Dynamics Of Mechanical Systems Research Articles

PREFACE

The object of the scientific and technical conference "Applied Mechanics and System Dynamics" is the analysis of the current state, trends and prospects for the development of applied mechanics and system dynamics with the aim of improving technology and production and creating new-generation equipment.The conference addresses topical issues of development and research on the problems of mechanical engineering, strength and dynamics of mechanical systems.

A novel feature selection method to boost variable predictive model–based class discrimination performance and its application to intelligent multi-fault diagnosis

Effective and efficient incipient fault diagnosis is vital to the maintenance and safe application of large-scale key mechanical system. Variable predictive model–based class discrimination is a recently developed multiclass discrimination method and has been proved to be potential tool for multi-fault detection. However, the vibration signals from dynamic mechanical system always present non-normal distribution so that the original variable predictive model–based class discrimination might produce the inaccurate outcomes. An improved variable predictive model–based class discrimination method is introduced at first in this work. At the same time, variable predictive model–based class discrimination will suffer computation difficulty in the case of high-dimension input features. Therefore, a novel feature selection method based on similarity-fuzzy entropy is presented to boost the performance of the variable predictive model–based class discrimination classifier. In this method, the ideal feature vectors are optimized to acquire more accurate similarity-fuzzy entropies for the input features. And, the one with the largest similarity-fuzzy entropy value is removed to refine input feature subset. Moreover, the optimal input features are repeatedly evaluated using the improved variable predictive model–based class discrimination classifier until the expected results are achieved. Finally, the incipient multi-fault diagnosis model for a hydraulic piston pump is established and verified by experimental test. Some comparisons with commonly used methods were made, and the results indicate that the proposed method is more effective and efficient.

Mixed mechanical-metrological approach to quantify the fractographic damage in mechanical components subjected to cyclic loading

The purpose of this paper is to present a mixed mechanical-metrological procedure, based on a fractographical approach, capable of correlating the fracture deformation behaviour with the fatigue loading history. The degradation mechanisms, which are related to the degree of fatigue damage, are identified from the changes in the dynamic response of the mechanical system. These changes, recorded during the tests by means of uniaxial acceleration sensors, are compared to different surface texture parameters, namely height parameters and material/void parameters, determined for both parts of the fracture surfaces after fatigue damage, and with the force needed for complete failure. The results show a direct relationship between the degree of fatigue damage, accounted for by the changes in the uniaxial acceleration sensors, and the surface texture parameters. This connection between the mechanical system dynamics and the surface metrology can provide a more precise fitness-for-service assessment.

Investigation of rigid dynamic systems on the example of modelling a tape drive mechanism

The features of modeling the dynamics of mechanical systems on the example of the operation of the tape drive mechanism related to real technological processes are stated. An approach to solving stiff systems of differential equations by the numerical-analytical method is noted. The approach is based on solving systems of higher-order differential equations using elementary functions using procedures for precision search for the roots of the characteristic polynomial of the system. A mathematical model of the tape drive mechanism of a VCR is given as an example of a precision electromechanical object.

Asymptotic Invariant Surfaces for Non-Autonomous Pendulum-Type Systems

Invariant surfaces play a crucial role in the dynamics of mechanical systems separating regions filled with chaotic behavior. Cases where such surfaces can be found are rare enough. Perhaps the most famous of these is the so-called Hess case in the mechanics of a heavy rigid body with a fixed point. We consider here the motion of a non-autonomous mechanical pendulum-like system with one degree of freedom. The conditions of existence for invariant surfaces of such a system corresponding to non-split separatrices are investigated. In the case where an invariant surface exists, combination of regular and chaotic behavior is studied analytically via the Poincare-Mel’nikov separatrix splitting method, and numerically using the Poincare maps.

Learning to Model the Dynamics of Mechanical Systems with the Method of Solving Educational and Research Problems

The methodological features of using software systems for modeling the dynamics of mechanical systems for solving educational research problems are considered. The traditionally established approach to studying the foundations of modeling the dynamics of technical systems is largely based on mastering the corresponding mathematical tools. With regard to modeling the dynamics of systems of solids, the mentioned approach involves, first of all, the development of skills in the preparation of ordinary differential equations (ODEs). At the same time, the formation of a mechanical calculation scheme as an «object of application of mathematics» becomes a natural stage of mathematical research, and the selection of simplifying assumptions that allow one or another idealization to correspond to a real object is carried out consciously taking into account the desire for certain internal properties of the mathematical model (for example, type and order of the ODE system). An important feature of modern systems for modeling the dynamics of solid’s systems is the ability to describe the object under study directly in terms of the subject area. This feature provides an increase in the effectiveness of modeling in solving design and engineering and scientific research problems and allows you to save a qualified specialist from a laborious routine. At the same time, as experience shows, in the process of solving educational and research problems, due to the mentioned features of modern software, students have certain difficulties in mastering the fundamental conceptual base of the corresponding discipline (physics, electrical engineering, theoretical mechanics, theory of automatic control, fundamentals of computer aided design). The article gives an example of an educational research task focused on overcoming these difficulties.

Динамика механизма удержания оправки прошивного стана трубопрокатного агрегата

The paper presents the results of the vibrodiagnostics of a centering machine mechanism for holding piercing mill mandrel N1 of the pipe-rolling plant (PRP) 350. In the paper, it is established that vibration acceleration of a bearing roller lever of the centering machine mechanism for holding piercing mill mandrel during milling of an Æ282х50 mm shell, steel 20 reaches 5…12 m/s2, and of the upper roller’s vibration frequency is 33.3 Hz. The paper presents the results of the thickness measuring of the Æ282х50 shell, steel 20 after using the piercing mill N1 350. The results shows the distinctive influence of the dynamics of the milling holding mechanism rod. The system is put forth for calculating the energy-power parameters during the realization of the technical process for making shells of the required specifications in a piercing mill. The paper establishes the value of the milling axial resistance to the flow of the milled metal (taking the calibration values into account). The paper presents a refined system for making a dynamic model for the piercing bill milling holding mechanism rod with the milling calibration parameters taken fully included. A differential equation for the milling rod movement is made, specifically for the dynamic model of the PRP piercing mill mechanical system. The dynamic values of the mechanical system are refined, which is used as a starting point for solving the tasks dealing with the analysis of the PRP piercing mill milling rod’s vibroactivity state. In order to decrease rod vibroactivity levels, the paper recommends choosing rational milling calibration and to set the shell milling modes using mechanical system dynamics modelling during the corresponding stages of the design of technological processes. The paper pro-poses a scheme for modernization of the PRP 350 piercing bill exit side by switching the centering machine rod system holding bridges gear to proportional hydraulics. Keywords: piercing mill, vibration diagnostics, thickness measurement, piercing, sleeve; difference in wall thickness, energy-power parameters, calibration, mandrel, vibroactivity, dynamics, mandrel retention mechanism.

Information Dynamic Correlation of Vibration in Nonlinear Systems.

In previous studies, information dynamics methods such as Von Neumann entropy and Rényi entropy played an important role in many fields, covering both macroscopic and microscopic studies. They have a solid theoretical foundation, but there are few reports in the field of mechanical nonlinear systems. So, can we apply Von Neumann entropy and Rényi entropy to study and analyze the dynamic behavior of macroscopic nonlinear systems? In view of the current lack of suitable methods to characterize the dynamics behavior of mechanical systems from the perspective of nonlinear system correlation, we propose a new method to describe the nonlinear features and coupling relationship of mechanical systems. This manuscript verifies the above hypothesis by using a typical chaotic system and a real macroscopic physical nonlinear system through theory and practical methods. The nonlinear vibration correlation in multi-body mechanical systems is very complex. We propose a full-vector multi-scale Rényi entropy for exploring the chaos and correlation between the dynamic behaviors of mechanical nonlinear systems. The research results prove the effectiveness of the proposed method in modal identification, system dynamics evolution and fault diagnosis of nonlinear systems. It is of great significance to extend these studies to the field of mechanical nonlinear system dynamics.

Методи розв'язування початкової задачі з двосторонньою оцінкою локальної похибки

Багато прикладних задач, наприклад для проектування радіоелектронних схем, автоматичних систем управління, розрахунку динаміки механічних систем, задачі хімічної кінетики загалом зводяться до розв'язування нелінійних диференціальних рівнянь і їх систем. Точні розв'язки досліджуваних задач можна отримати лише в окремих випадках. Тому потрібно використовувати наближені методи. Під час дослідження математичних моделей виникає потреба знаходити не тільки наближений розв'язок, але й гарантовану оцінку похибки результату. Використання традиційних двосторонніх методів Рунге-Кутта призводить до істотного збільшення обсягу обчислень. Ланцюгові (неперервні) дроби набули широкого застосування у прикладній математиці, оскільки вони за відповідних умов дають високу швидкість збіжності, монотонні та двосторонні наближення, мають слабку чутливість до похибки заокруглення. У роботі виведено методи типу Рунге-Кутта третього порядку точності для розв'язування початкової задачі для звичайних диференціальних рівнянь, що базуються на неперервних дробах. Характерною особливістю таких алгоритмів є те, що за певних значень відповідних параметрів можна отримати як нові, так і традиційні однокрокові методи розв'язання задачі Коші. Запропоновано розрахункові формули другого порядку точності, які на кожному кроці інтегрування дають змогу без додаткових звертань до правої частини диференціального рівняння отримати не тільки верхні та нижні наближення до точного розв'язку, а також дають інформацію про величину головного члена локальної похибки. Для практичної оцінки похибки на кожному кроці інтегрування у разі використання односторонніх формул типу Рунге-Кутта порядку p застосовують двосторонні обчислювальні формули порядку (p–1). Зауважимо, що використовуючи запропоновані розрахункові формули в кожному вузлі сітки будуть отримані декілька наближень до точного розв'язку, порівняння яких дає корисну інформацію, зокрема в питанні вибору кроку інтегрування, або в оцінці точності результату.

Advances in Mechanical Systems Dynamics

Modern dynamics was established many centuries ago by Galileo and Newton before the beginning of the industrial era [...]

Human Driver Interaction with Self-Balancing Vehicles’ Dynamics

This paper deals with a research activity concerning two-wheel self-balancing vehicles, with particular reference to the interaction between the driver and the vehicle’s dynamics. The usefulness and the flexibility of this kind of vehicle make it a very interesting device for smart mobility. In particular, a dynamical model of a two wheeled self-balancing vehicle and of his driver is presented here. It consists of a Multibody model of a real vehicle, designed and built in the Mechatronics and Mechanical Systems Dynamics lab. of our University, and of a driver model with 3 driven joints. The overall 3D model developed allows simulating the interaction between human (driver) and machine (vehicle), taking into consideration also the coupling between longitudinal motion and turn. The vehicle’s control system has been synthesized using the pole placement approach, starting from a simplified 2 dof planar model of the vehicle, considering the driver fixed with vehicle chassis. Through proper linearization, a state space description has been obtained and used to tune pole position, not only for stability but also for optimal response. Through co-simulation between the controller (modelled in Matlab-Simulink) and the vehicle-driver system (modelled with MSC.Adams) several tests have been performed on the full model, to assess its behaviour under different conditions like set point following and disturbance rejection, considering both a passive and an active driver. As far as the influence of the driver on the vehicle’s dynamics is concerned, the paper shows that it is possible to detect the dynamic forces exerted by the driver on the vehicle. According to these signals, control strategies to switch the vehicle in safe mode can be implemented. In the paper, some issues related to safety have been highlighted.

Vibration based modelling of acoustic emission of rolling element bearings

Vibration response has been extensively used for fault diagnosis, condition monitoring and root cause analysis of issues in the smooth operation of mechanical systems. In recent years, acoustic emission (AE) measurement and analysis have found significant applications in the field of in-situ as well as off-site fault diagnosis and condition monitoring of machines. To monitor vibration or AE of system, sensors are placed close to rolling element bearing (REB), but in fact, REBs themselves are sometimes the source of the problem in the machinery. As such, in all the dynamic mechanical systems, REBs are one of the most critical components, in regards to their usefulness as well as failure. This has led to extensive analytical and experimental research on REBs. To study the dynamic features and inherent characteristics of REBs, many researchers have formulated multi-body dynamic models of REBs. The results of these models have been well supported by experimental evidence. Contrary to this, very few attempts can be located in literature, which aim at modelling of acoustic emission of REBs and hence this paper is tasked with the same. A novel approach for AE modelling is used in this paper, and the proposed model is a blend of multi-body dynamic model and asperity based acoustic emission model of REB. The dynamic model of REB is solved to compute the contact deformations and thus contact forces. From these contact forces and lubricant film thickness; asperity forces and their deformations are computed and then fused into the AE model to compute the root mean square (rms) value of resultant AE signal. The developed model is deployed for analyzing the effect of load, speed, and radial clearance on AE. The results show that AE increases as load increases, it increases as speed increases up to a certain value and then decreases, and finally, as clearance increases, the AE decreases.

Model Reduction for Second‐Order Dynamical Systems Revisited

AbstractSecond‐order control systems are used to describe the dynamics of mechanical and vibrational systems, and in particular, their response to excitations. In this article, we discuss model order reduction (MOR) of such systems. A particular focus is on preserving the second‐order structure and physical properties such as stability and passivity.

Improved Damping and High Strength of Graphene-Coated Nickel Hybrid Foams.

Direct growth of graphene on the metal surface opens a door for obtaining high-performance composites in a simple way. In order to obtain both high strength and enhanced damping property of the porous metal, we prepared graphene-coated nickel hybrid foams by chemical vapor deposition technique and investigated the static and dynamic mechanical properties using a dynamic mechanical analyzer and vibration testing systems in detail. We found that the presence of graphene layers could greatly improve both mechanical strength and damping properties of nickel foams. The graphene-coated nickel hybrid foams exhibited high yield strength, compressive modulus, and damping ratio, increased by 46, 22, and 53% in comparison with those of nickel foams. Such significant graphene reinforcement in mechanical and damping properties is mainly attributed to the strong interfacial bonding, remarkable confinement effect, and rich interfaces in hybrid foams. By virtue of its high mechanical strength and enhanced damping properties, the graphene/nickel hybrid foams have great potential to be used as multifunctional composite materials in many fields.

Well posed formulations of holonomic mechanical system dynamics and design sensitivity analysis

Manifold theoretic ordinary differential equations of motion for holonomic mechanical systems that depend on problem data, or design variables, are shown to be well posed; i.e., they have a unique solution that depends continuously on problem data. It is proved that these differential equations are equivalent to the d’Alembert variational formulation and the index 3 Lagrange multiplier formulation of differential-algebraic equations of motion, which are also shown to be well posed. These results provide a foundation for dynamic system design sensitivity analysis, which requires differentiability of solutions of the equations of motion with respect to design variables.

T2-ETS-IE: A Type-2 Evolutionary Takagi–Sugeno Fuzzy Inference System With the Information Entropy-Based Pruning Technique

We introduce a new nonlinear system identification technique, leveraging the benefits of the Type-2 Evolutionary Takagi–Sugeno (T2-ETS) fuzzy system. The major advantage of our proposed system identification technique is mainly due to its ability to learn-from-scratch while accommodating the footprint-of-uncertainties (FoUs). To support its mission to achieve a reasonably high prediction accuracy for uncertain nonlinear dynamic systems, we also introduce a new type reduction method to convert Type-2 fuzzy systems into their Type-1 counterparts. As a part of its efficient pruning strategy, the proposed system incorporates the concept of information entropy to avoid over fitting, which is a highly undesirable issue in modeling. We demonstrate the effectiveness of our system identification technique in achieving a delicate balance between minimizing the complexity of the acquired fuzzy model and maximizing the prediction accuracy. To highlight the efficacy of our algorithm, we employ a set of challenging pH neutralization data, known for its substantial nonlinearity, in addition to the dynamics of a nonlinear mechanical system. We conclude our research by conducting a rigorous comparative study to quantify the relative merits of our proposed technique with respect to the previous ETS algorithm (as its predecessor), the well-known KM-type reduction technique, and the higher-order discrete transfer functions, widely implemented in most conventional mathematical modeling techniques.

Multipoint Constraints with Lagrange Multiplier for System Dynamics and Its Reduced-Order Modeling

A general formulation is presented to linear multipoint constraints, underlying that the linkages of mechanical system dynamics are governed by kinematic constraint conditions. Both rigid and interpolated multipoint constraints are then described in a formulation based on the Lagrange multiplier adjunction. The proposed formulation can directly offer reaction forces, which are essential information to modeling linkages of mechanical components. In particular, in the interpolated multipoint constraints, the proposed formulation is more numerically stable than the conventional master–slave formulation that has invertible issues with respect to choice of the constraint nodes. The other aim of the work is to condense the original equations of motion into degrees of freedom at certain nodes only, named as condensation nodes, for better computational and modeling efficiencies. In the proposed Lagrange multiplier based formulation, accuracy of the reduced model can be improved by dynamic correction. The performance of the proposed method is theoretically evaluated by comparing the master–slave elimination, which is the most widely used approach of the multipoint constraints, and it is demonstrated through numerical examples.

Inverse dynamics of underactuated flexible mechanical systems

AbstractAn alternative approach to the inverse dynamics of flexible mechanical systems is presented. In contrast to a sequential discretization in space and time a simultaneous space‐time discretization is applied to the problem of inverse dynamics of underactuated systems. In particular, a space‐time finite element formulation will be compared with a formulation which is based on the method of characteristics. Numerical examples are presented which underline the importance of solving this class of problems in space and time simultaneously.

Matched Disturbance Rejection for a Class of Nonlinear Systems

In this paper, we present a method to robustify asymptotically stable nonlinear systems by adding an integral action that rejects unknown additive disturbances. The proposed approach uses a port-Hamiltonian (pH) representation of the open-loop dynamics, which, relying on the asymptotic stability property, is guaranteed to exist. The integral action controller preserves the pH structure, and, by adding a suitable cross term between the plant and the controller states to the closed-loop energy function, it avoids the unnatural coordinate transformation used in the past. The controller is shown to be robust against some common types of modeling uncertainty, including unknown friction dynamics in mechanical systems.

Lateral Dynamics of Walking-Like Mechanical Systems and Their Chaotic Behavior

A detailed mathematical analysis of the two-dimensional hybrid model for the lateral dynamics of walking-like mechanical systems (the so-called hybrid inverted pendulum) is presented in this article. The chaotic behavior, when being externally harmonically perturbed, is demonstrated. Two rather exceptional features are analyzed. Firstly, the unperturbed undamped hybrid inverted pendulum behaves inside a certain stability region periodically and its respective frequencies range from zero (close to the boundary of that stability region) to infinity (close to its double support equilibrium). Secondly, the constant lateral forcing less than a certain threshold does not affect the periodic behavior of the hybrid inverted pendulum and preserves its equilibrium at the origin. The latter is due to the hybrid nature of the equilibrium at the origin, which exists only in the Filippov sense. It is actually a trivial example of the so-called pseudo-equilibrium [Kuznetsov et al., 2003]. Nevertheless, such an observation holds only for constant external forcing and even arbitrary small time-varying external forcing may destabilize the origin. As a matter of fact, one can observe many, possibly even infinitely many, distinct chaotic attractors for a single system when the forcing amplitude does not exceed the mentioned threshold. Moreover, some general properties of the hybrid inverted pendulum are characterized through its topological equivalence to the classical pendulum. Extensive numerical experiments demonstrate the chaotic behavior of the harmonically perturbed hybrid inverted pendulum.