Real Mechanical Systems Research Articles

Influence of imperfections on the stability of a multi-disc friction system

This paper studies the impact of geometrical imperfections (gaps in the links, center distance, inclination angle, etc.) on the stability and the dynamic behavior of mechanical systems exhibiting friction-induced vibrations (braking systems, clutches, etc.). It comes further to two papers relating to improved modeling of friction and separation at the interface of a rotor-stator system. The latter is a phenomenological model which is composed of an embedded beam on which a disc is mounted, called the stator, in contact with another disc called the rotor. The phenomenological mechanical system used in this paper is a new version of the latter model taking into account some of the geometrical imperfections present in real mechanical systems. In the proposed model, the rotor and stator discs have the ability to move radially thanks to the gaps in the links. The inclination angle of the rotor disc and a center distance between the stator and the rotor discs are also introduced. The inclusion of these three geometrical imperfections induces additional complex phenomena that have a strong impact on the stability and dynamic behavior of the mechanical system, because the coupling of the imperfections with the rotor rotation gives rise to a non-autonomous dynamical system. Consequently, stability studies of fixed points must be replaced by stability studies of periodic orbits involving the construction of a monodromy matrix. In conclusion, significant differences in the values of the bifurcation point and the levels of the associated instabilities can be observed, unlike in a study that does not take geometrical imperfections into account.

Identification and damage detection of beam-like structure using vibration signals based on simulated model, real healthy state and deep convolutional neural network

Condition monitoring of mechanical systems, such as structures and rotating machines is always a major challenge. This paper is presented a new method for damage detection of real mechanical systems in presence of the uncertainties such as modeling errors, measurement errors, varying loading conditions, and environmental noises based on a simulated model and real healthy state. In this method, data of a real healthy system is used to updating the parameters of the simulated model. Some parts of the signals that are not related to the nature of the system are removed using the complete ensemble empirical mode decomposition method. A deep convolutional network is designed to learn damage-sensitive features from raw frequency data of simulated model and real healthy state. Raw frequency data is extracted from vibration signals using the power spectral density method. In order to train the proposed deep network, raw frequency data of the simulated model andreal healthy state are used. Then, raw frequency data of the real model are used to test the proposed deep network. The proposed method is validated using an experimental beam structure. The results show that using the proposed algorithm for identification and damage detection of the beam-like structure has more accuracy with respect to the other comparative methods

Calculating spin correlations with a quantum computer

We calculate spin correlation functions using IBM quantum processors, accessed online. We demonstrate the rotational invariance of the singlet state, interesting properties of the triplet states, and surprising features of a state of three entangled qubits. This exercise is ideal for remote learning and generates data with real quantum mechanical systems that are impractical to investigate in the local laboratory. Students learn a wide variety of skills, including calculation of multipartite spin correlation functions, design and analysis of quantum circuits, and remote measurement with real quantum processors.

Функциональные компенсаторы в приводах машин

Real mechanical systems are characterized by real parameters, which include primary manufacturing and assembly errors, force and temperature deformations, and abnormal operating modes, the full knowledge of which is unknown when designing systems. Incomplete knowledge about the object is compensated by using coefficients entered into calculation formulas. The coefficients form the basis of reference literature and are obtained on the basis of generalization of experience in creating objects that are similar in design and purpose. This statistical technique is used to increase the margin of safety, but it does not allow us to obtain optimal performance criteria for the design of mechanical drives in particular. It is proposed to use the principle of designing mechanical systems by giving them the property of adaptation to real parameters at the design stage. The means of adaptation is an additional motion of links to the main one, implemented in particular by functional compensators. An algorithm for the synthesis of a compensator is given on the example of the basic scheme of a friction planetary gearbox

Dynamic Smoothing Effect in Non-Linear Dynamic System under Polyharmonic External Excitation

The effect of the polyharmonic external excitation causes the emergence or onset of novel properties in the system. The article devoted into the oscillations induced in a rigid system by the polyharmonic external excitation. The analysis of the results obtained in this research confirms that the systems with the nonlinear elastic characteristics are rather sensitive to the changes introduced into the external excitation according to the law. Therefore, some assumptions, for instance, those concerning the monoharmonic nature of changes in the external excitation, which are commonly used in studying the real mechanical systems, are not always correct.

Research of the manipulator dynamics installed on an elastic basis

In many scientific articles on construction topics, the problem of building density has recently been considered [1, 2]. When working construction equipment in the construction of such objects there is a problem of safety of work. For example, in work [3, 4] the possibility of an excavator with an offset digging axis is presented. But, such research for construc-tion cranes and construction robots is not enough. The elasticity of metal structures of real mechanical systems manipulators greatly affects their work [5]. When lifting cargo manipulator in its metal construction generated vibrations due to the complex dynamics of the machine. Fluctuations cargo the cause errors in its position and reduce life of the machine. For eliminate fluctuation make use of the dampers and devices regulate speed of the working body of the manipulator [5, 6]. It is necessary to develop the dynamic and mathematical models of the boom of the manipulator, which is mounted on an elastic base. The mathematical model must take into ac-count the parameters of the rigidity of the support arm of the manipulator, the mass of the jet and the load, as well as its geometrical parame-ters. The basic method of compiling the dynamic equations of motion, the Lagrange equations are used. The boundary conditions for the so-lution of the obtained differential equations for the angle of rotation the deformed prop were the boundary values of the displacements and the angle of rotation of the cantilever beam within the boundary of the strength of its cross-section.

The importance of dynamic behaviour of vibrating systems on the response in case of non-Gaussian random excitations

Dynamic response of vibrating system subjected to non-Gaussian random loads was investigated through a set of numerical simulation on several lumped systems aimed to determine whether and in what form the dynamic behaviour of a vibrating system transfers or masks non-Gaussianity features of the input to the output response. Indeed, in several numerical and experimental activities performed on a Y-shaped specimen it was observed how the system response, both in terms of displacement or stress, changed according to an input variation (stationary and non-stationary Gaussian and non-Gaussian load time histories) and according to a change of the system frequency response function. Moreover, it was observed that even if the system was excited in its frequency range, the response remains unchanged and similar to the input in case of non-stationary and non-Gaussian load, removing preliminarily the possibility to use spectral methods for damage evaluation, going necessarily back to a more “expensive” time-domain analysis. Since the system response characteristics may change significantly according to the input excitation features and to the dynamic system parameters allowing, in some cases, the use of spectral techniques for fatigue damage evaluation also in case of non-Gaussian input loads, the aim of this paper is to understand whether and how the dynamic behaviour of a generic mechanical system transforms the non-Gaussian input excitations into a Gaussian response. To this aim several numerical displacement responses of 1-dof lumped systems characterized by different frequency response functions (resonance frequency position and damping) were analysed and investigated for different stationary and non-stationary Gaussian and non-Gaussian excitations. In such a way, it was possible to a-priori establish under what circumstances the frequency-domain approaches can be adopted to compute the fatigue damage of real mechanical systems.

Optimization problem and efficient partitioning algorithm for transitions to finer-scale models in adaptive resolution simulation of articulated biopolymers

Adaptive coarse graining of highly complex biomolecular systems is conducted by either imposing constraints on the system model to generate a coarser model, or releasing certain constraints from it to create a higher fidelity one. This paper addresses some of the challenges of transitions to finer-scale models. It is shown that the kinetic energy associated with ignored modes of motion during the coarse graining process must be estimated and put back into the simulation. As such, unlike real mechanical systems, transitioning back to a finer biomolecular model may result in an infinite number of solutions. Herein, an optimization-based approach subject to the satisfaction of impulse–momentum balance and desired kinetic energy is presented to arrive at a physically meaningful state of the system immediately after the transition. In order to reduce the cost of formulating and solving this optimization problem, generalized velocities of the system are partitioned into two categories: independent joint velocities associated with the released joints, and dependent joint velocities associated with the rest of the joints. This paper further develops a divide-and-conquer algorithm to efficiently perform this partitioning process and express dependent velocities in terms of independent ones. The presented method is highly parallelizable and avoids the construction of the mass and Jacobian matrices of the entire system, resulting in a significant improvement in computational efficiency.

Synthesis of Sine-on-Random vibration profiles for accelerated life tests based on fatigue damage spectrum equivalence

Abstract In many real life environments, mechanical and electronic systems are subjected to vibrations that may induce dynamic loads and potentially lead to an early failure due to fatigue damage. Thus, qualification tests by means of shakers are advisable for the most critical components in order to verify their durability throughout the entire life cycle. Nowadays the trend is to tailor the qualification tests according to the specific application of the tested component, considering the measured field data as reference to set up the experimental campaign, for example through the so called “Mission Synthesis” methodology. One of the main issues is to define the excitation profiles for the tests, that must have, besides the (potentially scaled) frequency content, also the same damage potential of the field data despite being applied for a limited duration. With this target, the current procedures generally provide the test profile as a stationary random vibration specified by a Power Spectral Density (PSD). In certain applications this output may prove inadequate to represent the nature of the reference signal, and the procedure could result in an unrealistic qualification test. For instance when a rotating part is present in the system the component under analysis may be subjected to Sine-on-Random (SoR) vibrations, namely excitations composed of sinusoidal contributions superimposed to random vibrations. In this case, the synthesized test profile should preserve not only the induced fatigue damage but also the deterministic components of the environmental vibration. In this work, the potential advantages of a novel procedure to synthesize SoR profiles instead of PSDs for qualification tests are presented and supported by the results of an experimental campaign.

Multi-body contact in non-linear dynamics of real mechanical systems

The considerable number of real mechanical systems operates in conditions of multi-body contact. Very often, elastic properties in contact areas couldn’t be neglected, so the elastic deformations exist in contact area of each two deformable bodies in contact. When there are two or more contacts at the same time and rotations and/or translations of contact bodies, these conditions cause the continuous changes of contact areas’ geometry, friction, load distribution and other parameters. Therefore, the problem of non-linear dynamics of mechanical system becomes very complex.In this paper, the new approach for analyzing the non-linear dynamics of mechanical systems with multi-body contacts will be presented. In this approach, the contact bodies in mechanical systems are simulated with basic geometric deformable bodies coupled with elements with time-varying stiffness and damping. The main principles of mathematical phenomenological mapping are used for multi-body contact reduction to simple single-degree of few-degrees of freedom systems with total stiffness as main characteristic. The cases of two and three basic geometric bodies in contact are modeled to enable the investigation of influence of main parameters (stiffness, damping, external load, friction coefficient) in non-linear dynamics of multi-body contacts. The Finite Element Analysis is used to calculate the time-varying contact deformations, total stiffness and external load distribution.A particular attention is paid to the presentation of new approach application on real mechanical systems with multi-body contacts, such as gears and ball bearings. The analyses of non-linear dynamics of a particular gear pair and a particular ball bearing will illustrate the capabilities and advantages of presented new approach for comfortable and qualitative analysis of nonlinear dynamic behavior of real complex mechanical systems.

Adaptive robust image-based visual servoing control of robot with unknown actuator hysteresis

This paper investigates the image-based visual servoing (IBVS) manipulator system with unknown hysteresis nonlinearity by utilizing the uncalibrated eye-to-hand configuration. Compared with the conventional IBVS system, the unknown actuator hysteresis nonlinearity, which widely exists in the real physical mechanical systems and significantly limits the performances of the robotic system, is fully considered. The problem of unknown actuator nonlinearity prevents direct input of existing controllers and will result in some challenging difficulties in control design. In this paper, an adaptive IBVS control scheme, which takes the unknown actuator hysteresis into account, is presented. Without the prior knowledge of both the intervals of hysteresis parameters and the bound of the dynamic disturbance term, a novel adaptive algorithm is developed to estimate the unknown parameters on-line. The image tracking errors are guaranteed to converge to a small neighborhood of the origin. Simulations and comparative experiments are carried out to test the performance of the proposed scheme.

Modal Identification Using OMA Techniques: Nonlinearity Effect

This paper is focused on an assessment of the state of the art of operational modal analysis (OMA) methodologies in estimating modal parameters from output responses of nonlinear structures. By means of the Volterra series, the nonlinear structure excited by random excitation is modeled as best linear approximation plus a term representing nonlinear distortions. As the nonlinear distortions are of stochastic nature and thus indistinguishable from the measurement noise, a protocol based on the use of the random phase multisine is proposed to reveal the accuracy and robustness of the linear OMA technique in the presence of the system nonlinearity. Several frequency- and time-domain based OMA techniques are examined for the modal identification of simulated and real nonlinear mechanical systems. Theoretical analyses are also provided to understand how the system nonlinearity degrades the performance of the OMA algorithms.

Dynamic and energy analysis of frictional contact instabilities on a lumped system

When dealing with complex mechanical systems, the frictional contact is at the origin of significant changes in their dynamic behavior. The presence of frictional contact can give rise to mode-coupling instabilities that produce harmonic friction induced vibrations. Unstable vibrations can reach large amplitude that could compromise the structural and surface integrity of the system and are often associated with annoying noise emission. The study of this kind of dynamic instability has been the subject of many studies ranging from both theoretical and numerical analysis of simple lumped models to numerical and experimental investigation on real mechanical systems, such as automotive brakes, typically affected by such issue. In this paper the numerical analysis of a lumped system constituted by several degrees of freedom in frictional contact with a slider is presented, where the introduction of friction can give rise to an unstable dynamic behavior. Two different approaches are used to investigate the effects of friction forces. The first approach, the Complex Eigenvalues Analysis, allows for calculating the complex eigenvalues of the linear system that can be characterized by a positive real part (i.e. negative modal damping). The complex eigenvalues and eigenvectors of the system are investigated with respect to friction. In the second approach a non linear model has been developed accounting for the stick–slip–detachment behavior at the interface to solve the time history solution and analyze the unstable vibration. The effects of boundary conditions and of system parameters are investigated. Results comparison between the two different approaches highlights how nonlinearities affect the time history solution. The lumped model allows for a detailed analysis of the energy flows between the boundary and the system during self-excited vibrations, which are at the origin of the selection between the predicted unstable mode.

Dynamic modeling of flexible multibody system using a meshing method

Multi-rigid-body system dynamics can be used to investigate the dynamics of a mechanical system of rigid bodies while the finite element method is often utilized to model the quasi-static elastic deformations of an elastic structure. However, neither of these two methods can resolve the real dynamics of a mechanical system when both rigid displacements and elastic deformations coexist. Therefore, this article proposes a meshing method to simulate the mechanical system with uniform mass point movements. To split the specified solid structure into a set of regularly distributed dynamic units, one can assume that the mass density of the structure is evenly distributed within the whole concrete volume and the elasticity and damping of the material are isotropic. Then the whole solid structure of each component can be divided into a number of tetrahedrons the vertexes of which are the points with the mass parameters. The original distances between every pair of adjacent points are supposed to be identical, and the stiffness and the damping coefficients are introduced to formulate the internal and external dynamics of the adjacent mass points. To illustrate the correction and effectiveness of the method, the dynamics problems of a number of regular elastic bodies are investigated with large rigid displacements accompanying elastic deformations. Computer simulations demonstrate that this method is especially useful for real mechanical systems where the rigid displacements and elastic deformations coexist.

Robust Adaptive Fuzzy Control of MIMO Nonlinear Systems with Higher-Order and Unmatched Uncertainties

In this paper, a robust adaptive fuzzy controller is designed for the output tracking control problem of mu lti -input mult i-output (MIMO) nonlinear systems with higher-order and un matched uncertainties. For real mechanical systems, the strength of the unmatched uncertainties is bounded by the pth-order polynomials in states, in contrast to other works assuming that these uncertainties are bounded by the first-order polynomials in states. Based on the combination of the H ∞ optimal control with fuzzy systems and some feasible adaptation laws, the proposed robust adaptive fuzzy controller can not only guarantee that all the signals in the whole closed-loop systems are bounded, but also obtain that the output tracking performance of M IMO nonlinear uncertain systems is well established. A series of computer simulat ions are illustrated to demonstrate the validity of the proposed control scheme.

Application of simple adaptive control to water hydraulic servo cylinder system

Although conventional model reference adaptive control (MRAC) achieves good tracking performance for cylinder control, the controller structure is much more complicated and has less robustness to disturbance in real applications. This paper discusses the use of simple adaptive control (SAC) for positioning a water hydraulic servo cylinder system. Compared with MRAC, SAC has a simpler and lower order structure, i.e., higher feasibility. The control performance of SAC is examined and evaluated on a water hydraulic servo cylinder system. With the recent increased concerns over global environmental problems, the water hydraulic technique using pure tap water as a pressure medium has become a new drive source comparable to electric, oil hydraulic, and pneumatic drive systems. This technique is also preferred because of its high power density, high safety against fire hazards in production plants, and easy availability. However, the main problems for precise control in a water hydraulic system are steady state errors and overshoot due to its large friction torque and considerable leakage flow. MRAC has been already applied to compensate for these effects, and better control performances have been obtained. However, there have been no reports on the application of SAC for water hydraulics. To make clear the merits of SAC, the tracking control performance and robustness are discussed based on experimental results. SAC is confirmed to give better tracking performance compared with PI control, and a control precision comparable to MRAC (within 10 μm of the reference position) and higher robustness to parameter change, despite the simple controller. The research results ensure a wider application of simple adaptive control in real mechanical systems.

The energy level shifts, wave functions and the probability current distributions for the bound scalar and spinor particles moving in a uniform magnetic field

We discuss the equations for the bound one-active electron states based on the analytic solutions of the Schrodinger and Pauli equations for a uniform magnetic field and a single attractive $\delta({\bf r})$-potential. It is vary important that ground electron states in the magnetic field differ essentially from the analogous state of spin-0 particles, whose binding energy was intensively studied more than forty years ago. We show that binding energy equations for spin-1/2 particles can be obtained without using the language of boundary conditions in the $\delta$-potential model developed in pioneering works. We use the obtained equations to calculate the energy level displacements analytically and demonstrate nonlinear dependencies on field intensity. We show that the magnetic field indeed plays a stabilizing role in considered systems in a case of the weak intensity, but the opposite occurs in the case of strong intensity. These properties may be important for real quantum mechanical fermionic systems in two and three dimensions. We also analyze the exact solution of the Pauli equation for an electron moving in the potential field determined by the three-dimensional $\delta$-well in the presence of a strong magnetic field. We obtain asymptotic expressions for this solution for different values of the problem parameters. In addition, we consider electron probability currents and their dependence on the magnetic field. We show that including the spin in the framework of the nonrelativistic approach allows correctly taking the effect of the magnetic field on the electric current into account. The obtained dependencies of the current distribution, which is an experimentally observable quantity, can be manifested directly in scattering processes, for example.

Scalar and spinor particles with low binding energy in a strong stationary magnetic field in two and three dimensions

On the basis of analytic solutions of Schrodinger and Pauli equations for a uniform magnetic field and a single attractive $\delta({\bf r})$-potential the equations for the bound one-active electron states are discussed. It is vary important that ground electron states in the magnetic field essentially different from the analog state of spin-0 particles that binding energy has been intensively studied at more then forty years ago. We show that binding energy equations for spin-1/2 particles can be obtained without using of a well-known language of boundary conditions in the model of $\delta$-potential that has been developed in pioneering works. Obtained equations are used for the analytically calculation of the energy level displacements, which demonstrate nonlinear dependencies on field intensities. It is shown that in a case of the weak intensity a magnetic field indeed plays a stabilizing role in considering systems. However the strong magnetic field shows the opposite action. We are expected that these properties can be of importance for real quantum mechanical fermionic systems in two- and three-dimensional cases.

Orthogonal Function Techniques for the Identification of Nonlinear Mechanical Systems

Real world mechanical systems present nonlinear behavior and in many cases simple linearization in modeling the system would not lead to satisfactory results. Coulomb damping and cubic stiffness are typical examples of system parameters currently used in nonlinear models of mechanical systems. This paper uses orthogonal functions to represent input and output signals. These functions are easily integrated by using a so-called operational matrix of integration. Consequently, it is possible to transform the nonlinear differential equations of motion into algebraic equations. After mathematical manipulation the unknown linear and nonlinear parameters are determined. Numerical simulations, involving single and two degree-of-freedom mechanical systems, confirm the efficiency of the above methodology.

On the identification of non-linear mechanical systems using orthogonal functions

Real world mechanical systems present non-linear behavior and in many cases simple linearization in modeling the system would not lead to satisfactory results. Coulomb damping and cubic stiffness are typical examples of system parameters currently used in non-linear models of mechanical systems. This paper uses orthogonal functions to represent input and output signals. These functions are easily integrated by using a so-called operational matrix of integration. Consequently, it is possible to transform the non-linear differential equations of motion into algebraic equations. After mathematical manipulation the unknown linear and non-linear parameters are determined. Numerical simulations, involving single and two degree-of-freedom mechanical systems, confirm the efficiency of the above methodology.