Elastic Suspension Research Articles

Application of the ellipse of elasticity theory to the functional analysis of planar compliant mechanisms

In the last decades, a wide range of methods have been proposed for the analysis of compliant mechanisms. In this investigation, the theory of the ellipse of elasticity is tailored to the linear kinetostatic analysis of flexible systems. The proposed approach exploits the antiprojective polarity transformations of the conic associated to the generic two-port elastic suspension. According to the presented method, the elastostatic features of flexible elements with complex geometries, and of compliant mechanisms with serial, parallel, and hybrid topologies, can be represented by a unique geometric entity. As a consequence, the deflection analysis problem is reduced to a geometric problem with a straightforward solution. A specific procedure is developed both at the element and at the mechanism levels, to completely describe field of displacements and loads distribution in the elastic suspension. The application of the method is exemplified considering the analysis of different flexures and of a compliant four-bar linkage.

Three-Dimensional Performance Evaluation of Hemispherical Coriolis Vibratory Gyroscopes

In this paper, the oscillation patterns and characteristics of gyroscopic reaction to rotation-induced Coriolis force and phase relations are reviewed by examining the main principles of operation of Coriolis vibratory gyroscopes based on the dynamic relations and proposed improvements in performance using parameter changes. Coriolis vibratory gyroscopes (CVGs) are among the most modern applicable gyroscopes in position detection that have replaced traditional gyroscopes due to some great features of the design of vibrating proof mass and elastic suspension. Given the key characteristics of capacitive versus piezoelectric excitation technologies for determining the vibration type in sensors, their operating principles and equations have completely changed. Therefore, two-dimensional finite element analysis is required to evaluate their optimal performance. Since the sensor space is constantly vibrating, a general equation is presented in this paper to explain the impact of parameters on the frequency of different operating modes. The main purposes of building vibrating gyroscopes are replacing the constant spinning of the rotor with a vibrating structure and utilizing the Coriolis effect, based on which the secondary motion of the sensitive object is generated according to the external angular velocity.

Vertical vibrations of a freight car as a uniaxial carriage from a wave of unevenness of the path

The paper gives the results of mathematical modeling of movement of a loaded wagon with elastic suspension under viscous friction force equivalent to the dry friction force. Parameters of vertical relative forced vibrations have been found, which are stipulated by the wave of road irregularity.

Modelling and calculation of stumulated oscillation for a crushing plant with vibration

The paper presents the results of the mathematical modelling of external stimuli to improve the efficiency of the removal of grain material from the grinding zone. Thus, the authors proposed to improve the evacuation conditions of the finished product from the working chamber of the crushing plant, as one of these solutions to improve the grinding process in crushers. As a result of creation of external vibrating influence. For this purpose, the calculation chart for modelling the proceeding process of the crushing plant body movement is created which takes into account weight and sizes of the crusher, weight, angular velocity of rotation and eccentric piece location, as well as rigidity of an elastic suspension on which the crusher is established. For the solution of the posed problem, we used methods of analytical mechanics, the Lagrange equation of the second kind, for the mechanical system with two degrees of freedom. As a result of calculations amplitude-frequency characteristics of mechanical system are determined. The conclusion about the choice of the angular velocity of the eccentric rotation for creation of necessary external stimulating influence on the crushing system and improvement of conditions of evacuation of a ready product from a working zone is given. The resonance frequencies of firstand second-order system vibrations and the vibrator frequency are determined to achieve resonance frequencies. Keywords: vibration, modelling, Lagrangian equations of the second kind, grinding, crushing plant.

Исследование динамики механической системы с нелинейным упругим подвесом и спектральный анализ результатов

The article considers the dynamics of a nonlinear mechanical system under the action of a kinematic perturbation on it. The object's vibration isolation system is described by a rigid cubic power characteristic and is based on compensation of external perturbations — the introduction of an additional elastic element with negative stiffness into the suspension. Numerical modeling of the system is performed, the results of which are analyzed by the method of spectral analysis, based on the representation of the correlation function on a small time interval by a square polynomial. As a result of the analysis, it is found that in the pre-resonant and resonant regions, the general solution should consist of three components: a subharmonic of the order of 1/3, the fundamental harmonic, and the third harmonic. It is noted that only the subharmonic of the order of 1/3 and the fundamental harmonic are important in the resonant zone. It is also noted that even simple nonlinear mechanical systems in the study of dynamics should use approximate analytical and numerical methods in combination with spectral analysis, since traditional methods of nonlinear mechanics are not adapted to solving problems taking into account a relatively large number of harmonic components that appear due to nonlinearity.

Магнитная система одноосного инерционного магнитожидкостного акселерометра

Today, a physical problem of engineering design of inertial magnetic fluid accelerometers to measure dynamic processes is relevant. The main drawback of modern sensors is the nonlinear characteristic of the forced response, which limits the application area of the sensors to the case of quasi-static action (tilt angle sensor). The reason of nonlinearity is the design of the magneto-mechanical system of the elastic suspension of the inertial mass made in the form of a pair of permanent ring magnets. This drawback can be eliminated by designing an axisymmetric electromagnetic system that generates a magnetic field with a linear intensity gradient along the symmetry axis. Thus, the paper is devoted to this problem and experimental approvement of the results on a laboratory sensor prototype. The Monte Carlo algorithm is used to calculate electromagnetic system containing permanent magnets and magnetizing coils. The algorithm is implemented using the C++ programming language. Measurements of the most important parameters of the magnetic field from the point of view of the purpose of the study are carried out on the assembled model of the electromagnetic system of the accelerometer. The calculation of electromagnetic system that generate permanent magnetic field with linear intensity gradient along the symmetry axis is carried out. The applicability of the Monte Carlo method to solve similar engineering problems is shown. The measurements of the magnetic field strength of a given configuration have been made. The force of the magnetic field acting on the test sensitive element with a constant magnetic moment is measured. A comparison of the calculated magnetic field with the field of a real system is carried out. It shows satisfactory agreement between the calculated data and the real ones. A linear dependence of the restoring force on the displacement coordinate of a body with a constant magnetic moment from the equilibrium position is shown. The linearization of the response of the mechanical part of the magnetic fluid accelerometer is achieved by choosing the desired configuration of its electromagnetic system, which allows making reliable measurements of both static and dynamic quantities.

ОЦЕНКА АКТУАЛЬНОСТИ ИСПОЛЬЗОВАНИЯ РЕКУПЕРАТИВНОЙ ПОДВЕСКИ С ЛИНЕЙНЫМ ЭЛЕКТРОМАГНИТНЫМ ГЕНЕРАТОРОМ В КОНСТРУКЦИИ ЛЕСОВОЗНОГО АВТОМОБИЛЯ

The relevance of increasing the efficiency of a logging vehicle by using regenerative shock absorbers in the design of its suspension is sub-stantiated. The analysis of scientific works of foreign authors involved in research in the field of recuperation of various types of energy in the shock absorbers of vehicle suspensions has been carried out. Possible options for the appearance of a disturbing force and deformation in hydraulic shock absorbers and elastic suspension elements of a logging vehicle during its movement along an insufficiently equipped logging road are described. A mathematical de-scription of the processes occurring in the sus-pension system of a timber vehicle equipped with hydraulic shock absorbers and spring sus-pension is presented. The dependences of the change in the power dissipated by the hydraulic shock absorber in various frequency ranges are given. A perspective scheme of a linear elec-tromagnetic generator installed in the suspension of a timber vehicle is proposed. Its device, principle of operation, as well as advantages are described. The tasks are formulated, the solution of which will allow the prototype of the modified design of the regenerative shock ab-sorber to be put into mass production.

Research of ergonomic parameters of ambulance buses

The article considers a mathematical model of the movement of an ambulance bus, with the placement of stretchers in it for transporting the wounded with an elastic suspension system of stretchers. The results of tests of the bus movement on a section of road with a profiled cobblestone coating are presented. Calculated and experimental graphs of changes in vibration accelerations at the points of attachment of the stretcher to the bus body were obtained. Recommendations are given for improving the bus springing system and the stretcher elastic suspension system. Keywords: ambulance bus, bus springing system, stretcher, stretcher suspension, vibration load, vibration acceleration

Elastic Obstacle-Surmounting Pipeline-Climbing Robot with Composite Wheels

Regular inspection and maintenance can ensure safe working conditions of transport pipelines without leakage and damage. Pipeline-climbing robots can be used for rapid inspection of pipelines, effectively reducing labor costs and time consumption. For the annular pipelines outside spherical tanks, the special distribution and installation form presents more high obstacles, and puts forward higher requirements for the robot’s climbing performance and obstacle-surmounting ability. An elastic obstacle-surmounting pipeline-climbing robot with composite wheels is proposed in this paper. The designed elastic shock-absorbing suspension mechanisms and composite wheels were designed to increase the stability and obstacle-surmounting ability of the robot. The adjustable robot frame and rotating joint mechanisms allowed the robot to adapt to pipelines of different diameters and radians. Force analysis and simulation of obstacle surmounting by the robot were performed. Experiments were conducted on a 110-mm diameter pipeline to test the payload performance and obstacle-surmounting ability of the robot. With its elastic shock-absorbing suspension mechanisms, the pipeline-climbing robot could carry a 30 kg payload and stably climb the pipeline. The maximum height of obstacles surmounted by the composite wheels of the robot was 20 mm. In the process of surmounting obstacles, the velocity and inclination angle of the robot could remain relatively stable. This novel composite wheels and mechanisms can improve the performance of the pipeline-climbing robot and solve the problem of surmounting high obstacles. By carrying various equipment and instruments, the robot can promote the automated maintenance and inspection of complex pipelines.

Simulation of a multifunctional micromechanical gyroscope

The possibility of constructing a multifunctional inertial navigation device based on a hybrid-type modulation micromechanical gyroscope is considered. A mathematical model of the device ("heavy" gyroscope) as a high-quality three-dimensional oscillatory system is constructed. It is numerically shown that, under certain conditions, the reaction of the system to the motion of an object has, along with precession, the observed nutation, which carries information about the linear motion of the gyroscope base. It is noted that the possibility of measuring linear accelerations is ensured by the presence of a small symmetrical distance between the axes of the elastic suspension relative to the center of mass of the sensing element. The results obtained make it possible to implement a two-component angular velocity meter and a two-component linear acceleration meter in one device.

Non-linear Isolator for Vibration and Force Transmission Control of Unbalanced Rotating Machines

PurposeThe objective of this paper is to investigate with simulations how non-linear spring and non-linear damper components of isolators can be employed to effectively reduce both the oscillations and the force transmitted to ground in the whole spinning range of unbalanced rotating machines.MethodsThe principal goal of this paper is twofold. First, to present a concise and consistent formulation based on the harmonic balance approach for the vibration response of spinning machines mounted on linear/non-linear, softening/hardening, un-tensioned/pre-tensioned springs and linear/non-linear dampers. Second, to provide a comprehensive overview of the vibration and force transmission control with non-linear isolators specifically tailored to unbalanced machines.ResultsThe study has shown that, the best vibration isolation is provided by a pre-tensioned linear and cubic softening spring combined with a linear and negative quadratic damper. The pre-tensioned spring should be designed in such a way as it holds the weight of the machine and thus produces on the vibrating machine a symmetric elastic restoring force proportional to the linear and cubic powers of the displacement. The cubic softening stiffness should then be tuned to minimise the frequency, and thus the amplitude, of the resonant response of the fundamental mode of the machine and elastic suspension system, while preserving stability and a desired static deflection. In parallel, to reduce the force transmission to ground above the fundamental resonance frequency, the negative quadratic damping effect should be tailored to maximize the energy absorption at higher frequencies.ConclusionThe study has shown that non-linear spring and non-linear damper components can be effectively employed to control the vibration and force transmission in the whole spinning range of the machine. In particular, a pre-tensioned softening cubic non-linear spring can be used to mitigate the vibration and force transmission at low frequencies, close to the fundamental natural frequencies of the elastically suspended machine. Also, a negative quadratic non-linear damper can be used to tailor the energy dissipation of the isolator in such a way as to have high damping at low frequencies and low damping at higher frequencies, which enhances the vibration and force transmission control at low frequencies and, rather importantly, mitigates the force transmission at higher frequencies.

Methodology of Force Parameters Justification of the Controlled Steering Wheel Suspension

The methodology for selecting the main force parameters of nonlinear non-conservative suspension for the main performance characteristics of wheeled vehicles has been developed based on the longitudinal-angular oscillations. The following has been established: a) change limits of static deformation of the elastic suspension system and its other parameters at which the basic operational characteristics for various ranges of amplitude change are satisfied; b) the amplitude of the initial perturbation of oscillations depending on the shape of the inequality and its entry speed; c) the influence of the main characteristics of damping devices on the amplitude-frequency characteristics. The results of this work can be a basis for the choice of such parameters of the considered controlled suspension, which ensure the stability of the vehicle along the curved sections of the road, its controllability, etc.

Non-Linear Oscillations of the Channel Wall Filled with a Viscous Liquid Induced by the Vibrating Foundation

The paper considers the issues of mathematical modelling nonlinear vibrations for the wall of a narrow parallel walled channel filled with a viscous incompressible liquid. The upper channel wall is a rigid rectangular plate supported by nonlinear spring with a cubic restoring force, while the bottom one is a fixed rigid rectangular plate. The case of nonlinear oscillations of the upper channel wall due to channel’s foundation vibration has been investigated in the frame of hydroelasticity problem. The main attention is paid to the consideration of steady-state nonlinear oscillations for the upper channel wall and the creeping motion of the liquid in the channel. The liquid layer reaction acting on the upper channel wall is found and the channel’s wall nonlinear oscillation equation is obtained taking into account the energy dissipation due to the liquid viscosity. It was shown that this equation coincided with the Duffing one. The solution of the nonlinear oscillation equation was carried out by the harmonic balance method. Based on the found solution, the hydroelastic response of the channel wall on a nonlinear elastic suspension to the channel foundation vibration was determined.

Circumferentially rotatable inspection robot with elastic suspensions for bridge cables

PurposePeriodic inspection of bridge cables is essential, and cable-climbing robots can replace human workers to perform risky tasks and improve inspection efficiency. However, cable inspection robots often fail to surmount large obstacles and cable clamps. The purpose of this paper is to develop a practical cable inspection robot with stronger obstacle-surmounting performance and circumferential rotation capability.Design/methodology/approa/chA cable inspection robot with novel elastic suspension mechanisms and circumferential rotation mechanisms is designed and proposed in this study. The supporting force and spring deformation of the elastic suspension are investigated and calculated. Dynamic analysis of obstacle surmounting and circumferential rotation is performed. Experiments are conducted on vertical and inclined cables to test the obstacle-surmounting performance and cable-clamp passing of the robot. The practicality of the robot is then verified in field tests.FindingsWith its elastic suspension mechanisms, the cable inspection robot can carry a 12.4 kg payload and stably climb a vertical cable. The maximum heights of obstacles surmounted by the driving wheels and the passive wheels of the robot are 15 mm and 13 mm, respectively. Equipped with circumferential rotation mechanisms, the robot can flexibly rotate and successfully pass cable clamps.Originality/valueThe novel elastic suspension mechanism and circumferential rotation mechanism improve the performance of the cable inspection robot and solve the problem of surmounting obstacles and cable clamps. Application of the robot can promote the automation of bridge cable inspection.

Модифицирование спортивных подвесных систем для использования в реабилитационном процессе

В работе представлен обзор литературы, посвященной использованию спортивных подвесных систем в реабилитационном процессе. Подвесная терапия, или cлинг-терапия, — это метод физической реабилитации с использованием разнообразных систем подвеса всего тела или конечностей. Эти системы в настоящее время широко используются как в восстановительном лечении, так и в тренировочном процессе. Обсуждается возможное модифицирование спортивных подвесных систем путем использования эластичных подвесов. Применение эластичных подвесов в спортивных вариантах подвесных систем позволяет не только выявить слабое звено в скелетно-мышечной цепи, но и откорректировать его, используя разнообразные динамические упражнения. Так, использование эластичных подвесов дает возможность активизировать более слабые мышечные группы, чередуя выполнение динамических и статических упражнений. При этом врач имеет возможность проследить за тем, чтобы в выполнении движения не участвовали другие, более сильные мышечные группы. Включение в выполнение движения компенсаторных мышц является сигналом к завершению или изменению условий выполнения упражнений. Таким способом возможно сформировать и натренировать правильный двигательный паттерн у пациента, не прилагая больших усилий. Применение эластичных подвесов дает возможность увеличивать или уменьшать нагрузку, не изменяя количество повторений упражнения и, соответственно, не изменяя длительность занятия.

Вращательное и поступательное галопирование призм в воздушном потоке

In experiments in a wind tunnel, oscillations of three prisms with a rectangular cross section are studied. The prisms are located perpendicular to the velocity vector of the incoming flow and are limited from the ends by end plates that prevent air flow. The elastic suspension allows body oscillation with six degrees of freedom. It turned out that under the action of the air flow, two modes of oscillation of prism realized: translational oscillations in the direction perpendicular to the generatrix of prismatic bodies and the flow velocity, and rotational oscillations around an axis that is parallel to the generatrix, passes through the center of the prism and is perpendicular to the velocity of the incoming air flow. The tension of the two springs included in the elastic suspension is measured by the strain gauge method during the oscillation. The calibration experiment makes it possible to link the amplitudes of spring tension oscillations and phase shift with the amplitudes of rotational and translational oscillations of prisms. It turned out that a prism with a height-to-width ratio of 0.22 in the flow is subject to rotational oscillations. An increase in the ratio of height to width to 0.36 leads to a decrease in the amplitude of rotational oscillations and the appearance of translational ones. The ranges of existence of rotational and translational oscillations overlap. A further increase in the ratio of height to width to 0.43 is accompanied by intensive translational galloping.

Rotational and translational galloping of prisms in the air stream

In experiments in a wind tunnel, oscillations of three prisms with a rectangular cross section are studied. The prisms are located perpendicular to the velocity vector of the incoming flow and are limited from the ends by end plates that prevent air flow. The elastic suspension allows body oscillation with six degrees of freedom. It turned out that under the action of the air flow, two modes of oscillation of prism realized: translational oscillations in the direction perpendicular to the generatrix of prismatic bodies and the flow velocity, and rotational oscillations around an axis that is parallel to the generatrix, passes through the center of the prism and is perpendicular to the velocity of the incoming air flow. The tension of the two springs included in the elastic suspension is measured by the strain gauge method during the oscillation. The calibration experiment makes it possible to link the amplitudes of spring tension oscillations and phase shift with the amplitudes of rotational and translational oscillations of prisms. It turned out that a prism with a height-to-width ratio of 0.22 in the flow is subject to rotational oscillations. An increase in the ratio of height to width to 0.36 leads to a decrease in the amplitude of rotational oscillations and the appearance of translational ones. The ranges of existence of rotational and translational oscillations overlap. A further increase in the ratio of height to width to 0.43 is accompanied by intensive translational galloping. Keywords: galloping, bluff body, wind tunnel, strain gauge, translational oscillations, rotational oscillations.

Influence of hull oscillations on loads in the power train of a crawler vehicle

This paper considers the experience of creating a dynamic model of the power train of a crawler vehicle taking into account the hull oscillations on an elastic suspension. A tractor with a conventional caterpillar is analyzed as an example. The research is carried out on the numerical method of modeling dynamic processes on the basis of solving the system of differential equations of motion by the Runge-Kutta method. The power train is represented in the system of differential equations as a set of concentrated masses and elastic connections between them, and the hull of the tractor is represented by five masses according to the considered degrees of freedom. In this research, we acknowledged cases of vehicle starting under different conditions of resistance to motion and under the drawbar pull of different magnitudes. According to the results of the analysis, we have estimated the influence of hull oscillations of the crawler tractor on the loads acting in the power train during the starting process.

Improvement of Machine Protection against Vibration

The need to improve the methods of vibration protection for power plants and technological equipment is substantiated in the article. When using the traditional elastic suspension for the vibration isolation efficiency, the stiffness of the suspension should be minimal, but to limit the mobility of the object protected from vibration, it should be, in contrast, maximum. In order to eliminate this contradiction and increase the efficiency of the vibration isolation mechanisms, the use of additional special devices in the form of stiffness compensators is proposed. A theoretical substantiation of the advantages of stiffness compensators based on the analysis of the vibration isolation mechanisms force characteristics is given. It is proved that the vibration-isolating mechanisms with stiffness compensators significantly change the function of the force transmitted to the base of the mechanism protected from vibration. An expression for evaluating the efficiency of using vibration isolators with stiffness compensators as compared with conventional spring-loaded elastic mechanisms is presented. Design of the vibration isolator with stiffness compensators on the basis of spherical rolling bodies is proposed. Theoretical materials confirming the effectiveness of the proposed technical solution are given. Vibration isolating mechanisms with stiffness compensators provide stable equilibrium of the vibration system, as well as allow to change the total stiffness of the vibration isolator and set the shape of the force characteristic. As a result, it is possible to change the frequency of natural vibrations of the system without changing its carrying capacity.

High-performance inline RF MEMS switch for application in 5G mobile networks

This article presents the results of the design and analysis of a radio-frequency switch made using microelectromechanical systems technology. The device is the capacitive switch with a hybrid type of contact, in which the movable electrode of the structure – the metal membrane is part of the microwave signal line of the coplanar waveguide. The switch design is characterized by a high capacitance ratio and low contact resistance. The zig-zag elastic suspension is used to reduce the value of the pull-down voltage – 2 V and the switching time ∼ 7 us. The central resonant frequency of the switch is 3.8 GHz. In this case, in the open state, the value of the insertion loss is not more than -0.2 dB and the isolation value in the close state is not less than -55 dB. The effective frequency range is the S-band, as well as the C-, X- and Ku-band, in which the isolation value is at least -30 dB. The presented inline RF MEMS switch is suitable for use in various types of ground and satellite communications, in particular for devices and systems of 5G mobile networks.