Flexible Spring Research Articles

A Novel Fast Contact Operating Mechanism of the Medium and Low Voltage Hybrid DC Current Limiting Circuit Breaker

In order to solve the problem of the slow initial speed caused by the large mass of the bistable permanent magnetic actuator (PMA) in the traditional bistable permanent magnetic–electromagnetic repulsion mechanism (PM-ERM), a novel fast contact operating mechanism is proposed by using the flexible spring system (SS) between the PMA and the ERM. The novel structure can separate the mass of the PMA and the ERM at the initial phase of the interrupting process, improve the initial speed of the contact and increase the initial opening distance of the contact. Firstly, the paper conducts an extensive investigation and analysis of the principle of the existing fast operating mechanism and points out the advantages and disadvantages of the existing mechanism. In order to meet the requirement of fast interrupting and improve the service life of the mechanism, a novel mechanism is proposed. And then, the working principle of the novel mechanism is introduced. The cooperative relationship between the ERM and the PMA and the working principle and performance parameter requirements of the ERM, SS and PMA are analyzed and designed. Finally, the feasibility of the novel mechanism is verified by the experiment. The results show that the opening distance of the novel operating mechanism can reach 2.25 mm in 1 ms. Compared with 1.24 mm of the traditional operating mechanism, it improves the initial opening distance of the contact by 81.5% and is conducive to the rapid interruption of the Hybrid DC current-limiting circuit breaker (HDCCLCB).

Theoretical and experimental investigation of flexible air spring stiffness in a tuned liquid column gas damper for vertical vibration control

This study investigates the effectiveness of equivalent linear air spring stiffness in a Vertical Tuned Liquid Column Gas Damper (VTLCGD) for reducing vertical structural vibrations, particularly considering different sealing conditions. The VTLCGD system, designed with a single sealed vertical air column, allows flexible frequency tuning by adjusting the air spring stiffness. It aims to be used in low-frequency structures where conventional VTLCGD designs with two sealed ends are less efficient. The geometric configuration and working principle of the VTLCGD are first described. The equation of motion is derived using liquid dynamic equilibrium and the pressure-volume relationship, with expressions for natural frequency and control force validated through shaking table tests conducted with varying VTLCGD lengths. Experimental investigations are conducted to examine the parameters affecting damper performance using pressure data. The system's vibration reduction performance is then numerically evaluated on a cantilevered floor subjected to human walking. The numerical results, based on the equation of motion for liquid displacement and natural frequency, show good agreement with experimental data, which confirms the effectiveness of using linearized air spring stiffness for frequency tuning. The effects of total liquid length and height difference on control force are further investigated, and a polytropic index of 1.2 is determined for the VTLCGD frequency formula. The VTLCGD system achieves a maximum vibration reduction of 52.63 % in acceleration response on the cantilevered floor compared to the uncontrolled case. Moreover, the variation in stiffness due to changes in the sealing condition is presented to validate the damper's adaptability over a wide frequency range.

Design and Optimisation of Bionic Frog Hind Limbs

With the deepening of human exploration of the Earth, more and more survey tasks are being carried out in unstructured environments. Biomimetic robots that can replace humans in completing related tasks under harsh conditions have gradually become a hot topic in robot development. Therefore, developing a biomimetic robot with a wide range of activities, strong mobility, excellent obstacle crossing ability, and rapid avoidance response has important theoretical research significance and broad application prospects. This paper focuses on frogs as the research object,research is conducted from the perspective of institutional design, aiming to design a frog like jumping robot with strong obstacle crossing ability and good environmental adaptability. In terms of overall structural design, a M-shaped structure based on linear bearings was proposed to ensure the stability of the robot during takeoff and landing; In terms of leg structure design, C-shaped flexible springs are used to integrate the calf, ankle joint, and foot into one, which can play a buffering role when the robot lands; In terms of transmission structure design, Propose to control the compression cycle of the jumping leg through a cam to achieve continuous jumping of the robot. The relevant research results indicate that the structural principle of the designed frog like jumping robot is correct, and the jumping effect is relatively good.For the sake of ideals, this paper provides a certain theoretical basis and basis for further research on bionic jumping robots.

Free Undamped Motion in Spring Mass System

Assume that a mass m is fastened to the free end of a flexible spring that is hanging vertically from a rigid support [5]. Naturally, the mass of the spring will determine how much it stretches or elongates; different weight masses will stretch the spring in different ways. The spring itself exerts a restoring force F that is proportional to the amount of elongation s and opposed to the direction of elongation, according to Hooke's law. Put simply. When a mass m is connected to a spring, the mass extends the spring by a certain amount, reaching an equilibrium where the restoring force ks balances the mass W. Remember that [6] defines weight. w = mg (0.3.1) the condition of equilibrium is mg = −ks (0.3.2) or mg − ks = 0 (0.3.3) In the event that the mass deviates from its equilibrium position by an amount x, the spring's restoring force is equal to k(x + s). We can associate Newton's second rule with the net, or resultant, force of the restoring force and the weight W is balanced by the restoring force ks, provided that there are no retarding forces operating on the system and that[6] the mass vibrates free of other external forces—free motion. Remember that [6] defines weight. (ⅆ^2 x)/(ⅆt^2 )= -k(s + x) + mg (0.3.5) = −kx + mg − ks = −kx (0.3.5) The spring's restoring force works in the opposite direction of motion, as shown by the negative sign. Additionally, we follow the tradition that displacements recorded in positive values below the equilibrium position [6].

Modeling and comfort analysis of arrayed air cushion mattress for pressure ulcer prevention and assisted repositioning

Assisting immobile individuals with regular repositioning to adjust pressure distribution on key prominences such as the back and buttocks is the most effective measure for preventing pressure ulcers. However, compared to active self-repositioning, passive assisted repositioning results in distinct variations in force distribution on different body parts. This incongruity can affect the comfort of repositioning and potentially lead to a risk of secondary injury, for certain trauma or critically ill patients. Therefore, it is of considerable practical importance to study the passive turning comfort and the optimal turning strategy. Initially, in this study, the load-bearing characteristics of various joints during passive repositioning were examined, and a wedge-shaped airbag configuration was proposed. The airbags coupled layout on the mattress was equivalently represented as a spring-damping system, with essential model parameters determined using experimental techniques. Subsequently, different assisted repositioning strategies were devised by adjusting force application positions and sequences. A human-mattress force-coupled simulation model was developed based on rigid human body structure and equivalent flexible springs. This model provided the force distribution across the primary pressure points on the human body. Finally, assisted repositioning experiments were conducted with 15 participants. The passive repositioning effectiveness and pressure redistribution was validated based on the simulation results, experimental data, and questionnaire responses. Furthermore, the mechanical factors influencing comfort during passive assisted repositioning were elucidated, providing a theoretical foundation for subsequent mattress design and optimization of repositioning strategies.

Development of a software tool for remote control of knowledge

The purpose of this study was to develop and implement an information system for evaluating and testing students' knowledge in order to simplify the process of creating tests and evaluating the educational achievements of teachers. In the course of the work, a review of existing computer training programs, an analysis of the market of modern analogues was carried out, and on the basis of the obtained data, functional and non-functional requirements for the developed software product were formulated. Based on the requirements, technical and software tools were chosen for the development of the program, namely the JavaScript programming language and the ReactJS framework for the development of the client part of the web application, which allows for quick and convenient development of interactive user interfaces and guarantees the stable operation of the system. The server part of the application is implemented using the powerful and flexible Spring framework, which allows you to create scalable and high-performance web applications.
 To achieve the goal, the following tasks are solved in the work: registering a new user, editing user data, logging in and out of the system, viewing/creating/editing/deleting a study group, viewing students of a selected group, viewing/creating/editing/deleting/ publishing a test, viewing/creating/editing an exercise in a separate test, receiving all exercises in a selected test, assigning a test to a selected group, the ability to view/take tests assigned to the user (his group), the ability to check exercises and assign a grade (some exercises may be evaluated by the system automatically if the teacher gave the correct answer for comparison), the ability to view the result for the passed test. A MySQL database was designed and built according to the described data model that corresponds to the third degree of normalization. The structural and functional scheme of the system has been developed. There are three user roles: administrator, teacher, student. Great importance was attached to ensuring the simplicity and ease of use of the user's product, as this plays a key role in the use of the software. In the process of developing the program, great attention was paid to creating an intuitive and comfortable interface.
 As a result, an information system for automated testing was created, which successfully fulfills the assigned tasks and meets all the specified requirements, and is also fully ready for practical implementation. The obtained results can be used both to integrate the program into the educational process and to provide students with the opportunity to acquire practical skills

Design optimization of a flexure spring used in small-sized ultra-precise optical instrument

Small-sized ultra-precise optical devices require compact compliant ortho-planar springs (COPS) aka. flexure springs, for precise, frictionless linear motion which depends highly on the design. A self-developed arm-hinge-linked design, named “Panto-style” flexure spring was optimized by selecting 5 design parameters (thickness: t, hinge width: W, arm length 1 and 2: L1 and L2, arm angle: Ө) and constructing sets of design of experiments (DOEs).Signal-to-noise ratio (SNR) and response surface model (RSM) regression were obtained in terms of axial deformation. The highest response from the main effects plot was the thickness (t), followed by hinge width (W). The angle of the arm (Ө), was considered a non-relevant parameter.The parameters optimization was implemented with constraint input and output. Kinetostatic performances (axial/radial deformations, and stress) were predicted, validated, and compared (RSM, KNN, FE simulations, and experiments) using the optimized design.The average value of KNN and RSM (KNN + RSM) increased the accuracy of axial deformation value compared to RSM alone. To conclude, RSM design parameter optimization followed by KNN + RSM has successfully predicted the output results (axial/radial deformation and stress) confirmed both numerically and experimentally.

An Experimental Investigation of Fatigue Performance for A Flexure Spring

In order to prevent a free-piston Stirling cryocooler failure during mission life, the flexure spring's fatigue life is most critical and important. In the current research, an effort is made to examine fatigue life. The fatigue life testing of cryocooler flexures is frequently discussed in the literature. However, more information is needed about the economic approach and hardware needed for the testing. This research paper adopts the FEA approach of flexure spring and outlines the criteria for flexure fatigue testing. A moving coil linear motor was also designed and selected for the oscillating shaft and bending special-purpose flexure spring stack to validate stiffness criteria. The 108 no. of cycles required to validate the fatigue limit were also attained using the approach in a few days when testing at a relatively high frequency.

Numerical Analysis of Cracked Double-Beam Systems

Based on elasticity theory, this paper discusses the static analysis of a cracked double-beam system in the presence of a Winkler-type medium. It is further assumed that the double-beam system is constrained at both ends by elastically flexible springs with transverse and rotational stiffness. Using a variational formulation, the governing static equations are derived and solved using analytical and numerical approaches. In the first approach, closed-form solutions for the displacement functions are obtained based on the Euler–Bernoulli beam theory. In the second approach, the Cell Discretisation Method (CDM) is performed, whereby the two beams are reduced to a set of rigid bars connected by elastic constraints, in which the flexural stiffness of the bars is concentrated. The resulting stiffness matrix is easily deduced, and the governing equations of the static problem can be immediately solved. A comparative analysis is performed to verify the accuracy and validity of the proposed method. The study focuses on the effect of various parameters, including crack depth and position, boundary conditions, elastic medium and slenderness. The validity of the proposed analysis is confirmed by comparing the current results with those obtained from other approaches. In particular, the results obtained by closed-form solution and CDM are compared with the Finite Element Method (FEM). The accuracy of the results was assessed by making comparisons with results found in the literature and reported in the bibliography. It was shown that the proposed algorithm provides a simple and powerful tool for dealing with the static analysis of a double-beam system. Finally, some concluding remarks are made.

A high-sensitivity fiber Bragg grating sensor for displacement measurement in structural health monitoring.

Displacement measurement is of great significance to monitor the crack variation and ensure the health of building structures. Aiming at the problems of low sensitivity and high temperature error of fiber Bragg grating (FBG) displacement sensors in displacement monitoring, this paper presents an adjustable cantilever beam displacement sensor with the FBGs as the sensing element. The sensor adds double FBGs on the relative surfaces of the equal-strength cantilever beam, which increases the bending deformation on the FBG of the beam surface to improve the sensitivity and realize the temperature compensation of the sensor. By adding an adjustable external rod structure between a flexible spring and a fixed foot stand, the sensor can regulate the range of initial crack width for different occasions. A theoretical analysis of the displacement sensor is performed, and the simulation analysis and optimization design for the structural parameters of the cantilever beam elastic sensitive element are implemented by adopting SolidWorks and ANSYS software. Finally, a displacement testing platform is constructed to test its performance. Experimental results show that this design has a high sensitivity coefficient of 39.47 pm/mm and a temperature coefficient of 1.04 pm/°C in the range of initial crack width from 0 to 110mm or from 0 to 130mm depending on different monitoring situations. Furthermore, good linearity, hysteresis delay, repeatability, and temperature compensation performance have also been demonstrated.

PDMS-filled micro-spring Fabry-Perot cavity for temperature sensing.

A highly sensitive fiber-tipped temperature sensor based on polydimethylsiloxane (PDMS)-filled spring Fabry-Perot (FP) cavity has been proposed and experimentally demonstrated. The spring FP cavity is first fabricated on the fiber endface by the two-photon polymerization lithography. After that, PDMS is filled into the cavity to drive the elongation of the flexible spring and thus to functionalize high-performance temperature sensing. Benefiting from the large thermal expansion coefficient of PDMS, the proposed sensor exhibits a maximal temperature sensitivity of 704.3 pm/°C with excellent operating repeatability and stability. Besides, by selecting a proper spring constant k, the FP sensitivity can be precisely adjusted in the range of 100-700 pm/°C. Thanks to the advantages of high fabrication accuracy and designable property, the proposed sensor could promote numerous usages for customizable temperature sensing.

Theoretical and experimental investigations on free vibration characteristics of arbitrary spatially closed-coupled plates

A semi-analytical method and related experiments are present in this paper to investigate the free vibration characteristics of the closed-coupled plates with arbitrary spatial coupling angles and curved edges, which are the widely used structural form but researched for the first time. By combining the penalty function method with flexible setting virtual spring stiffness functions and the comprehensive relative motion relation matrices along the edges of the plates system, various types of boundary and spatial coupling connection conditions in practical engineering can be constructed. The semi-analytical solution formulas for the entire vibration model are established by using the first-order shear deformation theory (FSDT) and the two-dimensional Jacobian differential quadrature method (JDQM). To fulfill the requirements of integral operations for displacement approximation functions, the irregular domain mapping technique is employed to transform the irregular solving domain into the regular basic domain. The accuracy and applicability of the present method in predicting eigenfrequencies and mode shapes are proved by hammer modal tests concerning four pyramid/frustum-like built-up plates, comparisons with results from the open literature, as well as the finite element method (FEM) simulations of several specially designed cases. Moreover, many meaningful conclusions are drawn regarding the effects of spatial geometric parameters on the free vibration characteristics of spatially closed-coupled plates with curved edges.

Simulation analysis of effect of wheel out-of-roundness on dynamic stress of coil springs in metro vehicles

Many Chinese metros experienced numerous fatigue failures of the coil springs in the suspension of vehicles. The field test results presented in our previous work showed that wheel out-of-roundness (OOR) was responsible for the failure of the coil springs. It is believed that the most effective countermeasure to eliminate wheel OOR is to reprofile wheel. The fatigue life of coil springs is an important reference for determining the reprofiling parameters. A sophisticated vibration model for train and track with flexible coil springs and flexible track was established and validated with field test results. The effects of wheel OOR and P2 resonance on the coil spring can be evaluated with this model. The relationship between wheel OOR and coil spring dynamic stresses was determined using multibody simulation (MBS). The fatigue life of the coil springs was evaluated using the parameters of the amplitude of the wheel OOR and the mileage. Under the premise of finding a balance between improving the service life of the coil springs and reducing the cost of reprofiling the wheel, viable proposals were made to solve the problem of coil spring fracture.

Study on the Influencing Factors and Forming Process Selection of Sheet Metal Bending Spring Back Defects

In recent years, with navigation, aviation, chemical manufacturing, and automobile bodies increasing requirements for lightweight, high efficiency, and energy saving, quality requirements in the selection of materials and manufacturing process are also improved. However, there is an unavoidable elastic deformation in the process of plastic bending deformation of the panel veneer, and the accuracy of the workpiece is impacted by the spring back phenomenon, which causes dimensional and shape inaccuracies in the panel veneer. The purpose of this paper is to summarize and analyze the phenomenon of flexural spring back caused by material selection and processing techniques and to discuss the solution of the flexion bounce problem from the material selection, processing method, and machining mold, which can be applied to avoid material wastage.

On vibrations of functionally graded double wishbone structural systems

In the framework of dynamic finite element methodology, this articleinvestigates the free and forced vibration behaviors of functionally graded double wishbone structural systems considering the deformability of links and joints. Due to the advantages of the functionally graded materials (FGMs), the double wishbone control arms are modeled as a plane functionally graded frame based on the Timoshenko beam theory (TBT). The power law is adopted to model the through-thickness material gradation. Based on the power gradation law, analytical expressions for the equivalent material stiffnesses and the equivalent inertia are derived. On the other hand, joint deformability is modeled using flexible translational and rotational springs. The dynamic equations of motion are derived based on the Hamiltonian principle. Based on the isoparametric Timoshenko plane frame element, a displacement-based dynamic finite element model is developed. The accuracy of the developed numerical procedure is verified for both free and forced vibration behaviors and good agreement is obtained. Numerical results are obtained and discussed. The results show the significant effects of the FGM distributions on the free and forced vibration behaviors. The developed procedure and the obtained results are supportive of the design and manufacturing processes of such structural systems.

3D printed passive end-effector for industrial collaborative robotic arms

The work focuses on the design and prototyping of a novel end-effector for a collaborative robotic arm allowing to grab and drag industrial packages without lifting them. The proposed solution consists of a passive 3D-printed end-effector manufactured using carbon fibre reinforced Onyx material. Thanks to the entirely passive mechanical actuation that exploits the compliance of the main chassis, this end-effector features a simple, scalable, and inexpensive structure. This lightweight end-effector is specifically designed for small and low payload collaborative robotic arms. Specifically, the proposed end-effector includes three main parts. First, a thin blade, with the main function of separating boxes that are close to each other. Second, a rocker arm - rod mechanism, which allows an opposable bracket to be moved in order to grab the correspondent package. This is proportionally and passively actuated by the contact pressure between the package, during its grip, and a paddle (third part), which is composed of a flat leverage and three flexural springs to counterbalance the pushing force. This paddle and the main body of the gripper were designed as a single part exploiting 3D printing manufacturing capabilities. Moreover, we implemented a Simscape dynamic model that predicts the functionality of the end-effector during standard operations. The work shows how to design, develop and validate a new low cost, passive end-effector mainly oriented to collaborative robots. The final prototype demonstrates its entire functionality, and proves fabricability through 3D printing, thus minimizing production costs, weight, and time.

A compact quasi-zero-stiffness device for vibration suppression and energy harvesting

In this study, a novel compact energy harvesting dynamic vibration absorber (EHDVA) with quasi-zero-stiffness (QZS) characteristics is engineered for both vibration suppression and energy harvesting under low frequency. The QZS EHDVA is composed of a negative stiffness magnetic spring (NSMS), a spiral flexure spring (SFS) and coils. Firstly, the analytical expressions of the force and stiffness of the NSMS are derived by using the equivalent magnetic charge method, and the restoring force of the SFS is analyzed with finite element method. The electromechanically coupled equations are then solved using the Harmonic Balance Method (HBM), and the effect of system parameters on both the performances of vibration suppression and energy harvesting is investigated in detail. Finally, the prototype of the QZS EHDVA is fabricated, and an experiment is carried out to verify the theoretical model. According to the testing findings, the QZS EHDVA is able to suppress vibration in the low frequency region between 3.7 Hz and 6.1 Hz. In addition, the maximum output power of 1.51 mW is achieved under a load resistance of 300Ω at a driving frequency of 4.5 Hz.

Dynamic response of a damaged bridge model traversed by a heavy point mass

The dynamic response of a single-span, damaged bridge model traversed by a point mass whose magnitude is comparable to that of the underlying girder is studied for the purpose of detecting structural damage. Damage is represented in the form of vertical cracks running across the girder's web, which modifies the eigenproperties of the original intact girder. The weight of the mass during its traverse time also modifies the eigenproperties of the girder and its motion produces an additional damping effect. Both features are modelled as Dirac delta distributions, one accounting for the spatial discontinuity in the slope of the deflection, and the other for the temporal discontinuity as the point mass moves forward with constant velocity. Although each type of discontinuity has been treated in the past, their combined effect has not been satisfactorily addressed. Next, a novel time-marching scheme is introduced for treating the temporal discontinuity, where the mass, stiffness and damping of the girder are all updated at the end of a given time interval. Then, the equations of motion are cast as a first-order, matrix differential equation. A parametric study has shown that two eigenvalue-eigenfunction pairs are sufficient for convergence purposes. Following modal synthesis, the transient velocities at any point on the girder during both forced and free vibration regimes are processed by the short-time Fourier transform as a means for detecting changes in the resulting spectograms that are attributable to damage. Finally, support failure is also examined by the introduction of flexible translational springs at the ends. The methodology developed here can be used to identify damage from the recorded kinematic spectrograms at any station on the span of the girder due to a travelling mass. In closing, this work finds applications in structural health monitoring of structures, which is a contemporary and challenging problem facing the engineering profession.

Modeling of a detailed bow spring centralizer description in stiff-string torque and drag calculation

Flexible bow spring centralizers are commonly used in the drilling industry to ensure a good centralization of casings inside the borehole. A bow spring centralizer consists of multiple bows evenly spaced around the tubular. They are attached to the casing at multiple locations via connections or rings, and run-in hole such that the bows are sliding against the borehole. To provide a good centralization, the bows must be stiff enough to push the casing away from the borehole. Also, it must be flexible enough to avoid large contact forces and consequently friction forces that can cause excessive drag. This paper aims to present a theoretical model for bow-spring centralizers and its implementation in a stiff-string torque and drag model based on the finite element method.Our modeling approach assumes that the flexible centralizer bows are identical. Each bow acts independently from the others and could be in contact with the borehole or not, depending on the lateral displacement and orientation of the centralizer. The bow force follows a power law based on a constant stiffness and a stiffness power coefficient that are computed based on test measurements provided by the manufacturer.When introduced in a stiff-string torque and drag model, the contact forces are computed on each individual bow. For drag forces, the bows are assumed to be non-rotating inside the borehole, so the axial friction force at a bow spring is related to the algebraic sum of all bow contacts. When the casing is rotating inside the centralizer, a tangential friction force is generated between the casing and bow spring rings. It is related to the resultant contact force i.e., the vector sum of all bow contacts.An example of the calibration for a bow-spring centralizer is studied in this paper. The theoretical bow-spring model showed its capacity to have a good interpretation of the measurements. It also showed the importance of specifying the testing condition with regards to the possible clearance between the casing and centralizer rings. The finite element torque and drag model is firstly validated against another model. When applied to a case study of running in hole a casing string with bow-spring centralizers, the model shows its effectiveness to describe the casing centralization along the wellbore as well as the tension variations at the surface.

Design and Simulation Analysis of a Reverse Flexible Harvesting Device for Fresh Corn

Aiming at the problem of grain breakage during the harvesting of fresh corn, this paper theoretically analyzes the collision process between the ear picking device and the corn ear, and a flexible ear picking structure composed of flexible materials and buffer springs is determined. Combined with a new harvesting method that reverses the growth direction from top to bottom, a reverse flexible ear plucking device for fresh corn was designed. We used the ADAMS software to simulate the ear picking process of fresh corn, analyze the contact force between the rigid structure and flexible buffer structure under different picking claw speeds and stalk feeding speeds, and obtain the optimal parameter combination: the picking claw speed was 2 m/s, and the stalk feeding speed was 1 m/s. On the basis of the simulation, a reverse flexible fresh corn harvesting bench was built, and the optimal operating parameters were obtained from the test: the speed of ear picking claws was 2.11 m/s; the number of ear picking claws was four; the thickness of the flexible body was 4.52 mm; the stem feeding speed was 1.04 m/s; the corresponding grain breakage rate was 0.128%, which was far lower than the national standard (0.5%); and the ear impurity content was 0.3%, which was far lower than the national standard (2%). The results are consistent with the simulation results, proving that the model is reliable. This research achieved the harvest of fresh corn ears with a low grain damage rate, verified the possibility of reverse flexible ear picking, and provided a reference for the research and development of low-damage fresh corn harvesting machines.