Spring Constant Research Articles

Multi-Frequency Acoustic Levitation and Trapping of Particles in All Degrees of Freedom.

Stabilization of the position and orientation of non-spherical, sub-wavelength particles in mid-air is required for using acoustic levitation forces in applications such as automation of micro manufacturing processes, 3-D scanning, and inspection. Acoustic locking has previously been demonstrated by time-multiplexing of different acoustic traps at the same frequency. In this case, the magnitude of the acoustic levitation forces and the stabilizing torque are coupled by the ratio of the durations during which the different traps are applied and cannot be adjusted independently assuming operation at maximum power. This work presents a compact device that uses a method for independently adjusting the vertical trapping forces and the stabilizing torque using two different ultrasonic frequencies. A 40-kHz vertical standing wave is used to generate levitation forces that counteract the gravitational force. Additionally, a 25-kHz horizontal standing wave is used to generate a tunable stabilizing torque. Using this method, objects made from high-density materials across a wide range of geometries can be locked acoustically with increased stability compared with state-of-the-art methods. This is demonstrated by locking tin cuboids with a density of 7.3 g/cm3 and plastic cuboids with average side lengths between 0.9 and 3.5 mm. The experimental results demonstrate torsional spring constants of up to 50 nN · m/rad and an orientation stability of <7.5°.

A heaving system with two separated oscillating water column units for wave energy conversion

A theoretical model based on the linear potential theory is presented for two heaving oscillating water column (OWC) devices separated by a gap. The model includes relative motion and phase control between the devices and trapped water columns, and the hydrodynamic performance of the dual-OWC system thence evaluated. Matching conditions are employed along the common interfaces, and the power take-off model and motion equations of the OWC devices are incorporated into the solution procedure. At the top of each chamber, a Wells turbine is installed to extract wave power. To achieve the optimal overall power extraction performance, a numerical strategy of successive approximation is utilized to seek the optimal turbine damping combinations for the separated units. The effects of lip-wall draft and chamber breadth on the performance of a fully-free heaving dual-OWC system are explored. In view of the deficiency of a fully-free heaving system, two alternative optimization strategies are proposed, one focusing on the control of relative motion and phase between the water columns and the heaving devices, the other on utilizing resonance phenomenon inside the gap, achieved by tuning imposed linear spring constants and gap distance, respectively. It is shown that the control between heave motion of devices and water columns inside the chambers is beneficial for extracting more power over a broader range of wave frequencies. Moreover, enhanced extraction is likely over a wider range of wave conditions when the gap distance to wavelength triggers a sloshing mode inside the gap.

Towards the Development of Variable Elasticity Devices

Humans and animals utilize stiffness-altering faculties and elastic structures embedded within their musculoskeletal systems which allow them to manipulate and locomote within natural, dynamic environments. Hence, arming soft robots with mechanisms that accord them stiffness and elasticity is a pivotal step towards realizing machines closer to biological structures. While there is research in the domain of variable stiffness in soft robotics, variable elasticity is an area that is yet to be thoroughly investigated. This article presents the design, manufacturing, and performance demonstration of a novel device for addressing this key challenge: enabling a mechanism to reversibly modify its elasticity along a specific direction of motion. The device which we call the variable elasticity soft module (VESMo) is based on low-cost commercially available polymers and operates via pneumatic actuation. A significant application of our device is its capability of storing and returning energy of adjustable levels of intensity, like the role of biological springs in animals. Our experiments verify that the spring constant of the VESMo can be increased by more than 194% depending on the properties of the constitutive polymers and thepressure effected by the vacuum regulator. Finally, the performance of the device in two demonstrative mechanisms is presented.

Coarse-grained CFD-DEM simulations of fluidization with large particles

Detailed validation coarse-grained CFD-DEM model in the open source code MFIX is performed. Metrics used include fluidization behavior, minimum fluidization velocity, averaged pressure drop, mean and rms particle velocity. The choice of the spring constant alters fluidization dynamics. Of drag correlations tested, the Tang et al. (2015) formed poorly overall at low superficial velocities of 2 Umf and 3 Umf and exceptionally well at 4 Umf suggesting it is suitable at higher velocities. A deterioration in the predicted minimum fluidization velocity is noticed using the coarse-grained model. A trend of reducing error of average pressure drop with increasing statistical weight is observed at low gas velocities. The mean particle velocities profiles for the coarse grain and conventional CFD-DEM models do not show appreciable differences unlike rms profiles that exhibit a reducing trend with increasing statistical weight. Some gain on the wall clock time required to complete a case were recorded.

Exponentially Enhanced Single‐Photon Cross‐Kerr Nonlinearity in Quantum Optomechanics

AbstractStrong cross‐Kerr nonlinearity at the single‐photon level is crucial for various quantum applications, but usually very difficult to achieve. In this work, an efficient method to generate and exponentially enhance the cross‐Kerr nonlinearity in quantum optomechanics of two optical cavities coupled to a common mechanical resonator is proposed. Through periodically modulating the mechanical spring constant, a nonlinear two‐phonon drive can be acquired to amplify the mechanical zero‐point fluctuations. As a result, the exponentially enhanced cross‐Kerr interaction between the two optical modes can be realized via the amplified mechanical motion. The distinct feature of this scheme is that a true enhancement of cross‐Kerr nonlinearity can be achieved at the single‐photon level. As intriguing applications, it is also also proposed to generate anticorrelated photon blockade and stabilize one‐photon Fock state based on the enhanced nonlinearity. The present work may provide an appealing way for creating strong cross‐Kerr coupling.

Solution to the Fokker-Planck equationfor slowly driven Brownian motion: Emergent geometry and a formula for the corresponding thermodynamic metric.

Considerable progress has recently been made with geometrical approaches to understanding and controlling small out-of-equilibrium systems, but a mathematically rigorous foundation for these methods has been lacking. Towards this end, we develop a perturbative solution to the Fokker-Planck equationfor one-dimensional driven Brownian motion in the overdamped limit enabled by the spectral properties of the corresponding single-particle Schrödinger operator. The perturbation theory is in powers of the inverse characteristic timescale of variation of the fastest varying control parameter, measured in units of the system timescale, which is set by the smallest eigenvalue of the corresponding Schrödinger operator. It applies to any Brownian system for which the Schrödinger operator has a confining potential. We use the theory to rigorously derive an exact formula for a Riemannian "thermodynamic" metric in the space of control parameters of the system. We show that up to second-order terms in the perturbation theory, optimal dissipation-minimizing driving protocols minimize the length defined by this metric. We also show that a previously proposed metric is calculable from our exact formula with corrections that are exponentially suppressed in a characteristic length scale. We illustrate our formula using the two-dimensional example of a harmonic oscillator with time-dependent spring constant in a time-dependent electric field. Lastly, we demonstrate that the Riemannian geometric structure of the optimal control problem is emergent; it derives from the form of the perturbative expansion for the probability density and persists to all orders of the expansion.

Perbaikan Sistem Pelacakan Panel Surya Menggunakan Penyesuaian Posisi Massa Tambahan

This study aims to obtain an effective solar panel tracking mechanism using energy-efficient electric actuators. Furthermore, we designed and implemented a semi-active solar tracking system. A tracking system is proposed to control solar panel orientation using a moving mass, a spring system, and an actuator. The weight of the moving mass and the spring constant are optimized to reduce actuator size. A stepper motor was used for this case. This electric drive is not the prime mover of the solar tracker; hence, it works against mass elements lighter than solar panel weight as used in the active solar tracker. Experimental results suggest that the average power required by the stepper motor is 0.21% of the energy generated by the solar tracking system. The results indicate that the proposed solar panel tracker works satisfactorily to control solar panel orientation.

Design and Performance Analysis of Lamina Emergent Torsional Joints Based on Double-Laminated Material Structure

Flexibility and accuracy are two key aspects of the performances of compliant joints. In order to obtain high flexibility while maintain high accuracy, this paper proposes a design method to improve the tensile stiffness of Lamina Emergent Torsional (LET) joint by utilizing double-laminated material structure. The joint is made of a LET joint and a layer of flexible H18 aluminum foil fixing on it (called double-laminated LET, DL-LET). The kinetostatic model for the joint is given, and the equations needed to calculate the equivalent spring constant are derived. The model is verified using finite element analysis (FEA). The results obtained through two different ways coincide with each other very well. The results show that DL-LET and LET joints have similar bending stiffness, while the tensile stiffness of the DL-LET joint is much larger than that of the LET joint. The results are validated by tensile tests. Finally, to further demonstrate the extension of this idea, a DL-Triple-LET joint is presented and compared to the Triple-LET joint.

Generalized three-body harmonic oscillator system: ground state

In this work we report on a 3-body system in a d−dimensional space ℝd with a quadratic harmonic potential in the relative distances rij = |ri −rj| between particles. Our study considers unequal masses, different spring constants and it is defined in the three-dimensional (sub)space of solutions characterized (globally) by zero total angular momentum. This system is exactly-solvable with hidden algebra sℓ4(ℝ). It is shown that in some particular cases the system becomes maximally (minimally) superintegrable. We pay special attention to a physically relevant generalization of the model where eventually the integrability is lost. In particular, the ground state and the first excited state are determined within a perturbative framework.

Modeling and Simulation of PID Controller-Based Active Suspension System for A Quarter Car Model

The most common automotive suspension systems have been used passive components with fixed damping coefficient and spring constant. They are two separate functions to reach a compromise between drive quality and handling performance. Because of the limit of structures, the passive suspension system could hardly enhance the two features at the same time. In recent years, the active suspension system has been widely used in a vehicle which can overcome the limitations of the passive suspension systems. Since there are many advantages to make the vehicle operate safer and quieter than the passive suspension system. The aim of this study is to develop a linear mathematical model of active and passive suspensions systems for quarter car models subjected to different road profiles using a Proportional Derivative Integral (PID) controller. After modeling and simulation of the suspension system using Matlab/Simulink, this study has been able to determine the parameter of PID controllers of active suspension in many different road surfaces and vehicle speeds to improve driving comfort. Another new point of this study is the Graphical User Interfaces to be a successful design. The users can enter the input parameters for Matlab processing and get the results, which can make system analysis faster and more convenient. The main outcomes of this paper are performed to investigate and compare the response between active and passive suspension systems. Through the analysis of the simulation results, this research has demonstrated the feasibility, reliability, and they can be applied to propose a further improvement of the kinematic and dynamic characteristics of the vehicle active suspension system.

Multi‐Parameter Optimized Triboelectric Nanogenerator Based Self‐Powered Sensor Network for Broadband Aeolian Vibration Online‐Monitoring of Transmission Lines

AbstractOverhead transmission lines are vulnerable to aeolian vibrations that threaten the operation of the power grid. A triboelectric nanogenerator (TENG) based self‐powered system offers a desirable way for vibration online‐monitoring with potential for large‐scale deployment. In this work, a self‐powered sensor network constructed by active vibration sensor (AVS) units with a spring‐mass based TENG (S‐TENG) is reported for effective energy harvesting and broadband vibration sensing. The basic TENG with structural parameters is first discussed from the aspects of efficiency and response characteristics, then the spring constant and mass weight are also adjusted for S‐TENGs with different optimal operation regions, thus the overall vibration amplitude and frequency response are further enhanced by the mutual compensation of S‐TENGs with a weight allocation strategy. Furthermore, the S‐TENGs are combined with external circuits to compose the AVS units, which are deployed in a distributed manner on a simulated transmission line to demonstrate a self‐powered wireless warning system and an aeolian vibration mapping system, enabling abnormal vibration warnings and vibration distribution monitoring over the whole line. This work represents a novel strategy for utilizing TENG technology for transmission line aeolian vibration monitoring and provides valuable guidance for further sensor network construction and power grid visualization.

Equivalent Electronic Circuit of a System of Oscillators Connected with Periodically Variable Stiffness

In this paper, we have shown an electronic circuit equivalence of a mechanical system consisting of two oscillators coupled with each other. The mechanical design has the effects of the magnetic spring force resistance force, and the spring constant of the system is periodically varying. We have shown that the system’s state variables, such as the displacements and the velocities, under the effects of different forces, lead to some nonlinear behaviors, like a transition from the fixed point attractors to the chaotic attractors through the periodic and quasi-periodic oscillations. We have verified those numerically obtained phenomena using the analog electronic circuit of this mechanical system.

Proposal of forceps force limiter design using leaf spring buckling

To prevent accidents in minimally invasive surgeries, force limiters have been developed for forceps grippers. When a force limiter is in use, if the absolute value of its spring constant is reduced, the risk of damage to the organs decreases. This paper proposes the use of a leaf spring buckling mechanism as a force limiter for forceps. The results obtained indicate that the spring constant of a buckled leaf spring is lower than that of a normal coil spring. Furthermore, the use of a leaf spring allows the independent adjustment of its thickness and width, based on the stress and force values. This enables an easy calibration of the threshold value. In the experiments, the spring constant of the buckled leaf spring was 1.5 times 10^{-1} N/mm, which is half of that of a normal coil spring. After calibrating the gripping force, it was confirmed that the force limiter reduced the extent of damage to the dummy organs in the ex vivo experiments.

Two orders agreement between stiffness measurement of µ-scale beam with analytical, macroscopic predictions

Miniaturization technology for creating three-dimensional structures is constantly advancing, reaching a processing accuracy of several µm. Therefore, it is questionable whether it is possible to obtain the stiffness of spring constant derived from macroscopic bending model and from macroscale parameters such as Young's modulus in this small region. To test the goodness of the macroscale model, we fabricated a micro-scale beam and an electrostatic actuator, applied an AC voltage to make the beam resonate, and measured the resonant frequency of the beam. The resonance frequencies were measured through changes in bias voltage. By the constant voltage dependence of the resonance frequency, we measured the soft-spring effect, and also measured the stiffness spring constant of the beam without the soft-spring effect. We demonstrate that the stiffness of a beam of a few µm can be accurately calculated from the macroscale analytical solution if the beam dimensions are known.

A classical analog for defects in quantum band formation

When many individual atoms come together to form a solid, their interaction splits their electronic energy levels to form continuous bands separated by forbidden energy ranges known as band gaps. Introducing defects in a solid results in new electron energy levels that may lie inside the bandgaps. The presence of these defect levels is the heart of the semiconductor-based devices that play a significant role in the modern world. Quantum mechanics provides the best description of interacting atoms. However, band formation is not unique to small-scale atomic interactions but rather is a result of the wave-nature of Schrödinger's equation, which governs quantum mechanics. Using oscillations in a mass-spring system, we present a table-top, classical analog to the quantum system illustrating how defects in a one-dimensional lattice produce changes to the band structure. A pair of masses connected by a spring plays the role of a single atom. Interactions between “atoms” are introduced with weak coupling springs producing two distinct frequency bands from the translational and fundamental modes. Defects are introduced by altering an oscillator pair's total mass or internal spring constant. We provide the theoretical groundwork and experimental verification of the model along with a discussion of the value and limitations of the model as a macroscopic tool to visualize the microscopic world.

A classical model for perfect transfer and fractional revival based on q-Racah polynomials

It is shown how choices based on the q-Racah polynomials for the masses and spring constants along a chain give new systems that exactly allow dispersionless end-to-end transmission of a pulse as well as periodic splitting of the initial momentum between the first and last mass. This “Newton's cradle” provides a classical analog of quantum spin devices that exhibit perfect state transfer and fractional revival.

Mechanical frequency control in inductively coupled electromechanical systems

Nano-electromechanical systems implement the opto-mechanical interaction combining electromagnetic circuits and mechanical elements. We investigate an inductively coupled nano-electromechanical system, where a superconducting quantum interference device (SQUID) realizes the coupling. We show that the resonance frequency of the mechanically compliant string embedded into the SQUID loop can be controlled in two different ways: (1) the bias magnetic flux applied perpendicular to the SQUID loop, (2) the magnitude of the in-plane bias magnetic field contributing to the nano-electromechanical coupling. These findings are quantitatively explained by the inductive interaction contributing to the effective spring constant of the mechanical resonator. In addition, we observe a residual field dependent shift of the mechanical resonance frequency, which we attribute to the finite flux pinning of vortices trapped in the magnetic field biased nanostring.

Theory of Harmonic Oscillations: A Gross Error in Physics

Theory of Harmonic Oscillations: A Gross Error in Physics

Theoretical study on Three-dimensional mechanical stability of tensegric manipulator

The goal of this research is to realize a large robot arm over 20 meters long. In the previous study, we discussed the load reduction of a multi-stage robot, the control algorithm of the arm, and the balancing of moments and forces in a simple model. Based on the above, this paper develops theoretical equations for how the spring constant and tension on the wire are related to the direction of arm movement. We have succeeded in finding a posture that provides stable moment balancing.

Vibration Analysis of Dynamical System with Flat-band Like Structure

It has been reported that a system of spring-masses connected in the form of a ladder has a flat-band dispersion relation in which the eigenfrequency degenerates for certain translational degrees of freedom by appropriately selecting the spring constants and masses of the mass points. In this study, we show that, by considering the nonlinearity of the spring in this structure, it is possible to construct a mobile localized vibration mode which is stable and robust to perturbations.