Igor Fernandez de Bustos

• Professor (Associate) at University of the Basque Country

In this work, a new algorithm for solving symmetric indefinite systems of linear equations is presented. It factorizes the matrix into the form LDLt using Jacobi rotations in order to increase the pivot's absolute value. Furthermore, Rook's pivoting strategy is also adapted and implemented. In determinate compatible systems, the computational cost...

There are several common procedures used to numerically integrate second-order ordinary differential equations. The most common one is to reduce the equation’s order by duplicating the number of variables. This allows one to take advantage of the family of Runge–Kutta methods or the Adams family of multi-step methods. Another approach is the use of...

Apart from other options, a common procedure to integrate order 2 Ordinary Differential Equations (ODEs) present in Multibody systems is to reduce the order of the ODE by duplicating the number of variables. This leads to apply the well-known family of Runge-Kutta (RK) methods. Other approach, commonly used in structural mechanics, is the use of me...

This article falls within the scope of topology optimization for Additive Manufacturing processes and proposes an alternative strategy to prevent the phenomenon known as the Dripping Effect. The Dripping Effect is when an overhang constraint is imposed on topology optimization processes for Additive Manufacturing and is defined as the formation of...

The stability of integrators dealing with high order Differential Algebraic Equations (DAEs) is a major issue. The usual procedures give rise to instabilities that are not predicted by the usual linear analysis, rendering the common checks (developed for ODEs) unusable. The appearance of these difficult-to-explain and unexpected problems leads to m...

The direct integration method by central differences (DIMCD) is an explicit method of order two for integrating the equations governing the dynamic analysis of multibody systems. So far, development has focused only on verifying the quality of the results. In this paper, it is shown that in addition to providing optimal results, it is also competit...

This paper presents an infill topology optimization procedure to generate lightweight porous structures by the Sequential Element Rejection and Admission (SERA) method. The proposed procedure evaluates the material volume of small neighbourhoods guaranteeing the presence of material within each of them by means of a set of local volume constraints....

The deformed energy method has shown to be a good option for dimensional synthesis of mechanisms. In this paper the introduction of some new features to such approach is proposed. First, constraints fixing dimensions of certain links are introduced in the error function of the synthesis problem. Second, requirements on distances between determinate...

This paper presents the mathematical developments required to introduce both linear springs and dampers into the second order Newmark method for the integration of Multibody System Dynamics (MBSD) for bidimensional problems. The advantage of the Newmark approach is that it integrates directly the second order differential equations found in MBSD, t...

The paper examines the application of a general minimum distance error function to the dimensional kinematic synthesis of bidimensional mechanisms. The minimum distance approach makes it possible to solve the problem maintaining the same generality as that of the minimum deformation energy method while solving the problems that occasionally appear...

This work presents a computational procedure for direct integration of Topology Optimization and Additive Manufacturing (AM) technologies for compliant mechanisms design. Many topologically optimized geometries present manufacturing problems derived from the lack of self-supporting capacities and require sacrificial support material for 3D printing...

A methodology for integrating rigid body dynamics for the analysis of multibody systems is presented. The novelty lies in the fact that the equation system is solved directly by means of central differences as a second-order integration method. To obtain the best achievable convergence, the equilibrium is solved iteratively by the exact Newton meth...

Uniform bolt load is critical to achieve leak-free service in pressure vessel gasketed joints. In a previous work, the authors presented the tetraparametric assembly method, which enabled to obtain a uniform final load distribution in a one-pass tightening sequence. The accuracy of the method was proved by finite element analysis and experimental t...

The use of the classical Newmark method for the integration of Multibody System Dynamics (MBSD) is presented. This approach has the advantage of directly integrating the second order differential equations which appear in MBSD and, thus, does not require duplication of the variables, reducing the computational cost. The resolution of each step is p...

The aim of this document is to show a method for the introduction of node to node requirements in the dimensional synthesis of mechanisms when using the minimum distance approach. The presented method allows one to introduce a requirement on the distance of two points belonging to different elements of the linkage, which has multiple practical appl...

This work falls within the scope of computer-aided optimal design, and aims to integrate the topology optimization procedures and recent additive manufacturing technologies (AM). The elimination of scaffold supports at the topology optimization stage has been recognized and pursued by many authors recently. The present paper focuses on implementing...

The minimal least squares solutions is a topic of interest due to the broad range of applications of this problem. Although it can be obtained from other algorithms, such as the Singular Value Decomposition (SVD) or the Complete Orthogonal Decomposition (COD), the use of LDU factorizations has its advantages, namely the computational cost and the l...

The method of the lower deformation energy has been successfully used for the synthesis of mechanisms for quite a while. It has shown to be a versatile, yet powerful method for assisting in the design of mechanisms. Until now, most of the implementations of this method used the dimensions of the mechanism as the synthesis variables, which has some...

One of the most successful general methods for the synthesis of mechanisms is that based in the deformed position problem, which has seen uninterrupted development on the last 20 years. The advantages of this formulation are its versatility (can solve prescribed and unprescribed timing problems, different kind of requirements, works with any mechan...

The deformed position problem is the basis for methods dealing both with synthesis and analysis of mechanisms. This paper analyzes how nonlinear restrictions can be introduced into the method so that it can be used to represent restrictions in the distance between two arbitrary points in the mechanism. The applications of this algorithm range from...

Several analytical models have been proposed to estimate the load distribution and the deformation of slewing bearing assemblies in wind turbine generators (WTGs). Even though they are a useful tool for designers as a first approach, most of them assume rigid rings and rigid supporting structures, leading to inaccurate results; even if compliance i...

This paper presents an algorithm for the factorization of indefinite symmetric matrices that factors any symmetric matrix AA into the form LDLTLDLT, with DD diagonal and LL triangular, with its subdiagonal filled with zeros. The algorithm is based on Jacobi rotations, as opposed to the widely used permutation methods (Aasen, Bunch–Parlett, and Bunc...

In this work we discuss the introduction of restrictions in the kinematical optimization of mechanisms, using the deformed position problem. This method has shown a great degree of versatility, allowing to solve both prescribed and not prescribed timing problems. The algorithm leads to an error function which is the sum of several error functions,...

En los últimos años se han publicado varios métodos analíticos para estimar la distribución de cargas y la deformación de los ensamblajes de rodamientos de vuelco en aerogeneradores. Pese a ser útiles para obtener resultados preliminares, la mayoría de estos métodos supone anillos y estructuras de soporte rígidos, lo cual conduce a resultados impre...

In bolted joints, bolts are tightened to a uniform preload in order to improve their operational behavior. This preload is not easy to achieve due to several phenomena that occur during the tightening sequence; in the case of wind generator bolted joints, which present a gap between the contact surfaces of the flanges, the elastic interaction is by...

This paper presents the kinematical features of an inversion of the double linked fourbar for morphing wing purposes. The structure of the mechanism is obtained using structural synthesis concepts, from an initial conceptual schematic. Then, kinematic characteristics as instant center of rotation, lock positions, dead point positions and uncertaint...

This study developed a framework for the shape optimization of aerodynamics profiles using computational fluid dynamics (CFD) and genetic algorithms. A genetic algorithm code and a commercial CFD code were integrated to develop a CFD shape optimization tool. The results obtained demonstrated the effectiveness of the developed tool. The shape optimi...

This work shows first the way by which an inversion of the double linked fourbar has been obtained in order to use it as actuation mechanism for an UAV morphing wing after a short structural synthesis step. Then, the kinematical capabilities of this mechanism are outlined and graphically derived: instant center of rotation, lock positions and uncer...

This paper presents a general method for the second order local mobility analysis of kinematical chains using closure equations. As it is known, one can obtain the mobility of a mechanism as the nullspace of its Jacobian Matrix. But in the event of a singular configuration, not all of the linear combinations of these vectors represent finite moveme...

In previous publication, the authors developed a theoretical model to evaluate the static load capacity of four contact point slewing bearings. The method culminated in the formulation of an acceptance surface in the load space, in such a way that the validity of a load combination is assured by an inside-surface checking. In the present work a mul...

This paper presents a metamodel that enables estimation of the elastic interaction that occurs in the bolted joints of a wind generator tower during the tightening sequence. In this kind of joint, there is a gap between the contact surfaces of the flanges. The metamodel is composed of four parameters, which are enough to simulate the response of th...

Vibratory dynamics of variable geometry trusses (VGT) is studied and a tool is developed to efficiently estimate the dynamic properties of VGTs throughout their movement. A procedure for estimating the variation of natural frequencies and vibration modes of VGTs during their movement, making it unnecessary to recalculate them at all positions but j...

This paper presents a novel numerical approach to solving the inverse dynamics of variable geometry trusses (VGTs) with elastic elements, allowing designers to accurately and efficiently determine motor action requirements, the time-dependent behavior of the structure, and the contribution of vibration modes to the motion. The dynamic equations hav...

One important problem in the dynamic analysis of Variable Geometry Trusses (VGTs) is the evolution of frequencies and vibration modes in different positions along their movement, which usually involves large changes in their geometry. The calculation of modes and frequencies in every position may result in a prohibitive computational cost when usin...

This paper presents the derivation of the general static load-carrying capacity of three row roller slewing bearings under axial load and tilting-moment. This calculation is a true generalization of Rumbarger's method and provides an acceptance curve in the load space. This acceptance curve provides an approximate quick way for the design and selec...

This paper presents a novel numerical approach to solving the inverse dynamics of variable geometry trusses (VGTs) with elastic elements, allowing designers to accurately and efficiently determine motor action requirements, and the time-dependent behavior of the structure. The dynamic equations have been simplified by assuming that movements of the...

This paper presents a method for the generalized rigid-body guidance dimensional synthesis of planar linkages. The error function is based on the elastic energy stored in a finite element model of the linkage, built with rod-type elements, when it is forced to fulfil the synthesis data. The best linkage dimensions are the ones that give the minimum...

This paper presents a calculation of the general static load-carrying capacity of four-contact-point slewing bearings under axial, radial, and tilting-moment loads. This calculation is based on a generalization of Sjovall and Rumbarger's equations and provides an acceptance surface in the load space. This acceptance surface provides a solid basis t...

This work tries to represent the general static load-carrying capacity of four-contact-point stewing bearings under general loading This representation is based on a generalization of Sjovall and Rumbarger's equations and provides an acceptance surface in the load space This acceptance surface provides the key set of acceptance curves for the desig...

This paper presents an improved approach to the optimum dimensional synthesis of planar linkages based on an elastic strain-energy error function, according to which the optimum link dimensions are those which result in the minimum energy when the linkage is forced to comply with the synthesis data. This method is suitable for any kind of kinematic...

This paper presents a novel numerical approach to solving the inverse dynamics of variable geometry trusses (VGTs) with elastic elements, allowing designers to accurately and efficiently determine motor action requirements, and the time-dependent behavior of the structure. The dynamic equations have been simplified by assuming that movements of the...

In the bolted joints of wind generator flanges there is a gap between the contact surfaces of the flanges. This involves a nonlinear behavior of the system during the tightening sequence of the joint. This phenomenom, in addition with the elastic interaction, makes it difficult to achieve a uniform bolt preload at the end of the assembly process. T...

This paper presents a theoretical model to calculate the general static load-carrying capacity of four-contact-point slewing bearings under axial, radial and tilting-moment loads, compared with preliminary results obtained from a detailed parametric finite element model of the bearing. The theoretical model is based on a generalization of Sjoväll a...

This paper presents a method for the second order analysis of the mobility of a mechanism (i.e., the identification of the first order infinitesimal motions of the mechanism), based on the compatibility of the acceleration restrictions. This second order analysis allows one to numerically or analytically obtain the limitations of the movement of a...

In this paper, two procedures are described to identify the optimal damping element locations invariable geometry trusses and to improve their behavior when dynamic loads are applied. In simple structures subjected to well-identified actions, obtaining an optimal location for damping elements can be relatively easy. However, as the geometry of the...

The second order mobility analysis of mechanisms is a complicated problem that can be approached in a direct way via the analysis of the compatibility of the acceleration field. This paper will present a simple, numerical approach to retrieve the restrictions imposed to the movement that are derived from the second order (curvature) restrictions. T...

In this paper an error function for optimum dimensional synthesis of mechanisms using genetic algorithms is presented. This function is general for its use with any mechanism with R and P joints. This minimization function is established as the quadratic addition of the minimum linear or angular distance to the synthesis positions which can be achi...

Among existing kinematic analysis methods of mechanisms, the techniques based on finite elements represent a generally applicable alternative which enable a wide variety of problems to be solved, including linear (velocities, accelerations, jerk, ...) and non-linear ones (position). To modelize a mechanism via these techniques, the link element may...

In this paper, a data acquisition system that simultaneously allows the recording of cutting forces and cutting tool position (coordinates X, Y and Z) is presented. Thus, the geometry of the surface being machined and the values of the cutting forces generated during the surface milling can be correlated. In this manner, two usual problems in milli...

This paper presents two new finite elements and its application in solving some problems in linear kinematic analysis of mechanisms. These elements highly increase the simplicity of the finite element method when applied in the resolution of velocity, acceleration, jerking and further derivatives. Likewise, it could also be used to solve some meshi...

A diagnostic system of the milling process through the cutting forces and cutting tool position (coordinates X, Y, and Z) simultaneously collected is detailed in this paper. After the milling test, the cutting forces generated during the machining and the machine position where they occurred can be correlated. After collecting and recording of both...

The use of finite elements in both kinematic analysis and synthesis of mechanisms has shown good performance. Its only drawback is the need for an initial reasonable quality solution. To address this topic, the use of genetic algorithms with a finite-element-based error function is proposed in this paper. This approach has not only shown good beh...

A new general approach for the solution of the path planning problem has been developed in environments with obstacles. On the one hand, this strategy can be applied to mobile robots and on the other hand it can be used to solve the planning of high redundant multibody systems in their Configuration Space. The approach is based on the concept of Ar...

This paper looks at a method for the analysis of highly redundant multibody systems (e.g. in the case of cellular adaptive structures of variable geometry) in environments with obstacles. It is sought to solve the inverse problem in successive positions of multibody systems, avoiding the obstacles in its work environment; i.e. the computation of th...

This paper looks at a method for the analysis of highly redundant multibody systems (e.g., in the case of cellular adaptive structures of variable geometry) in environments with obstacles. Our aim is to solve the inverse kinematics in successive positions of multibody systems, avoiding the obstacles in its work environment. The multibody systems ar...

The present article looks at a method of analysing the behaviour of highly redundant multibody systems (e.g. in the case of cellular adaptive structures of variable geometry) in environments with obstacles. It is sought to solve the inverse problem in successive positions of variable-geometry structures, avoiding the obstacles in its work environme...

The present article looks at a method of analysing the behaviour of highly redundant multibody systems (e.g. in the case of cellular adaptive structures of variable geometry) in environments with obstacles. It is sought to solve the inverse problem in successive positions of variable-geometry structures, avoiding the obstacles in its work environme...

The present article looks at a method of analysing the behaviour of highly redundant multibody systems (e.g. in the case of cellular adaptive structures of variable geometry) in environments with obstacles. It is sought to solve the inverse problem in successive positions of variable-geometry structures, avoiding the obstacles in its work environme...

This paper deals with the optimum synthesis of mechanisms including apparent stiffness restrictions. These kind of restrictions are of interest in some problems such as that of the suspension of vehicles where a progressive or regressive effect is to be achieved. Provided that a mechanism is composed of non-deformable links and a spring, it can be...

1. Abstract The use of genetic algorithms has proven itself to be an efficient tool for the synthesis of mechanisms, as shown in plenty of references. In the workgroup on multibody analysis and design of the Escuela Superior de Ingenieros de Bilbao, a particular development has shown a great degree of efficiency in the optimization of kinematic cha...

1. Abstract The work presented in this article is structured in three parts, focusing its attention on the reduction of the execution time required by the GA to accomplish the evolutive process when the error function is very complex. In order to do it, several strategies will be presented and studied. In the first one, a theoretical approach to de...

INTRODUCCIÓN Los rodamientos de vuelco (Slewing bearings, en nomenclatura internacional) son rodamientos de grandes dimensiones cuyos campos de aplicación van desde generadores de energía eólica, grúas, tanques, centros de torneado… En general se utilizan en casos en los que se ven implicados elementos funcionales de grandes dimensiones. Es muy com...

1 — A new modelling for mechanical systems is considered in this work, in order to arrange the kinematics in a direct and elegant way. We are describing this modelling and applying it particularly to the velocity and acceleration analysis of 2D mechanisms.