Andrei Craifaleanu

Theoretical and Experimental Studies on Magnetic Dampers

The proper operation and reliability of numerous mechanical devices depends on reducing the vibrations of embedded components, modeled as multi-degree-of-freedom dynamic systems. This can be achieved by using various types of absorbers. The design of such devices is conditioned by the understanding of the variation of their technical characteristics with the constructive parameters. The present paper is dedicated to a special type of dampers, based on the use of the magnetic phenomenon. However, available empirical formulae for the damping characteristics of magnetic dampers do not reveal all significant dependencies. Based on theoretical, numerical and experimental methods, the paper brings a number of contributions concerning the relation between the damping characteristics of a magnetic damper and some of its constructive parameters. Variation curves, useful both for theoretical studies and practical applications, are plotted.

Study of Vibrations of a Robotic Arm, Using the Lagrange Equations with Respect to a Non-inertial Reference Frame

The paper studies the free vibrations of a robotic arm, located on a rotating platform. The robotic arm is modeled as a system with a finite number of degrees of freedom, consisting of elastically coupled rigid bodies. The differential equations of the free vibrations are obtained using the Lagrange equations formalism, in a generalized form, valid with respect to a non-inertial reference frame. The influence of the kinematic parameters of the platform motion upon the eigenfrequencies of the robotic arm is analyzed, considering two configurations of the system.

Reduction of Arbitrary Rigid Bodies to Inertially Equivalent Discrete Systems of Material Points

In a previous paper of the authors, a general method was presented for the reduction of a rigid plane plate to a discrete system of material points, with equivalent inertial properties (mass, center of mass, tensor of inertia). The present paper generalizes the method for rigid bodies of arbitrary shape, i.e. for material volumes, as well as for curved shells. It is shown that a homogenous ellipsoid can be reduced to a system of seven material points placed in significant geometrical points of the body. Next, starting from the concept of ellipsoid of inertia, an equivalent homogenous ellipsoid is determined for an arbitrary body. The method simplifies considerably the calculation of various mechanical quantities, such as moments and products of inertia with respect to rotated Cartesian coordinate systems, angular momentum and kinetic energy, of rigid bodies part of all types of mechanical devices or structures.

Caveats in Modeling the Elasto-Plastic Behavior of Materials to Alternate Loads

Bilinear hysteretic models are an attractive choice in modeling the elasto-plastic behavior of various materials to alternate loads, due to their simplicity and ease of interpreting the results. However, choosing the parameters of the model without taking into account some restrictions can lead to highly unrealistic results. These restrictions are analyzed, and the allowable ranges for the model parameters are determined. The conclusions can be used for a wide range of plastic and composite materials. The significant errors that can occur in the case of the inadequate selection of model parameters are illustrated by a practical application.

Use of Equimomental Systems in Calculating Inertial and Dynamic Quantities of Plane Plates

The paper proposes a method for the reduction of an arbitrary-shape plane plate to a symmetrical discrete system of material points, with the same center of mass and the same tensor of inertia. It is shown, first, that an elliptical plate can be reduced to a symmetrical system of five material points, with a spatial distribution directly related to the shape of the plate. The results are subsequently generalized for plane plates of arbitrary shape. By using the reduction procedure, various mechanical quantities can be calculated more simply, as compared to the traditional methods. The proposed method finds application in the dynamic, vibration and structural analysis of complex mechanical systems that include rigid plane plates, such as industrial robots.

Generalization of the Lagrange Equations Formalism, for Motions with Respect to Non-Inertial Reference Frames

The paper presents an original generalization of the Lagrange equations of the second kind, for motions with respect to reference frames in arbitrary motions. The traditional form of the equations is modified by adding certain supplementary terms. Calculation methods are presented for these terms and some conclusions useful in practical applications are drawn. For validation, the new formalism is illustrated on the application of the Foucault pendulum. The results are in full agreement with those obtained by traditional methods. The formalism can be used to determine the motions of various mechanical systems, with respect to large size movable bodies (such as planets or orbital stations), that are not influenced by the relative motion of the studied parts.

Analytic-Experimental Method for Determining the Eccentricity of a Cantilever Rotor

Various mechanical systems contain highspeed rotating bodies, which are affected by small eccentricities. During operation, such shape irregularities are the cause of vibrations that can produce malfunctioning, as well as early wear development in the bearings and in other parts of the devices. In order to control and reduce these undesirable effects, the eccentricity of the rotors must be determined, which, due to their geometrical complexity, can be seldom achieved by direct measurement. The paper proposes an analytic-experimental method for determining the eccentricity of a cantilever rotor, based on the statistical processing of data obtained by measuring the vibrations of its bearing. The application of the method is illustrated on a laboratory testing model built by the authors.

Study on Vibration Transmission, with Application to the Calibration of a Measuring Stand

The paper studies the vibration transmitted by a mechanical oscillating system to its fixing device. The influence of the mechanical characteristics (inertial and elastic) of the device on the quantities specific to the free and forced vibration, respectively, of the principal system, is analyzed. In this context, the paper investigates the possibility to correlate the vibrations of the mechanical system with the vibrations measured on the fixing device. The conclusions of this study can be used for the calibration of vibration measuring stands. In the final part, a practical application is presented, aimed to compare the theoretical results with the data obtained by measurements performed on an experimental model built by the authors.

Virtual Laboratory for the Study of Kinematics in Engineering Faculties

In engineering faculties, kinematics is studied during the first year, providing the basic knowledge for understanding, modeling and designing mechanical systems. The traditional method of teaching kinematics uses drawings and mathematical equations to explain the motion of rigid bodies forming various mechanisms. From the experience of the authors, due to this approach students often tend to regard kinematics as excessively abstract, having difficulties in understanding the correspondence between analytical expressions and the actual behavior of mechanisms. The Virtual Laboratory of Kinematics VLK is an attempt to overcome these difficulties, by allowing students to visualize and interactively modify the motion and configuration of basic mechanisms. VLK consists of a package of software applications, which has been tested in theoretical mechanics classes during the past few years. The favorable feedback received from students encouraged the authors to improve it gradually and, recently, to completely re-write it, also implementing additional features and capabilities.