Measurement of Tangential Contact Hysteresis During Microslip

2004 ◽  
Vol 126 (3) ◽  
pp. 482-489 ◽  
Author(s):  
Sergio Filippi ◽  
Adnan Akay ◽  
Muzio M. Gola
Keyword(s):  
Measurement System ◽  
Measurement Errors ◽  
Small Amplitude ◽  
Contact Stiffness ◽  
Tangential Force ◽  
Systematic Errors ◽  
Relative Displacement ◽  
Tangential Contact ◽  
Measurement Artifacts ◽  
Contact Parameters

This paper describes a measurement system designed to determine the hysteresis that develops between two surfaces as a result of small-amplitude tangential relative motion. Hysteresis is determined by measuring the tangential force and relative displacement of the contacting surfaces as they oscillate. These measurements also produce values of contact parameters such as friction coefficient and tangential contact stiffness. Although these parameters depend on the tribological properties, most of them also exhibit strong sensitivity to measurement errors. The measurement system described here avoids or at least reduces many of the measurement artifacts. This paper validates the measurement system by analyzing and estimating potential errors and describes corrections to systematic errors where possible.

Experimental Verification of Friction Behaviors Under Periodically-Varied Normal Force by Developing a Two-Directional Friction Test System

2015 ◽  
Author(s):  
Kunio Asai ◽  
Muzio M. Gola
Keyword(s):  
Contact Pressure ◽  
Contact Area ◽  
Normal Force ◽  
Contact Stiffness ◽  
Tangential Force ◽  
Test System ◽  
Dissipated Energy ◽  
Friction Test ◽  
Force Coefficient ◽  
Tangential Contact

In order to achieve more accurate friction damping of turbine blades equipped with shroud covers and under-platform dampers, it is necessary to clarify such friction behaviors as tangential contact stiffness, micro-slips, and dissipated energy, under periodically varied normal force instead of constant normal force. Although some analytical studies were reported on the contact mechanics under alternating normal force, only minimal research has been conducted on the experimental verification of such behaviors, as friction tests were commonly done under constant normal force. In this study, we developed an original two-directional friction test system that can apply any combination of alternating normal and tangential forces by changing the displacement-controlled loading direction. In this system, relative displacement and contact force were measured simultaneously by using a laser Doppler displacement sensor and force transducers of the strain gage type. By using our original test system, we examined the dissipated energy under constant normal force and periodically-varied normal force whose amplitude is the same as that of tangential force with no phase difference. We then obtained a new finding that dissipated energy depends on alternating normal force under the same mean normal force and alternating tangential force. More specifically, when the tangential force coefficient, defined as the ratio of the amplitude of alternating tangential force to mean normal force, is large enough to cause a macro-slip, dissipated energy under variable normal force is smaller than that under constant normal force. Conversely, when tangential force coefficient is small in the micro-slip region, dissipated energy under variable normal force is larger than that under constant normal force. This behavior was successfully reproduced by FE analysis based on a macro-slip model, where an array of macro-slip elements was used to describe micro-slip behavior. It was found that alternating normal force makes it easier to cause a micro-slip in a certain area of the contact surface under variable normal force, resulting in higher dissipated energy than at constant normal force when tangential force coefficient is small. In this study, basic friction data were also obtained regarding the tangential contact stiffness with variations in contact pressure, as well as the relation between a micro-slip and the tangential force coefficient. Tangential contact stiffness increases as contact pressure increases. In addition, tangential contact stiffness increases with the nominal contact area, but is not proportional to the area. The non-dimensional slip range (corresponding to the ratio of slip range to stick displacement) was confirmed as being described in a unified form against different contact area (6 and 18 mm2) and contact pressure ranging from 3 to 40 MPa.

Evaluation of Friction Damping in Dovetail Root Joints Based on Dissipation Energy on Contact Surfaces

2009 ◽  
Author(s):  
Kunio Asai ◽  
Shigeo Sakurai ◽  
Takeshi Kudo ◽  
Norihiko Ozawa ◽  
Taizo Ikeda
Keyword(s):  
Contact Force ◽  
Contact Stiffness ◽  
Relative Displacement ◽  
Contact Angles ◽  
Forced Response ◽  
Contact Forces ◽  
Friction Damping ◽  
Normal Contact ◽  
Tangential Contact ◽  
Contact Surfaces

It is necessary to increase and estimate friction damping at contact interfaces to reduce vibratory stresses in turbines. The hysteresis behavior between tangential contact force and relative displacement should be precisely estimated to improve the accuracy of fiction-damping estimates. There is a difficulty in establishing a general model of hysteresis because tangential contact stiffness depends on many parameters, such as normal contact force, contact geometry, surface roughness, and wear status. We discuss a procedure to empirically calculate friction damping in dovetail root joints using the tangential contact stiffness estimated from measured natural frequencies and the micro-slip model whose coefficients were experimentally obtained from special fretting tests. Instead of the multi-harmonic balance methods, we calculated the friction damping on the basis of the energy dissipation at contact surfaces to discuss the effects of the tangential contact stiffness on several physical values, i.e., tangential and normal contact forces, natural frequency, and micro-slip. In our model, the linear forced response analysis was conducted by taking into consideration the non-linearity between the tangential contact force and the relative displacement by defining the actual and imaginary tangential contact stiffness. We confirmed that the numerically calculated damping ratios are quantitatively in very good agreement with the measured ones under different contact angles, input gravity levels, and contact forces. This indicates that if the tangential contact stiffness is accurately estimated, friction damping with our method can be precisely estimated under different test conditions. We also showed that the estimated tangential contact stiffness for dovetail root joints are smaller than those obtained by the fretting tests at high input gravity. This is probably because the contact interface partially separates during a cyclic loading in the former case; this results in the decrease of the contact area and contact stiffness.

Measurement of Contact Parameters of Flat on Flat Contact Surfaces at High Temperature

2012 ◽  
Author(s):  
D. Botto ◽  
M. Lavella ◽  
M. M. Gola
Keyword(s):  
Friction Coefficient ◽  
Vibration Amplitude ◽  
Contact Stiffness ◽  
Relative Displacement ◽  
Wear Behaviour ◽  
Test Rig ◽  
Contact Parameter ◽  
Contact Surfaces ◽  
Contact Parameters ◽  
Flat Contact

In aircraft engines the blade resonant vibration amplitude is normally reduced by increasing the structural damping by using, for example, tip shrouds. These devices dissipate the energy generated at the contact surfaces between the relative motion and the friction force. Contact parameters, principally the friction coefficient and contact stiffness, are required to characterize the dynamics of shrouded blade system. Moreover, if at these contact surfaces severe wear occurs, a loss of interference takes place and the energy dissipated by the shroud decreases. Consequently the blade vibration amplitude increases and a catastrophic blade failure could take place. In this work a test rig for the contact parameter measurements and micro wear characterization of flat-on-flat contact surfaces has been developed. The test rig works at high temperatures of up to 1000 °C, by means of induction heating. One of the specimens was attached to the rig frame, basically an inertial mass and four springs, and subsequently excited by an electromagnetic shaker. The second specimen was allowed to approach the first specimen and to rotate in such a way than the geometric contact between the two surfaces occurred at three points. In this way a real “flat to flat” contact was obtained. The two surfaces were kept in contact by means of a constant normal load. The tangential contact force was measured by a force sensor while the relative displacements between the contact surfaces were measured by two laser vibrometers. The relative displacement was kept under control by acting on the shaker force. Tangential force and relative displacement were used to describe the hysteresis loop and, consequently, to obtain the friction coefficient and contact stiffness during the wear process. The temperature is feedback controlled by using two thermocouples placed within the specimens near the contact surfaces. The expected results are the contact parameters and the wear behaviour of real flat-on-flat contact surfaces. The aim of this work is to describe the design principle of the test rig and present the initial measurements.

Precise on-line Measurement of Lattice Vectors

1990 ◽  
Vol 48 (1) ◽  
pp. 530-531
Author(s):  
W.J. de Ruijter ◽  
Sharma Renu
Keyword(s):  
Electron Microscope ◽  
Measurement Errors ◽  
Dynamic Range ◽  
Structural Information ◽  
Statistical Parameter ◽  
Systematic Errors ◽  
Geometric Distortion ◽  
Crystal Silicon ◽  
Camera System ◽  
On Line

Established methods for measurement of lattice spacings and angles of crystalline materials include x-ray diffraction, microdiffraction and HREM imaging. Structural information from HREM images is normally obtained off-line with the traveling table microscope or by the optical diffractogram technique. We present a new method for precise measurement of lattice vectors from HREM images using an on-line computer connected to the electron microscope. It has already been established that an image of crystalline material can be represented by a finite number of sinusoids. The amplitude and the phase of these sinusoids are affected by the microscope transfer characteristics, which are strongly influenced by the settings of defocus, astigmatism and beam alignment. However, the frequency of each sinusoid is solely a function of overall magnification and periodicities present in the specimen. After proper calibration of the overall magnification, lattice vectors can be measured unambiguously from HREM images.Measurement of lattice vectors is a statistical parameter estimation problem which is similar to amplitude, phase and frequency estimation of sinusoids in 1-dimensional signals as encountered, for example, in radar, sonar and telecommunications. It is important to properly model the observations, the systematic errors and the non-systematic errors. The observations are modelled as a sum of (2-dimensional) sinusoids. In the present study the components of the frequency vector of the sinusoids are the only parameters of interest. Non-systematic errors in recorded electron images are described as white Gaussian noise. The most important systematic error is geometric distortion. Lattice vectors are measured using a two step procedure. First a coarse search is obtained using a Fast Fourier Transform on an image section of interest. Prior to Fourier transformation the image section is multiplied with a window, which gradually falls off to zero at the edges. The user indicates interactively the periodicities of interest by selecting spots in the digital diffractogram. A fine search for each selected frequency is implemented using a bilinear interpolation, which is dependent on the window function. It is possible to refine the estimation even further using a non-linear least squares estimation. The first two steps provide the proper starting values for the numerical minimization (e.g. Gauss-Newton). This third step increases the precision with 30% to the highest theoretically attainable (Cramer and Rao Lower Bound). In the present studies we use a Gatan 622 TV camera attached to the JEM 4000EX electron microscope. Image analysis is implemented on a Micro VAX II computer equipped with a powerful array processor and real time image processing hardware. The typical precision, as defined by the standard deviation of the distribution of measurement errors, is found to be <0.003Å measured on single crystal silicon and <0.02Å measured on small (10-30Å) specimen areas. These values are ×10 times larger than predicted by theory. Furthermore, the measured precision is observed to be independent on signal-to-noise ratio (determined by the number of averaged TV frames). Obviously, the precision is restricted by geometric distortion mainly caused by the TV camera. For this reason, we are replacing the Gatan 622 TV camera with a modern high-grade CCD-based camera system. Such a system not only has negligible geometric distortion, but also high dynamic range (>10,000) and high resolution (1024x1024 pixels). The geometric distortion of the projector lenses can be measured, and corrected through re-sampling of the digitized image.

Performance Characteristics of Methods for the Bacteriological Examination of Water

1993 ◽  
Vol 27 (3-4) ◽  
pp. 1-13 ◽  
Author(s):  
Arie H. Havelaar ◽  
Siem H. Heisterkamp ◽  
Janneke A. Hoekstra ◽  
Kirsten A. Mooijman
Keyword(s):  
Sensitivity And Specificity ◽  
Measurement Errors ◽  
Systematic Errors ◽  
General Concept ◽  
Growth Characteristics ◽  
Performance Characteristics ◽  
Logarithmic Scale ◽  
Bacteriological Examination ◽  
Membrane Filters

The general concept of measurement errors is applied to quantitative bacteriological counts on membrane filters or agar plates. The systematic errors of these methods are related to the growth characteristics of the medium (recovery of target organisms and inhibition of non-target organisms) and to its differential characteristics (sensitivity and specificity). Factors that influence the precision of microbiological counts are the variation between replicates, within samples, between operators and between laboratories. It is also affected by the linearity of the method, the verification rate and, where applicable, the number of colonies subcultured for verification. Repeatability (r) and reproducibility (R) values can be calculated on the logarithmic scale.

scholarly journals Micromechanism of the Breakage of Two Spherical Gypsum Particles under Normal–Tangential Contact Conditions

2021 ◽  
Vol 11 (9) ◽  
pp. 4039
Author(s):  
Yiran Niu ◽  
Lin Li ◽  
Yanwei Zhang ◽  
Shicai Yu ◽  
Jian Zhou
Keyword(s):  
Tangential Force ◽  
Coarse Grained ◽  
Spherical Particles ◽  
Contact Conditions ◽  
Normal Contact ◽  
Tangential Contact ◽  
Theoretical Predictions ◽  
Tangential Forces ◽  
Predicted Values ◽  
The Relationship

Contact breakage of particles makes a large difference in the strength of coarse-grained soils, and exploring the characteristics within the process of the breakage is of great significance. Ignoring the influence of particle shape, the micromechanism of two spherical particles breaking under normal–tangential contact conditions was investigated theoretically and experimentally. Through theoretical analysis, the breakage form, the shape and size of the conical core, and the relationship between the normal and tangential forces at crushing were predicted. Particle contact tests of two gypsum spheres were carried out, in which the breakage forms, features of the conical cores and the normal and tangential forces at crushing were recorded for comparison with the predicted values. The test results and the theoretical predictions showed good agreement. Both the analysis and test demonstrate that the presence of tangential forces causes the conical core to assume the shape of an oblique cone, and the breakage form to change. Moreover, with increasing normal contact force, the tangential force needed for crushing increases gradually first and then decreases suddenly.

The elastic contact influences on passive walking gaits

Robotica ◽  
2010 ◽  
Vol 29 (5) ◽  
pp. 787-796 ◽  
Author(s):  
Feng Qi ◽  
Tianshu Wang ◽  
Junfeng Li
Keyword(s):  
Coulomb Friction ◽  
Dynamic Models ◽  
Contact Stiffness ◽  
Contact Forces ◽  
Hertz Contact ◽  
Walking Gait ◽  
Routes To Chaos ◽  
Coulomb Friction Law ◽  
Contact Parameters ◽  
Passive Model

SUMMARYThis paper presents a new planar passive dynamic model with contact between the feet and the ground. The Hertz contact law and the approximate Coulomb friction law were introduced into this human-like model. In contrast to McGeer's passive dynamic models, contact stiffness, contact damping, and coefficients of friction were added to characterize the walking model. Through numerical simulation, stable period-one gait and period-two gait cycles were found, and the contact forces were derived from the results. After investigating the effects of the contact parameters on walking gaits, we found that changes in contact stiffness led to changes in the global characteristics of the walking gait, but not in contact damping. The coefficients of friction related to whether the model could walk or not. For the simulation of the routes to chaos, we found that a small contact stiffness value will lead to a delayed point of bifurcation, meaning that a less rigid surface is easier for a passive model to walk on. The effects of contact damping and friction coefficients on routes to chaos were quite small.

scholarly journals Measuring turbulence and gas motions in galaxy clusters via synthetic Athena X-IFU observations

2018 ◽  
Vol 618 ◽  
pp. A39 ◽  
Author(s):  
M. Roncarelli ◽  
M. Gaspari ◽  
S. Ettori ◽  
V. Biffi ◽  
F. Brighenti ◽  
...  
Keyword(s):  
Measurement Errors ◽  
Velocity Dispersion ◽  
Emission Measure ◽  
Systematic Errors ◽  
X Ray ◽  
Fitting Method ◽  
Metal Abundance ◽  
Centroid Shift ◽  
Hydrodynamical Simulations ◽  
Field Unit

Context. The X-ray Integral Field Unit (X-IFU) that will be on board the Athena telescope will provide an unprecedented view of the intracluster medium (ICM) kinematics through the observation of gas velocity, ν, and velocity dispersion, w, via centroid-shift and broadening of emission lines, respectively. Aims. The improvement of data quality and quantity requires an assessment of the systematics associated with this new data analysis, namely biases, statistical and systematic errors, and possible correlations between the different measured quantities. Methods. We have developed an end-to-end X-IFU simulator that mimics a full X-ray spectral fitting analysis on a set of mock event lists, obtained using SIXTE. We have applied it to three hydrodynamical simulations of a Coma-like cluster that include the injection of turbulence. This allowed us to assess the ability of X-IFU to map five physical quantities in the cluster core: emission measure, temperature, metal abundance, velocity, and velocity dispersion. Finally, starting from our measurements maps, we computed the 2D structure function (SF) of emission measure fluctuations, ν and w, and compared them with those derived directly from the simulations. Results. All quantities match with the input projected values without bias; the systematic errors were below 5%, except for velocity dispersion whose error reaches about 15%. Moreover, all measurements prove to be statistically independent, indicating the robustness of the fitting method. Most importantly, we recover the slope of the SFs in the inertial regime with excellent accuracy, but we observe a systematic excess in the normalization of both SFν and SFw ascribed to the simplistic assumption of uniform and (bi-)Gaussian measurement errors. Conclusions. Our work highlights the excellent capabilities of Athena X-IFU in probing the thermodynamic and kinematic properties of the ICM. This will allow us to access the physics of its turbulent motions with unprecedented precision.

scholarly journals Assimilation of river discharge in a land surface model to improve estimates of the continental water cycles

2018 ◽  
Vol 22 (7) ◽  
pp. 3863-3882 ◽  
Author(s):  
Fuxing Wang ◽  
Jan Polcher ◽  
Philippe Peylin ◽  
Vladislav Bastrikov
Keyword(s):  
Iberian Peninsula ◽  
Land Surface ◽  
Measurement Errors ◽  
River Discharge ◽  
Water Footprint ◽  
Human Impacts ◽  
Land Surface Model ◽  
Systematic Errors ◽  
Balance Model ◽  
Surface Model

Abstract. River discharge plays an important role in earth's water cycle, but it is difficult to estimate due to un-gauged rivers, human activities and measurement errors. One approach is based on the observed flux and a simple annual water balance model (ignoring human processes) for un-gauged rivers, but it only provides annual mean values which is insufficient for oceanic modelings. Another way is by forcing a land surface model (LSM) with atmospheric conditions. It provides daily values but with uncertainties associated with the models. We use data assimilation techniques by merging the modeled river discharges by the ORCHIDEE (without human processes currently) LSM and the observations from the Global Runoff Data Centre (GRDC) to obtain optimized discharges over the entire basin. The “model systematic errors” and “human impacts” (dam operation, irrigation, etc.) are taken into account by an optimization parameter x (with annual variation), which is applied to correct model intermediate variable runoff and drainage over each sub-watershed. The method is illustrated over the Iberian Peninsula with 27 GRDC stations over the period 1979–1989. ORCHIDEE represents a realistic discharge over the north of the Iberian Peninsula with small model systematic errors, while the model overestimates discharges by 30–150 % over the south and northeast regions where the blue water footprint is large. The normalized bias has been significantly reduced to less than 30 % after assimilation, and the assimilation result is not sensitive to assimilation strategies. This method also corrects the discharge bias for the basins without observations assimilated by extrapolating the correction from adjacent basins. The “correction” increases the interannual variability in river discharge because of the fluctuation of water usage. The E (P−E) of GLEAM (Global Land Evaporation Amsterdam Model, v3.1a) is lower (higher) than the bias-corrected value, which could be due to the different P forcing and probably the missing processes in the GLEAM model.

Multi-gnss as a combination of gps, glonass and beidou measurements carried out in real time

2015 ◽  
Vol 50 (4) ◽  
pp. 217-229 ◽  
Author(s):  
Zbigniew Siejka
Keyword(s):  
Real Time ◽  
Measurement Errors ◽  
Systematic Errors ◽  
Measurement Point ◽  
Height Determination

Abstract In this paper the advantages of using combination of different GNSS including GPS, GLONASS and BeiDou with respect to singe GPS are presented. It was shown that an improvement of satellite conditions at the chosen measurement point due to increase of the number of visible satellites has an impact on RTK measurement errors. Additionally, it was shown that there are systematic errors in RTK measurements that can be eliminated to get more precise results of them, especially in the case of height determination.

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