Ilaria Palomba

Model updating in flexible-link multibody systems

The dynamic response of flexible-link multibody systems (FLMSs) can be predicted through nonlinear models based on finite elements, to describe the coupling between rigid- body and elastic behaviour. Their accuracy should be as high as possible to synthesize controllers and observers. Model updating based on experimental measurements is hence necessary. By taking advantage of the experimental modal analysis, this work proposes a model updating procedure for FLMSs and applies it experimentally to a planar robot. Indeed, several peculiarities of the model of FLMS should be carefully tackled. On the one hand, nonlinear models of a FLMS should be linearized about static equilibrium configurations. On the other, the experimental mode shapes should be corrected to be consistent with the elastic displacements represented in the model, which are defined with respect to a fictitious moving reference (the equivalent rigid link system). Then, since rotational degrees of freedom are also represented in the model, interpolation of the experimental data should be performed to match the model displacement vector. Model updating has been finally cast as an optimization problem in the presence of bounds on the feasible values, by also adopting methods to improve the numerical conditioning and to compute meaningful updated inertial and elastic parameters.

A Ranking Method for the Selection of the Interior Modes of Reduced Order Resonant System Models

Resonant system design and optimization is usually supported by finite element models. Large dimensional models are often needed to achieve the desired accuracy in the representation of the vibrational behaviour at the frequency of interest. Unfortunately, large dimensional models are frequently too cumbersome to be actually useful, mainly at the optimization stage. On the other hand, the choice of the most appropriate reduction strategy and dimension for a reduced-order model is generally left to designers’ experience. Having recognized the effectiveness and spreading of the Craig Bampton reduction technique, the aim of this paper is to propose a rigorous ranking method, called Interior Mode Ranking (IMR), for the selection of the interior normal modes of the full order model to be inherited by the reduced order one. The method is aimed at finding the set of interior modes of minimum dimensions which allows achieving a desired level of accuracy of the reduced order model at a frequency of interest. The method is here applied to a resonator widely employed in industry: an ultrasonic welding bar horn, which is usually designed to operate excited in resonance. The results achieved through the application of the IMR method are compared with those yielded by other ranking techniques available in literature in order to prove its effectiveness.Copyright

Energy-Based Optimal Ranking of the Interior Modes for Reduced-Order Models under Periodic Excitation

This paper introduces a novel method for ranking and selecting the interior modes to be retained in the Craig-Bampton model reduction, in the case of linear vibrating systems under periodic excitation. The aim of the method is to provide an effective ranking of such modes and hence an optimal sequence according to which the interior modes should be progressively included to achieve a desired accuracy of the reduced-order model at the frequencies of interest, while keeping model dimensions to a minimum. An energy-based ranking (EBR) method is proposed, which exploits analytical coefficients to evaluate the contribution of each interior mode to the forced response of the full-order system. The application of the method to two representative systems is discussed: an ultrasonic horn and a vibratory feeder. The results show that the EBR method provides a very effective ranking of the most important interior modes and that it outperforms other state-of-the-art benchmark techniques.

In-Operation Structural Modification of Planetary Gear Sets Using Design Optimization Methods

Planetary gears are a crucial component in the drives of automation systems and robots. The vibrational behavior of these components can lead to detrimental structural-mechanical effects including fatigue, comfort and acoustics. As the system parameters can change during operation due to wear and damage, configuration changes need to be designed during the operation to avoid vibrational problems. Possible deviation of system parameters is especially true for the stiffness parameters of the gear mesh and bearings. Lumped-parameter models are efficient yet accurate and are used to ascertain eigenfrequencies as well as frequency responses of planetary gear sets. Using these models, the change in system parameters due to damage accumulation is modeled. Thereafter, in operation configuration changes are calculated with numerical optimization methods to reduce undesired vibrational behavior. As exact parameter values are not know, these are considered uncertain using interval methods. These methods will be shown with a generic benchmark example, yet can be used in a wide range of industrial applications.

Application of a Parametric Modal Analysis Approach to Flexible-Multibody Systems

It is widely recognized that modal analysis is an effective tool for the study, modeling, design, control and understanding of mechanical systems. However, its applicability is limited to linear or linearized systems. The validity of linearized models is bounded in an infinitesimal neighborhood of the linearization point (operating point). A series of modal analysis is therefore required to calculate the system modal properties if the operating point varies, as in the case of multibody systems, which typically show gross motion.

An Updating Method for Finite Element Models of Flexible-Link Mechanisms Based on an Equivalent Rigid-Link System

This paper proposes a comprehensive methodology to update dynamic models of flexible-link mechanisms (FLMs) modeled through ordinary differential equations. The aim is to correct mass, stiffness, and damping matrices of dynamic models, usually based on nominal and uncertain parameters, to accurately represent the main vibrational modes within the bandwidth of interest. Indeed, the availability of accurate models is a fundamental step for the synthesis of effective controllers, state observers, and optimized motion profiles, as those employed in modern control schemes. The method takes advantage of the system dynamic model formulated through finite elements and through the representation of the total motion as the sum of a large rigid-body motion and the elastic deformation. Model updating is not straightforward since the resulting model is nonlinear and its coordinates cannot be directly measured. Hence, the nonlinear model is linearized about an equilibrium point to compute the eigenstructure and to compare it with the results of experimental modal analysis. Once consistency between the model coordinates and the experimental data is obtained through a suitable transformation, model updating has been performed solving a constrained convex optimization problem. Constraints also include results from static tests. Some tools to improve the problem conditioning are also proposed in the formulation adopted, to handle large dimensional models and achieve reliable results. The method has been experimentally applied to a challenging system: a planar six-bar linkage manipulator. The results prove their capability to improve the model accuracy in terms of eigenfrequencies and mode shapes.

A Model Reduction Strategy for Flexible-Link Multibody Systems

In this paper a novel strategy is presented to perform the reduction at system level of flexible-link multibody models based on the equivalent rigid-link system modeling approach. Such a strategy is aimed at obtaining reduced models ensuring an accurate description of the full-order model dynamics in a frequency range of interest and in a wide subset of the workspace. Starting from the well-known Craig-Bampton reduction technique, and the interior mode ranking method a configuration-dependent reduction transformation is formulated, which allows obtaining a minimum-size reduced model, accurately describing the dynamics of interest. The proposed strategy has been validated by applying it to the model of a flexible-link planar manipulator driven by three motors.

Experimental Evaluation and Comparison of Low-Cost Adaptive Mechatronic Grippers

Nowadays, robotic systems are not an exclusive of the industry environment anymore. Indeed, in the last decades, they assumed an important role in other application fields such as medicine (e.g. robot-assisted surgery) and agriculture (e.g. fruit picking). To meet the requirements of these new fields of application, this transition has involved both an adaptation of old-technologies and the development of new ones.