Time-resolved Force Measurements Research Articles

Force measurements near a natural frequency of a measurement system using inverse filters

Accurate time-resolved force measurements for complex experimental systems are important for minimizing erroneous and misleading data. These measurements become difficult when a natural frequency of the system is in or near the expected frequency domain of the time-varying force being applied. In the cases where it is not possible to avoid this occurrence, the experimenter typically abandons the setup. This work presents an inverse filter method to compensate for the dynamic response of the measurement system. A two degree-of-freedom measurement system is used to obtain force measurements with dominant forcing frequencies above and below the first natural frequency of the system. The results show that inverse filtering can be used along with digital low pass filters to correct amplification and phase shift due to the dynamic response of the measurement system to within ±4.0 of total forcing amplitude and ±5.0∘. A simple cam follower mechanism is proposed as a method of low-frequency dynamic testing.

Time-Resolved Force Measurements to Determine Positioning Tolerances for Impulse-Based Indentations

High-throughput experimentation methods determine characteristic values, which are correlated with material properties by means of mathematical models. Here, an indentation method based on laser-induced shock waves is presented, which predicts the material properties, such as hardness and tensile strength, by the induced plastic deformation in the substrate material. The shock wave pushes a spherical indenter inside a substrate material. For reproducible indentations, the applied load is of importance. To compare different processes and process parameters, the measured plastic deformation is normalized by the applied load. However, eccentric irradiation leads to altered beam profiles on the surface of spherical indenters and the angle of incidence is changed. Thus, the influence of eccentric irradiation is studied with an adapted time-resolved force measurement setup to determine the required positioning tolerances. The spherical indenter is placed inside a cylindrical pressure cell to increase the laser-induced shock pressure. From the validated time-resolved force measurement method we derive that deviations from the indentation forces are acceptable, when the lateral deviation of the beam center, which depends only on the alignment of the setup, does not exceed ± 0.4 mm. A vertical displacement from the focus position between -3.0 mm and + 2.0 mm still leads to acceptable deviations from the indentation force.

Tailoring the Pressure Profile of TEA-CO2 Laser-Induced Shock Waves for Mechanical Forming and Separation Processes

For laser shock processes, the acting pressure can be increased by confining the propagation of the laser-induced plasma. Water or glass is commonly used as confinement for laser shock waves induced by Nd:YAG-lasers. This is not possible for the longer wavelength of TEA-CO2 lasers due to higher absorption coefficients. Instead, the acting pressure can be manipulated with a pressure cell above the workpiece. Two different pressure cells were designed to test the versatility of this concept. A cylindrical pressure cell design was used to confine the propagation of the laser-induced plasma and a parabolic pressure cell design was used to reflect the shock wave back to the workpiece. The effect of the pressure cells was analysed by time-resolved force measurements and evaluated for maximum force and force duration. This study shows that the cylindrical pressure cell strongly increases the maximum force while the parabolic pressure cell maximises the duration of force application. Furthermore, the pressure cells have been applied to the laser shock-based processes laser shock punching and LiSE hardness measurement. The cylindrical pressure cell strongly enhances the results of both processes, while the parabolic pressure cell shows only a minor effect.

Development of a transient thrust stand with sub-millisecond resolution.

A transient thrust stand has been developed to offer 0.1 ms time-resolved force measurements up to 22 N. The system uses a predictor-based subspace system identification (PBSID) algorithm to obtain a high order state space model of the thrust stand. The state space model defines high-frequency vibration modes within the thrust stand. The high-frequency vibration modes are necessary to provide the time response of 0.1 ms. Thruster forces are then estimated using an augmented Kalman filter (AKF) to combine sensor traces from four accelerometers, a velocity sensor, and a displacement transducer. Fusing low-frequency displacement data with high-frequency acceleration measurements provides accurate force data from 0 kHz to 10 kHz. Combining the AKF with the PBSID state space model inherently attenuates external noise sources such as pumps. The transient thrust stand uses a torsional configuration to minimize influence from external vibrations and achieve high force resolution independent of thruster weight. Results demonstrated that the system was capable of obtaining dynamic thrust profiles with less than 5% error and a time resolution of 0.1 ms. To date, no thrust stand is capable of measuring up to 22 N forces with a time response of 10 kHz.

Undulatory microswimming near solid boundaries

The hydrodynamic forces involved in the undulatory microswimming of the model organism C. elegans are studied in proximity to solid boundaries. Using a micropipette deflection technique, we attain direct and time-resolved force measurements of the viscous forces acting on the worm near a single planar boundary as well as confined between two planar boundaries. We observe a monotonic increase in the lateral and propulsive forces with increasing proximity to the solid interface. We determine normal and tangential drag coefficients for the worm, and find these to increase with confinement. The measured drag coefficients are compared to existing theoretical models. The ratio of normal to tangential drag coefficients is found to assume a constant value of 1.5 ± 0.1(5) at all distances from a single boundary, but increases significantly as the worm is confined between two boundaries. In response to the increased drag due to confinement, we observe a gait modulation of the nematode, which is primarily characterized by a decrease in the swimming amplitude.

Particle-Image Velocimetry and Force Measurements of Leading-Edge Serrations on Owl-Based Wing Models

High-resolution Particle-Image Velocimetry (PIV) and time-resolved force measurements were performed to analyze the impact of the comb-like structure on the leading edge of barn owl wings on the flow field and overall aerodynamic performance. The Reynolds number was varied in the range of 40,000 to 120,000 and the range of angle of attack was 0° to 6° for the PIV and −15° to +20° for the force measurements to cover the full flight envelope of the owl. As a reference, a wind-tunnel model which possessed a geometry based on the shape of a typical barn owl wing without any owl-specific adaptations was built, and measurements were performed in the aforementioned Reynolds number and angle of attack range. This clean wing model shows a separation bubble in the distal part of the wing at higher angles of attack. Two types of comb-like structures, i.e., artificial serrations, were manufactured to model the owl's leading edge with respect to its length, thickness, and material properties. The artificial structures were able to reduce the size of the separation region and additionally cause a more uniform size of the vortical structures shed by the separation bubble within the Reynolds number range investigated, resulting in stable gliding flight independent of the flight velocity. However, due to increased drag coefficients in conjunction with similar lift coefficients, the overall aerodynamic performance, i.e., lift-to-drag ratio is reduced for the serrated models. Nevertheless, especially at lower Reynolds numbers the stabilizing effect of the uniform vortex size outperforms the lower aerodynamic performance.

High-Speed Particle Image Velocimetry and Force Measurements of Bio-Inspired Surfaces

To evaluate the influence of the velvet-like surface mimicking the structure on the suction side of barn owl wings on the flow field and on the aerodynamic performance of the wing, high-speed particle image velocimetry and time-resolved force measurements were performed. The Reynolds number was varied in the range of , and the range of the angles of attack was for the particle image velocimetry measurements and for the force measurements. The flow over a clean-wing model whose geometry corresponds to that of the owl wing without any special adaptations was investigated as a reference case for the same Reynolds number and angle of attack range. This clean wing possesses a laminar separation bubble as the dominant flow feature. Two artificial surfaces were selected to mimic the natural surface concerning the length, density, and thickness of the filaments. The surfaces were able to reduce flow separation. Although this reduction of the separation region might have a positive influence on the pressure drag, the aerodynamic performance of the models with the artificial surfaces was significantly reduced due to the increased skin-friction drag. Furthermore, the models equipped with the velvets possessed a reduced susceptibility to changes in Reynolds number and angle of attack concerning the aerodynamic performance. It can be stated that the velvet surfaces stabilize the flow field at low Reynolds numbers, enabling the owl to fly more slowly and thus more silently.

High-Resolution Nanomechanical Mapping Using Interferometric-Force-Sensing AFM Probes

In this paper, we demonstrate high-resolution mapping of composite surfaces based on their nanomechanical properties by employing an atomic force microscope probe that can resolve high-frequency tip-sample interaction forces in tapping-mode atomic force microscopy (AFM) (TM-AFM). Time-resolved force measurements are achieved by a small integrated interferometric high-bandwidth grating force sensor at the end of the cantilever beam. The probes are batch fabricated using optical lithography and are used in an AFM system with no further modification. The fabricated devices are characterized and grating-force-sensor signals and their measured spectra confirm that probes with integrated high-bandwidth force sensors can successfully resolve high-frequency tip-sample interaction forces. We utilize the capability of our probes to form images by recording the amplitude of the higher harmonics of the time-resolved tip-sample interaction forces with lock-in detection. These images show that our probes can successfully map, with high spatial resolution, the mechanical contrast due to different materials and structural differences in composite surfaces.

Modeling, design, and analysis of interferometric cantilevers for time-resolved force measurements in tapping-mode atomic force microscopy

Cantilevers with interferometric high bandwidth force sensors can resolve nonlinear tip-sample interaction forces in tapping-mode atomic force microscopy. In this paper, we provide a detailed analysis of time-resolved force measurements using such cantilever. We first model the probe as a coupled spring-mass system and investigate its steady state dynamics under tapping-mode imaging conditions. Next, we analyze the optical response of the interferometric force sensor: Diffraction patterns as a function of tip displacement are obtained both analytically and by simulations. Finally, the frequency response of the force sensor is calculated, and the effects of the sensor geometry variations on the sensor mechanical response are analyzed.

The weight of a falling chain, revisited

A vertically hanging chain is released from rest and falls due to gravity on a scale pan. We discuss the various experimental and theoretical aspects of this classic problem. Careful time-resolved force measurements allow us to determine the differences between the idealized problem and its implementation in the laboratory. We observe that, in spite of the upward force exerted by the pan on the chain, the free end at the top falls faster than a freely falling body. Because a real chain exhibits a finite minimum radius of curvature, the contact at the bottom results in a tensional force, which pulls the falling part downward.

Flat-Plate Interaction with the Near Wake of a Square Cylinder

B LUFF bodies are integral components of aircraft, high-speed trains, automobiles, and many forms of industrial equipment. The minimization of mean and fluctuating force levels generated by bluff bodieswhen placed in afluid streamhas the benefits of reducing drag, vibration, and radiated sound. It is therefore very important that a good understanding of the flowfield about bluff bodies be obtained to achieve these aims. This Note explores how lowReynolds number bluff-body wake interference can affect the generation of unsteady flowand force. The case chosen for study is the interaction of a square cylinder and an infinitely thin flat plate. A rigid square cylinder is one of the most basic forms of a bluff body and when placed in a uniform fluid stream has been shown to exhibit strong vortex shedding, resulting in fluctuating forces and the radiation of sound in the form of an aeolian tone. Previous fluid dynamic experimental studies [1,2] exhibit this strong vortex shedding over a wide range of Reynolds number (10–10). Numerical studies investigating the fluid dynamics [3–6] also confirm this behavior. Despite the wealth of experimental data available for circular cylinders, experimental or numerical data for square cylinders are rare. Available studies include the work of Inoue [7], who performs a numerical simulation of compressible flow about a square cylinder at Re 150. Zhou et al. [8] use an upstream plate to suppress fluctuating lift on a square cylinder. They find that there is an optimal position and size for the upstream plate for effective lift suppression. Studies concerning the control of noise from a circular cylinder are more common. Recent numerical studies [9,10] investigate the use of a splitter plate attached to the base of a circular cylinder. These studies show that vortex shedding can disappear once the splitter plate achieves a certain length. Numerical solutions of the compressible unsteady Navier–Stokes equations for tandem square cylinders [11] show that significant force and noise reduction can occur if the cylinders are placed at a critical spacing in a region in which vortex shedding from the upstream cylinder is suppressed. If this separation distance is increased, the force and noise increase rapidly, due to the reestablishment of upstream vortex shedding and the associated vortex impingement on the downstream cylinder. Other work includes the experimental time-resolved force measurements of tandem bluff bodies by Sakamoto et al. [12] and Alam and Zhou [13], which were used to investigate the phase difference between the aerodynamic forces of each body in the vortex-shedding regime (i.e., the interbody spacing was such that vortex shedding was allowed to occur from each body). In each case, the phase varied linearly with separation distance. Further, Alam and Zhou developed a theoretical model based on the convective properties of isolated bluff-body wakes that agrees reasonably with experimental results. This Note will consider the case of an infinitely thin flat plate placed in the near wake of a square cylinder at a Reynolds number of Re 150. To the author’s knowledge, there have been no previous investigations of the interaction of a thin flat plate with the near wake of a square cylinder. The Note is structured as follows. After outlining the numerical approach (Sec. II), a solution of the incompressible Navier–Stokes equations for the single square cylinder case is presented and validated against available experimental and numerical results (Sec. III). A second solution is then presented that includes the downstream plate (Sec. IV), and the flow and force results are analyzed. The Note concludes with a summary of the key results.