Electric heater mathematical model for cyber-physical systems

The article discusses the heat and mass transfer dynamic model for an electric heater with lumped parameters, which allows transient processes simulation for the main influences. The proposed model is recommended to be used in cyber-physical systems for forecasting and evaluating the effectiveness of control systems integrated into a single information management system. The developed model can be used by specialists for the analysis and synthesis of control systems for balanced ventilation systems or industrial air conditioners. As an example, a numerical simulation of transient processes along the action main channels for an electric heater HE 36/2 manufactured by VTS CLIMA was carried out. The significant advantage of the proposed model is the possibility for using it for the synthesis and analysis of multidimensional control systems.

Lumped-Parameters Thermal Network of PM Synchronous Machines for Automotive Brake-by-Wire Systems

Thermal analysis represents a key factor in electrical machine design due to the impact of temperature increase on insulation lifetime. In this context, there has been a wide investigation on thermal modeling, particularly for machines used in harsh working conditions. In this perspective, brake-by-wire (BBW) systems represent one of the most challenging applications for electrical machines used for automotive smart actuators. Indeed, electro-actuated braking systems are required to repeatedly operate the electric machine in high overload conditions in order to limit the actuator response time, as well as to enhance gravimetric and volumetric specific performance indexes. Moreover, BBW systems often impose unconventional supply conditions to the electric machine, consisting of dc currents in three-phase windings to keep the rotor fixed during the braking intervals. However, a dc supply leads to uneven temperature distributions in the machine, and simplified thermal models may not accurately represent the temperature variations for the different machine parts. Considering such unconventional supply conditions, this paper initially investigates the applicability of a conventional lumped-parameters thermal network (LPTN) based on symmetry assumptions for the heat paths and suitable for surface-mounted PM synchronous machines used in BBW systems. An extensive test campaign consisting of pulses and load cycle tests representative of the real machine operations was conducted on a prototype equipped with several temperature sensors. The comparison between measurements and predicted average temperatures, together with insights on the unbalanced heat distribution under the dc supply obtained by means of finite element analyses (FEA), paved the way for the proposal of a phase-split LPTN with optimized parameters. The paper also includes a critical analysis of the optimized parameters, proposing a simplified, phase-split lumped-parameters thermal model suitable to predict the temperature variations in the different machine parts for PM synchronous electric machines used in BBW systems.

Recent Developments in the Modelling of Transformer Windings

The paper provides a review of the modelling techniques used to simulate the frequency response of transformer windings. The aim of the research and development of modelling methods was to analyze the influence of deformations and faults in the windings on the changes in the frequency response. All described methods are given with examples of the modelling results performed by the authors of this paper and from literature sources. The research is prefaced with a thorough literature review. There are described models based on lumped parameters with input data coming from direct calculations based on the winding geometry and obtained from FEM modelling software and models considering the wave phenomena in the windings. The analysis was also performed for practical problems in winding modelling: the influence of windings other than the modelled one and the influence of parallel wires in a winding.

Development of an electrical analogue for modeling natural vibrations of a viscoelastic structure with piezoelectric element

This paper focuses on the development of an equivalent electrical model with lumped parameters capable of describing the natural vibrations of an electromechanical system comprising a viscoelastic structure with a piezoelectric element attached to its surface. The important advantage of the model is that it takes into account the energy losses associated with the viscoelastic properties of the material of the main structure. Two versions of the equivalent electric analogue of the initial electro-viscoelastic system in the form of electric circuits, the elements of which are described by the real or complex quantities, are considered. The approaches to the formulation of the problem of natural vibrations in the developed electric analogue are based on Kirchhoff’s laws for electric circuits and Ohm’s law for alternating current. Special attention is paid to the identification of model parameters. A procedure for determining the parameters for the equivalent electrical model is based on the results gained from the solution of a coupled problem of natural vibrations of the initial electromechanical system; problem formulation is also given here. The effectiveness and reliability of the developed equivalent electric models with lumped parameters for the determination of complex eigenfrequencies of the electromechanical system containing energy dissipation elements are demonstrated by analyzing the behavior of structures in the form of a rectangular plate and a semi-cylindrical shell.

A Lumped Parameter Approach for Analysing a Metamaterial Beam Based Piezoelectric Energy Harvester Around Fundamental Resonance

This paper proposes a lumped parameter approach to simplify the modelling of a metamaterial based PEH to predict its energy harvesting performance around the fundamental resonance. The metamaterial based PEH consists of a host beam with a piezoelectric patch bonded at the clamped end. A series of local resonators are attached onto the host beam. In the first case study, the local resonators are modelled as mass-spring systems. By applying Rayleigh’s method and approximating the fundamental mode shape by the static deflection, the host beam is represented by a SDOF system. The equivalent lumped parameters are assumed to concentrate at the tip of the host beam and their explicit expressions are presented. Though the local resonators are identical, they have different influences on the host beam when being attached at different positions. To reflect the interaction degree (i.e., reacting force) between the local resonator and the host beam, a scaling factor that is a function of the attaching position is derived. On the other hand, due to the action of the local resonators, the fundamental mode shape of the host beam is actually changed. Based on the linear superposition principle, the static deflection approximated fundamental mode shape is corrected and the electromechanical coupling coefficient that is sensitive to the slope of the mode shape is updated to improve the accuracy. Based on the derived equivalent lumped parameters and correction factors, a multiple-degree-of-freedom (MDOF) model is constructed to predict the dynamic behavior of the metamaterial based PEH with mass-spring resonators. A corresponding finite element model is built to verify the developed MDOF model. In the second case study, the local resonators are modelled as practical parasitic beams. The parasitic beams are converted into equivalent lumped systems as well. However, the lumped parameters are the effective parameters at the beam tip. For the force interaction at the root of a parasitic beam, a factor is derived to correct the reaction force when a parasitic beam is represented by a SDOF mass-spring system. Using the reaction force correction factor, a MDOF model for the metamaterial based PEH with beam-like resonators is also established and verified by the finite element model.