utilizing the thinnest possible airfoil section. On the other hand, the transition between the circular mount and the first airfoil profile is referred as blade-root region, which carries highest loads along the blade. In this investigation, an efficient procedure is developed for mapping NACA airfoil wind-turbine blades into ANCF thin plate models. The procedure concerns a complete wind turbine blade structure, blade-root as well as the blade-span regions with non-uniform and twisted nature. As a result, the slope discontinuity problem arises in both chord-wise and span-wise directions, and consequently presents numerical errors in dynamic simulation. The paper investigates the methods of modeling slope discontinuity resulting from the variations of the cross-sectional layouts across the blade. The developed method is applied for the gradient-deficient thin plate element in order to account for structural discontinuity. In addition, the aerodynamic loads are precisely expressed and the aerodynamic characteristics of such blades are examined with the ANCF and with the classical finite element method. The static and dynamic solutions of different operating conditions are obtained and results are compared with those obtained using ANSYS code. Both the limitations and advantages of using the ANCF in modeling large size wind turbine blades are concluded and discussed. A Dynamics for Design (DFD) procedure is presented with numerical example concerning large-rotation, large deformation wind turbine blades.

FLOATING FRAME OF REFERENCE AND ABSOLUTE NODAL COORDINATE FORMULATIONS IN THE LARGE DEFORMATION ANALYSIS OF ROBOTIC MANIPULATORS: A COMPARATIVE EXPERIMENTAL AND NUMERICAL STUDY

This paper describes the use of flexible multibody system approaches in the dynamic modeling of interconnected rigid-elastic robotic manipulators. Two approaches are used to establish the flexible robot dynamic model; the floating frame of reference formulation (FFR) and the absolute nodal coordinate formulation (ANCF). The ANCF is used with two different methods for formulating the elastic forces; basic continuum mechanics approach (ANCF-BC) and elastic line method (ANCF-EL). The simulation results show that the use of the nonlinear FFR and the ANCF-EL improves the performance of the beam element in the modeling of flexible robotic manipulators. In the case of simple large deformation shape, the simulation results obtained show a good agreement between the FFR and the ANCF solutions. In the case of thin and stiff beams, the coupled deformation modes that result from the use of the ANCF-BC can be a source of numerical problems. These problems can be avoided using the implicit Hilber-Hughes-Taylor (HHT) integration method. On the other hand, HHT integrator does not capture high frequency axial modes when the FFR is used; RADAU5 method is used instead. The experimental results of the direct dynamics model are effectively used in this study to validate the numerical solutions.Copyright

Dynamic Modeling of a Flexible Cantilever Beam: An Experimental Technique

This paper describes an investigation of real time dynamic modeling method for a flexible cantilever beam, as an approximation of a robot flexible link, using experimental measurement techniques. The beam is equipped with a number of strain gauges to measure the corresponding nodal flexibilities and using them to obtain its real-time dynamic model. Two methods are proposed; the 1st method is based on approximating the beam deflection by a 4th order polynomial curve while the 2nd one is based on the solution of its Eulerbernoulli equation. The polynomial constants are obtained by real-time estimation using the readings of the strain gauges. These readings are used to estimate the beam temporal solution in the 2nd method. The error in the beam tip deflection is reduced to 0.01% by relocating the last strain gauge at 12.5% instead of 30% from its tip. Both methods show good agreement with the general beam theory and results.Copyright

Computational Design Scheme for Wind Turbine Drive-Train Based on Lagrange Multipliers

The design optimization of wind turbines and their subsystems will make them competitive as an ideal alternative for energy. This paper proposed a design procedure for one of these subsystems, which is the Wind Turbine Drive-Train (WTDT). The design of the WTDT is based on the load assumptions and considered as the most significant parameter for increasing the efficiency of energy generation. In industry, these loads are supplemented by expert assumptions and manipulated to design the transmission elements. In contrary, in this work, the multibody system approach is used to estimate the static as well as dynamic loads based on the Lagrange multipliers. Lagrange multipliers are numerical parameters associated with the holonomic and nonholonomic constraints assigned in the drive-train model. The proposed scheme includes computational manipulations of kinematic constraints, mapping the generalized forces into Cartesian respective, and enactment of velocity-based constrains. Based on the dynamic model and the obtained forces, the design process of a planetary stage of WTDT is implemented with trade-off’s optimization in terms of gearing parameters. A wind turbine of 1.4 megawatts is introduced as an evaluation study of the proposed procedure, in which the main advantage is the systematic nature of designing complex systems in motion.

Selective Generalized Coordinates Partitioning Method for Multibody Systems With Non-Holonomic Constraints

The goal of this research work is to extend the method of generalized coordinates partitioning to include both holonomic and nonholonomic constraints. Furthermore, the paper proposes a method for selective coordinates for integration instead of identifying a set of independent coordinates at each integration step. The effectiveness of the proposed method is presented and compared with full-coordinates integration as well as generalized co-ordinates partitioning method. The proposed method can treat large-scale systems as one of the main advantages of multi-body systems.Copyright

Development and Validation of Multibody Model of Wind Energy System

The wind energy is observed as an essential and powerful energy resource for the socio-economic development. It is proposed that the small-size wind turbines can demonstrate the innovative solution for the wind energy conversion for low speed regions. An innovative design, control, and monitoring processes require accurate and validated dynamic model of such turbines. In this investigation, the flexible multibody dynamics approach is used to extend the traditional method of dynamic modeling of small-size wind turbines. A systematic approach is developed based on Floating Frame of Reference formulation (FFR) that includes the dynamics of the flexible blades as well as the aerodynamic loads. Beam element is used to model the blade structure with variable twist angle and the corresponding generalized aerodynamic forces are developed. In order to counteract the effect of the geometric stiffening, the coupling terms in the expression of axial strain energy are taken into account. An experimental test-rig equipped with wind generator is used for the FFR model validation. The equipment gives a maximum discharge flow of 10 [m/s] in a 500 [mm] diameter duct. The dynamic effect of the twist angle of 30 [cm] diameter of rotor blades is studied based on the measured rotor speed of the wind turbine. High sensitivity multi-axis accelerometers are used to measure the induced vibration and the data points are collected via data acquisition card of 16 bit resolution. The comparison of experimental results and numerical solution shows a very good agreement and consequently the wind turbine model obtained is suitable for stress analysis, structural and control design. It is concluded that the FFR formulation is best suited for large rotation and small deformation problems, which coincide with the operational conditions of small-size wind energy systems.Copyright

Exact linearization by feedback of state dependent parameter models applied to a mechatronics demonstrator

The paper develops an exact linearization by feedback approach for State Dependent Parameter (SDP), Proportional-Integral-Plus (PIP) control. The method is demonstrated using a simple automated belt driven by a DC motor equipped with a single board Reconfigurable Input-Output (sbRIO-9631) card, within a Field Programmable Gate Array (FPGA), and with a real time processor for control. The demonstrator is first modeled using a discrete-time SDP model structure, in which the parameters are functionally dependent on measured system states. An exact linearization step returns a linear model with unity coefficients, which is subsequently used to design a PIP control algorithm based on linear system design strategies, including pole assignment and optimal linear quadratic design. Preliminary experimental results demonstrate that the new approach yields an acceptable control performance for the nonlinear system.