Igor Fernández de Bustos

Calculation of General Static Load-Carrying Capacity for the Design of Four-Contact-Point Slewing Bearings

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 to compute acceptance curves for the design and selection of bearings of this kind.

A Tetraparametric Metamodel for The Analysis and Design of Bolting Sequences for Wind Generator Flanges

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 the flange under the tightening loads of the bolts. Even though the behavior of the joint is nonlinear because of the gap, the parameters are obtained from two simple linear elastic analyses of a finite element (FE) model of the flange. The corresponding loss of load in the bolts has been estimated for various sequences with minimum computational cost. Thus, there is no need for costly experimental measurements or nonlinear FE simulations.

Eigensensitivity-Based Optimal Damper Location in Variable Geometry Trusses

In this paper, two procedures are described to identify the optimal damping element locations in variable 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 structures becomes more complex, the number of elements increases, and the frequency range of external actions is wider, finding the optimal location of dampers along the system becomes a difficult task. Furthermore, if the structure varies its geometry in successive positions, such as folding, unfolding, or any other movement, another level of complexity is added to the problem. The two procedures presented in this paper are based on calculating the effectiveness indices obtained from the derivatives of the eigenfrequencies of the dynamic eigenproblem with regard to parameters like stiffness or damping.

Eigensensitivity Analysis in Variable Geometry Trusses

T HE adaptive structures of variable geometry are light mechanical systems capable of modifying their geometry and mechanical properties to adapt to different operating conditions. There are different kinds of mechanical variable geometry systems [1], amongwhich stand out the variable geometry trusses (VGTs) [2– 5]. These structures are a subset of the former, generally comprising a large number of biarticulated bars to form a complex truss. Some of these bars are active elements; that is, their length can vary in a controlled way to enable the actuation of the VGT. One of the most important problems to be solved in VGTs is vibration, essentially due to two factors. On the one hand, they are generally slimline structures, making them easily excitable at low frequencieswith large amplitudes, whichmight interferewith correct VGT operation, thereby harming its accuracy, and even resulting in collisions with environmental obstacles [5–7]. On the other hand, as VGTs may have highly different configurations throughout their operation, the dynamic properties (natural frequencies and vibration modes) also change to a large extent. There have been numerous contributions onvibratory dynamics of VGTs. There are a few works, like those of Keane and Bright [8], Keane [9], andNair andKeane [10], which opt for optimum redesign of the structure geometry using evolutionary methods to determine structural geometries presenting a better dynamic response; the most widely accepted procedure for improving and/or controlling dynamic properties is the inclusion of active, semiactive, or passive elements to control its dynamic response. In this sense, Bilbao et al. [11] carried out a detailed revision of the state of the art and proposed a new methodology for the optimal location of damping elements. This Note further contributes to vibratory dynamics of VGTs, describing a tool developed to efficiently estimate the dynamic properties of VGTs (frequencies and modes) throughout their movement, by responding to two needs. First, the information that frequencies and modes supply is often sufficient to foresee the dynamic behavior without having to perform costly direct dynamic analyses, as verified in [12]. Second, should said analyses be necessary, they can be approached from the modal superposition viewpoint, for which a tool that efficiently estimates natural frequencies and vibration modes is necessary. A linear estimation is proposed tomodel the variation of these dynamic properties throughout the VGTevolution, so that there is no need to calculate them per position but only for a fraction of these positions, whichmay result in considerable computational saving. Thus, a methodology estimating the value of natural frequencies and vibration modes in a new position from their value in the immediately prior position is employed. This is done by differentiating natural frequencies and vibration modes with respect to nodal coordinates at the starting position and developing a first-order series around the starting position to extrapolate the values of natural frequencies and vibration modes for a new position.

Solving the Minimum Distance Problem for the Synthesis of Mechanisms

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 mechanism, being only limited by computational cost); its great convergence; and its efficiency not only when optimizing simple mechanisms, but also for complex mechanisms when starting from a good initial guess. This allows one to adapt machinery for new tasks in an easy way like is needed, for example, in packaging industry. The method (as many others) is based on the synthesis point concept, which is related to a set of requirements to be accomplished in a possible configuration of the mechanism. The main caveat of the deformed position problem is derived from the fact that, when used for mechanism synthesis, it is an approximation of the real task to optimize, and this leads to the problem that it can converge to mathematical solutions which are useless. This happens when optimizing complex mechanisms via sequential quadratic programming algorithms without a good initial guess, or when using explorative methods such as genetic algorithms. In both cases, the algorithm will favour low stiffness mechanisms, due to the fact that they can reach any requirement with high deformation, but low deformation energy. To solve this problem, here the use of a minimum distance problem is proposed, where one tries to reach the minimum distance that the mechanisms is able to achieve to the considered requirement. In order for this idea to be suitable for multiple requirements in a single synthesis point, a weighted square distance summation is used. This should solve the stiffness issue while keeping all the advantages of the deformed position problem, at the cost of an increase on the convergence cost. Although developed for bidimensional problems, a three dimensional generalization should be easy to formulate. In this presentation this function is presented, along with some considerations on its resolution via a sqp algorithm using Lagrange multipliers. Furthermore, some initial experimental results are presented which allows one to figure out the future performance of the function when used as a basis for mechanism synthesis.

On Classical Newmark Integration of Multibody Dynamics

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 performed in a full Newton approach, instead of using less efficient quasi-Newton approaches. This requires the analytic computation of derivatives, but improves in convergence and precision. An implementation for 2D problems using Newton-Euler formalism and cartesian coordinates has been developed to test the system. An example is included.

Static Load Carrying Capacity in Four Contact Point Slewing Bearings: Theoretical and Preliminary Finite Element Calculations

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 Sjovall and Rumbarger’s equations and provides an acceptance surface in the load space. The finite element model is based on the modelization of the balls via nonlinear traction-only equivalent spring concept. The aim is to validate the theoretical model to be used as an acceptance curve generator for slewing bearing design.© 2010 ASME

A Tetraparametric Metamodel for the Simulation and Optimization of Bolting Sequences for Wind Generator Flanges

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. This work presents a methodology which, based on a metamodel created for such purpose, enables the optimization of the tightening sequence; i.e. it calculates the load to be applied to each bolt in order to achieve a desired uniform preload at the end of the tightening sequence. This optimization is done with a minimum computational cost, avoiding costly experimental measurements or nonlinear FE simulations. Besides, the methodology also takes into account that the load for any bolt must be below its yield point, and therefore calculates a two-pass sequence if necessary.Copyright

A Numerical Method for the Second-Order Mobility Analysis of Mechanisms

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. This algorithm can be easily applied to bi and three dimensional mechanisms and delivers a good degree of efficiency. The results of this analysis can be employed to improve the efficiency of other algorithms which present lack of convergence in the vicinity of singular configurations.

An Error Function for Optimum Dimensional Synthesis of Mechanisms Using Genetic Algorithms

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 achieved by the mechanism. To get this distance, a non-linear function must be iteratively solved, leading to a high computational cost function. In order to reduce the computational cost, variable complexity functions techniques can be applied. Solutions obtained with this genetic algorithm are a good starting point for further numerical optimization methods.