Flexible Displacement Research Articles

Design and performance analysis of a flexible-hinged piezoelectric driving dispenser

Piezo-driven dispensers are precision dispensing devices for trace amounts of fluid and are widely used in the microelectronics packaging field. However, the preloading mechanism of piezo-driven dispensers easily loosens in high-frequency operation, and the design accuracy of the transmission ratio of the flexible displacement transmission mechanism (DTM) requires improvement. To address the aforementioned problems, we designed a self-locking preloading mechanism with an adjustable preloading amount for piezo-driven flexible transmission dispensers and investigated the method of designing the transmission ratio considering the non-expected directional deformation (parasitic deformation). First, the principle of the preloading mechanism was analyzed, and a method for adjusting the droplet diameter based on the preloading amount was proposed. Second, an asymmetric flexible-hinge compliance matrix calculation method was proposed, a transmission ratio model of the DTM was established, and the influence law of the structural parameters on the transmission ratio was comparatively analyzed using ANSYS software. Based on the output displacement requirement, transmission ratios were designed and structural parameters were determined. Finally, based on the piezoelectric coupling simulation, a piezo-driven dispenser was manufactured, and a test platform was built to conduct the relevant tests. The simulation and test results demonstrated that the maximum relative errors of the transmission-ratio calculated by the proposed transmission-ratio model were 1.54% and 3.6%, respectively, compared to the simulation and test results, confirming that the model was correct. Single-factor tests confirmed that a preloading mechanism can fix and preload the piezostack and that the droplet diameters can be adjusted with the preloading amounts. The operating frequency was up to 800 Hz with a diameter of 0.30 mm and a consistency of 4.32%, which meet the requirements of dispensing efficiency in the microelectronics packaging field. This study has practical significance for enhancing the transmission ratio design accuracy and dispensing performance of dispensers.

A Self-Powered Flexible Displacement Sensor Based on Triboelectric Effect for Linear Feed System.

The detection and feedback of displacement and velocity significantly impact the control accuracy of the linear feed system. In this study, we propose a flexible and self-powered displacement sensor based on the triboelectric effect, designed for seamless integration into linear feed systems. The displacement sensor comprises two parts, the mover and stator, operating in a sliding mode. This sensor can precisely detect the displacement of the linear feed system with a large detection range. Additionally, the sensor is capable of real-time velocity detection of linear feed systems, with an error rate below 0.5%. It also offers advantages, such as excellent flexibility, compact size, stability, easy fabrication, and seamless integration, with linear feed systems. These results highlight the potential of the self-powered displacement sensor for various applications in linear feed systems.

A Novel Reflection-Mode Fabry–Perot Cavity Antenna With Broadband High Gain and Large Beam-Scanning Angle by Janus Partially Reflective Surface

Operational mechanism and design methodology of a novel reflection-mode (R-mode) Fabry–Perot cavity antenna (FPCA) are proposed in this article. Unlike common transmissive-mode (T-mode) FPCAs, the R-mode one places the feed antenna outside the cavity and introduces a Janus partially reflective surface (PRS), reducing the coupling between the feed and the FP cavity, while obtaining flexible displacement freedom of the feed to achieve a large beam scanning angle. The proposed R-mode FPCA employs a compact triple-layered Janus PRS, a simple ground plane, and a linearly polarized microstrip feed. The Janus PRS is applied to achieve bidirectional asymmetric transmission from the outside to the inside of the cavity to ensure the excitation efficiency and gain enhancement. In addition, a beam scanning model is proposed to obtain the spatial position of the feed and the maximum beam scanning angle under the specific antenna size. Finally, a proof-of-concept prototype is designed, fabricated, and measured at X-band. The measurement results agree well with the simulation, the 3 dB gain bandwidth of 19.7% is achieved. The peak gain in this range is 17.35 dBi and a large 3-D beam scanning range of [−35°, 35°] is also obtained.

3D flexible displacement sensor for highly sensitive movement measurement assisted by the terahertz imaging system

Aiming at the difficulty of accurately calibrating the sample position in the terahertz (THz) imaging process, especially in the defect imaging detection and the precise characterization of the edge profile, a flexible and highly sensitive 3D terahertz displacement sensor with a resolution of up to 1 μm was proposed by the artificial electromagnetic metamaterials. The high resolution of the flexible sensor can be attributed to the used artificial electromagnetic metamaterials with the enhancing sensitivity of THz sensors as well as the flexible substrate with the high fitting to the target. Unlike the laser displacement sensor with a complex and large volume of the generating device, the proposed flexible sensor with a simple structural design is composed of only a fixed layer and a displacement indicating layer. The fixed layer is composed of the Mylar flexible substrate layer and the metal split resonator ring on it, and the displacement indicating layer is composed of the Mylar flexible substrate layer and the metal indicator lines on it. By using this unique double-layer structure, high-sensitivity measurement of displacement can be achieved by measuring the moving amount of the metal indicator line corresponding to the valley change in the THz transmission of the displacement sensor. The results demonstrate that the sensitivity of the displacement sensor can reach 145 GHz/μm, the quality factor Q can reach 194.67, and the quality factor figure of merit can reach 6.25 μm−1. Compared with the mature commercial displacement sensors and laser displacement sensors, the proposed sensor can have the characteristics of compact structure, simple preparation process, high-sensitivity, and flexibility, which can offer certain advantages for the realization of high-precision, miniaturization, and distributed sensing systems in the future.

Performance of Modular-Reinforced Soil-Retaining Walls for an Intercity Railway during Service

In order to investigate the mechanical behavior of reinforced soil-retaining walls during service, this paper carried out a long-term remote observation test for 6 years on the modular-reinforced soil-retaining wall of the Qingrong intercity railway in eastern China’s Shandong Province. During the construction period, earth pressure boxes, flexible displacement meters, settlement pipes and displacement meters were buried to observe the soil pressure, reinforcement strain, horizontal displacement and settlement of the reinforced earth-retaining wall, respectively, for a long time; then, the results were analyzed to summarize its variation law. The results show that the reinforced earth-retaining wall was stable after one year of construction. It was determined that the strain of reinforcement in each layer decreased with time, culminating in a value of less than 0.88 percent during the 6th year. The maximum horizontal displacement of the wall was 11.43 mm and the maximum settlement of the wall top was 46.77 mm, which were 0.15% and 0.60% of the wall height, respectively. These research results can be applied to the construction and design of reinforced soil-retaining walls in high-speed railways. The effects of the elastic modulus of filler, the tensile modulus of reinforcement and the reinforcement length on the characteristics of the retaining wall were analyzed in the numerical simulation with PLAXIS2D. The results and analysis show: the elastic modulus of filler and reinforcement length have a significant effect on the horizontal displacement of the retaining wall. The results of this experiment can be referenced for engineering projects.

Free vibration analysis of multi-layer rectangular plate containing magnetorheological fluid and flexible core layers rested on Winkler-Pasternak foundation

Magneto-rheological (MR) fluids viscosity can be varied by changing the magnetic field intensity. Therefore, they can improve structural rigidity and damping property. The current study presents a free vibration analysis of a multilayer rectangular plate with two layers of MR fluid and a flexible core layer, rested on a Winkler-Pasternak foundation based on exponential shear deformation theory (ESDT). In this theory, the exponential functions are applied in terms of thickness coordinates to include the effect of transverse and inertial rotational shear deformation. The flexible core displacement is modeled via the second-order Frostig model. The Hamilton’s principle is used to derive the equations of motion. These equations are solved using the Navier method to obtain the natural frequencies of the plate. The accuracy of the derived equations is validated, and the obtained results are compared with a specific case. Finally, the results show that by applying and increasing the magnetic field intensity, the natural frequencies and loss factor increase. With the increase in the mode number for each specific magnetic field intensity, the natural frequency increases and the loss factor decreases. The natural frequencies and loss factor decrease with the increase of the MR layer thickness to overall thickness ratio and the flexible core layer thickness to overall thickness ratio. The natural frequencies increase when the parameters of the foundation increase.

Numerical investigation on arching effect surrounding deep cylindrical shaft during excavation process

Predicting the inner displacements of deep vertical shafts during the excavation process has been a difficult task considering the geological, structural, and constructional influences. In fact, the two-dimensional (2D) analytical solution based on the retaining wall model remains insufficient for understanding the actual behavior during an excavation. This is because the deformation of vertical shafts becomes complicated due to the unexpected arching effect brought about by the three-dimensional (3D) flexible displacements occurring in the excavation process. Previous analytical solutions only considered the limit equilibrium. Therefore, the present study deals with a 3D soil-structure simulation by considering the displacements of a cylindrical shaft and the mechanical behavior of the surrounding soil as well as the geometry of the cylindrical structure. Moreover, this mechanical behaviors of the surrounding soil and shaft are controlled by the shaft stiffness; hence, the relationships among the shaft stiffness, mechanical behavior of the surrounding soil (in terms of earth pressure coefficient), and shaft displacement were investigated. A cylindrical model, 120 m in depth and 20 m in diameter, was positioned at the center of a sand domain, and each excavation step was performed at an interval depth of 20 m. A 3D finite difference method analysis was applied using the modified Cam-Clay (MCC) model to represent the soil behavior. As a result, the present study provides a new normalized lateral earth pressure theory for excavated shafts by considering the 3D arching effect obtained from parametric studies using various levels of shaft stiffness. From a comparison with the analytical solutions of previous studies (Terzaghi, 1943a; Prater, 1977; Cheng & Hu, 2005), it is found that the previous studies underestimated the earth pressure acting on the cylindrical shaft because they did not consider the accurate arching effect.

Bidirectional Drive with Inhibited Hysteresis for Piezoelectric Actuators.

Piezoelectric actuators with a flexible displacement amplification structure are widely used in the fields of precision driving and positioning. The displacement curve of conventional piezoelectric actuators is asymmetrical and non-linear, which leads to large non-linear errors and reduced positioning accuracy of these piezoelectric actuators. In this paper, a bidirectional active drive piezoelectric actuator is proposed, which suppresses the hysteresis phenomenon to a certain extent and reduces the non-linear error. Based on the deformation theory of the beam, a theoretical model of the rhombus mechanism was established, and the key parameters affecting the drive performance were analyzed. Then, the static and dynamic characteristics of series piezoelectric actuators were analyzed by the finite element method. A prototype was manufactured and the output performance was tested. The results show that the actuator can achieve a bidirectional symmetric output of amplification displacement, with a maximum value of 91.45 μm and a resolution of 35 nm. In addition, compared with the hysteresis loop of the piezoelectric stack, the nonlinear error is reduced by 62.94%.

Development of a low-voltage driven non-resonant three-DOF eyeball-like piezoelectric actuator

In this work, a low-voltage driven non-resonant three degree-of-freedom (DOF) eyeball-like piezoelectric actuator is proposed. Elliptical motions on the driving feet are formed from the pushing and pulling actions of the flexible displacement amplification (FDA) mechanism in the piezoelectric actuator. There are three types of elliptical movements to drive the spherical rotor around three coordinate axes while driving the different groups of piezoelectric stacks. The principles of the three-DOF rotations are analysed by theoretical and simulation methods. Fabrication of a miniature piezoelectric prototype of 34mm × 34mm × 34mm is conducted. Under a driving voltage of 40 the maximum rotary velocities of the rotor around X, Y and Z axes reach to 62.5 r min−1, 65 r min−1 and 46 r min−1 at 1.5 kHz. High resolutions around X and Y axes up to 2.5 and 5 are obtained. The remarkable comprehensive performances enable much potential applications of this three-DOF eyeball-like piezoelectric actuator in precision pointing, attitude adjustment and bionic eye positioning systems.

Development of a Flight Mechanics Simulation Computer based on a Flexible Aircraft Model for a Regional Aircraft

The changes on aircraft structures and the increased use of advanced and light materials have led to the design of more efficient and flexible aircraft. This implies that rigid body dynamics is no longer sufficient to describe the aircraft behaviour in atmospheric flight. Coupling between structural and rigid body dynamics should be included, due to frequencies of structural modes. In this work, an analytical method, based on a mixed Newtonian-Lagrangian approach, is used to derive a simplified model of a flexible aircraft. Moreover, flexible displacements and torsional variables, starting from the Lagrange’s equations, are discretized by means of a finite number of generalized coordinates. This approach allows to derive directly a finite-order system of ordinary differential equations, making it less complex and suitable for real time simulation and control law synthesis. The main objective of the proposed methodology is the real-time implementation on a “flyable” hardware, for experimental tests, including sensor models. In detail, accelerometers on selected wing sections are design to measure the effect of flexibility in terms of bending and torsional deformations. A simplified low-order model is designed for a regional aircraft, including different masses and flight conditions. Moreover, only two symmetrical bending modes and one torsional mode are considered in the flexibility definition. Finally, the hinge moments acting on the control surfaces are evaluated. The hinge moment is calculated as the aerodynamic torque generated on the hinge axis by the variation of the pressure distribution acting on the control surfaces. A gust response of this aircraft is mainly analysed, considering both a discrete gust model and a continuous model. This research is performed within the ASTIB project, which has received funding from the Clean Sky 2 Joint Undertaking under the European Union’s Horizon 2020 research and innovation program under grant agreement CSJU – GAM REG 2014-2015.

Real-time implementation of a parameterized Model Predictive Control for Attitude Control Systems of rigid-flexible satellite

Rigid-flexible satellites are aerospace systems with flexible parts attached to their structures, such as antennas or solar panels. Attitude Control Systems (ACS) of satellites are responsible for spatial orientation concerning a fixed reference for executing maneuvers. As a result, ACS can lead to problems in flexible structures, especially in large-scale movements, as undesired vibrations may be induced in the system, which can impair the satellite’s mission. Then, ACS must be designed to carry out attitude control efficiently while regarding several satellite operating restrictions. In this paper, a parameterized Model Predictive Control (MPC) strategy is proposed for the ACS of a rigid-flexible satellite. The parameterized MPC can provide attitude tracking performance as well as meeting operational constraints to limit the maximum allowable flexible displacement of the structure. Besides, the proposed controller also deals with the saturation of the electric motor command variable. Another relevant feature of the proposed control strategy is the parameterization of MPC, which reduces the complexity of the optimization problem enabling short computation times and allowing real-time implementation. A Hardware-in-the-Loop (HIL) platform is used to validate the proposed control scheme in an embedded system as well as evaluate the closed-loop performance, robustness, and control feasibility. Numerical and experimental results emphasize the efficiency of the parameterized MPC strategy, and a comparison with a Linear Quadratic Regulator (LQR) is performed.

Multi-floater-mooring coupled time-domain hydro-elastic analysis in regular and irregular waves

In this study, a time-domain hydro-elastic model is developed to solve the floater-connector-mooring coupled system. The frequency-domain model is first devised with the discrete-modulus-based method in which the deformable floating structure is modeled with multiple rigid bodies connected by high-order beam elements. The corresponding multi-body hydrodynamic coefficients and loads are estimated by 3D potential theory with the coupling stiffness matrix based on the theory of the Euler-Bernoulli beam and Saint-Venant torsion. The time-domain hydro-elastic model with mooring dynamics is then subsequently developed with multi-body Cummins equation with high-order rod-FE (Finite Element) mooring elements connected to relevant floaters. The present frequency- and time-domain models are validated through comparisons with published experimental and frequency-domain results for a VLFS (Very Large Floating Structure) without mooring lines. The present method directly solves the hydro-elastic problem with mooring lines without using the conventional modal superposition method, for which wet modes with mooring need to be obtained in a priori through cumbersome iterations. The developed hydro-elasticity model is also very useful when complex inner structure-connection conditions, such as discontinuity by multiple hinged joints, are involved. Such an example is also numerically tested, and reliable results are obtained. Vertical flexible displacements, bending and torsional moments, shear forces, and mooring tensions in regular and irregular wave conditions are systematically analyzed and compared with rigid-body and without-mooring cases.

High-speed 3D digital image correlation for rolling deformation of a tire sidewall and measuring dynamic contact patch length.

Tires play a vital role in a vehicle's operational stability, comfort, and security. However, due to the influence of test equipment and tire operating conditions, the perception of rolling tire characteristics is still in the stage of gradual improvement, especially the analysis of sidewall rolling deformation and dynamic contact peculiarities of tires/road interactions, which has restricted the analysis of rolling energy dissipation and the accurate observation of tire forces. In this paper, the high-speed stereo-vision system was created by high-speed cameras, and the relative rigid and flexible displacement, strain, and trajectory trend of marker points and the real-time global displacement field of the sidewall during the tire-rolling cycle were acquired utilizing the improved digital image correlation algorithm under different rolling velocities. Meanwhile, the periodic dissipation of the strain concentration region was observed, and the phenomenon of strain resonance appeared at the overlap of the periods. The relative flexibility strain and shear strain of the marker point were obtained on the plane element, which resulted in the relative flexibility major principle strain of the plane element, and then it achieved recognition of the leading and trailing points of the contact patch and the accurate measurement of dynamic contact patch length.

Dynamic Modeling and Residual Vibration Suppression of the Redundantly-Actuated Cable Driving Parallel Manipulator

An improved input shaping (IS) scheme was proposed for the redundantly actuated cable driving parallel robots (CDPRs) to suppress the residual vibration (RV). To make the design of the RV suppression convenient, the flexible displacements of the moving platform were taken as the generalized coordinates considering the axial deformation of cables, and rigid-flexible dynamic model of generalized redundantly actuated CDPRs was established with the Newton-Euler equation and the Newton's law. Then to cope with time-variant vibration frequencies of the CDPRs due to the variable lengths of cables, the technique that combined the one- to three-order zero vibration (ZV) IS with the particle swarm optimization (PSO) and the controller was proposed to suppress the RV. At last, to validate the effectiveness the proposed method, the simulations were carried out in a redundantly actuated CDPR that has six degree-of-freedom CDPR and seven driving cables with the proposed method, the results show that the RVs can be reduced significantly.

Adaptive finite element analysis with local mesh refinement based on a posteriori error estimate of element energy projection technique

PurposeThis study aims to propose a general and efficient adaptive strategy with local mesh refinement for two-dimensional (2D) finite element (FE) analysis based on the element energy projection (EEP) technique.Design/methodology/approachIn view of the inflexibility of the existing global dimension-by-dimension (D-by-D) recovery method via EEP technique, in which displacements are recovered through element strips, an improved element D-by-D recovery strategy was proposed, which enables the EEP recovery of super-convergent displacements to be implemented mostly on a single element. Accordingly, a posteriori error estimate in maximum norm was established and an EEP-based adaptive FE strategy of h-version with local mesh refinement was developed.FindingsRepresentative numerical examples, including stress concentration and singularity problems, were analyzed; the results of which show that the adaptively generated meshes reasonably reflect the local difficulties inherent in the physical problems and the proposed adaptive analysis can produce FE displacement solutions satisfying the user-specified tolerances in maximum norm with an almost optimal adaptive convergence rate.Originality/valueThe proposed element D-by-D recovery method is a more efficient and flexible displacement recovery method, which is implemented mostly on a single element. The EEP-based adaptive FE analysis can produce displacement solutions satisfying the specified tolerances in maximum norm with an almost optimal convergence rate and thus can be expected to apply to other 2D problems.

Rotating blade-casing rubbing simulation considering casing flexibility

In the traditional rubbing model, the overall displacement (rigid body displacement) of the casing is always taken into account, while the local flexible deformation is either ignored or simply assumed as a spring element. Due to the small thickness of the casing (about 2–4 mm), there may exist a large error for predicting the normal rubbing force using the traditional model, which can lead to the error when the local deformation and wear extent are calculated. Aiming at this phenomenon, this paper deduces an improved rotating blade-casing rubbing model based on elastic compatibility conditions. During the derivation, the centrifugal stiffening, spin softening and rubbing softening are considered and the quasi-static bending displacement of blade is calculated based on the theory of mechanics of materials. The casing is regarded as a flexible ring with spring support in the radial direction, and the displacements are composed of rigid-body and flexible displacements. Ignoring the effects of the kinetic energy, according to Hamilton principle, the structural stiffness of the casing under the quasi-static condition is obtained. The proposed model is verified by comparing with the experimental data obtained from both rigid casings and flexible casings in published references. Based on a rotating-blade-flexible-casing system, the rubbing-induced vibration behaviors from both finite element (FE) model in ANSYS software and the proposed model are figured out and compared with each other for testing the effectiveness of the proposed model again. A frequency sweep is performed in order to better understand the resonances of the blade and casing. Vibration responses obtained from the traditional rubbing model and the proposed model are also compared with each other so that the advantages of the proposed model is emphasized. The comparison results show that the normal rubbing forces obtained from the proposed model are closer to the experimental results because the proposed rubbing model can accurately describe the flexible deformations of the casing under both quasi-static and dynamic conditions. The rubbing-induced blade vibration responses obtained from the traditional and proposed rubbing models agree well, however, the dynamic rubbing forces obtained from the proposed model are smaller than those from the traditional model. In addition, different combined nodal-diameter modes of the casing can be excited under different rotating speeds.

Slip Line Theory Based Stability Analysis on the Influence of Deep Excavation on Adjacent Slope

The impact of deep excavation to the stability of adjacent slope is evaluated based on the slip line theory. Stress field of slope under various excavation conditions is simulated by finite element method, while slip line field is determined by non-associated flow rule. Factor of safety is obtained by integrating the skid-resistance and the shear stress on each slip line, and the slip line with minimum factor of safety corresponds to the critical slip surface. Two typical displacement constraint boundaries are considered. The results indicate that the critical slip surface moves towards to the slope surface and develops downwards. The factor of safety decreases with the excavation process. For flexible displacement constraint boundary, large deformation of supporting pile causes obvious variation of critical slip surface and factor of safety. In terms of the stiff displacement constraint boundary with internal supports, deep excavation only has limited effect on the slope stability.

Robust output feedback attitude tracking control for rigid-flexible coupling spacecraft

This paper investigates the robust attitude tracking control problem for a rigid-flexible coupling spacecraft. First, the dynamic model for a rigid-flexible coupling spacecraft is established based on the first-order approximation method to fully reveal the coupling effect between rigid movement and flexible displacement when the spacecraft is in rapid maneuver. In the condition that flexible vibration measurements are not available, an robust output feedback controller which is independent of model is presented using Lyapunov method with considering state-independent disturbances. To resolve the chattering problem caused by the discontinuous sign function, a modified continuous output feedback controller is proposed by introducing functions with continuous property. Rigorous proof is achieved showing that the proposed control law ensures asymptotic stability and guarantees the attitude of a rigid-flexible spacecraft to track a time-varying reference attitude based on angle and angular velocity measurements only. Finally, simulations are carried out to verify the simplicity and effectiveness of the proposed control scheme.

Integrating Communities: How Spatial Patterns Matter?

Social exclusion is a key issue in the European Cohesion Policy 2014-2020. Despite the magnitude of the problem and the importance recognized by the literature to the spatial component of the city in supporting effective inclusion, policy documents still lack of attention on spatial patterns and their influence on integration. This paper discusses how spatial patterns may influence the outcomes of urban policies addressed to social inclusion, with a particular focus on Roma minorities. Recommendations will be supported by the findings from two case studies located in a Southern European metropolitan area, Reggio Calabria, and include: 1) Avoiding concentration of minorities through appropriate displacement, planned on case-by-case approach and discussed with the interested community; 2) Supporting flexible displacement through appropriate rules and planning regulations; 3) Avoiding displacement of minorities in areas lacking physical and social connectivity.

STUDY OF THE TARGETING ERROR FOR PERCUTANEOUS NEEDLE INSERTION INTO SOFT PHANTOM MATERIAL

Percutaneous needle insertion is widely used in minimally invasive procedures, in which the flexible needle is steered to reach a specific target inside the human body. The targeting error is due to a combination of flexible needle deflection and target displacement in soft tissue and only a very limited number of studies have focused on both two factors. This paper presents a targeting error calculation method which incorporates an energy-based needle deflection model into a soft tissue finite-element (FE) model. The needle insertion process is discretized into several increments on the basis of the quasi-static method. Needle deflection in each step is obtained by the needle-soft tissue interaction model which is applied into the FE model as the displacement input. A 2D-planar FE model is used to model the target displacement by imposing needle distribution forces and needle deflection at different steps on the appointed reference nodes. The soft tissue is modeled as a non-linear hyperelastic material with geometrical non-linearity. Uniaxial tensile strength tests are utilized to determine the soft tissue parameters. Needle targeting experiments are conducted to validate the simulation results. Results show that the proposed method can predict the needle targeting errors while the averaged prediction error stays below 0.4[Formula: see text]mm. At last, we conduct different experiments to compensate the obtained targeting error and thus, reaching preferable effects.