Alexandru Dadalau

Expedient modeling of ball screw feed drives

Ball screw feed drives are the most commonly used mechanism to provide linear motion in high speed machine tools. Position accuracy and the achievable closed loop bandwidth of such drive systems are usually limited by the structural vibration modes of the mechanical components. Higher order plant models allow for a better understanding of the system dynamics, improve the design process of feed drives and are essential for the development of sophisticated control strategies. The ball screw shaft, describing a complex flexible structure, is probably the most significant component concerning structural vibration modes of a feed drive. In this paper, the behavior of the shaft and its dominant influence at different operating and coupling conditions is particularly addressed. Using a hybrid modeling technique, the main characteristics of the shaft are derived and projected onto a clearly arranged and versatile lumped mass model. Simulative and experimental examinations are conducted and a parameter analysis is performed. The presented model proofs to be accurate for a great range of parameters and in addition allows for a physical interpretation of the dominant structural vibration modes of a feed drive.

Modeling linear guide systems with CoFEM: equivalent models for rolling contact

Today’s machine tools are highly complex mechatronic systems capable to exert large translational and rotatory movements. In most cases rolling bearings are used to connect the moving parts to each other. As full FE models of rolling bearings can consume a large amount of degrees of freedom (DOF) efficient methods for reducing the DOF consuming rolling elements to more simple equivalent models are needed. As an example a linear guide system is used. A special feature of the considered linear guide is that the runner block consists of three separate parts, which are hold together only by pretension and friction. FE simulations of such linear guide system were not reported before in the literature. Beside the full FE model three equivalent contact models are presented. The first two equivalent contact models feature novel characteristics. Advantages and disadvantages of the equivalent models are discussed using as reference a slice of the full model and simulation results of static stiffness. The validation of the numerical models is also done using the general analytical solution of Hertz.

Parametric modeling of ball screw spindles

In the product development process numerical optimization can successfully be applied in the early product design stages. In the very common case of ball screw drives, the dynamical behavior is most depending on the geometrical shape of the ball screw itself. Properties like axial and torsional stiffness, moment of inertia, maximum velocity and acceleration are determined not only by the servo motor but also by screw diameter, slope and ball groove radius. Furthermore coupling effects between the design variables make the optimization task even more difficult. In order to capture these effects, efficient numerical (usually FEM or MBS) models are needed. In this work a new more accurate and efficient method of computing the axial and torsional stiffness of ball screw spindles is presented. We analytically derive parametric equations which depicts most of the dependencies of stiffness on geometrical parameters of the screw. Furthermore, we enhance the analytical model with an identified function, which increase the accuracy even more. The presented analytical model is validated against FEM model and catalog data with the help of numerous examples.

Numerical Analysis of Relaxation Test Based on Prony Series Material Model

In performing an experimental analysis it is always important to take into account different parameters influencing the results. Boundary conditions in addition to the specimen size in case of nonlinear materials could be even more effective. Hence, a full analysis of these parameters before doing any test on the real material seems necessary. In this paper, these effects are numerically analyzed, using ANSYS APDL coding. Samples are cylindrical elastomers becoming ready for a relaxation test in order to get Prony series of the material. The influences of friction and applied displacement in addition to the area-length ratio have been investigated and the optimal values in order to do an appropriate relaxation test are proposed.

A new adaptive penalization scheme for topology optimization

In the product development process topology optimization can successfully be applied in the early product design stages. In this work a new penalization scheme for the SIMP-method (Solid Isotropic Material with Penalization) is presented. One advantage of the presented method is a linear density-stiffness relationship, which has advantages for self-weight or eigenfrequency problems. The optimization problem is solved through derived optimality criteria (OC), which is also introduced in this paper. The derived OC uses no sensitivities of the optimization function but is equivalent to the classical OC in the case of no penalization. In the case with penalization we present an objective function for the penalty factor. By maximizing the objective function in each iteration, we get an adaptive penalty factor. Numerical experiments show, that the adaptive penalty factor leads to better optimization results then a fixed penalty factor. The presented topology optimization method is implemented in the commercial FEM package ANSYS under the name TopoAD. One useful extension of TopoAD is the concept of “meta elements”, which is also presented in this paper.

Bottom-Up Component Oriented FE-Modelling of Machine Tools

This work presents a new method for efficient FE modelling of machine tools and their mechanical components, called CoFEM (Component oriented Finite Element Modelling). It uses predefined component models, which, similar to modern CAD software, are gradually and hierarchically assembled to a more complex FE model using a bottom-up technique. The implementation and testing of CoFEM is done in the ANSYS environment. In this paper the modelling methodology and practical examples of modelling complex ball screw feed drive systems as well as single components such as rolling contact linear guides are presented. Advantages of the presented CoFEM modelling method compared with standard modelling methods are reduction of complex models to simpler subcomponents, decrease of modelling error probability, more flexibility regarding model changes and intuitive management of model versions.

Component oriented and automatic generation of FE models for parallel kinematics

This paper presents an algorithm to automatically generate the finite element models for parallel kinematics. The algorithm translates the geometric constraint information of each component to equations. The relative positions between components can be determined by solving those equations. The algorithm is independent of the kinematic structure. It has been already implemented in component oriented finite element modeling software and has been tested on some practical examples.

Automatische Generierung von MPC-Kontakt anhand der Kontaktknoten zwischen FE-Baugruppen

Kurzfassung Mit der Steigerung der Computerleistung werden die Finite-Elemente (FE)-Modelle immer komplexer. Damit verbunden ist ein höherer Modellierungs- und Änderungsaufwand von solchen Modellen, insbesondere im Falle von vielen Versionen desselben Modells. Mit Hilfe einer komponentenorientierten Modellierung lässt sich der Aufwand drastisch reduzieren, wobei gleichzeitig die Fehleranfälligkeit sinkt. Die Voraussetzung bei der komponentenorientierten FE-Modellierung ist jedoch eine möglichst einfache aber flexible Definition der Modellschnittstellen, sodass die Kopplung der Komponenten automatisiert erfolgen kann. Der Kopplungsalgorithmus muss dabei insbesondere nichtkonforme Netze sehr unterschiedlicher Art zuverlässig unterstützen können. Im vorliegenden Text wird eine neuartige, kontaktknotenbasierte Methode zur automatisierten Kopplung von nichtkonformen FE-Netzen mit Hilfe von Multi-Point-Contraints (MPC)-Kontaktelementen vorgestellt.