Effects Of Spring Stiffness Research Articles

A3-DOF frog-inspired quasi-zero stiffness isolator and its vibration control performance

To pursue a nonlinear isolator with simpler structure, better load adaptability, and wider quasi-zero stiffness (QZS) region, a 3-DOF bionic vibration isolation device is proposed and analyzed inspired by the superior landing performance of the frog's leg structure. The mechanism's dynamical equation is established using Lagrange's principle. The dynamic model is validated using ADAMS simulation. The effects of spring stiffness and rod length on static mechanical characteristics are analyzed. The vibration attenuation performance of the structure is analyzed under independent three-directional excitation and three-directional coupled excitation. Compared with the typical X-shaped QZS isolator and the traditional QZS isolator, the designed structure's advantages is demonstrated. By tuning the parameters and building a control route based on variable-stiffness dielectric elastomer, optimization of the device's vibration isolation performance under coupled excitation was accomplished.

Robotic compliant grinding of curved parts based on a designed active force-controlled end-effector with optimized series elastic component

High-accuracy, fast-response, and low-overshoot force control are important to guarantee the material removal accuracy and surface quality of robotic compliant grinding. In order to achieve the above target, this study develops an active compliant force-controlled end-effector based on a series elastic actuator for the robotic grinding of curved parts. Firstly, a decoupled robotic grinding system composed of an industrial robot and an end-effector is developed, and a novel force-controlled end-effector is designed by adding an elastic component between the servo motor and the load to improve compliance. Secondly, the influences of the elastic component and grinding tool stiffness on the stability of the force-controlled end-effector system are analyzed by establishing a contact model of the compliant end-effector and the transfer function of the entire force control system. Then, the stiffness of the grinding tool and the elastic component are optimized with full consideration of the system cutoff frequency and the end-effector compliance. To improve the force tracking accuracies of the developed compliant end-effector, a proportional-integral (PI) controller with first-order differential force feedforward control is designed. Finally, grinding experiments are conducted for verification. The effects of spring stiffness and grinding tool stiffness on the force control system are tested, which match well with the theoretical analysis. Grinding results show that the maximum force control error of the compliant force-controlled end-effector is decreased by 70% compared to that of the rigid force-controlled end-effector, and the overshoot of the force control is reduced from 30% to almost 0 under the same response speed. The maximum and average absolute grinding depth errors using the designed end-effector are reduced by 57.2% and 58.6%, respectively, compared with those of the traditional rigid end-effector, and the average surface roughness of the finished part is reduced by 19.2%. Which demonstrates the effectiveness and advantages of the proposed compliant force-controlled end-effector.

Human motion energy harvesting backpack using quasi-zero stiffness mechanism

In this study, a quasi-zero stiffness energy harvesting backpack (QZS-EHB) is proposed. The bistable quasi-zero stiffness mechanism is constructed by paralleling a pair of positive stiffness springs and a pair of negative stiffness springs to make the vibration system more easily excited by low-frequency human motion and generate snap-through action. The bidirectional vibration is mechanically modulated into unidirectional higher speed rotation, thus improving the electromechanical conversion efficiency. The theoretical model of the bistable system is established by using the Lagrange functional method to verify the bistable mechanism. A prototype is manufactured to validate the advantages of the design. The effects of spring stiffness, load weight, and motion speed on the performance of the harvester are investigated through a series of experiments. The results show that the peak voltage is 5.11 V and the peak power is 2.37 W, and the average power of the harvester is 0.77 W, with the load of 5 kg and the speed of 10 km/h. The QZS-EHB can light up a combination of LED lamps with a total power of 6 W, charge the cell phone, and enable self-powered localization and wireless information transmission, when people are jogging with the load of 2 kg. These tests verify that the proposed design can be used for emergency power consumption of people's outdoor activities.

Dynamics coupling analysis between elastic supporting structure and TLD with and without slat screen

The slat screen (SS) has been widely used in tuned liquid damper (TLD) to increase damping and suppress structural vibration. This study proposes a linked-spring screen that has a movable screen elastically connected to the inner wall. Laboratory experiments of elastic supporting structure with TLD were first conducted on a hexapod table to obtain structural dynamics response under different conditions. Wavelet transform and wavelet-based bicoherence are used to analyze the nonlinear characteristics of sloshing waves. Meanwhile, a two-way coupling numerical model was validated to accurately predict the nonlinear coupling interaction between structure and TLD. Effects of the SS on reducing the structural vibration were numerically evaluated together with the interactions among elastic structure, TLD and SS. Finally, effects of spring stiffness on TLD with linked-spring screen were studied. Findings show that SS can not only enhance the internal dissipation by creating vortexes but also break waves through the perforation. Compared with conventional TLD, screen with Se = 0.75 and D/L = 0.15 can reduce the maximum displacement by 37.86 %. Besides, the linked-spring screen can further improve the damping performance because of the enhanced shear flow and turbulence intensity when it was moving. The optimal damping effect can be achieved for K = 500 N·m−1 where the further reduction ratio is 29.80 %.

Machine condition monitoring enabled by broad range vibration frequency detecting triboelectric nano-generator (TENG)-based vibration sensors

Vibration analysis is an efficient method to monitor machine condition status. Different types of vibration sensors, such as microelectromechanical, and piezoelectric accelerometers have been used to measure vibrations, but face the problems of relying on external power and high cost. Recently, triboelectric nano-generator (TENG)-based vibration sensors have attracted attention to solve these problems. However, previous studies on TENG-based mechanical vibration sensors are limited to a low-frequency range (less than 200 Hz), which is below industry machine condition monitoring requirements (often 10–1000 Hz). This work aims at enabling TENG-based vibration sensors for higher frequencies and a broad range of frequency detection through structural design supported by numerical simulations. Numerical simulation results indicate that the frequency detection range is controlled by structural design and can be easily expanded for high-frequency detection by reducing the size and improving the shape of the structure. Spring-assisted TENG-based vibration sensors with the possibility of detecting the vibration within 0–1200 Hz, which covers the major mechanical failures and imperfections in vibrational frequency ranges, are prepared according to the structural design and numerical simulation results. The experimental results show that the developed sensor successfully detects signals within the frequency range of 0–1200 Hz. Due to optimized structural symmetry and effective spring stiffness, the two spring-assisted (TS) structures generate higher electric signal output (up to 200 V and 0.9 µA). The prepared TENG vibration sensors are further compared with a high-quality commercial vibration sensor in terms of vibrational signal response and detecting bearing defects. The results show that the prepared TENG vibration sensors can provide at least the same function as the commercial vibration sensor and demonstrate a promising potential to detect machine working conditions.

Study on vibration transfer characteristics of liquid filled double-walled cylindrical shells with elastic connection

In order to study the vibration isolation characteristics in water, based on the Flügge theory, a double-walled cylindrical shell model with spring connection is established using the wave propagation method. The fluid inside the inner shell is considered in the model. The reliability of the theoretical method is verified by comparing the calculation results of the mean square velocity with those of the finite element method. The effects of spring stiffness, spring number, fluid load, and inter-shell fluid thickness on vibration transmission of inner and outer shells are studied. The results show that the fluid loading effect of the water medium inside the inner shell can act on the inner shell and the outer shell simultaneously, while the fluid loading effect of the outboard fluid only acts on the outer shell. Under the condition of keeping the total spring stiffness unchanged, increasing the number of springs can reduce the vibration transmission from the inner shell to the outer shell, especially the vibration transmission from the inner shell to the outer shell at low frequencies. The “vibration short circuit” effect easily occurs in the inter-shell water, which is independent of the thickness of inter-shell water. When the elastic connection stiffness is small, the inter-shell water plays a leading role in vibration transmission in the whole frequency range. When the stiffness of elastic connection is large, the inter-shell water plays a leading role in vibration transmission at low frequencies, while the elastic connection plays a leading role in vibration transmission at high frequencies.

Free vibration analysis of three-layer thin cylindrical shell with variable thickness two-dimensional FGM middle layer under arbitrary boundary conditions

In this paper, a unified method is developed to analyze free vibrations of the three-layer functionally graded cylindrical shell with non-uniform thickness. The middle layer is composed of two-dimensional functionally gradient materials (2D-FGMs), whose thickness is set as a function of smooth continuity. Four sets of artificial springs are assigned at the ends of the shells to satisfy the arbitrary boundary conditions. The Sanders’ shell theory is used to obtain the strain and curvature-displacement relations. Furthermore, the Chebyshev polynomials are selected as the admissible function to improve computational efficiency, and the equation of motion is derived by the Rayleigh–Ritz method. The effects of spring stiffness, volume fraction indexes, configuration on of shell, and the change in thickness of the middle layer on the modal characteristics of the new structural shell are also analyzed.

Intercalated ion tuning of the cross-plane thermal transport properties of graphite

The effects of the intercalated ion concentration on the cross-plane thermal conductivity and the thermal boundary conductance in the graphite/lithiated graphite interface are investigated from molecular dynamics simulations. At low ion concentration, the cross-plane thermal conductivity of the lithiated graphite is lower than that of the pristine graphite. However, as the intercalated ion concentration increases, the cross-plane thermal conductivity increases rapidly, even exceeding that of the pristine graphite at high ion concentration. By analyzing the variations of the cross-plane elastic constants and phonon dispersion relation with the intercalated ion concentration, it is found that the intercalated ions significantly increase the phonon irradiation heat flux along the cross-plane direction. Our study further shows that the variation of the intercalated ion concentrations can also modulate the thermal boundary conductance in the graphite/lithiated graphite interface. The non-equilibrium molecular dynamics simulations show that the thermal boundary conductance between graphite and lithiated graphite decreases as the lithiation level increases, which would worsen the thermal performance of Li-ion batteries. A one-dimensional atomic chain model is proposed to elaborate on how the effective spring stiffness of material influences the interfacial transmission of phonons with different frequencies. This work provides a quantitative calculation of the cross-plane thermal conductivity and thermal boundary conductance in intercalated graphite samples and is also extremely important for the thermal management and structural design of lithium-ion batteries.

Dynamics of a beam with multiple spring/mass attachments using binary asymptotic admissible functions

The dynamics of an Euler–Bernoulli beam, with multiple spring/mass attachments, is investigated in this paper. A novel analytical approach for determining the natural frequencies and mode shapes of the system is presented. The formulation is applicable for any parameter value of the attached mass or spring stiffness. The calculation is performed using a minimal binary set of admissible functions for each spring/mass connection, with extremal values (zero or infinity) of the parameter. For example, to study a beam with n intermediate spring/mass connections, only 2 n admissible functions are required. These functions are used in a Rayleigh–Ritz-based energy formulation. The small number of functions used in the formulation leads to an efficient computational procedure. The results from the proposed formulation are compared with those from a finite element simulation, for different boundary conditions. The results obtained by the two methods are in excellent agreement for all boundary conditions as well as for different parameter ranges. Detailed design studies, on the effect of spring stiffness and lumped mass values, as well as their locations, on the natural frequencies and mode shapes, have been carried out. Design charts have also been generated to aid the designer of such structures.

Wave energy dissipation of a submerged horizontal flexible porous membrane under oblique wave interaction

An analytical model associated with oblique wave interaction with a submerged horizontal flexible porous membrane is presented under the assumption of linearized small amplitude and structural response in finite water depth. The expansion formula associated with Green's functions using fundamental source potentials based on reduced wave equation is derived. Further, a physical problem of oblique wave interaction with a moored finite horizontal submerged flexible porous membrane on wave energy dissipation is illustrated to analyse the different design parameter based on matched eigenfunction expansion method. The roots of the complex dispersion relation are obtained by applying a perturbation scheme and the accuracy of the numerical computation is demonstrated by analysing the convergence of reflection, transmission, and dissipation coefficients for different spring stiffness and porous-effect parameters. Further, the correctness of the present solution is checked by validating against analytical, numerical boundary element method, and experimental data available in the literature. The effects of spring stiffness, porous-effect parameter, submergence depth, structural length, angle of incidence, and flow pattern on reflection, transmission, dissipation coefficients, membrane deflection, vertical force, and contour plots are analysed. The present analysis on different design parameters will be helpful for better understanding for engineers to design as an effective breakwater/wave absorber.

Dynamic Analysis and Optimization of the Planar Model of the Trolleybus Škoda 21Tr

The article deals about modelling, dynamic analysis and optimization of stiffness and damping parameters of the main suspension of the Skoda 21Tr trolleybus. The trolleybus is excited by a ride on a rough road modelled using the Shinozuka method with the specified spectral power density. After examining the impact of tire stiffness and damping on the effective values of driving comfort characteristics, dynamic tire-to-road forces, and relative displacements between sprung and unsprang mass, the effect of spring stiffness and damping of dampers in main suspension are investigated. After selecting appropriate optimization parameters, the stiffness and damping parameters of the main suspension are optimized using the MATLAB Optimization Toolbox. The objective function is the sum of the effective values of the suspension mass acceleration and its angular acceleration. The results are the improved driving comfort without increasing the dynamic forces between the tires and the road and the relative displacements between the sprung and unsprung masses.

Anisotropic nanoscale and sub-nanoscale friction behaviors between phosphorene and silicon tip

Understanding the frictional properties of phosphorene is essential for reliable fabrication and sustainable operation of phosphorene-based nanotechnology devices. Although recent studies have revealed that phosphorene exhibits anisotropic frictional characteristics, the detailed mechanisms are not well analyzed, and the influence of some experimental parameters (e.g., spring stiffness, tip load force, and tip size), which are very sensitive to atomic frictional forces, were not considered. This study was carried out to address the above shortcomings. The anisotropic frictional behavior of phosphorene and its detailed mechanism were analyzed using potential energy profiles. Also, the effects of spring stiffness and tip load force on the stick-slip behaviors were investigated. Furthermore, we studied the sub-nanoscale stick-slip behavior during the nanoscale slip motion. The nanoscale and sub-nanoscale stick-slip phenomena were originated from the tip's behavior of passing over the bond between the phosphorus atoms and over the puckered honeycomb structure along the zigzag and armchair directions. We utilized a simple one-dimensional model to explain the energy profiles. The influence of tip size on the stick-slip behavior was also examined and found related to the initial nanoscale slip velocity. As the tip diameter decreased, a high-frequency sub-nanoscale stick-slip phenomenon and shorter nanoscale slip duration were identified.

Modelling neutral gear rattle for a light commercial vehicle

Acoustic levels have a significant influence on the ride comfort of road vehicles. Among the others, gear rattling noise is a significant problem faced by the car industry. Automotive powertrains are under investigation to reduce and isolate the torsional vibrations responsible f or g ear rattling. T his work addresses the problem of reducing gear rattle while the engine is idling. The aim is to reduce the rattle index by introducing the pre-damper clutch plate instead of a conventional clutch plate that uses torsional vibration springs. A Matlab/Simulink model is developed to estimate the effect of spring stiffness on the rattle index of the system. The output of the model is validated experimentally and the accuracy of the Simulink model is reported. The rattle index was successfully decreased with the help of a pre-damped clutch plate, and the model is found to be accurate enough to estimate the rattle index.

Topological design of compliant orthogonal displacement amplification mechanism under the unidirectional input force

The orthogonal displacement amplification mechanism is used to output and amplify the displacement perpendicular to the direction of the input force, and its configuration often uses a typical bridge-type. However, the bridge-type amplifier to achieve orthogonal shift conversion must enter the bidirectional symmetric input forces, otherwise the output will produce parasitic displacement. In view of this problem, the topology optimization method is used to find the new configuration of the displacement amplification mechanism, so that it can still realize the orthogonal displacement transformation under the unidirectional input force condition. Based on the solid isotropic material with penalization (SIMP) topological description method, the ratio of output and input displacements is maximized as the objective function, the ratio of parasitic displacement and output displacement as one of constraint functions, and the topological optimization mathematical model of the compliant orthogonal displacement amplifier is established under the unidirectional input force. The sensitivity information of the objective and constraint functions is deduced by the adjoint matrix method, and the optimization problem is solved by the method of moving asymptotes (MMA). The topology optimization results of orthogonal displacement amplifier are given through numerical examples, and the effect of spring stiffness on the topology optimization result is also discussed. Finally, the parasitic motions of the displacement amplification mechanism obtained from topology optimization and the bridge-type amplification mechanism are compared through the finite element analysis and experiment. Finite element simulation and experiment confirm the correctness and validity of the proposed method.

Vibration characteristics and thermoelastic analysis of the supersonic composite laminated panel with arbitrary elastic boundaries

The novelty of this study is to present a theoretical approach to investigate the dynamic behaviors of the laminated panels under arbitrary elastic boundary conditions. The motion equations of panels considering the first order piston theory are derived using Hamilton principle. A solution of computing the vibration characteristics of a panel with arbitrary elastic boundaries is proposed based on the Rayleigh–Ritz method, in which the admissible functions are constructed by a set of characteristic orthogonal polynomials employing the Gram–Schmidt process; the support boundary is modeled by introducing the technology of artificial springs. The effects of spring stiffness and different boundaries on the dynamic characteristics and thermal aeroelastic behaviors are presented in detail. Numerical results show that the small ply angle and large spring stiffness are helpful to improve the aerodynamic stability. Multiple new phenomena have been observed, e.g. the phenomena of mode jumping and the alterations of coupled mode orders. Moreover, the thermal loads and aerodynamic loads play an opposite effect on the stability of composite panels.

Effects of Multiple Factors on Water Hammer Induced by a Large Flow Directional Valve

© 2018 Journal of Mechanical Engineering. All rights reserved. The flow gain of the large flow poppet directional valve presently used on hydraulic-powered support is large, so water hammer occurs easily when the poppet valve closes. Thus, the hydraulic system, its components, and human safety are seriously threatened. To solve this problem, a plane-sealed large flow directional valve with different throttle windows, which must be taken into consideration when the mathematical model is established, is designed. The effects of spring stiffness and the shape of the throttle window on the hydraulic shock induced by the valve are analysed with the combination of simulation and experiments. It is obvious that the bigger the spring stiffness is, the greater the water hammer is produced. When the spring stiffness continues to increase, the valve becomes instable and causes much stronger water hammer. The area gains of the valves with different throttle windows (round type, triangular type, rectangle combined type) are different, and the corresponding instances of water hammer differ accordingly. Compared with the common round throttle window, the triangular window produces the lowest shock. Furthermore, the effects of the closing time and the type of control curve of the main valve on the water hammer are explored. It is helpful for the proportional control of the large flow water directional valve in the future. This study provides valuable references for the design of the large flow water valve and the corresponding control of water hammer.

An Evolutionary Soft-Add Topology Optimization Method for Synthesis of Compliant Mechanisms With Maximum Output Displacement

This paper presents an evolutionary soft-add topology optimization method for synthesis of compliant mechanisms. Unlike the traditional hard-kill or soft-kill approaches, a soft-add scheme is proposed in this study where the elements are equivalent to be numerically added into the analysis domain through the proposed approach. The objective function in this study is to maximize the output displacement of the analyzed compliant mechanism. Three numerical examples are provided to demonstrate the effectiveness of the proposed method. The results show that the optimal topologies of the analyzed compliant mechanisms are in good agreement with previous studies. In addition, the computational time can be greatly reduced by using the proposed soft-add method in the analysis cases. As the target volume fraction in topology optimization for the analyzed compliant mechanism is usually below 30% of the design domain, the traditional methods which remove unnecessary elements from 100% turn into inefficient. The effect of spring stiffness on the optimized topology has also been investigated. It shows that higher stiffness values of the springs can obtain a clearer layout and minimize the one-node hinge problem for two-dimensional cases. The effect of spring stiffness is not significant for the three-dimensional case.

Vibration and Instability Analysis of Double-Carbon Nanotubes System Conveying Fluid

AbstractVibration and instability analysis of a fluid-conveying double-carbon nanotube system (DCNTS) is researched in this article. The system is composed of two single-walled carbon nanotubes, and the two carbon nanotubes are assumed to be connected by an elastic spring medium. Nonlocal elasticity theory and Euler-Bernoulli beam theory are employed in the equation modeling of the system. The nonlocal effect on the in-phase (synchronous) and out-of-phase (asynchronous) vibration of fluid-conveying DCNTS is discussed in detail. Explicit expressions of critical-flow velocity are given for both in-phase and out-of-phase vibration. It is found that the nonlocal parameter plays an important role in the natural frequency and critical-flow velocity for both the in-phase and out-of-phase vibration. An increase in the nonlocal parameter has an obvious reducing effect on the natural frequency and critical-flow velocity. For the case of out-of-phase vibration, the effect of spring stiffness reduces the nonlocal effect.

Climate loads in insulating glass units: comparison of theory and experimental results

The verification of insulating glass units in ultimate limit state often gives rise to the question of how to take into account the edge seal in the design of the glass panes. Usually the edge seal is calculated as immovable, as this is a more conservative assumption. A flexible edge seal, as to be expected under realistic conditions, leads to a lower climate load and therefore to lower stresses in the glass. In order to determine the influence of a flexible support on the verification of the ultimate limit state under the applicable standards in Germany, various setups of insulating glass units were subjected to cyclically recurring temperatures of $$-$$ 18 to $$+53\,^{\circ }\hbox {C}$$ in a climate chamber. In this procedure, the atmospheric pressure was measured as well as the pressure in the cavity, as were the deformations of the edge seal orthogonally to the glass panes. Based on these, a comparison of analytical calculations of the climate load and the experimentally determined climate load is conducted. By means of the experimentally determined pressure difference in the cavity and the measured deformations of the edge seal, an effective spring stiffness in tension of the edge seal under the climatic test conditions was calculated using a finite element (FE) model. On the basis of an effective spring stiffness in tension assumed in a FE simulation, the influence of a flexible edge seal on the design of the glass panes is determined and discussed.

An experimental study on the effects of spring stiffness on the combustion and dynamic characteristics of a linear engine

We investigated the effects of the stiffness of springs applied to linear compressor chambers experimentally. The applied springs could prevent conflict between the engine piston head and engine head cover as well as be available to save the regenerative energy. The linear engine bore size was 30 mm, the maximum stroke was 31 mm and effective stroke volume of a cylinder was 25.45 cc. The spring stiffness was varied: 0, 0.5, 1.00, 2.9 and 14.7 N/mm. The linear engine was fueled with a pre-mixture combined with LPG (propane 99%) and air. As an experimental result, higher spring stiffness affected growth in regenerative energy and stroke. Also, IMEP was increased by rising stroke. Finally, increased IMEP and regenerative energy made more electricity than no spring.