Model Of Mechanical System Research Articles

Torsion‐free connections of second‐order maximally superintegrable systems

AbstractSecond‐order (maximally) conformally superintegrable systems play an important role as models of mechanical systems, including systems such as the Kepler–Coulomb system and the isotropic harmonic oscillator. This paper is dedicated to understanding non‐ and semi‐degenerate systems. We obtain “projective flatness” results for two torsion‐free connections naturally associated to such systems. This viewpoint sheds some light onto the interrelationship of properly and conformally (second‐order maximally) superintegrable systems from a geometrical perspective. It is shown that the semi‐degenerate secondary structure tensor can be viewed as the Ricci curvature of a natural torsion‐free connection defined by the primary structure tensor (and similarly in the non‐degenerate case). It is also shown that properly semi‐degenerate systems are characterised, similar to the non‐degenerate case, by the vanishing of the secondary structure tensor.

MATHEMATICAL MODELING OF THE DYNAMICS OF THE AEROELASTIC "PIPELINE – PRESSURE SENSOR" SYSTEM

This paper proposes mathematical models of mechanical systems "pipeline - pressure sensor" designed to control the pressure of the working medium in the combustion chambers of engines. In such systems, to mitigate the impact of vibration accelerations and high temperatures, the sensor is connected to the engine using a pipeline and is located at some distance from it. The movement of the working medium is described by linear models of fluid and gas mechanics. To describe the dynamics of an elastic sensitive element, linear models of the mechanics of a solid deformable body are used. Based on linear differential equations with partial derivatives, mathematical formulations of problems are proposed that correspond to three-dimensional models of pressure measurement systems in gas-liquid media for some pipeline cross-sectional shapes, namely, for a pipeline with a rectangular cross-section, with a section in the form of a sector and in the form of a ring. By introducing integral characteristics, the solution of problems is reduced to studying one-dimensional models. Equations have been obtained that make it possible to determine the pressure of the working medium in the combustion chamber at each moment of time by the value of deformation of the sensitive element of the sensor. Analytical and numerical-analytical methods for solving the corresponding initial-boundary value problems for systems of differential equations are proposed. In the analytical approach, the solution of the problem is reduced to solving a differential equation with a deviating argument. The numerical-analytical study of the problem is based on the application of the Galerkin method. Also, a numerical experiment was carried out and examples of calculating the deformation of the sensitive element of the sensor in the case of rigid fastening when specifying specific values of the mechanical parameters of the system are presented, also during setting the law of change in the excess pressure of the working medium in the engine.

Data-free non-intrusive model reduction for nonlinear finite element models via spectral submanifolds

The theory of spectral submanifolds (SSMs) has emerged as a powerful tool for constructing rigorous, low-dimensional reduced-order models (ROMs) of high-dimensional nonlinear mechanical systems. A direct computation of SSMs requires explicit knowledge of nonlinear coefficients in the equations of motion, which limits their applicability to generic finite-element (FE) solvers. Here, we propose a non-intrusive algorithm for the computation of the SSMs and the associated ROMs up to arbitrary polynomial orders. This non-intrusive algorithm only requires system nonlinearity as a black box and hence, enables SSM-based model reduction via generic finite-element software. Our expressions and algorithms are valid for systems with up to cubic-order nonlinearities, including velocity-dependent nonlinear terms, asymmetric damping, and stiffness matrices, and hence work for a large class of mechanics problems. We demonstrate the effectiveness of the proposed non-intrusive approach over a variety of FE examples of increasing complexity, including a micro-resonator FE model containing more than a million degrees of freedom.

Balance equations for physics-informed machine learning

Using traditional machine learning (ML) methods may produce results that are inconsistent with the laws of physics. In contrast, physics-based models of complex physical, biological, or engineering systems incorporate the laws of physics as constraints on ML methods by introducing loss terms, ensuring that the results are consistent with these laws. However, accurately deriving the nonlinear and high order differential equations to enforce various complex physical laws is non-trivial. There is a lack of comprehensive guidance on the formulation of residual loss terms. To address this challenge, this paper proposes a new framework based on the balance equations, which aims to advance the development of PIML across multiple domains by providing a systematic approach to constructing residual loss terms that maintain the physical integrity of PDE solutions. The proposed balance equation method offers a unified treatment of all the fundamental equations of classical physics used in models of mechanical, electrical, and chemical systems and guides the derivation of differential equations for embedding physical laws in ML models. We show that all of these equations can be derived from a single equation known as the generic balance equation, in conjunction with specific constitutive relations that bind the balance equation to a particular domain. We also provide a few simple worked examples how to use our balance equation method in practice for PIML. Our approach suggests that a single framework can be followed to incorporate physics into ML models. This level of generalization may provide the basis for more efficient methods of developing physics-based ML for complex systems.

An optimized dynamic model improved deep discriminative transfer learning network for fault detection in rotation vector reducers

In recent years, recognized fault types using artificial intelligence (AI) models has gradually become one of the mainstream directions in the field of mechanical fault diagnosis. However, it is very difficult to obtain relatively complete fault samples, which limits the application of AI models for complex mechanical systems, such as rotation vector (RV) reducers. To address this issue, physical model-based fault sample generation methods attracted many attentions but still an open problem: the difference in fault samples between numerical simulation and measurement of a physical system needs to be well decreased. Therefore, this article proposes an improved deep discriminative transfer learning network (IDDTLN) for RV reducer fault diagnosis. The presented network is driven by an optimized dynamic model. Firstly, the measurement normal signal and whale optimization algorithm (WOA) are utilized to update the dynamic model parameters of the RV reducer. Secondly, the updated numerical model is employed to calculate simulation fault samples. Finally, simulation samples and unlabeled measurement fault samples are used to train IDDTLN. The trained IDDTLN can accurately identify the unknow measurement fault samples. The data obtained from RV reducer test rigs are utilized to explore the feasibility of the proposed method, and the classification accuracies reach 99.8 %.

A noise generative network to reduce the gap between simulation and measurement signals in mechanical fault diagnosis

Data-driven artificial intelligence models play an important role in mechanical fault diagnosis. Generally, it is difficult to collect relative complete fault samples, which limits the application of artificial intelligence models for complex mechanical systems. To address this issue, numerical model-based or called physical model-based fault sample generation methods attracted many attentions but still an open problem: the difference in fault samples between numerical simulation and measurement of a physical system needs to be well decreased. Therefore, a noise generative network (NGN) for mechanical fault classification is developed. First, the NGN is trained using the simulation and measurement normal samples. The simulation fault samples are further fed into the trained NGN to obtain more solid simulation fault samples with minor differences from measurements of mechanical systems with faults. Second, deep convolutional neural network is trained by solid simulation fault samples, and the test samples of unknown fault types will be finally recognized. Finally, validation experiments using rotation vector reducers, bearings, and rotors classified test samples with average accuracies of 99.5%, 95.7%, and 99.9%, respectively. They indicate that the proposed NGN model effectively reduces the difference between the simulation and measurement samples to lead more precision results for fault classification in mechanical systems.

A systematic methodology for port-Hamiltonian modeling of multidimensional flexible linear mechanical systems

This article introduces a novel systematic methodology for modeling a class of multidimensional linear mechanical systems that directly allows to obtain their infinite-dimensional port-Hamiltonian representation. While the approach is tailored to systems governed by specific kinematic assumptions, it encompasses a wide range of models found in current literature, including ℓ-dimensional elasticity models (where ℓ = 1, 2, 3), vibrating strings, torsion in circular bars, classical beam and plate models, among others. The methodology involves formulating the displacement field using primary generalized coordinates via a linear algebraic relation. The non-zero components of the strain tensor are then calculated and expressed using secondary generalized coordinates, enabling the characterization of the skew-adjoint differential operator associated with the port-Hamiltonian representation. By applying Hamilton's principle and employing a specially developed integration by parts formula for the considered class of differential operators, the port-Hamiltonian model is directly obtained, along with the definition of boundary inputs and outputs. To illustrate the methodology, the plate modeling process based on Reddy's third-order shear deformation theory is presented as an example. To the best of our knowledge, this is the first time that a port-Hamiltonian representation of this system is presented in the literature.

A Relationship Between Spin and Geometry

In physics, spin is often seen exclusively through the lens of its phenomenological character: as an intrinsic form of angular momentum. However, there is mounting evidence that spin fundamentally originates as a quality of geometry, not of dynamics, and recent work further suggests that the structure of non-relativistic Euclidean three-space is sufficient to define it. In this paper, we directly explicate this fundamentally non-relativistic, geometric nature of spin by constructing non-commutative algebras of position operators which subsume the structure of an arbitrary spin system. These “Spin-s Position Algebras” are defined by elementary means and from the properties of Euclidean three-space alone, and constitute a fundamentally new model for quantum mechanical systems with non-zero spin, within which neither position and spin degrees of freedom, nor position degrees of freedom within themselves, commute. This reveals that the observables of a system with spin can be described completely geometrically as tensors of oriented planar elements, and that the presence of non-zero spin in a system naturally generates a non-commutative geometry within it. We will also discuss the potential for the Spin-s Position Algebras to form the foundation for a generalisation to arbitrary spin of the Clifford and Duffin–Kemmer–Petiau algebras.

Electronic mechanical braking system executive mechanism design, calculation, and modeling based on dynamic control

Introduction: As science and technology develop, automobiles are moving toward intelligence and electrification and need better braking systems.Methods: To improve the braking system’s response speed and braking effect, a longitudinal dynamics control system for automobiles based on the electronic mechanical braking system was proposed, and the electronic mechanical braking system was improved through automatic disturbance rejection control.Results: The experimental results show that the time required for achieving the target clamping force in the electronic mechanical braking system using self-disturbance rejection control and proportional integral differential control is only 0.01 s, but there is an issue of excessive control in the proportional integral differential system between 0.12 s and 0.2 s, while the self-disturbance rejection controller does not have this problem. Meanwhile, regardless of the interference applied, the electronic mechanical braking system with automatic disturbance rejection control can ensure that the clamping force does not fluctuate. In the joint simulation experiment, the expected acceleration and actual acceleration can remain consistent, and if the expected braking force is 9000 N, then the actual braking force of the electronic mechanical brake (EMB) is also 9000 N.Discussion: The above results indicate that the vehicle longitudinal dynamics control system using the electronic mechanical braking system not only responds fast but also has a good braking effect, avoiding the problem of excessive control and improving the driving experience.

Air tightness detection method in parallel for aerospace: mechanical design, system modeling and optimum control

To address the problems of high cost, complex operation, and low efficiency of existing equipment for aerospace, a simple but efficient multichannel air tightness detection device is designed. A physical system model is constructed for the process of inflation, deflation, and inflation with leakage. The expression between the inflation/deflation rate and the valve area is obtained. Through modeling the intersection and rotation of spatial curves, the relationship between the valve area and the valve core angle is derived, and the optimal valve core angle calculation method is proposed to achieve precise rate control of inflation and deflation. Simulation experiments and numerical analysis demonstrate the superiority of the proposed system scheme, the effectiveness of the control method, as well as the accuracy of the mathematical model. For the tested object of 0.3 L, the target pressure of 400 KPa, and the inflation and deflation rate of 75 Kpa/min, by using four channels with a 10 s interval for sequential operation and adjusting valves every 60 s, the efficiency of inflation and deflation is more than 3.5 times that of a single device with a single circuit. Its performance is not much different from real-time automatic control equipment, but the economy is greatly improved.

Study of high power steam turbine forced oscilla-tions near operating frequency

Problem. Forced oscillations of the turbine unit-foundation-base system near the operating frequency are considered. Goal. The purpose of the work is to study forced vibrations of the turbine unit-foundation-base system near the operating frequency range to assess the vibration state of the system and determine the causes of increased vibrations. The object of the study is the turbine unit-foundation-base system. The system consists of a single reinforced concrete foundation on which a steam turbine and generator are installed. The subject of the study is the amplitude-frequency dependences of forced oscillations of the turbine unit-foundation-base system. Methodology. The study was carried out using vibration methods and the finite element method. Also worth noting is the use of original methods developed directly by the author for constructing models of complex mechanical engineering systems. Results. As a result of the research, three-dimensional finite element models of low-pressure cylinder housings, the foundation and the entire turbine unit-foundation-base system were built. The conducted research allows us to draw a conclusion regarding the reasons for the increased level of vibration near the operating frequency and directions for their prevention. Originality. Regarding the methods for constructing a model of the turbine unit-foundation-base system, it should be noted that they are unique. The features of the applied modeling method make it possible to take into account the variable interaction between the low-pressure cylinder bodies and the foundation. Fixpoints are also taken into account. Previous studies of the turbine unit-foundation-base system did not allow us to determine the causes of increased vibrations of the shaft line supports. Practical significance. The results of the work relate to direct practical application. As a result of the work, conclusions were drawn about the ways to increase the vibration reliability of the turbine unit-foundation-base system and further directions for research.

Lagrangian operator inference enhanced with structure-preserving machine learning for nonintrusive model reduction of mechanical systems

Complex mechanical systems often exhibit strongly nonlinear behavior due to the presence of nonlinearities in the energy dissipation mechanisms, material constitutive relationships, or geometric/connectivity mechanics. Numerical modeling of these systems leads to nonlinear full-order models that possess an underlying Lagrangian structure. This work proposes a Lagrangian operator inference method enhanced with structure-preserving machine learning to learn nonlinear reduced-order models (ROMs) of nonlinear mechanical systems. This two-step approach first learns the best-fit linear Lagrangian ROM via Lagrangian operator inference and then presents a structure-preserving machine learning method to learn nonlinearities in the reduced space. The proposed approach can learn a structure-preserving nonlinear ROM purely from data, unlike the existing operator inference approaches that require knowledge about the mathematical form of nonlinear terms. From a machine learning perspective, it accelerates the training of the structure-preserving neural network by providing an informed prior (i.e., the linear Lagrangian ROM structure), and it reduces the computational cost of the network training by operating on the reduced space. The method is first demonstrated on two simulated examples: a conservative nonlinear rod model and a two-dimensional nonlinear membrane with nonlinear internal damping. Finally, the method is demonstrated on an experimental dataset consisting of digital image correlation measurements taken from a lap-joint beam structure from which a predictive model is learned that captures amplitude-dependent frequency and damping characteristics accurately. The numerical results demonstrate that the proposed approach yields generalizable nonlinear ROMs that exhibit bounded energy error, capture the nonlinear characteristics reliably, and provide accurate long-time predictions outside the training data regime.

Seamless Function-Oriented Mechanical System Architectures and Models

One major challenge of today’s product development is to master the constantly increasing product complexity driven by the interactions between different disciplines, like mechanical, electrical and software engineering. An approach to master this complexity is function-oriented model-based systems engineering (MBSE). In order to guide the developer through the process of transferring requirements into a final product design, MBSE methods are essential. However, especially in mechanics, function-oriented product development is challenging, as functionality is largely determined by the physical effects that occur in the contacts of physical components. Currently, function-oriented MBSE methods enable either the modeling of contacts or of structures as part of physical components. To create seamless function-oriented mechanical system architectures, a holistic method for modeling contacts, structures and their dependencies is needed. Therefore, this paper presents an extension of the motego method to model structures, by which the seamless parametric modeling of function-oriented mechanical system architectures from requirements to the physical product is enabled.

The C&C² Approach as a Thinking Tool in Mechatronic Systems

In recent times, interest in cross-domain system modeling has seen a significant increase. Despite the proven success of the Contact and Channel Approach (C&C2-Approach) in mechanical system modeling, a procedure for cross-domain applications has been largely absent. In this research, we discuss how mechatronic systems can be modeled with the C&C2-Approach. Based on extensive literature research, which allowed us to identify cross-domain reference models, we are introducing the integration of bond graphs into the C&C2-Approach. The principles of bond graph theory make it possible to represent embodiment function relations (EFRs) in non-mechanical domains. For this purpose, only a few extensions to the key elements of the C&C2-Approach are required: On the one hand, the information about the predominant direction of the energy flow is integrated into the C&C2-Model, while, on the other hand, we add the information about whether the EFR is static or dynamic. These adaptations offer the further possibility of building a bridge to mathematical models. At this point, a bond graph can be derived from the C&C2-Model and used to analyze the systems’ behavior in a simulation. This research therefore supports developers in modeling mechatronic systems and enables simulations at an early stage of product development.

QUALITATIVE METHODS IN MATHEMATICAL MODELING OF COMPLEX MECHANICAL SYSTEMS WITH DISSIPATION

QUALITATIVE METHODS IN MATHEMATICAL MODELING OF COMPLEX MECHANICAL SYSTEMS WITH DISSIPATION

An Investigation of Stability, Controllability and Observability of a Three Degree of Freedom Translational Mechanical System using State Space Approach

State-space modelling approach which is essentially time-domain developed in the late 1960s is a new approach to the analysis and design of complex control systems. Several researches have carried out modelling and analysis of mechanical systems with a number of degrees of freedom of movement using state space approach among which is the work of Sivak and Darina (2012) who modelled a system with two degrees of freedom. In this paper, therefore, we provide an extension of the work of Sivak and Darina to model and analyse a three degree of freedom translational mechanical system using state-space approach. The system was first presented in equivalent free body diagrams, then Newton's second law of motion was used to derive its equations of motion. The State-space formulation in the controllable canonical form obtained from the time-domain differential equations is adopted and the Laplace transform method was used in the analysis to determine the poles (natural frequencies) of the system using two numerical examples in MATLAB software. The software was also used to determine the controllability and observability matrices of the system. The stability, controllability and observability of the system were then discussed from the poles, controllability matrix and observability matrix respectively. Tables of numerical values and line graphs were used to present the results obtained from the analysis. Finally, in these results, the system was found to be stable, controllable and observable suggesting that a state feedback ( pole placement ) control design for the system is possible.

Nonlinear interactions between vibration modes with vastly different eigenfrequencies

Nonlinear interactions between modes with eigenfrequencies that differ by orders of magnitude are ubiquitous in various fields of physics, ranging from cavity optomechanics to aeroelastic systems. Simplifying their description to a minimal model and grasping the essential physics is typically a system-specific challenge. We show that the complex dynamics of these interactions can be distilled into a single generic form, namely, the Stuart-Landau oscillator. With our model, we study the injection locking and frequency pulling of a low-frequency mode interacting with a blue-detuned high-frequency mode, which generate frequency combs. Such combs are tunable around both the high and low carrier frequencies. By discussing the analogy with a simple mechanical system model, we offer a minimalistic conceptual view of these complex interactions originating the frequency combs, together with showcasing their frequency tunability.

A More Accurate Systems Modelling and Simulation Framework in Design and Optimization of A System During the Conceptual Phase

Modelling and simulation of complex mechanical systems involving multi-simulation environment, with great accuracy is essential as part of the conceptual design phase of a system under design. The co-simulation between system level model with various subsystems based on Model Based Design (MBD) and component level model is a perfect example. These mathematical models have distinct features such as the type of differential equations used to represent its physics, boundary conditions etc. In this study we use MBD methodology to develop a simulation model that can drive product development and optimization of mechanical systems. We also incorporate a 3-D Computational Fluid Dynamics (CFD) model as one of its subsystem into the System Level (SL) model architecture. This is done by creating a co-simulation interface between these two different modelling environments and exchange boundary conditions via a specific interface. The interaction between multi-domain models through system simulation together with the detailed fluid flow and thermal analysis of the component through CFD is finally explained. Finally, the dynamic behaviour of the complete system and its temporal and spatial scales is shown to be captured in more detail.

Creation and research of internal combustion engines dynamic models in OpenModelica

Problem. Torsional vibrations of the internal combustion engine crankshaft are the result of uneven torque due to gas pressure in the cylinders, as well as due to inertial forces of engine moving parts. To analyze torsional vibrations, it is necessary to have an adequate mathematical model of the engine mechanical system that takes its dynamic characteristics into account. Goal. Developing methodology for determining the mass-inertial parameters of connecting rod mechanisms in the internal combustion engines and building dynamic models based on the Openmodelica environment. Developing the Modelica language algorithm for calculating natural frequencies and forms of the dynamic model oscillations. Methodology. The elastic and inertial parameters of the dynamic scheme elements are determined by their energy equivalence to the mechanical system. The construction of a dynamic and mathematical model is implemented using the Modelica programming language. Results. Based on the proposed methodology, dynamic models of straight and V internal combustion engines were built in the Openmodelica environment. Calculation of system oscillation natural frequencies and forms was carried out. The results obtained were compared with data from other sources and analyzed from the physical feasibility point of view. Originality. The proposed methodology for determining the mass-inertial parameters of the connecting rod mechanisms in the internal combustion engines and the way to build dynamic models based on them has been shown. An algorithm has been developed in Modelica language, and natural oscillation frequencies and forms were calculated. Practical value. The developed models can be used as a part of the higher-level dynamic machine models, as well as for determining the parameters of engine crankshaft torsional vibrations.

A data-driven approach for plasticity using history surrogates: Theory and application in the context of truss structures

Data-driven methods and algorithms show immense potential for future advancements in the modeling and simulation of complex mechanical systems. However, in order to actually exploit this potential, the methods must be extended to consider inelastic and path-dependent material behavior—a step that appears more complex than in conventional material modeling, where this can be achieved with the help of additional, mostly internal, history variables. The effect of such history variables must thereby be transferred to the data-driven framework. This is achieved in the present paper by defining an appropriate history surrogate as well as a so-called propagator. The history surrogate contains tangible quantities that represent the backward path–uniquely in the ideal case–and enrich the conventional database entries of matching pairs of stresses and strains. The propagator defines the update of the history surrogate from one discrete time step to another. As a major advantage, the newly developed method retains the structures of the data-driven algorithm for elastic material behavior and therefore allows a rather straightforward extension of preexisting program codes. Thus, for instance, heterogeneous problems in which purely elastic and elastoplastic materials are present can be solved without further significant coding effort. Furthermore, several material classes covering different inelastic phenomena such as plasticity with isotropic and kinematic hardening as well as phase transformations in shape memory alloys can be considered in our framework.