Elastic Links Research Articles

Adaptive selective-invariant control of tracking electric drives with elastic kinematic transmissions

Currently, high quality indicators of adaptive versions of selective-invariant electromechanical systems designed to control the speed in a wide range have been obtained. Thus, it lays the groundwork for effective use of the proposed synthesis methods and obtained structural solutions in the systems of contour-positional and tracking control of angular displacements of the working elements of technological machines. The implemented structural-parametric synthesis is based on the methods of the theory of modal control, reduction of regulators, the principles of selective invariance, separation of the rates of movement of local subsystems, adaptive, contour-positional and tracking control. The study has been carried out by detailed computational experiments with models of synthesized electromechanical systems. The features of synthesis and functioning of adaptive selective-invariant systems with elastic kinematic links in the tracking and positioning modes are described. The combination of the principles of tracking, selective-invariant and adaptive control in the structure of a single electromechanical system makes it possible to fully provide new opportunities for the implementation of high-precision dynamic control of working machines.

Stochastic analysis of lattice, nonlocal continuous beams in vibration

In this paper, we study the stochastic behavior of some lattice beams, called Hencky bar-chain model and their non-local continuous beam approximations. Hencky bar-chain model is a beam lattice composed of rigid segments, connected by some homogeneous rotational elastic links. In the present stochastic analysis, the stiffness of these elastic links is treated as a continuous random variable, with given probability density function. The fundamental eigenfrequency of the linear difference eigenvalue problem is also a random variable in this context. The reliability is defined as the probability that this fundamental frequency is less than an excitation frequency. This reliability function is exactly calculated for the lattice beam in conjunction with various boundary conditions. An exponential distribution is considered for the random stiffness of the elastic links. The stochastic lattice model is then compared to a stochastic nonlocal beam model, based on the continualization of the difference equation of the lattice model. The efficiency of the nonlocal beam model to approximate the lattice beam model is shown in presence of rotational elastic link randomness. We also compare such stochastic function with the one of a continuous local Euler-Bernoulli beam, with a special emphasis on scale effect in presence of randomness. Scale effect is captured both in deterministic and non-deterministic frameworks.

Research of the electrical complex of a conveyor with two wire drums

The electrical equipment and control system of the conveyor conveyor electric drive are considered. The functional and structural diagrams were drawn up. The analysis of the operation of one-and two-drum electric drives is carried out. Structural diagrams of the mechanical part of the conveyor were obtained. A mathematical description was compiled and modeling of the investigated electric drive was carried out. The structure and model of the elastic link are compiled taking into account the friction forces. The use of a smoothing filter in the speed reference circuit makes it possible to eliminate fluctuations in the system from the reference signal. A mathematical model of the electrical complex has been compiled and its modeling has been carried out. The results obtained confirm the effectiveness of the application of the corrective coupling based on the elastic moment signal.

Frictional Impact-Contacts in Multiple Flexible Links

Multiple impacts of 2D (planar) open-loop robotic systems composed of [Formula: see text] elastic links and revolute joints are studied in this paper. The dynamic equations of motion for such systems are derived by the Gibbs-Appell recursive algorithm, while the regularized method is employed to model the impact-contact mechanism. The Timoshenko beam theory is used to model the transverse vibrations of the links. Also, both the structural damping and air damping are considered to enhance the modeling accuracy. The system joints are assumed to be frictionless and slack-free, but friction force is included for the links colliding with the ground. The [Formula: see text]-flexible-link system considered goes through a flight phase and an impact phase during its motion. In the impact phase, new equations of motion are derived by including the terms caused by the viscoelastic forces in the system’s differential equations. Owing to the extremely short acting time of the impact force, the related differential equations can be solved only via special treatment, i.e. by detecting the exact moment of impact. To this end, entering or leaving the impact phase is analyzed and controlled with high precision by a special computational algorithm presented in this work. To demonstrate the efficacy and precision of the algorithm developed, computer simulations are conducted to study the dynamic behavior of a 3-link robotic mechanism. To investigate the effect of mode shape on the elastic deformation of links, four different mode shapes are used in the simulations and their results are compared.

An optimization-based approach for elasticity-aware trajectory planning of link-elastic manipulators

Elastic manipulators often result from lightweight construction or safety requirements in human–robot-collaboration scenarios. In many cases, vibration-damping becomes necessary to enable stable and precise operation, which imposes high demands on controllers. A fundamental challenge for link-elastic manipulators with general kinematics and no dedicated damping actuators is the potential inability of a joint to control the vibration of a link depending on the manipulator’s configuration. Numerous control concepts assume a sufficiently high ability to control vibrations by, for example, dedicated actuators or special kinematic structures. This work presents an online, optimization-based motion planning approach with three methods for maximizing this ability for link-elastic manipulators. The planning algorithm utilizes modified cost functions to incorporate the controllability of vibrations by prioritization and adaptive activation of competing objectives. The effectiveness of the approach is demonstrated on a real manipulator with 3 actuated DoFs and two elastic links in different disturbance scenarios. The results show that the amplitudes of vibrations caused by disturbances decay noticeably faster than with conventional motion planning.

Passive Nonreciprocity in a System of Asymmetrical Rotational Oscillators

In this paper we investigate an elastically linked, nonlinear, in-plane rotator system and experimentally study its nonreciprocal impulse response. The nonlinearity of the system arises from the angled elastic linkage in rotational motion. A chain of rotators coupled with such linkages reaches an acoustic vacuum when the pretension of the elastic links vanish, leading to large nonlinearity tunable via small pretension. Using an analytical model and experimental exploration, we observe a broadband nonreciprocity in a weakly pretensioned, asymmetric, three-rotator system. In addition, we use a nonlinear normal-mode (NNM) analysis, capturing the main qualitative dynamics of the response, to explain the observed nonreciprocity mechanism. The analysis shows that equal applied impulses, combined with energy-dependent frequency and mode shapes, result in robust nonreciprocity features, contrary to the reciprocal response present in the linear counterpart of this system.

Present problems of vibration isolation in heavy mining machines at long-term cyclic loads

Abstract. An integrated approach was used, including the construction of a mathematical model and the results of lengthy industrial tests of heavy mining machines with rubber elastic bonds. The issues of vibration isolation of heavy machines operating in extreme conditions, i.e. with prolonged cyclic loads and the influence of an external aggressive environment inherent in mining and processing enterprises. As an example, we con-sider vortex mixers with a vibration isolation system containing rubber elements. During long-term operation, the mass of the mixer does not remain constant; its increase is associated with the sticking of the initial product on the moving parts of the ma-chine. The location of such machines in the sinter factory at + 10.4 m, as well as the change in time of rotational symmetry of the drum rotation imposes certain requirements on the vibration isolation system: the system must be "soft" and stable in time, i.e. during 9-10 years of operation, its stiffness and dissipative parameters should not go beyond the permissible values. In order to reduce the aging effect, type 2959 rubber based on natural caoutchouc with a reinforced protective group was used, while the instability of the main mechanical parameters was taken into account in the developed theory of vibration isolation of machines. On the basis of the developed simulation model and the Boltzmann-Volterra integral relations with kernels of relaxation and aftereffect, an equation was worked out, which made it possible to take into account the rubber viscoelastic properties in full volume; in this equation, stiffness operator of elastic suspension in the machine is written by using fractional exponential function of the Yu. Rabotnov's type; on the basis of the mathematical model, the basic parameters of the machine under the study were calculated; in particular, for the vortex mixer, the time dependences of amplitude of the mixer housing vibrations and coefficient of vibration isolation efficiency were calculated with taking into account aging of elastic link material in the ma-chines; the calculation results were compared with the results of industrial tests of the vortex mixer operation lasting for 16 years. The theory and method for calculating vibration isolation systems with rubber elastic links for heavy mining machines were developed with taking into account material structure changes due to the effects of aging. The paper considers an example of calculating the mixer vibration isolation system taking into account rubber aging; the magnitude of the change in time of the main mechanical parameters was obtained experimentally over 16 years. This made it possible to determine temporary changes in the amplitude of oscillations of the mixer body and the coefficient of efficiency of the vibration isolation system. It was shown that the mixer vibration isolation system remained effective for 9-10 years, after which the mechanical characteristics of the rubber went beyond the permissible values and the system lost its functional pur-pose, and the amplitude of the mixer body exceeded the existing sanitary standards.

Calculation of rubber-metal silent-blocks under quasi-static loading

Abstract. In this paper, an algorithm for calculating rubber-metal silent blocks (hinges) under the action of a lateral quasi-static load is presented. Silent blocks of a welded type made of new brands of rubbers, which are widely used in vibration machines of various types as elastic links, are considered. A calculation is given for a very long hinge, for which the length is large compared to its outer diameter. In the calculation, it was assumed that there are no axial displacements, and the angular and radial displacements can be represented as a product of arbitrary functions of the radial coordinate and the sine and cosine of the angular coordinate, respectively. The relationship between these functions is obtained from the condition of rubber incompressibility. From the condition of the minimum total energy of the system, we have a linear inhomogeneous differential equation of the third order for one of these functions. By solving it under known boundary conditions, we obtain final expressions for the radial and angular displacement, and, consequently, for the displacement of the inner cage. With taking these expressions into account, a solution was also obtained for the hinge, the length of which cannot be considered infinite in comparison with its diameter. In this case, axial displacements should also be considered. Besides, it is assumed that the functions of the radial coordinate for the radial and angular displacement can be represented as a linear combination of the corresponding functions for the long hinge. The corresponding function for axial displacement can be found from the condition of volume constancy. The linear combination coefficients are obtained from a system of two linear algebraic equations, to which the minimum condition for the total energy of the system leads. The exact expression for the movement for the short hinge is rather cumbersome. But for the most common sizes of rubber-metal hinges, you can use a series expansion of the expression for displacement and thus get a fairly simple formula. By comparing the resulting expression with the expression for displacement of the long hinge, you can see that the formula for the infinitely long hinge can only be used if a certain condition is met that binds the dimensions of the hinge. At the end of the paper, an example of calculating a rubber-metal element ШРМ-102, which is under the action of a radial load, is given. The rubber layer in it is made of a new medium-filled rubber made of natural rubber. The obtained value of the displacement of the inner cage is in good agreement with the experimental data.

Strong Connection between Elastic Body and Porous Link and Investigation for Actuator Application

Strong Connection between Elastic Body and Porous Link and Investigation for Actuator Application

DYNAMICS OF HEAVY VIBRATING MACHINES TAKING INTO ACCOUNT INSTABILITY IN TIME OF THEIR PARAMETERS

Underground mining of uranium ores consists of several technological processes, one of the most important of which is the release of broken rock from the working excavation zone and loading it into transportation vehicles. The issue of increasing the intensity of production requires a simultaneous increase in the productivity of all production processes, including the production of mineral raw materials. At the same time, it is necessary to create both a high-performance and a safe process. This problem is successfully solved by the use of vibration machines with elastic links made of elastomeric materials, which, along with an increase in productivity, can reduce energy consumption and the number of freezes. An integrated approach was used, which includes analytical studies and results of industrial tests of vibratory feeders for underground mining and delivery of uranium ores and building materials. On the basis of the developed algorithm and synergistic model of fatigue microfracture of rubber links in vibratory feeder, mathematical equations were obtained, which made it possible to describe dynamics of feeders with time-depending parameters; when solving the integro-differential equation of the oscillatory system, the dependence of the amplitude characteristics of the feeder on the time of its operation is obtained. An original algorithm and synergistic model were developed, and on their basis, a mathematical apparatus was created, which allowed determining change of amplitude of vibratory feeder oscillations during its operation. On the basis of analytical calculations, a method was developed and introduced for predicting changes of parameters change of oscillation amplitudes of vibratory feeder used for underground mining and feeding of uranium ores.

MODELING OF AIRCRAFT STEERING CONTROL SYSTEM WITH TRACTION ELECTRIC DRIVE BY USED AN ADAPTIVE FUZZY CONTROLLER

One of the main tasks of the last two decades is to find ways to optimize energy consumptions for aircrafts. The commercial aviation business is increasingly using environmental monitoring systems and electrical control by using AC and DC tires. One of the trends in the development of aircraft control systems is the replacement of hydraulic and pneumatic systems with electrical ones. The aerospace industry and airlines are interested in performing steering operations without major engines. This operation method allows to save fuel, reduce brake wear, eliminates towing and achieve decreasing of environmental pollution. In the future it is necessary to implement electric steering using a traction drive (TD) based on a synchronous motor with permanent magnets (PMSM). This system is powered by an available auxiliary power unit or other sources such as fuel cells or batteries. This study presents a highly efficient electric steering system as a modern solution for improving the ground operations of modern aircraft powered by main engines. The system was investigated using steering profiles for takeoff and landing. The study determined the effectiveness of its use for steering. The influence of external factors and the change of parameters of the electromechanical system of wheel with an elastic tire were investigated. The results of modeling the dynamic processes of an electromechanical system containing elastic links in the conditions of parametric perturbations confirmed the robust stabilization of dynamic control quality indicators based on the laws of fuzzy logic.

A Stiffness Variable Passive Compliance Device with Reconfigurable Elastic Inner Skeleton and Origami Shell

Devices with variable stiffness are drawing more and more attention with the growing interests of human-robot interaction, wearable robotics, rehabilitation robotics, etc. In this paper, the authors report on the design, analysis and experiments of a stiffness variable passive compliant device whose structure is a combination of a reconfigurable elastic inner skeleton and an origami shell. The main concept of the reconfigurable skeleton is to have two elastic trapezoid four-bar linkages arranged in orthogonal. The stiffness variation generates from the passive deflection of the elastic limbs and is realized by actively switching the arrangement of the leaf springs and the passive joints in a fast, simple and straightforward manner. The kinetostatics and the compliance of the device are analyzed based on an efficient approach to the large deflection problem of the elastic links. A prototype is fabricated to conduct experiments for the assessment of the proposed concept. The results show that the prototype possesses relatively low stiffness under the compliant status and high stiffness under the stiff status with a status switching speed around 80 ms.

Establishing patterns in the dynamic loading on the body of a semi­wagon with an elastic middle part of the girder beam

To reduce the dynamic loading and prolong the service life of a semi-wagon's girder beam by improving its fatigue strength, it has been proposed to improve its design. A special feature of the girder beam is that its middle part (the distance between the rear supports of auto-couplings) consists of a U-shaped profile, covered with a horizontal sheet above which an I-beam is located. Elastic elements are placed between the horizontal part of the U-shaped profile's shelf and the sheet. Mathematical modeling was performed to substantiate the proposed technical solution. A mathematical model has been constructed describing the fluctuations of the bouncing wagon. It has been established that the maximum vertical acceleration of the body is about 1.8 m/s 2 (0.18 g), and of the bogie ‒ about 9.0 m/s 2 (0.9 g). Based on our calculations, we can conclude that a wagon's movement is assessed as excellent. In this case, the use of the girder beam with elastic links makes it possible to reduce the dynamic load on a wagon, in comparison with the prototype, by almost 35 %. The main indicators of the strength of the improved load-bearing structure of a wagon have been determined. The maximum equivalent strains occur, in this case, in the upper horizontal sheet of the girder beam, and are 136.0 MPa, which are lower, by 20 %, than those of the prototype wagon. The results of the modal analysis of the load-bearing structure of a semi-wagon taking into consideration the improvement measures have demonstrated that their natural frequencies of oscillations are within the permissible limits. Our research could help reduce the dynamic loading on the load-bearing structures of wagons in operation, as well as design the innovative structures of rolling stock

Magnetic damped links to reduce internal seismic pounding in base-isolated buildings

A limited gap between closely spaced structural parts may induce internal pounding in seismically isolated structures, because of notable displacement at the level of the isolation system under severe earthquakes. A gap between a fixed-base elevator shaft and the surrounding building is presented here with reference to a reinforced concrete building located in the Sicilian town of Augusta. The building, comprising a basement and three storeys above the ground level, is seismically isolated at the top of rigid columns in the basement with a hybrid isolation system including elastomeric and sliding bearings, while a steel framed elevator shaft crosses the isolation level. Despite the gap, internal pounding may occur at all levels of the superstructure when the elevator with maximum load stops at the upper floors. To reduce structural pounding effects, a magnetic damped link (MDL) between adjacent corners of the elevator and the surrounding building is proposed. This is obtained as an in parallel combination of an eddy current damped link (ECDL) and an elastic helicoidal spring, and occupies less space than traditional passive dampers and transmits considerably less forces compared to a rigid link configuration. Specifically, an ECDL consists of an outer cylindrical copper tube, as conductor, and an inner tube, equipped with an array of axially magnetized and ring-shaped permanent magnets separated by iron pole pieces, as mover. The relative motion between conductor and magnets, during seismic loading, induces an eddy current producing electromagnetic damping. Given that viscoelastic linear behaviour can be hypothesized for the MDL, a simplified iterative design procedure of the ECDL is proposed, with optimization of the thickness and radius of the magnets, thereby enhancing magnetic flux and energy dissipation. The directionality of the near-fault ground motions is investigated through nonlinear seismic analysis, comparing no connection with four configurations of the interconnection: i.e., flexible and rigid elastic links, viscous and magnetic damped links.

Modeling and experimental analysis of a multi-rod parallel continuum robot using the Cosserat theory

Parallel continuum robots get their compliance and compactness from continuum rods while also having the stability and strength of parallel robots. Their potential to provide multi-degree-of-freedom articulation gives them versatility and makes them very useful in various applications. The purpose of this paper is to model a six link parallel continuum robot using the Cosserat theory. The single rod model is initially derived and experimentally verified with an average error of 12%. Then, the parallel continuum robot model is obtained by combining six elastic links, and eventually, some experiments are done on a real system to analyze the results of the obtained model.

MÔ HÌNH HÓA VÀ ƯỚC LƯỢNG PHẦN TỬ LIÊN KẾT ĐÀN HỒI TRONG CÁC HỆ TRUYỀN ĐỘNG ĐIỆN TỰ ĐỘNG NHIỀU ĐỘNG CƠ BẰNG PHƯƠNG PHÁP SỐ

The paper proposes a new approach for solving the problem of determining the optimal estimation model of the elastic linkage element in multi-motor automatic driving systems using the real interpolation method (RIM). Algorithms and programs based on the RIM have been built for a two-motor electromechanical driving model to approximate the original transfer function that describes the elastic linkage element containing inertialand transcendent components by the transfer function in a rational fraction form. Besides,providing a specific function form, the program also calculates estimation errors for different approximate transfer functions, thereby allowing to determine the structure and parameters of the optimal estimation model.

Cylindrical Line-Feeding Growth of Free-Standing Silicon Nanohelices as Elastic Springs and Resonators.

Three-dimensional (3D) construction of free-standing silicon (Si) nanohelices has been a formidable challenge for planar lithography and etching technology. We here demonstrate a convenient 3D growth and integration of Si nanohelices (SiNHs) upon bamboolike cylinders with corrugated sidewall grooves, where the indium catalyst droplets grow around the cylinders in a helical fashion, while consuming precoated amorphous Si (a-Si) thin film to produce crystalline Si nanowires on the sidewalls. At the end of each groove cycle, the droplets are enforced to linefeed/switch into the neighbor groove to continue a spiral growth of SiNHs with readily tunable diameter, pitch, aspect-ratio, and chiral/achiral symmetries. In addition, the SiNHs can be reliably released as free-standing units to serve as elastic links, supports and vibrational resonators. These results highlight the unexplored potential of high precision 3D self-assembly growth in constructing a wide range of sophisticated electromechanical, sensor, and optoelectronic functionalities.

Using Deep Learning to Predict Fracture Patterns in Crystalline Solids

Summary Fracture is a catastrophic process whose understanding is critical for evaluating the integrity and sustainability of engineering materials. Here, we present a machine-learning approach to predict fracture processes connecting molecular simulation into a physics-based data-driven multiscale model. Based on atomistic modeling and a novel image-processing approach, we compile a comprehensive training dataset featuring fracture patterns and toughness values for different crystal orientations. Assessments of the predictive power of the machine-learning model shows excellent agreement not only regarding the computed fracture patterns but also the fracture toughness values and is examined for both mode I and mode II loading conditions. We further examine the ability of predicting fracture patterns in bicrystalline materials and material with gradients of microstructural crystal orientation. These results further underscore the excellent predictive power of our model. Potential applications of this model could be widely applied in material design.

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The problems of calculating dynamic processes are widely used for a broad variety of complex ship mechanisms with elastic-deformable links. The dynamics of elastic ship mechanisms is a complex set of mechanical and physical phenomena. No issue can be solved rationally when designing ship mechanisms without taking into account the requirements of strength and rigidity of individual links and ship mechanisms as a whole. During operation, the ship’s mechanisms are affected by various static and dynamic forces. To withstand the action of these forces, the ship’s mechanisms must have sufficient strength in general and in their individual parts. One of the criteria for the construction material strength is stress, and for the stiffness is displacement. But establishing that the stresses do not exceed the permissible value does not always allow us to conclude that the structure can safely exist. Therefore, the concepts of displacements, deformations and stresses are crucial in strength and stiffness calculations. This is especially important when designing ship mechanisms consisting of a variety of core elements. Since elastic inertial elements are widely represented in them, the calculation of dynamics is essential for them. Currently, the problems of nonlinear dynamics of thin-walled structures under the action of complex loads have become a necessary component of engineering analysis. The calculation of the dynamics of spatial ship mechanisms with nonlinear elastic links by the most promising numerical method allows us to accurately describe both the geometry and the nature of the loads applied to it and the elastic properties of the ship mechanisms material and to analyze their stress-strain state. As well as obtaining reliable data on the load-bearing capacity of anisotropic rod links, it makes it possible to make rational design decisions when designing specific ship mechanisms.

Mechanical Stepless Self-Regulating Transmission for Vehicles

The article discusses a mechanical stepless transmission capable of self-control in a wide range of gear ratios depending on the traction load of the vehicle. Mechanical stepless transmission is based on using angular oscillations of freewheel mechanisms (FWM) and elastic linkages (torsion shafts) enabling multiflow transformation of mechanical power, ensuring the automatic increase of torque on the output shaft of the transmission with a reduction in its frequency or smooth increase of its frequency with concurrent reduction of torque. The article gives basic mathematical dependencies and makes computer simulation of transmission operation. The article shows a Simulink design model that includes an engine block to create an incoming flow of torque and power, a transmission block with parallel branches of freewheels modules for smoothing and converting torque, and a block for determining torque, power, and efficiency at the output of the transmission. The graphs show that the use of parallel freewheel mechanisms allows us to smooth the flow of output torque and power, and greatly reduces the inertial performance of the transmission at the starting moment. The results of the calculations and their analysis show that the proposed self-controlled mechanical stepless transmission has a high torque ratio and ensures the continuous transfer of power to the output shaft with high efficiency. The obtained characteristics tell us that the proposed transmission has an advantage over mechanical transmissions because of the quick response at the moment of vehicle start and the ability to continuously deliver power and torque flow to the output shaft or drive wheels.