Flexible Spring Research Articles

A Novel MEMS Capacitive Microphone with Semiconstrained Diaphragm Supported with Center and Peripheral Backplate Protrusions.

Audio applications such as mobile phones, hearing aids, true wireless stereo earphones, and Internet of Things devices demand small size, high performance, and reduced cost. Microelectromechanical system (MEMS) capacitive microphones fulfill these requirements with improved reliability and specifications related to sensitivity, signal-to-noise ratio (SNR), distortion, and dynamic range when compared to their electret condenser microphone counterparts. We present the design and modeling of a semiconstrained polysilicon diaphragm with flexible springs that are simply supported under bias voltage with a center and eight peripheral protrusions extending from the backplate. The flexible springs attached to the diaphragm reduce the residual film stress effect more effectively compared to constrained diaphragms. The center and peripheral protrusions from the backplate further increase the effective area, linearity, and sensitivity of the diaphragm when the diaphragm engages with these protrusions under an applied bias voltage. Finite element modeling approaches have been implemented to estimate deflection, compliance, and resonance. We report an 85% increase in the effective area of the diaphragm in this configuration with respect to a constrained diaphragm and a 48% increase with respect to a simply supported diaphragm without the center protrusion. Under the applied bias, the effective area further increases by an additional 15% as compared to the unbiased diaphragm effective area. A lumped element model has been also developed to predict the mechanical and electrical behavior of the microphone. With an applied bias, the microphone has a sensitivity of −38 dB (ref. 1 V/Pa at 1 kHz) and an SNR of 67 dBA measured in a 3.25 mm × 1.9 mm × 0.9 mm package including an analog ASIC.

A temperature self-compensation submicron displacement fbg sensor with tilt parallel-suspended dual-optical fibers

A temperature self-compensating displacement sensor based on fiber Bragg grating (FBG) was developed to measure micro-displacement. This design is composed of a slider, two flexible springs, a probe, and two optical fibers. Both fibers, which are inscribed with FBGs, are tightly suspended in a tilt parallel manner and this structural design allows to tailor the displacement sensing range depending on different sensing requirements or ranges. Furthermore, the difference between the responses of two FBGs is sensitive to the micro axial-movement while insensitive to the temperature. The sensing model with the temperature compensated FBG-based displacement sensor is derived and introduced in detail. Experimental results demonstrate that the sensor’s sensitivity achieves 1518.6 pm/mm, and its range is 0–0.5 mm. The dynamic experiment indicates that the measured result of the designed sensor is in line with the values of a commercial laser displacement sensor which effectively validates the feasibility of the proposed sensor to measure a micro-displacement. Besides, the micro-displacement detection capability with the temperature self-compensation, the designed sensor can support temperature measurement within 20 °C− 50 °C.

Characteristics of a novel cylindrical arm spiral spring for linear compressor

The spring system is the key component of linear compressor, which is attractive in the field of household refrigeration due to its high efficiency and compact structure. Inspired by the traditional flexure spring, we proposed a novel cylindrical arm spiral spring for linear compressor with a comprehensive consideration on the cost, compactness and performance requirements. The design method of spring was introduced and different performance can be obtained by adjusting the internal radius, external radius, number of turns and wire diameter. The static displacement of spring was modelled by using FEA (Finite Element Analysis) method for various axial and radial force. And a specific fixture was built to measure the spring stiffness to verify the results obtained from FEA simulation. At last, the dynamic test of the linear compressor equipped with the proposed spring was conducted. The experimental results showed that the resonant frequency of linear compressor can meet the design requirements of 78 Hz without gas compressor, indicating that the application of this type of spring in the linear compressor is feasible.

A monolithic linear motion platform driven by a piezoelectric and fluidic pressure-fed dual mechanism.

This paper presents a novel dual-mode motion mechanism capable of achieving nanopositioning on a monolithic linear motion platform. Unlike conventional dual-mode stages that use piezoelectric (PZT)- and electromagnetic-combined or similar actuation mechanisms comprising two separate motion axes, the dual-mode actuation was developed by combining a PZT for a coarse motion and a fluidic pressure-fed mechanism (FPFM) for a fine motion and was implemented in a monolithic flexure stage fabricated by metal additive manufacturing. The FPFM actuates the flexure stage by pressuring the media in the fluidic channels created inside the flexure spring structures. Experimental tests were performed to investigate the performance of the dual-mode linear motion platform. The stiffness, damping, and frequency response functions of the dual-mode stage were experimentally characterized. The proportional-integral-differential control combined with dual-mode control was employed to control the position of the flexure stage while bidirectionally controlling the flow of compressed air for a fine motion. The FPFM motion showed a good response to 1nm stepwise input (every 10 psi), and it was implemented to provide up to ∼10nm fine motion along with the PZT coarse motion (1 µm). The hysteresis characteristics of the FPFM were also characterized and compensated to track the positioning error.

Electromagnetic Vibration Energy Harvester with Tunable Resonance Frequency Based on Stress Modulation of Flexible Springs.

This paper presents a compact electromagnetic vibrational energy harvester (EVEH) with tunable resonance frequency. The resonance frequency of the EVEH is tuned by adjusting the axial stress in the flexible polymeric springs, which is realized by physically pulling and pushing the springs. The stress tuning functionality is realized with a compact structure with small volume. The total frequency tuning range of the proposed EVEH is 56 Hz (74–130 Hz), which is 64% of the natural resonance frequency of the EVEH (88 Hz). It is found that the tensile stress increases the resonance frequency of the EVEH, while the compressive stress firstly reduces the resonance frequency and then increases the resonance frequency due to buckling.

Design Optimization of Flexure Springs for Free-Piston Stirling Engines and Experimental Evaluations with Fatigue Testing

The free-piston Stirling engine is a closed-cycle regenerative heat engine that converts heat energy into mechanical work, and requires a spring element for vibratory operations of the displacer and power pistons. In this study, the geometry of the flexural spring design was optimized through structural finite element analyses and fatigue test evaluations. First, we constructed a target design space considering the required natural frequency of the displacer spring assembly under the geometric constraints of total mass and module height. The design of experiments was employed to construct simulation cases for design factors such as the outer diameter, thickness, and number of spirals in the spring sheet. As a result, the optimized design values were obtained to satisfy the design requirements. We also fabricated a test spring specimen and conducted fatigue tests using a linear actuator system developed to have the same motion as the engine. The test results indicated that the optimized spiral spring had no fracture under operating conditions with the design piston amplitude, revealing the effectiveness of the design method.

Rapid Prototyping of Inertial MEMS Devices through Structural Optimization.

In this paper, we propose a novel design and optimization environment for inertial MEMS devices based on a computationally efficient schematization of the structure at the a device level. This allows us to obtain a flexible and efficient design optimization tool, particularly useful for rapid device prototyping. The presented design environment—feMEMSlite—handles the parametric generation of the structure geometry, the simulation of its dynamic behavior, and a gradient-based layout optimization. The methodology addresses the design of general inertial MEMS devices employing suspended proof masses, in which the focus is typically on the dynamics associated with the first vibration modes. In particular, the proposed design tool is tested on a triaxial beating-heart MEMS gyroscope, an industrially relevant and adequately complex example. The sensor layout is schematized by treating the proof masses as rigid bodies, discretizing flexural springs by Timoshenko beam finite elements, and accounting for electrostatic softening effects by additional negative spring constants. The MEMS device is then optimized according to two possible formulations of the optimization problem, including typical design requirements from the MEMS industry, with particular focus on the tuning of the structural eigenfrequencies and on the maximization of the response to external angular rates. The validity of the proposed approach is then assessed through a comparison with full FEM schematizations: rapidly prototyped layouts at the device level show a good performance when simulated with more complex models and therefore require only minor adjustments to accomplish the subsequent physical-level design.

Development of the Reduced-Scale Vehicle Model for the Dynamic Characteristic Analysis of the Hyperloop

This study addresses the Hyperloop characterized by a capsule-type vehicle, superconducting electrodynamic suspension (SC-EDS) levitation, and driving in a near-vacuum tube. Because the Hyperloop is different from conventional transportation, various considerations are required in the vehicle-design stage. Particularly, pre-investigation of the vehicle dynamic characteristics is essential because of the close relationship among the vehicle design parameters, such as size, weight, and suspensions. Accordingly, a 1/10 scale Hyperloop vehicle system model, enabling the analysis of dynamic motions in the vertical and lateral directions, was developed. The reduced-scale model is composed of bogies operated by Stewart platforms, secondary suspension units, and a car body. To realize the bogie motion, an operation algorithm reflecting the external disturbance, SC-EDS levitation, and interaction between the bogie and car body, was applied to the Stewart platform. Flexible rubber springs were used in the secondary suspension unit to enable dynamic characteristic analysis of the vertical and lateral motion. Results of the verification tests were compared with simulation results to examine the fitness of the developed model. The results showed that the developed reduced-scale model could successfully represent the complete dynamic characteristics, owing to the enhanced precision of the Stewart platform and the secondary suspension allowing biaxial motions.

A simplified computational model for seismic performance evaluation of steel plate shear wall-frame structural systems

The steel plate shear wall (SPSW)-frame structure is a high-performance lateral force-resisting system, which has been widely utilized in high-rise buildings, especially in seismic-prone regions. The complexity of SPSW modeling and the interaction between SPSWs and frame, make it very time-consuming and low-efficiency for the performance-based seismic performance evaluation of SPSW-frame systems. This paper developed a simplified computational analytical model of SPSW-frame system based on the lateral deformation characteristics of the system. The simplified flexure-shear (F-S) model was composed of the flexure springs and shear springs, to respectively simulate the behaviors of SPSW and frame. Also, the P-delta column was incorporated into the simplified model to account for the P-delta effect. The material parameters of the flexure spring and shear spring were calibrated by the response spectrum method. By employing the PEER full probability theory, the seismic performance evaluation of two 7- and 15-story SPSW-frame structures were carried out using the simplified F-S model and refined finite element method (FEM). The analytical results demonstrated that the simplified flexure-shear model can achieve nearly the same performance parameters, compared with the refined FEM. Furthermore, the repair cost and repair time of the SPSW-frame structures mainly came from the non-structural components.

Multiresponse Optimization for a Novel Compliant Z-Stage by a Hybridization of Response Surface Method and Whale Optimization Algorithm

A novel compliant z-stage is applied for positioning and indenting a specimen in nano/microindentation testing system. For an excellent operation, the proposed z-stage can concurrently satisfy multicriteria comprising high safety factor, small parasitic motion, and large output displacement. The key aims of this article are to present a novel design of the compliant z-stage as well as an effective integration methodology of Taguchi method, response surface method, weight factor calculation based on signal to noise, and the whale optimization algorithm to resolve a design optimal problem so as to enrich the quality performances of the proposed stage. Primarily, the z-stage is designed based on four-lever amplifier, compliant hinge shifted arrangement mechanism, zigzag-based flexure spring guiding mechanism, and symmetric six leaf hinges-based parallel guiding mechanism. Secondly, the number experiment data are achieved by the Taguchi method and finite element analysis. Subsequently, the regression functions among input variables and quality characteristics are formed by exploiting response surface method. In addition, the weight factors for every characteristic are defined. Additionally, the sensitivity analysis is accomplished for determining influences of input variables on quality responses. Ultimately, based on regression equations, the whale optimization algorithm is executed to define the optimal factors. The consequences indicated that the output deformation is about 454.55 μm and the safety factor is around 2.38. Furthermore, the errors among the optimal consequences and the confirmations for the safety factor and output deformation are 7.12% and 4.25%, correspondingly. By using Wilcoxon and Friedman methods, the results revealed that the proposed algorithm is better than the cuckoo search algorithm. Based on the quality convergence characteristics of hybrid approach, the proposed method is proficient for resolving complicated multiobjective optimization.

Closed-form solutions for vibrations analysis of cracked Timoshenko beams on elastic medium: An analytically approach

In this paper a novel analytically method for analysing the dynamic behaviour of Timoshenko beam model, resting on Winkler-type elastic soil, under simply-supported boundary condition and with a crack is proposed. The beam is also supposed to be constrained at the ends by elastically flexible springs, with transverse stiffness and rotational stiffness. Applying the Timoshenko beam theory and employing the auxiliary functions, the equation of motion is derived. The natural frequencies are obtained by applying the Euler–Bernoulli method and are derived by the corresponding auxiliary functions of the governing equation of the Euler–Bernoulli beam in free vibration. For different values of soil parameter, taking into account the effects of rotational and shear deformation and considering the presence of crack, typical results are presented, in order to demonstrate the efficiency of the proposed approach. Finally the obtained results are compared with some results available in the literature. It is shown that very good results are obtained. This approach is very effective for the study of vibration problems of Timoshenko beams. The novelty of the proposed approach is that although the auxiliary functions, used to find the solution to the dynamic problem of a Timoshenko beam, are different for the two theories applied, in both cases, the dynamic problem is traced to the study of an Euler - Bernoulli beam subjected to an axial load.

Analysis of the Protection Performance of Face Guard for Large Mining Height Hydraulic Support

With the increase of mining height, the problem of coal wall spalling in the working face gradually worsens. Hydraulic support and its face guard structure are the key pieces of equipment to restrain the coal wall spalling. However, at present, the hydraulic jack is mostly considered as rigid in the analysis of protection mechanism. This simplification cannot effectively reflect the true bearing state of the face guard. In order to improve the accuracy of analysis, this study considers the face guard jack as a flexible spring and establishes a rigid-flexible coupling analysis model of the face guard mechanism. First, based upon the multibody dynamics software ADAMS®, the multibody numerical model of the face guard of the hydraulic support was established. The influence of the two kinds of structures on the coal wall disturbance was analyzed and compared. Then, the rigid model was meshed. The hydraulic jacks were equivalent to the spring system, and the rigid-flexible coupling model was established. Based upon the application load on different positions of the rigid-flexible model, the load-bearing characteristics and hinge point force transfer characteristics of the two face guards were analyzed. The results show that the support efficiency of the integral type was higher than that of the split type. In the vertical support attitude, the dynamic disturbance of the coal wall, produced by the two kinds of face guards, was small. The four-bar linkage effectively improved the ultimate bearing capacity of the integral face guard. The results provide theoretical support for the design and optimization of the face guard.

Design and experimental validation of a vibration isolator with high-static low-dynamic stiffness and operating point variable property

Vibration isolator with high-static low-dynamic stiffness property has been researched extensively, but the isolator’s stability and performance will be deteriorated with the operation point variation. In this article, a vibration isolator that operation point can be variable was proposed, and it was constructed by combining a coil spring and flexible leaf springs with a negative stiffness magnet spring in parallel. Unlike previous studies, this article focuses on the realization of the high-static low-dynamic stiffness characteristic of the isolator, and the operation point of the vibration isolator can be varied in a certain range. The effects of configuration parameters on the negative stiffness are investigated in detail. Furthermore, the designing procedure to realize the linear negative stiffness with the expected magnitude and range was also developed. A prototype was installed and the vibration transmissibility of the system at different operation points was measured, the experimental results indicated that the isolator can be kept stable in different operation points, and the performance does not deteriorate with the variation of the operation point. The effectiveness of the designing procedure of the realization of linear negative stiffness with the expected magnitude and range and the variable of the operation point of the isolator was validated.

Optimization of material of flexure spring by finite element analysis

Abstract Flexure spring is thin metallic disc used to allow relative motion by bending between the piston and the fixed support in compressor body. The flexure spring deforms by the force applied by piston and come back to its original position. As spiral arms cut from its surface, flexing takes place. The main object of this article is to optimize the spring material to enhance the service life of spring. The present article analyzes five different copper based alloys as these materials are having elasticity property. Initially the model was prepared in Catia software. The Finite Element Analysis (FEA) was carried out by applying boundary conditions. As the total displacement of piston is 10 mm so force is applied at the central hole in such a way that the spring will deform for 5 mm from mean position. Due to applied load stresses will develop in the flexure. The equivalent stress was observed for chosen materials. The equivalent stresses were compared with permissible stress for that material by considering factor of safety (FoS). The cold drawn copper and the Beryllium copper UNS C (TH02) found suitable for flexure spring having the stress within permissible limit. As stiffness is also important property for spring. The deformation was observed in FEA for these two materials by applying 1 N force. The stiffness was calculated. The material was selected which will give maximum stiffness. It was found that the Beryllium copper UNS C (TH02) shows the maximum stiffness.

Material selection for long life and high durability for special purpose type of flexure bearing

A special type of flexure bearings are installed to support a compressor motor and a displacer within a cryocooler which is used in space applications. The fatigue life of spring is a critical factor for such applications, to ensure that the cryocooler does not fail. The flexure spring is used in the setup of an eccentric type of flexure bearing. The present study analyzes various significant parameters and properties in selecting the best suitable material to achieve finite-fatigue life. To avoid a failure of such critical component, batch testing is carried out. The three materials which are compared with respective SN-curve are a] beryllium copper, b] Stainless Steel (3 0 4) and c] Titanium. The study has been carried out to find the best suitable material for flexure bearing. Finite Element Analysis (FEA) is used to understand flexure springs stress and displacement.

Structure Design of Cable-Stayed Bridge Intelligent Detection Robot

Cables are the main load-bearing components of cable-stayed Bridges. The durability and reliability of cables are directly related to the safe operation and service life of the whole bridge. Aiming at the problem of cable detection and maintenance, a new type of cable detection robot is designed in this paper. To further enhance the stability of the robot, the structure adopts symmetrical arrangement to make the center of mass of the robot system coincide with the cable axis. According to the working condition of the robot, a flexible body spring that meets the parameter requirements is designed, which not only meets the required preload, but also meets the starting torque of the motor. The robot is simple in structure, standardized in parts, easy to assemble and disassemble, and has good obstacle clearance ability and detection efficiency.

Non-linear simplified models for seismic response estimation of a novel tall timber-concrete hybrid structural system

To better study the seismic performance of a novel high-rise timber-concrete (FaB) hybrid structural system, two non-linear simplified analytical models (i.e., Fixed Model and Controlled Model) are proposed in this paper. The timber-concrete FaB hybrid system mainly consists of a concrete frame-tube structure with large story height as the main structure, and several multi-story-high timber substructures on every concrete slab. The timber substructures are fixed to the main structure to form the Fixed Model (FM) or are connected by energy dissipation layers to form the Controlled Model (CM). To fully consider the different structural characteristics of the concrete main structure, timber substructures, and the connections in between, the FaB hybrid system is discretized and simulated with different non-linear parts in simplified models. For the concrete main structure, non-linear flexural springs and shear springs are adopted to simulate the flexural-shear behavior, while non-linear shear springs are used for simulating the timber substructures and energy dissipation layers. The model development procedure of the proposed simplified models is then presented in detail. Results from modal analysis, linear and non-linear time-history analyses of simplified models and refined finite element models of a 30-story timber-concrete FaB hybrid structure are compared and show good agreement. Specifically, the simplified models can satisfactorily predict the dynamic properties and seismic responses of the FaB hybrid system in linear and non-linear stages. The maximum difference between the simplified models and refined models varies from 2% to 20% for predicting the modal periods, floor displacement, acceleration, or base shear of the FaB system, which validates the accuracy of the simplified models. Moreover, by adopting the simplified models, the computation efficiency is also significantly enhanced, which is about 400 times faster than that of using the refined models. Outcomes of this study are expected to provide some references for future research and structure design for the novel timber-concrete hybrid system, which supports potential applications of such hybrid systems in tall buildings.

Design and Fabrication of a MEMS-Based Break Junction Device for Mechanical Strain-Correlated Optical Characterization of a Single-Molecule

Here, we propose a robust lab-on-a-chip system for multi-dimensional (electrical, optical, and mechanical) characterization of a single-molecule utilizing a Si micromachined micro-electromechanical-system (MEMS) chip. Our MEMS-based break junction (MEMS-BJ) utilizes conventional MEMS chip fabrication techniques to create an electrostatic comb actuator capable of trapping a single-molecule between two nanoscale metal electrodes with sub-nanometer displacement resolution. In order to achieve this functionality, components of the chip (e.g flexural spring, comb drive fingers) are delicately designed based on an analytical model and basic performance parameters are verified using a finite element analysis simulation and capacitive sensor measurements. Using this system, we are able to perform combined single-molecule Raman spectroscopy and molecular conductance measurements in real-time. Finally, we present a representative case study of the multi-dimensional characterization of a single-molecule junction by analyzing correlated electrical, optical, and mechanical information while mechanically modulating the strain on the junction which allows for direct observation of the interplay between molecular structure and electron transport. We believe that our MEMS-BJ system will enable a deeper multi-dimensional study at a single-molecule level promoting the development of new methods for chemical and biological sensor applications.

Origami-Inspired Radiation Pattern and Shape Reconfigurable Dipole Array Antenna at C-Band for CubeSat Applications

This article presents an antenna structure with a reconfigurable pattern and polarization for CubeSat applications. The proposed antenna is based on spatial-mapping origami theory and consists of a center-fed four-way Gysel power divider, delay lines, inside lamina emergent torsion (LET) joints, and four thick planar dipole antennas. The LET joints are used to distribute the mechanical stress of a rigid planar material to form a flexible planar spring structure. The proposed antenna has monopole-like omnidirectional linearly polarized gain patterns in planar mode. Its gain value is about 0.5 dBi at 5.8 GHz. In folded mode, the antenna has about a circularly polarized gain value of about 8.07 dBic and broadside radiation patterns. The measured cross-polarization suppression ratio is about 25 dB, and the axial ratio (AR) value is 1.13 dB at 5.8 GHz. The size of the antenna in planar mode with a cross-shape is $100\times 100\times0.5$ mm3, and its size is in folded mode is $32.5\times 32.5\times32.5$ mm3. The size of the antenna in inactive mode is $35\times 35\times 3$ mm3, and its total weight is only 4.73 g.

Experimental Investigation on a Novel Airfoil-Based Piezoelectric Energy Harvester for Aeroelastic Vibration.

This paper presents a novel airfoil-based piezoelectric energy harvester (EH) with two small square prisms attached to an airfoil. This harvester can achieve a two degree-of-freedom (DOF) plunge–pitch motions. Several prototypes of energy harvester were fabricated to explore the nonlinear aerodynamic response and the output performance in a wind tunnel. The experimental results showed that the longer the flexible spring was, the lower the critical velocity and frequency of the harvester were, and the better aerodynamic response and output performance could be achieved. The initial disturbance, the following limit-cycle oscillation, and the ultimate chaos of nonlinear response occurred, as increasing airflow velocity was increased. The overall output performance of the harvesters with a flexible spring having a thickness of 1 mm outperformed than that of the harvesters with a flexible spring having a thickness of 0.5 mm at a higher airflow velocity, while the tendency was opposite at a lower velocity. An optimum output voltage of 17.48 V and a power of 0.764 mW were harvested for EH-160-1 at 16.32 m/s, which demonstrated it possessed better performance than the other harvesters. When the capacitor was charged for 45 s and directly drove a sensor, it could maintain working for 17 s to display temperature and humidity in real time.