Quasi-static Deflection Research Articles

Quasi-static testing based structural modal parameter estimation

ABSTRACT Structural modal identification is generally implemented within a dynamic framework, requiring multidisciplinary knowledge and adequate operational experience. This preliminary study attempts to explore an easy-to-handle quasi-static alternative method for dynamics-based modal identification of beam-type structures. Acceleration time-history data are replaced by quasi-static deflections induced by slow moving loads. A concept of quasi-static deflection influence surface is proposed based on the theory of influence lines and the principle of virtual work. Its analytical expression is simplified into a deflection matrix by choosing specific points on the surface according to deflection measurement coordinates. The matrix form is divided by external loads to obtain a generalised quasi-static flexibility matrix, which is used to replace the inversion of the global stiffness matrix in the modal eigenvalue equation. The lumped-mass method is also employed to establish the mass matrix. Subsequently, the eigenvalue equation is analytically solved seeking for modal frequencies and mode shapeswithout performing modal tests. The feasibility of the proposed method has been successfully verified against three experimental examples including a continuous box girder with variable cross sections. It was observed that the modal frequencies and mode shapes estimated by the proposed method were very close to those given by the dynamically modal tests.

Quasistatic deflection analysis of slender ball-end milling cutter

In this study, a quasistatic force-deflection interaction model considering cutting and elastic force was proposed to analyze and compensate for the quasistatic deflection of slender ball-end milling cutter. The theoretical waveforms and peaks of cutting force considering the force-deflection interactions were consistent with the experimental results. The deflection of slender ball-end milling cutter significantly reduces the cutting force, and the Pearson's correlation coefficient between the difference in the peak cutting force and maximum deflection in radial is larger than that of in feed directions. An analysis of the machining error of a cylindrical surface revealed that the deflection of slender ball-end milling cutter had a considerable effect on the machining error, and the compensation of slender cutter deflection effectively reduced the amplitude and fluctuation of the machining error. This work can provide a useful guidance for machining error control in the ball-end milling process of mold surfaces with deep cavities.

Comparison of five different methodologies for evaluating ankle–foot orthosis stiffness

BackgroundThe mechanical properties of an ankle–foot orthosis (AFO) play an important role in the gait mechanics of the end user. However, testing methodologies for evaluating these mechanical properties are not standardized. The purpose of this study was to compare five different evaluation frameworks to assess AFO stiffness.MethodThe same 13 carbon composite AFOs were tested with five different methods. Four previously reported custom test fixtures (the BRUCE, KST, SMApp, and EMPIRE) rotated an AFO into dorsiflexion about a defined axis in the sagittal plane. The fifth method involved quasi-static deflection of AFOs into dorsiflexion by hanging weights (HW) from the footplate. AFO rotational stiffness was calculated as the linear fit of the AFO resistive torque and angular deflection. Differences between methods were assessed using descriptive statistics and a repeated measures Friedman with post-hoc Bonferroni–Holm adjusted Wilcoxon signed-rank tests.ResultsThere were significant differences in measured AFO stiffnesses between test methods. Specifically, the BRUCE and HW methods measured lower stiffness than both the EMPIRE and the KST. Stiffnesses measured by the SMApp were not significantly different than any test method. Stiffnesses were lowest in the HW method, where motion was not constrained to a single plane. The median difference in absolute AFO stiffness across methods was 1.03 Nm/deg with a range of [0.40 to 2.35] Nm/deg. The median relative percent difference, measured as the range of measured stiffness from the five methods over the average measured stiffness was 62% [range 13% to 156%]. When the HW method was excluded, the four previously reported test fixtures produced a median difference in absolute AFO stiffness of 0.52 [range 0.38 to 2.17] Nm/deg with a relative percent difference between the methods of 27% [range 13% to 89%].ConclusionsThis study demonstrates the importance of developing mechanical testing standards, similar to those that exist for lower limb prosthetics. Lacking standardization, differences in methodology can result in large differences in measured stiffness, particularly for different constraints on motion. Non-uniform measurement practices may limit the clinical utility of AFO stiffness as a metric in AFO prescription and future research.

Influence of the velocity on quasi-static deflections of industrial articulated robots

This article presents the measurement and analysis of the influence of velocity on the quasi-static deflections of industrial manipulators of three different manufacturers. Quasi-static deflection refers to the deflection of the end effector position of articulated robots during movement at low velocity along a predefined trajectory. Based on earlier reported observations by the authors, there exists a difference in the static and quasi-static deflections considering the same points along a trajectory. This work investigates this difference to assess the applicability of robotic compliance calibration at low velocities. For this assessment, the deflections of three industrial articulated robots were measured at different speeds and loads. Considering the similarity among the robot models used in this investigation, this work also elaborates on the potential influence of the measurement procedure on the measured deflections and its implications for the compliance calibration of articulated robots. For all industrial articulated robots in this investigation, the quasi-static deflections are significantly larger than the static ones but similar in trend. Additionally, the magnitude of the quasi-static deflections presents a proportional relationship to the Cartesian velocity.

High-Rate, High-Precision Wing Twist Actuation for Drone, Missile, and Munition Flight Control

This paper covers a new actuation and deflection controller configuration for high-aspect-ratio wings used on subsonic drones, missiles, and munitions. Current approaches to the flight control of these aircraft have unearthed challenges with friction, stiction, slop, bandwidth, and thick boundary layer nonlinearities, which degrade flight control accuracy—especially in terminal flight phases. The approach described in this paper uses directionally attached piezoelectric (DAP) actuators to actively twist a high-aspect-ratio wing for flight control. The DAP actuators were modeled analytically and computationally using linear finite element modeling. A 3″ (7.62 cm) chord × 15″ (38.1 cm) semispan rectangular wing with an NACA 0012 profile was built and structurally tested, demonstrating excellent agreement between theory and experiment. New actuation methods were used to overdrive the PZT-5H piezoelectric elements deep into the repoling range. This overdrive actuation rejuvenated the actuator elements and allowed for dramatically improved deflections with respect to configurations in previous years. Static testing demonstrated deflections in excess of ±1.6° in root-to-tip twist. Dynamic testing showed corner frequencies greater than 310 Hz. A series of wind tunnel tests at up to 180 ft/s (55 m/s, 123 mph, 107 kts, 198 kph) demonstrated excellent roll control authority, rapid manipulation of Clδ, and lift manipulation using quasi-static deflections. The paper concludes with a summary of implications for terminal guidance for drone, missile, and munition flight control in real atmospheres.

On quasi-static large deflection of single lap joints under transverse loading

This study aims to characterize the mechanical behavior of a carbon fiber reinforced plastics (CFRP)/aluminum (Al) adhesive bonded single lap joint (SLJ) subjected to transversal three-point bending load with different adherend materials and kinematic boundary conditions. The experimental results divulged that the boundary conditions had noticeable influence on the load bearing capacity of the joint; and the stiffness and peak load for the fixed-support condition were much higher than those for the simply-supported condition. The stress distribution in the adhesive layer varies under different boundary conditions, leading to the different morphology of the residual adhesive at the fracture surface. The different cracks in the adhesive layer were further analyzed by SEM under peel stress and shear stress loadings. The finite element (FE) models were developed by using the material properties characterized in-house here. It is found that the load displacement curves and the crack energies predicted by finite element analysis (FEA) was well correlated with those measured by the experiment in the designated four groups of adhesive joints. This study is anticipated to provide systematic understanding of adhesive joints with dissimilar adherend materials under different boundary conditions subject to transverse loading.

Wide Two-Degree-of-Freedom Static Laser Scanner with Miniaturized Transmission Mechanism and Piezoelectric Actuation.

In recent years, laser scanners have attracted significant attention for applications such as laser radars. However, the establishment of a two-degree-of-freedom scanner that can quasi-statically drive a large mirror with a large deflection angle has proven to be challenging. In this paper, we propose a laser scanner design and fabrication method by combining two unimorph piezoelectric actuators composed of piezoelectric single-crystal Pb(In1/2Nb1/2)O3-Pb(Mg1/3Nb2/3)O3-PbTiO3 and a miniature translation-rotation conversion mechanism with flexible polyimide hinges. The size of the entire scanner was 32 mm × 12 mm × 10 mm. We successfully demonstrated that the scanner could achieve a large quasi-static mechanical deflection angle amplitude of 20.5° in two axes with a 6-mm-square mirror.

Quasi-Static Compliance Calibration of Serial Articulated Industrial Manipulators

This article presents a procedure for the quasi-static compliance calibration of serial articulated industrial manipulators. Quasi-static compliance refers to the apparent stiffness displayed by manipulators at low-velocity movements, i.e., from 50 to 250 mm/s. The novelty of the quasi-static compliance calibration procedure lies in the measurement phase, in which the quasi-static deflections of the manipulator’s end effector are measured under movement along a circular trajectory. The quasi-static stiffness might be a more applicable model parameter, i.e., representing the actual manipulator more accurately, for manipulators at low-velocity movements. This indicates that the quasi-static robot model may yield more accurate estimates for the trajectory optimization compared with static stiffness in the implementation phase. This study compares the static and apparent quasi-static compliance. The static deflections were measured at discretized static configurations along circular trajectories, whereas the quasi-static deflections were measured under circular motion along the same trajectories. Loads of different magnitudes were induced using the Loaded Double Ball Bar. The static and quasi-static displacements were measured using a linear variable differential transformer embedded in the Loaded Double Ball Bar and a Leica AT901 laser tracker. These measurement procedures are implemented in a case study on a large serial articulated industrial manipulator in five different positions of its workspace. This study shows that the measured quasi-static deflections are bigger than the measured static deflections. This, in turn, indicates a significant difference between the static and apparent quasi-static compliance. Finally, the implementation of the model parameters to improve the accuracy of robots and the challenges in realizing cost-efficient compliance calibration are discussed.

Flight Dynamics of Transport Aircraft Equipped with Flared-Hinge Folding Wingtips

This paper studies the influence of flared-hinge folding wingtips on the aerodynamic derivatives and flight dynamics of a narrow-body transport aircraft. In addition, the influence of fold angle, hinge-line angle (flare angle), and wingtip size on wing loading is assessed. The Tornado vortex lattice method is used for aerodynamic predictions and to estimate the stability and control derivatives. First, the aircraft is assumed rigid, and different hinge angles, fold angles, and wingtip sizes are considered. Then, structural flexibility is considered by coupling Tornado with a linear structural finite element solver to facilitate quasi-static aeroelastic analysis. The quasi-static deflections method is used to study the flight dynamics of the flexible aircraft. The effect of the flared-hinge folding wingtips on the longitudinal and lateral-directional flight dynamic modes of the rigid and the flexible aircraft is compared and contrasted. Furthermore, the variations of longitudinal trim settings and roll response with flared-hinge folding wingtips are assessed.

Flexural fatigue life of woven carbon/vinyl ester composites under sea water saturation

The adverse effects of sea water environment on the fatigue life of woven carbon fiber/vinyl ester composites are established at room temperature in view of long-term survivability of offshore structures. It is observed that the influence of sea water saturation on the fatigue life is more pronounced when the maximum cyclic displacement approaches maximum quasi-static deflection, that is, the reduction in the number of cycles to failure are comparable between dry and sea water saturated samples at lower strain ranges (37% at 0.46% strain), but are drastically different at higher strain ranges (90% at 0.62% strain). Key damage modes that manifest during the fatigue loading is also identified, and a non-linear model is established for predicting low cycle fatigue life of these composites in dry and sea water saturated conditions.

A Biomimetic Fish Fin-Like Robot Based on Textile Reinforced Silicone.

The concept of merging pre-processed textile materials with tailored mechanical properties into soft matrices is so far rarely used in the field of soft robotics. The herein presented work takes the advantages of textile materials in elastomer matrices to another level by integrating a material with highly anisotropic bending properties. A pre-fabricated textile material consisting of oriented carbon fibers is used as a stiff component to precisely control the mechanical behavior of the robotic setup. The presented robotic concept uses a multi-layer stack for the robot’s body and dielectric elastomer actuators (DEAs) on both outer sides of it. The bending motion of the whole structure results from the combination of its mechanically adjusted properties and the force generation of the DEAs. We present an antagonistic switching setup for the DEAs that leads to deflections to both sides of the robot, following a biomimetic principle. To investigate the bending behavior of the robot, we show a simulation model utilizing electromechanical coupling to estimate the quasi-static deflection of the structure. Based on this model, a statement about the bending behavior of the structure in general is made, leading to an expected maximum deflection of 10 mm at the end of the fin for a static activation. Furthermore, we present an electromechanical network model to evaluate the frequency dependent behavior of the robot’s movement, predicting a resonance frequency of 6.385 Hz for the dynamic switching case. Both models in combination lead to a prediction about the acting behavior of the robot. These theoretical predictions are underpinned by dynamic performance measurements in air for different switching frequencies of the DEAs, leading to a maximum deflection of 9.3 mm located at the end of the actuators. The herein presented work places special focus on the mechanical resonance frequency of the robotic setup with regard to maximum deflections.

An Artificial Vibrissa-Like Sensor for Detection of Flows.

In nature, there are several examples of sophisticated sensory systems to sense flows, e.g., the vibrissae of mammals. Seals can detect the flow of their prey, and rats are able to perceive the flow of surrounding air. The vibrissae are arranged around muzzle of an animal. A vibrissa consists of two major components: a shaft (infector) and a follicle–sinus complex (receptor), whereby the base of the shaft is supported by the follicle-sinus complex. The vibrissa shaft collects and transmits stimuli, e.g., flows, while the follicle-sinus complex transduces them for further processing. Beside detecting flows, the animals can also recognize the size of an object or determine the surface texture. Here, the combination of these functionalities in a single sensory system serves as paragon for artificial tactile sensors. The detection of flows becomes important regarding the measurement of flow characteristics, e.g., velocity, as well as the influence of the sensor during the scanning of objects. These aspects are closely related to each other, but, how can the characteristics of flow be represented by the signals at the base of a vibrissa shaft or by an artificial vibrissa-like sensor respectively? In this work, the structure of a natural vibrissa shaft is simplified to a slender, cylindrical/tapered elastic beam. The model is analyzed in simulation and experiment in order to identify the necessary observables to evaluate flows based on the quasi-static large deflection of the sensor shaft inside a steady, non-uniform, laminar, in-compressible flow.

Sensitivity and accuracy of Casimir force measurements in air

Quantum electrodynamic fluctuations cause an attractive force between metallic surfaces. At separations where the finite speed of light affects the interaction, it is called the Casimir force. Thermal motion determines the fundamental sensitivity limits of its measurement at room temperature, but several other systematic errors contribute uncertainty as well and become more significant in air relative to vacuum. Here we discuss the viability of several measurement techniques in air (force modulation, frequency modulation, and quasi-static deflection), characterize their sensitivity and accuracy by identifying several dominant sources of uncertainty, and compare the results to the fundamental sensitivity limits dictated by thermal motion and to the uncertainty inherent to calculations of the Casimir force. Finally, we explore prospects for mitigating the sources of uncertainty to enhance the range and accuracy of Casimir force measurements.

Vibration suppression in high-speed trains with negative stiffness dampers

This work proposes and investigates re-centering negative stiffness dampers (NSDs) for vibration suppression in high-speed trains. The merit of the negative stiffness feature is demonstrated by active controllers on a high-speed train. This merit inspires the replacement of active controllers with re-centering NSDs, which are more reliable and robust than active controllers. The proposed damper design consists of a passive magnetic negative stiffness spring and a semi-active positioning shaft for re-centering function. The former produces negative stiffness control forces, and the latter prevents the amplification of quasi-static spring deflection. Numerical investigations verify that the proposed re-centering NSD can improve ride comfort significantly without amplifying spring deflection.

Normal impact of a low-velocity projectile against a taut string-like membrane

For the impact system in which a moving projectile transversely impacts against a taut fabric band, 1-D linearized model applies because of low-velocity, sufficient pretension, and the sizes of the objects. This projectile-to-band impact model can serve as the physical prototype of applications in engineering such as cable-membrane architectures and seat belts. In this fundamental work, the response properties under central and non-central impacts are investigated analytically from the viewpoint of wave propagations, while comparisons and verifications are made with finite element (FE) analysis. For a central impact after the first separation, band can catch up with the projectile such that a contact-impact state is re-established when m is in the small interval neighbouring m = 1. For a non-central impact, the projectile would be subjected to a combination of translation and rotation due to asymmetric wave propagations. From every certain instant, the projectile is subjected to an additional rotational acceleration (principal moment) with an abrupt or zero initial value in the anti-clockwise or clockwise direction. The swing amplitude of a small-j or a flat projectile is susceptible to significant fluctuations, and vice versa. The band with a rather large off-centre ratio for the impacted zone and a rather short length of the shorter segment would facilitate a larger accumulation of swing amplitude in a single direction soon after the impact. The linearized impact models proposed can be used to well describe the small-deflection responses for the system, based on 1-D wave propagations or the dependence of quasi-static band deflection on time if the impact duration is much longer than the double wave transit time for the band.

Experimental study and electromechanical model analysis of the nonlinear deformation behavior of IPMC actuators

This paper develops analytical electromechanical formulas to predict the mechanical deformation of ionic polymer–metal composite (IPMC) cantilever actuators under DC excitation voltages. In this research, IPMC samples with Pt and Ag electrodes were manufactured, and the large nonlinear deformation and the effect of curvature on surface electrode resistance of the IPMC samples were investigated experimentally and theoretically. A distributed electrical model was modified for calculating the distribution of voltage along the bending actuator. Then an irreversible thermodynamic model that could predict the curvature of a unit part of an IPMC actuator is combined with the electrical model so that an analytical electromechanical model is developed. The electromechanical model is then validated against the experimental results obtained from Pt- and Ag-IPMC actuators under various excitation voltages. The good agreement between the electromechanical model and the actuators shows that the analytical electromechanical model can accurately describe the large nonlinear quasi-static deflection behavior of IPMC actuators.

Scanning micromirror for large, quasi-static 2D-deflections based on electrostatic driven rotation of a hemisphere

A micromirror (mirror area 3.1mm2) for laser tracking applications is presented. The mirror, which is based on a hemisphere, is designed to achieve large quasi-static deflection around two rotational axes by adapting the principle of ultrasonic motors. Here, the deflection of the mirror is achieved by a periodic momentum transfer from a stage with electrostatically driven oscillations. Due to the periodic hemisphere-stage-contact, the system has multiple degrees of freedom and is non-linear. A simple model of stage-hemisphere-interaction is presented and verified in order to identify design rules and adequate excitation regimes.The actuator is fabricated in standard SOI-technology. The final system is excited as well in a non-resonant (2000Hz) as in a resonant mode (2900Hz). Thus excitation frequencies over a wide range are possible. For a resonant operation of the stage, a maximum quasi-static deflection of the mirror of up to +/−35.2° with a maximum angular velocity of 732°/s is demonstrated. In this case, the crosstalk (movement perpendicular to desired direction) is less than 22%. For the non-resonant operation the crosstalk is reduced significantly (less than 10%). In this case, a quasi-static deflection of +/−10.5° is found.

A Novel Electrostatic Actuator Class

Common quasi-static electrostatic micro actuators have significant limitations in deflection due to electrode separation and unstable drive regions. These actuators suffer from an operational instability, the so-called pull-in effect that limits the actuators’ travel range to one third of the electrode separation. High driving voltages and large electrode gaps are required to achieve large displacements. In our work, we present a novel electrostatic actuator class, which allows high deflections with nanometric electrode separation. The approach presented utilizes a bimorph like effective lever to transform electrostatic forces into deflection. It permits to make use of high electrostatic forces generated in small gaps and thus gives access to large actuator deflections. We demonstrate that quasi-static deflections as large as four times the gap size are possible.

Preliminary results of the feasibility of hydrogen detection by the use of uncoated silicon microcantilever-based sensors

Hydrogen is a key parameter to monitor radioactive disposal facility such as the envisioned French geological repository for nuclear wastes. The use of microcantilevers as chemical sensors usually involves a sensitive layer whose purpose is to selectively sorb the analyte of interest. The sorbed substance can then be detected by monitoring either the resonant frequency shift (dynamic mode) or the quasi-static deflection (static mode). The objective of this paper is to demonstrate the feasibility of eliminating the need for the sensitive layer in the dynamic mode, thereby increasing the long-term reliability. The microcantilever resonant frequency allows probing the mechanical properties (mass density and viscosity) of the surrounding fluid and, thus, to determine the concentration of a species in a binary gaseous. Promising preliminary work has allowed detecting concentration of 200 ppm of hydrogen in air with non-optimized geometry of silicon microcantilever with integrated actuation and read-out.

Quasi-static micromirror with enlarged deflection based on aluminum nitride thin film springs

Uniaxial electrostatically driven micromirrors with very large non-resonant rotation angles are presented. The mirrors achieve an analog deflection of about ±12° at voltages between 200 and 320V. At pull-in, a digital tilt angle of approx. ±21° is found. A mirror control for a nearly linear characteristic curve, by using a counter torque is approved. The key for large quasi-static deflections are novel aluminum nitride based thin film springs. The high mechanical strength of AlN enables the fabrication of thin but stable torsion springs. The mirror has a size of 1mm×1.2mm with a bending of less than 0.2μm and high surface quality (Ra<2nm). The rotational eigenfrequencies are found to be between 37 and 73Hz and the eigenfrequencies of the vertical mirror movement are between 1235 and 1751Hz.