Giuseppe Catania

A computer-aided prototype system for NC rough milling of free-form shaped mechanical part-pieces

Abstract A prototype computer-aided manufacturing module for rough milling of free-form mechanical moulds is proposed. The system allows direct modelling of the shape of the material to be removed, by starting from the geometry of the stock and of the final part-piece. A modelling engine, based on rational bivariate and trivariate tensor-product B-spline patches, was developed to ensure complete geometric coverage, allowing common analytic geometric items such as planes, quadrics, and blocks to be exactly modelled. Methods for the evolution of the milling layers, the choice of isoparametric NC tool-paths and their piecewise approximation are proposed; the procedures work in the context of three-axis machining by end-mill cutters. Technological considerations about the main cutting force the follow: it results that fine tuning of the milling feed rate can be computed by geometric evaluation of the depth and width of cut. To demonstrate the feasibility of the approach, an application example concerning mould manufacturing is reported.

Analytical Modelling and Experimental Identification of Viscoelastic Mechanical Systems

In the present study non-integer order or fractional derivative rheological models are applied to the dynamical analysis of mechanical systems. Their effectiveness in fitting experimental data on wide intervals of frequency by equivalent damping ratio valid for fractional derivative models is introduced, making it possible to test their ability in reproducing experimentally obtained damping estimates. A numerical procedure for the experimental identification of the parameters of the Fractional Zener rheological model is then presented and vibrations.

Global asymptotic stability of bone remodeling theories: a new approach based on non-linear dynamical systems analysis.

Mathematical tools for the analysis of nonlinear dynamical systems are applied to the study of stability of bone remodeling theories. As a practical application, the same problem studied by Harrigan and Hamilton (1992) and Cowin et al. (1994b) is analysed using these tools, and their findings on the necessary and sufficient conditions to ensure local asymptotic stability are easily confirmed. Using a general approach based on Lyapunovs method the same condition has been found to be necessary and sufficient also for the global asymptotic stability, thus confirming a result obtained by Harrigan and Hamilton (1994) by variational methods applied to finite-element models. The proof is based on the discretization of the spatial domain but the results for the continuum can be easily extrapolated.

Spectral modeling of vibrating plates with general shape and general boundary conditions

The analysis and design of lightweight plate structures require efficient computational tools, because exact analytical solutions for vibrating plates are currently known only for some standard shapes in conjunction with a few basic boundary conditions. This paper deals with vibration analysis of Kirchhoff plates of general shape with non-standard boundary conditions, adopting a Rayleigh-Ritz approach. Three different coordinate mappings are considered, using different kinds of functions: 1) trigonometric and polynomial interpolation functions for mapping the shape of the plate, 2) trigonometric and polynomial interpolation functions for mapping a constraint domain of general shape, 3) products of linearly independent eigenfunctions evaluated from a standard beam in flexural vibration for describing the transverse displacement field of the plate. Flexural free vibration analysis of different shaped plates is then performed using the same approach: skew, trapezoid and triangular plates, plates with parabolic curved edges, sectors of circular plates, circular and elliptic annular plates. Purely elastic plates are considered, but the method may also be applied to the analysis of viscoelastic plates. The results are compared with those available in the literature and using standard finite element analysis.

A Condensation Technique for Finite Element Dynamic Analysis Using Fractional Derivative Viscoelastic Models

Fractional derivative rheological models are known to be very useful for describing the viscoelastic behaviour of materials, especially of polymers, and when applied to dynamic problems, the resulting equations of motion, after a fractional state-space expansion, can still be studied in terms of modal analysis. The increase in matrix dimensions produced by this expansion, however, is often so fast as to make the calculations too cumbersome for finite element applications. This article presents a condensation technique based on the computation of two reduced-size eigenproblems. The rheological model adopted is the fractional Zener (fractional standard linear solid) model, but the same methodology can be applied to problems using different fractional derivative linear models.

Technical NoteGlobal asymptotic stability of bone remodeling theories: a new approach based on non-linear dynamical systems analysis

Mathematical tools for the analysis of nonlinear dynamical systems are applied to the study of stability of bone remodeling theories. As a practical application, the same problem studied by Harrigan and Hamilton (1992) and Cowin et al. (1994b) is analysed using these tools, and their findings on the necessary and sufficient conditions to ensure local asymptotic stability are easily confirmed. Using a general approach based on Lyapunovs method the same condition has been found to be necessary and sufficient also for the global asymptotic stability, thus confirming a result obtained by Harrigan and Hamilton (1994) by variational methods applied to finite-element models. The proof is based on the discretization of the spatial domain but the results for the continuum can be easily extrapolated.

Crack localization in non‐rotating shafts coupled to elastic foundation using sensitivity analysis techniques

The problem of damage and crack detection in structural components has acquired an important role in recent years. Since the presence of cracks in a structure may alter its vibrational characteristics, the estimation of such variations can be used to detect cracks and damage, and to monitor the integrity of structures. The use of fast, easy and inexpensive non‐destructive testing is thus a major task. In this paper, sensitivity analysis by measurement of the reduction of eigenfrequencies was utilized to localize a crack in a non‐rotating shaft coupled to an elastic foundation. The shaft was modeled by the finite element method and coupled to an experimentally identified foundation model. The detection of a crack with different depths and orientations was verified experimentally and a good agreement between actual and detected crack positions was achieved. Finally easiness, effectiveness, applicability of the method and its extensions are also shown.

A Multibody Motorcycle Model for the Analysis and Prediction of Chatter Vibrations

The chatter phenomenon, appearing during high speed cornering maneuvers performed by racing motorcycles, consists of a self-excited vertical oscillation of both the front and rear unsprung masses in the range of frequency between 17 and 22 Hz. The suspensions are not generally able to dampen the above vibrations which start from the rear wheel and suddenly propagate to the front wheel during the corner entry phase, making the vehicle’s handling unpredictable and, ultimately, weakening the overall performance, that is the lap time. It is not clear which is the determining factor causing this phenomenon. Therefore, numerical simulation on a three dimensional, multibody motorcycle model is proposed, taking into account the effects of the major parameters involved, in order to highlight which of them takes part in the vibration. Accurate models for tire and drivetrain have been developed, making it possible to consider tire carcass deformability, chain transmission in both traction and braking states, full drivetrain inertia and anti-hop clutch effect. A critical maneuver experimentally measured on the race track is analyzed. The modal response of the linearized system is evaluated for several configurations extracted from the maneuver. The above maneuver is then simulated with the model, showing the actual vibration uprising. A critical discussion of the possible physical interpretations of the phenomenon is given.Copyright

B-spline Shell Finite Element Updating by Means of Vibration Measurements

Within the context of structural dynamics, Finite Element (FE) models are commonly used to predict the system response. Theoretically derived mathematical models may often be inaccurate, in particular when dealing with complex structures. Several papers on FE models based on B-spline shape functions have been published in recent years (Kagan & Fischer, 2000; Hughes et al, 2005). Some papers showed the superior accuracy of B-spline FE models compared with classic polynomial FE models, especially when dealing with vibration problems (Hughes et al, 2009). This result may be useful in applications such as FE updating. Estimated data from measurements on a real system, such as frequency response functions (FRFs) or modal parameters, can be used to update the FE model. Although there are many papers in the literature dealing with FE updating, several open problems still exist. Updating techniques employing modal data require a previous identification process that can introduce errors, exceeding the level of accuracy required to update FE models (D’ambrogio & Fregolent, 2000). The number of modal parameters employed can usually be smaller than that of the parameters involved in the updating process, resulting in ill-defined formulations that require the use of regularization methods (Friswell et al., 2001; Zapico et al.,2003). Moreover, correlations of analytical and experimental modes are commonly needed for mode shapes pairing. Compared with updating methods using modal parameters as input, methods using FRFs as input present several advantages (Esfandiari et al., 2009; Lin & Zhu, 2006), since several frequency data are available to set an over-determined system of equations, and no correlation analysis for mode pairing is necessary in general. Nevertheless there are some issues concerning the use of FRF residues, such as the number of measurement degrees of freedom (dofs), the selection of frequency data and the ill-conditioning of the resulting system of equations. In addition, common to many FRF updating techniques is the incompatibility between the measurement dofs and the FE model dofs. Such incompatibility is usually considered from a dof number point of view only, measured dofs being a subset of the FE dofs. Reduction or expansion techniques are a common way to treat this kind of incompatibility (Friswell & Mottershead, 1995). A more general approach should also take into account the adoption of different dofs in the two models. As a matter of result, the adoption of B-spline functions as shape functions in a FE

A Coupled Theoretical-Experimental Dynamical Model for Chatter Prediction in Milling Processes

Productivity of high speed milling operations can be seriously limited by chatter occurrence. Several studies on this self-excited vibration can be found in the literature: simple models (1 or 2 dofs) are proposed, i.e. a lumped parameter model of the milling machine being excited by regenerative, time-varying cutting forces. In this study, a model of the milling machine is proposed: the machine frame and the spindle were modeled by an experimentally evaluated modal model, while the tool was modeled by a discrete modal approach, based on the continuous beam shape analytical eigenfunctions. The regenerative cutting force components lead to a set of Delay Differential Equations (DDEs) with periodic coefficients; DDEs were numerically integrated for different machining conditions. The stability lobe charts were evaluated using the semi-discretization method [6–7] that was extended to n dofs models (with n >2). Differences between the stability charts obtained by the low dofs models and the stability charts obtained by the new n dofs model are pointed out. Time histories and spectra related to the vibratory behavior of the system were numerically obtained to verify the effectiveness of the stability charts obtained with the n dofs modal model.Copyright