Mechanical Systems In Terms Research Articles

Analytical simulation of influential parameters affecting grooved wet clutches performance underdisengagement condition

Innovating new approaches and effective methods to improve the efficiency of mechanical systems in terms of energy losses and environmental effects serve as an attractive domain for researchers and industries. Wet clutches are widely used in power transmission systems in automotive and other tribological mechanisms. The wet clutch has two functional modes; under the engaged state, in which two disks come into contact to each other, and under disengagement the plates are located at a very short distance from each other, and oil flows between them. In disengaged state, the differential speed of driving and driven units causes oil shearing within the clearance which leads to transmission of certain amount of drag torque from the driving to the output shaft. This transferred drag torque is distinguished as power loss in form of heat. The governing physical relation based on continuity equation and Navier–Stokes equations reveals that in a certain rotational velocity, the pressure gradient at the outer radius of the clutch becomes null, and, in this circumstance, aeration occurs that is known as critical rotation speed. Experimental findings provide evidence that geometry manipulation and considering grooves over the frictional disk, reduces the critical rotational speed. But there is a shortage of physical analytical relations to predict the pressure gradient in grooved wet clutches. Therefore, this article is aimed to introduce analytical model to evaluate grooved wet clutches performance in terms of drag torque and critical rotational speed under single-phase flow condition.

Failure of Solid Lubricant W-S-C Coatings under Boundary Lubrication Conditions

A boundary lubrication regime imposes a significant challenge on mechanical systems in terms of both friction and wear. A standard approach to the boundary lubrication regime problems involves coating the contacting parts and lubrication with additivated lubricant. The presented paper explores the application of TMD-based coatings combined with a base oil and an organic-based friction modifier to provide a more environmentally friendly and cheaper solution. An investigation has been performed using a reciprocating tribometer across a range of applied loads, with post-test characterisation performed by a 3D optical profilometer, Raman microscopy, SEM, and TEM. Results show that the coating with higher hardness performs better and that the organic friction modifier increases coefficient of friction but decrease wear in the boundary lubrication regime. Moreover, it was established that without an external source of sulphur TMD-based coatings do not have a satisfactory performance in the boundary lubrication regime.

Second class constraints and the consistency of optimal control theory in phase space

As has been shown in the literature (Rothe and Rothe, 2010; Rothe and Scholtz, 2003), the description of a mechanical system in terms of canonical transformations together with the Hamilton–Jacobi equation for the S function is ill-defined when the system has second class constraints. In this case, Carathéodory’s integrability conditions are violated and either the corresponding Hamilton–Jacobi equation cannot be solved or their solutions do not describe the system at all. This can be remedied by enlarging the phase space so that the constraints become first class in the extended space. Another way to approach this problem, is to apply the Rothe–Scholtz method discussed in Rothe and Rothe (2010) and Rothe and Scholtz (2003), so that the constraints themselves become variables of a new canonical transformation. This method works when the elements of the Dirac matrix are constant. On the other hand, it has been shown that optimal control theory can be written in phase space as a mechanical system with second class restrictions (Itami, 2001; Hojman, 0000; Contreras et al., 2017; Contreras and Peña 2018). This implies that the description of control theory can become inconsistent in terms of the Hamilton–Jacobi equation. In this article we will use the description of Rothe–Scholtz to analyse a subclass of LQ linear-quadratic problems whose Dirac matrix is constant and to check if the integrability conditions can be fulfilled so as to not get inconsistencies.

Electronic Constant Twist Angle Control System Suitable for Torsional Vibration Tuning of Propulsion Systems

Currently, great emphasis on reducing energy consumption and harmful emissions of internal combustion engines is placed. Current control technology allows us to customize the operating mode according to the currently required output parameters, while the tuning of mechanical systems in terms of torsional vibration is often ignored. This article deals with a semi-active torsional vibroisolation system using pneumatic flexible shaft coupling with constant twist angle control. This system is suitable, as it is specially designed, for the tuning of mechanical systems where the load torque has fan characteristics (fans, ship propellers, pumps). The main goal of this research is to verify the ability of an electronic control system developed by us to maintain the pre-set constant twist angle of the used pneumatic flexible shaft coupling during operation. The constant twist angle control function was tested on a laboratory torsional oscillating mechanical system. Presented results show that the proposed electronic control system meets the requirements for its function, namely that it can achieve, sufficiently accurately and quickly, the desired constant twist angle of the pneumatic flexible shaft coupling. It is possible to assume that the presented system will increase the technical level of the equipment where it will be applied.

Reliability analysis of an end-bearing pile with account for friction forces on the pile surface

Introduction. The behavior of end-bearing piles in the foundation soil and the methodology for their reliability analysis, treated as operational safety measures applicable to a separate bearing element of a pile foundation, need clarification and further development. The weakness of the established reliability analysis methodology, focused on the bearing capacity of the foundation soil, is its failure to take account of each case of the soil behavior above rock or low compressibility soils pursuant to Construction rules and regulations 24.13330.2011. Taking account of the bearing capacity of this soil layer in respect of the load accommodation by an end-bearing pile (taking account of the pile weight) may improve its reliability by the criterion of the bearing capacity in combination with the soil behavior below the bottom tip of a pile. Nizhne-Suyanskiy Waterworks Facility had the mission to solve water household, energy and socio-economic problems. Materials and methods. The author analyzed piles made of any applicable materials; their reliability analysis methods are based on the possibility theory due to the limited amount of statistical information on controllable parameters to be entered into the limit state design model to verify the bearing capacity of the foundation soil. Results. The author presents the design formula to identify the parameters ensuring reliable failure-free behavior of an end-bearing pile in the foundation soil and in respect of the soil bearing capacity. The pile reliability analysis performed in respect of its bearing capacity (and focused on the strength of the pile material) is provided in the references section. The author uses two performance criteria to analyze the reliability of an end-bearing pile, given that an end-bearing pile is analyzed as a consistent mechanical system in terms of the reliability theory. Conclusions. The author has developed a methodology used to analyze the reliability of end-bearing piles. It is focused on the bearing capacity of the foundation soil below the bottom tip of a pile and along its length with a view to the quantitative assessment of its safe performance at the stage of design of a facility that has a piled footing; the groundwork has been laid for further research into the behavior of end-bearing piles and for the development of design regulations applicable to various types of piles that may differ in material, behavior, sinking techniques, etc.

The LAPW Method with Eigendecomposition Based on the Hari--Zimmermann Generalized Hyperbolic SVD

In this paper we propose an accurate, highly parallel algorithm for the generalized eigendecomposition of a matrix pair $(H, S)$, given in a factored form $(F^{\ast} J F, G^{\ast} G)$. Matrices $H$ and $S$ are generally complex and Hermitian, and $S$ is positive definite. This type of matrices emerges from the representation of the Hamiltonian of a quantum mechanical system in terms of an overcomplete set of basis functions. This expansion is part of a class of models within the broad field of Density Functional Theory, which is considered the golden standard in condensed matter physics. The overall algorithm consists of four phases, the second and the fourth being optional, where the two last phases are computation of the generalized hyperbolic SVD of a complex matrix pair $(F,G)$, according to a given matrix $J$ defining the hyperbolic scalar product. If $J = I$, then these two phases compute the GSVD in parallel very accurately and efficiently.

PROBABILISTIC ANALYSIS OF ANCHOR (DOWEL) PULL-OUT CAPACITY IN AERATED CONCRETE

Aerated concrete structures are widely used in construction as load-bearing or filler structures. The article describes the probabilistic approach to estimation of anchor (dowel) pull-out capacity. The article also presents the experimental studies of control samples from aerated concrete and diagrams “stress – strain”. The maximum permissible load values are obtained for the given batch of aerated concrete blocks based on the requirements of ensuring the specified reliability (probability of no-failure). Permissible load on the anchor (dowel) will also depend on the number of anchors in case of set of anchors as a conditional sequential mechanical system in terms of reliability theory. The design equations is given the reliability analysis of anchor (dowel) on pull-out force with limited statistical data and small number of control samples for using probabilistic and statistical approaches.

Many-Body Quantum Dynamics by the Reduced Density Matrix Based on Time-Dependent Density-Functional Theory.

We evaluate the density matrix of an arbitrary quantum mechanical system in terms of the quantities pertinent to the solution of the time-dependent density functional theory (TDDFT) problem. Our theory utilizes the adiabatic connection perturbation method of Görling and Levy, from which the expansion of the many-body density matrix in powers of the coupling constant λ naturally arises. We then find the reduced density matrix ρ_{λ}(r,r^{'},t), which, by construction, has the λ independent diagonal elements ρ_{λ}(r,r,t)=n(r,t), n(r,t) being the particle density. The off-diagonal elements of ρ_{λ}(r,r^{'},t) contribute importantly to the processes unaccessible via the density, directly or by the use of the known TDDFT functionals. Of those, we consider the momentum-resolved photoemission, doing this to the first order in λ, i.e., on the level of the exact exchange theory. In illustrative calculations of photoemission from the quasi-2D electron gas and isolated atoms, we find quantitatively strong and conceptually far-reaching differences with the independent-particle Fermi's golden rule formula.

Development of a promising system for diagnosing the frogs of railroad switches using the transverse profile measurement method

We have developed a system for diagnosing the frogs of railroad switches, based on the application of modern microcontrollers of the type ESP with high technical characteristics and the simultaneous use of the information technology IoT (Internet of Things). The proposed system has advantages over mechanical systems in terms of the accuracy of data, their operational processing and submission to user in order to analyze technical condition of frogs at railroad switches. The results of measuring the transverse profile of frogs at railroad switches make it possible to take scientifically-substantiated decisions regarding the need for recovery repair of frogs by the method of surfacing and for control over gradual decrease in their carrying capacity, for establishing their actual technical condition and residual resource.We carried out experimental-theoretical research into longitudinal profile of frogs at railroad switches laid on the reinforced concrete bars. It was established as a result that after passing 50–65 million tons of cargo (that corresponds to the medium degree of wear) the trajectory takes the shape of a bump. We observe sharp hollows on the reinforced concrete base in the zone where a wheel rolls from a rail wing onto the core, characterized by significant total inclination. Subsequently, when the passed cargo increases, the number of sinusoidal irregularities grows. At wear close to maximal (80–95 million tons passed), the percentage of unfavorable trajectories (sinusoidal and hollows) grows; at low wear, they make up 49.8 %, at a wear of 5–6 mm and larger – 88.3 %. Sometimes there is a transformation of the sinusoidal irregularities into the wave-shaped ones.We have established characteristic motion trajectories of the center of mass of the wheel over the frog depending on the wear of rail wings and the core of a frog and the passed cargo. A mathematical model was constructed for predicting the wear of frog profile depending on the total weight of passed cargo.

The solution of linear mechanical systems in terms of path superposition

We prove that the solution of any linear mechanical system can be expressed as a linear combination of signal transmission paths. This is done in the framework of the Global Transfer Direct Transfer (GTDT) formulation for vibroacoustic problems. Transmission paths are expressed as powers of the transfer matrix. The key idea of the proof is to generalise the Neumann series of the transfer matrix – which is convergent only if its spectral radius is smaller than one – into a modified Neumann series that is convergent regardless of the eigenvalues of the transfer matrix. The modification consists in choosing the appropriate combination coefficients for the powers of the transfer matrix in the series. A recursive formula for the computation of these factors is derived. The theoretical results are illustrated by means of numerical examples. Finally, we show that the generalised Neumann series can be understood as an acceleration (i.e. convergence speedup) of the Jacobi iterative method.

Application of Graphs in the Analysis of Vibrating 3-Dimensional Systems

Vibrating 3-dimensional mechanical systems are described by hybrid graphs. By dividing the hybrid graph into a tree and associated co-tree it is possible to describe in terms of matrices: across-flow-variables, stiffness and flexibility. The application of the formalism of graphs makes it possible to analyze mechanical systems in terms of dynamic characteristic and trajectory motion of determinate points.

Passivity-based Trajectory-tracking for Marine Craft with Disturbance Rejection

This paper presents a Hamiltonian model of marine vehicle dynamics in six degrees of freedom in both body-fixed and inertial momentum coordinates. The model in body-fixed coordinates presents a particular structure of the mass matrix that allows the adaptation and application of passivity-based control interconnection and damping assignment design methodologies developed for robust stabilisation of mechanical systems in terms of generalised coordinates. As an example of application, we follow this methodology to design a passivity-based tracking controller with integral action for fully actuated vehicles in six degrees of freedom. We also describe a momentum transformation that allows an alternative model representation that resembles general port-Hamiltonian mechanical systems with a coordinate dependent mass matrix. This can be seen as an enabling step towards the adaptation of the theory of control of port-Hamiltonian systems developed in robotic manipulators and multi-body mechanical systems to the case of marine craft dynamics.

Tolerance analysis by polytopes: Taking into account degrees of freedom with cap half-spaces

To determine the relative position of any two surfaces in a system, one approach is to use operations (Minkowski sum and intersection) on sets of constraints. These constraints are made compliant with half-spaces of Rn where each set of half-spaces defines an operand polyhedron. These operands are generally unbounded due to the inclusion of degrees of invariance for surfaces and degrees of freedom for joints defining theoretically unlimited displacements. To solve operations on operands, Minkowski sums in particular, “cap” half-spaces are added to each polyhedron to make it compliant with a polytope which is by definition a bounded polyhedron. The difficulty of this method lies in controlling the influence of these additional half-spaces on the topology of polytopes calculated by sum or intersection. This is necessary to validate the geometric tolerances that ensure the compliance of a mechanical system in terms of functional requirements.

From parametricity to conservation laws, via Noether's theorem

Invariance is of paramount importance in programming languages and in physics. In programming languages, John Reynolds' theory of relational parametricity demonstrates that parametric polymorphic programs are invariant under change of data representation, a property that yields "free" theorems about programs just from their types. In physics, Emmy Noether showed that if the action of a physical system is invariant under change of coordinates, then the physical system has a conserved quantity: a quantity that remains constant for all time. Knowledge of conserved quantities can reveal deep properties of physical systems. For example, the conservation of energy is by Noether's theorem a consequence of a system's invariance under time-shifting. In this paper, we link Reynolds' relational parametricity with Noether's theorem for deriving conserved quantities. We propose an extension of System F$\omega$ with new kinds, types and term constants for writing programs that describe classical mechanical systems in terms of their Lagrangians. We show, by constructing a relationally parametric model of our extension of F$\omega$, that relational parametricity is enough to satisfy the hypotheses of Noether's theorem, and so to derive conserved quantities for free, directly from the polymorphic types of Lagrangians expressed in our system.

Fuzzy Dynamic Reliability Model of Dependent Series Mechanical Systems

Conventional static fuzzy reliability models cannot be directly extended for dynamic reliability analysis of mechanical systems, which consist of correlative components with strength degradation, due to the difficulties in describing the strength degradation process of components under fuzzy load and considering the failure dependence between different components in a system in the possibility context. To deal with these problems, fuzzy dynamic reliability models of mechanical systems in terms of stress and strength are proposed in this paper, which take into account the degradation mechanism of mechanical components in the failure mode of fatigue. The proposed models can be used to represent the dynamic characteristics of fuzzy reliability and analyze the influences of the variation in the parameters of fuzzy stress and strength on the failure dependence of components in a system and the dynamic behavior of fuzzy system reliability. Besides, the explosive bolts for connection between launch vehicle and satellite are chosen as a representative example to illustrate the proposed method. The results show that different parameters of fuzzy stress have different influences on fuzzy system reliability and the failure dependence of components in a system.

Energy scale of the average stresses and physical properties of metals in the region of reversible and irreversible deformations

Expressing the specific energy increment of a mechanical system in terms of variations of the kinematic invariants of motion equations in the Lagrange form, a hypothesis has been proposed concerning the existence of new physical properties of materials that determine the mechanism of the self-organization of reversible and irreversible deformations, as well as the variation of the mechanical properties with consideration of the previous history of deformations and variations of the ambient conditions. An energy interpretation of the notion of “generalized force” has been proposed, as well as the energy scale of average stresses by analogy with the thermodynamic scale of temperatures with an example of their calculation for certain metals.

Stress, stress asymmetry and couple stress: from discrete particles to continuous fields

Explicit and closed expressions for the stress and couple-stress fields for discrete (classical) mechanical systems in terms of the constituents’ degrees of freedom and interactions are derived and compared to previous results. This is done by using an exact and general coarse graining formulation, which allows one to predetermine the resolution of the continuum fields. Since the full dynamics of the pertinent fields is considered, the results are not restricted to static states or quasi-static deformations; the latter comprise mere limiting cases, which are discussed as well. The fields automatically satisfy the equations of continuum mechanics. An explicit expression for the antisymmetric part of the stress field is presented; the question whether the latter vanishes, much like its nature when it does not, have been debated in the literature. Physical explanations of some of the obtained results are offered; in particular, an interpretation of the expression for the stress field provides an argument in favor of its uniqueness, yet another topic of debate in the literature. The formulation and results are valid for single realizations, and can of course be used in conjunction with ensemble averaging. Part of the paper is devoted to a biased discussion of the notion of coarse graining in general, in order to set the presented results in a certain perspective. Although the results can be applied to molecular (nanoscale included) and granular systems alike, the presentation and some simplifying assumptions (which can be easily relaxed) target granular systems. The results should be useful for the analysis of experimental and numerical findings as well as the development of constitutive relations.

Perturbation to Mei Symmetry and Adiabatic Invariants for Nonholonomic Systems in Terms of Quasi-Coordinates

Based on the concept of adiabatic invariant, the perturbation to Mei symmetry and adiabatic invariants for nonholonomic mechanical systems in terms of quasi-coordinates are studied. The definition of the perturbation to Mei symmetry for the system is presented, and the criterion of the perturbation to Mei symmetry is given. Meanwhile, the Mei adiabatic invariants for the perturbed system are obtained.

Unified symmetry of the holonomic system in terms of quasi-coordinates

This paper discusses the unified symmetry of a holonomic mechanical system in terms of quasi-coordinates under special infinitesimal transformations in which time is not varied. The differential equations of motion of the system are given. The definition and the criterion of the unified symmetry for the system are presented. A new conserved quantity, besides the Noether conserved quantity and the Hojman conserved quantity, is deduced from the unified symmetry. An example is iven to illustrate the application of the results.

Non Noether conserved quantity of the holonomic mechanical systems in terms of quasi-coordinates ——An extension of Hojman theorem

Using the Lie symmetry under infinitesimal transformations in which the time in not variable,a new conserved quantity of holonomic mechanical systems in terms of quasi-coordinates is studied.The differential equations of motion of the systems are established.Determining equations of Lie symmetry under infinitesimal transformations are given.The Hojman theorem is generalized.Finally,an example is given to illustrate the application of the results.