Modeling of Contact Area, Contact Force, and Contact Stiffness of Mechanical Systems With Friction

Tribology ◽  
2005 ◽  
Author(s):  
Jamil Abdo ◽  
Elhanafi Shamseldin
Keyword(s):  
Contact Force ◽  
Contact Area ◽  
Contact Stiffness ◽  
Surface Profile ◽  
Test Area ◽  
Contact Forces ◽  
Profile Data ◽  
Contact Parameter ◽  
Parameter Values ◽  
True Contact Area

It is well recognized that the contact stiffness, true contact area, and the contact force are among the key features in the study of friction system behavior. This paper presents the development of formulae for the mechanical component of dry-friction at the interface of two microscopic rough surfaces. Elastic deformation under the influence of the contact forces is considered. The elastic contact model formulation between interacting asperities is not assumed to occur only at asperity peaks, thus allowing the possibility of oblique contacts wherein the local contact surfaces are no longer parallel to the mean planes of the mating surfaces. It is shown that the approach enables the separation of the contact area into its normal and tangential projections and the contact force into its normal and tangential components. The mathematical model of contact is utilized to develop formulae for normal and tangential contact stiffness. The analytical method is used to estimate contact stiffness components. Contact parameter values for the sample are derived from the surface profile data taken from a 1.0-mm by 10-mm test area. The profile is measured using a Mahr profilometer. A computer program is written and used to analyze the profile data. The analysis yields the asperity density, average asperity radius, and the standard deviation for each test area.

scholarly journals Muscle Synergies May Improve Optimization Prediction of Knee Contact Forces During Walking

2014 ◽  
Vol 136 (2) ◽  
Author(s):  
Jonathan P. Walter ◽  
Allison L. Kinney ◽  
Scott A. Banks ◽  
Darryl D. D'Lima ◽  
Thor F. Besier ◽  
...  
Keyword(s):  
Contact Force ◽  
Contact Forces ◽  
Muscle Model ◽  
Patient Specific ◽  
Force Prediction ◽  
Model Parameter ◽  
Subject Specific ◽  
Rms Error ◽  
Parameter Values ◽  
Shape Tracking

The ability to predict patient-specific joint contact and muscle forces accurately could improve the treatment of walking-related disorders. Muscle synergy analysis, which decomposes a large number of muscle electromyographic (EMG) signals into a small number of synergy control signals, could reduce the dimensionality and thus redundancy of the muscle and contact force prediction process. This study investigated whether use of subject-specific synergy controls can improve optimization prediction of knee contact forces during walking. To generate the predictions, we performed mixed dynamic muscle force optimizations (i.e., inverse skeletal dynamics with forward muscle activation and contraction dynamics) using data collected from a subject implanted with a force-measuring knee replacement. Twelve optimization problems (three cases with four subcases each) that minimized the sum of squares of muscle excitations were formulated to investigate how synergy controls affect knee contact force predictions. The three cases were: (1) Calibrate+Match where muscle model parameter values were calibrated and experimental knee contact forces were simultaneously matched, (2) Precalibrate+Predict where experimental knee contact forces were predicted using precalibrated muscle model parameters values from the first case, and (3) Calibrate+Predict where muscle model parameter values were calibrated and experimental knee contact forces were simultaneously predicted, all while matching inverse dynamic loads at the hip, knee, and ankle. The four subcases used either 44 independent controls or five synergy controls with and without EMG shape tracking. For the Calibrate+Match case, all four subcases closely reproduced the measured medial and lateral knee contact forces (R2 ≥ 0.94, root-mean-square (RMS) error < 66 N), indicating sufficient model fidelity for contact force prediction. For the Precalibrate+Predict and Calibrate+Predict cases, synergy controls yielded better contact force predictions (0.61 < R2 < 0.90, 83 N < RMS error < 161 N) than did independent controls (-0.15 < R2 < 0.79, 124 N < RMS error < 343 N) for corresponding subcases. For independent controls, contact force predictions improved when precalibrated model parameter values or EMG shape tracking was used. For synergy controls, contact force predictions were relatively insensitive to how model parameter values were calibrated, while EMG shape tracking made lateral (but not medial) contact force predictions worse. For the subject and optimization cost function analyzed in this study, use of subject-specific synergy controls improved the accuracy of knee contact force predictions, especially for lateral contact force when EMG shape tracking was omitted, and reduced prediction sensitivity to uncertainties in muscle model parameter values.

scholarly journals Estimation accuracy vs. engineering significance of contact parameters for solid dampers

2017 ◽  
Vol 1 ◽  
pp. VLXC9F ◽  
Author(s):  
Chiara Gastaldi ◽  
Muzio M. Gola
Keyword(s):  
Numerical Models ◽  
Contact Stiffness ◽  
Point Of View ◽  
Contact Forces ◽  
Estimation Accuracy ◽  
Contact Friction ◽  
Experimental Frequency ◽  
Contact Parameter ◽  
Friction Parameters ◽  
Contact Parameters

AbstractAll numerical models of friction-damped bladed arrays require knowledge or information of contact-friction parameters. In the literature, these parameters are typically tuned so that the experimental Frequency Response Function (FRF) of a damped blade matches its numerical counterpart. It is well known that there exist multiple combinations of contact parameters capable of satisfying a given experimental-numerical FRF match. A better approach towards a finer tuning could be based on directly measuring contact forces transmitted between blade platforms through the damper: in this case friction coefficients are estimated through tangential over normal force components during those hysteresis segments which are safely identified as being in a slip condition. This has been applied by these authors to rigid bar (solid) dampers. Unfortunately, the four contact stiffness values (left and right damper-platform contact, normal and tangential) are more than the measurements available in the technique presented by these authors. Therefore, the problem is underdetermined. The purpose of this paper is twofold,i.e., to propose an alternative way to estimate contact stiffness values (i.e.thus solving the under-determinacy mentioned above) and to check the effective significance of such estimates from a practical engineering point of view. The contact parameter estimation technique proposed by these authors produces, for each contact parameter, a best-fit value and an uncertainty band. It will be shown that the uncertainty affecting each contact parameter results in an uncertainty on the equivalent damping and stiffness indicators at blade level which is lower than 5%.

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.

A study of the mechanics of microindentation using finite elements

1992 ◽  
Vol 7 (3) ◽  
pp. 618-626 ◽  
Author(s):  
T.A. Laursen ◽  
J.C. Simo
Keyword(s):  
Thin Film ◽  
Finite Element ◽  
Contact Area ◽  
Contact Stiffness ◽  
Surface Profile ◽  
Critical Examination ◽  
Actual Contact ◽  
Actual Contact Area ◽  
Straight Line ◽  
Film Substrate

In this paper the finite element method is used to explore the mechanics of the microindentation process. In the simulations discussed, aluminum and silicon are investigated both in their bulk forms and in thin film-substrate combinations. Among the quantities readily computed using this approach and given in this paper are hardness (computed using actual contact area), contact stiffness, effective composite modulus, and surface profile under load. Importantly, this investigation builds on previous work by providing a more critical examination of the amount of pileup (or sink-in) around the indenter in the fully loaded configuration, as well as the variation of the actual contact area during indenter withdrawal. A key conclusion of this study is that finite element simulations do not support the widely used assumption of constancy of area during unloading (for either bulk materials or thin film systems). Furthermore, the amount of pileup or sink-in can be appreciable. The implication of these findings is that for many situations the commonly used straight-line extrapolation of a plastic depth may render an estimate for the contact area that is quite distinct from the actual area. This assertion is demonstrated herein through comparison of hardnesses calculated using actual contact area with values calculated using the straight-line extrapolation of plastic depth.

scholarly journals Relationship of Catheter Contact Angle and Contact Force with Contact Area on the Surface of Heart Muscle Tissue in Cardiac Catheter Ablation

2021 ◽  
Author(s):  
Kriengsak Masnok ◽  
Nobuo Watanabe
Keyword(s):  
Contact Angle ◽  
Catheter Ablation ◽  
Contact Force ◽  
Contact Area ◽  
Heart Muscle ◽  
Contact Angles ◽  
Contact Forces ◽  
Logarithmic Function ◽  
Experimental Procedure ◽  
Relationship Of

Abstract Purpose The aims of this study were to develop an experimental procedure for setting the catheter angle with respect to the surface of the heart muscle and the catheter contact force and to investigate the catheter contact area on the heart muscle as a function of catheter contact angle and force. Methods Visualization tests were performed for 5 contact angles (0°, 30°, 45°, 60°, and 90°) and 8 contact forces (2, 4, 6, 10, 15, 20, 30, and 40 gf). Each experiment was repeated 6 times with 2 different commercially available catheter tips. Results The morphology of the contact area was classified into rectangular, circular, ellipsoidal, and semi-ellipsoidal. The correlation between contact force and contact area was a logarithmic function; increasing contact force was associated with increased contact area. At the same contact force, the correlation between contact angle and contact area was inverse; decreasing contact angle was associated with a corresponding increase in contact area. Conclusion Both the catheter contact angle and contact force substantially impact the contact area and morphology in catheter ablation procedures.

scholarly journals Measuring and Understanding Contact Area at the Nanoscale: A Review

2017 ◽  
Vol 69 (6) ◽  
Author(s):  
Tevis D. B. Jacobs ◽  
Ashlie Martini
Keyword(s):  
Continuum Mechanics ◽  
Contact Area ◽  
Contact Stiffness ◽  
Indirect Methods ◽  
Simulation Techniques ◽  
In Situ Electron Microscopy ◽  
Direct Measurements ◽  
True Contact Area ◽  
Single Contact

The size of the mechanical contact between nanoscale bodies that are pressed together under load has implications for adhesion, friction, and electrical and thermal transport at small scales. Yet, because the contact is buried between the two bodies, it is challenging to accurately measure the true contact area and to understand its dependence on load and material properties. Recent advancements in both experimental techniques and simulation methodologies have provided unprecedented insights into nanoscale contacts. This review provides a detailed look at the current understanding of nanocontacts. Experimental methods for determining contact area are discussed, including direct measurements using in situ electron microscopy, as well as indirect methods based on measurements of contact resistance, contact stiffness, lateral forces, and topography. Simulation techniques are also discussed, including the types of nanocontact modeling that have been performed and the various methods for extracting the magnitude of the contact area from a simulation. To describe and predict contact area, three different theories of nanoscale contact are reviewed: single-contact continuum mechanics, multiple-contact continuum mechanics, and atomistic accounting. Representative results from nanoscale experimental and simulation investigations are presented in the context of these theories. Finally, the critical challenges are described, as well as the opportunities, on the path to establishing a fundamental and actionable understanding of what it means to be “in contact” at the nanoscale.

scholarly journals Neuromusculoskeletal Model Calibration Significantly Affects Predicted Knee Contact Forces for Walking

2016 ◽  
Vol 138 (8) ◽  
Author(s):  
Gil Serrancolí ◽  
Allison L. Kinney ◽  
Benjamin J. Fregly ◽  
Josep M. Font-Llagunes
Keyword(s):  
Contact Force ◽  
Muscle Fiber ◽  
Model Calibration ◽  
Contact Forces ◽  
Patient Specific ◽  
Muscle Forces ◽  
Model Parameter ◽  
Neuromusculoskeletal Model ◽  
Leg Muscle ◽  
Parameter Values

Though walking impairments are prevalent in society, clinical treatments are often ineffective at restoring lost function. For this reason, researchers have begun to explore the use of patient-specific computational walking models to develop more effective treatments. However, the accuracy with which models can predict internal body forces in muscles and across joints depends on how well relevant model parameter values can be calibrated for the patient. This study investigated how knowledge of internal knee contact forces affects calibration of neuromusculoskeletal model parameter values and subsequent prediction of internal knee contact and leg muscle forces during walking. Model calibration was performed using a novel two-level optimization procedure applied to six normal walking trials from the Fourth Grand Challenge Competition to Predict In Vivo Knee Loads. The outer-level optimization adjusted time-invariant model parameter values to minimize passive muscle forces, reserve actuator moments, and model parameter value changes with (Approach A) and without (Approach B) tracking of experimental knee contact forces. Using the current guess for model parameter values but no knee contact force information, the inner-level optimization predicted time-varying muscle activations that were close to experimental muscle synergy patterns and consistent with the experimental inverse dynamic loads (both approaches). For all the six gait trials, Approach A predicted knee contact forces with high accuracy for both compartments (average correlation coefficient r = 0.99 and root mean square error (RMSE) = 52.6 N medial; average r = 0.95 and RMSE = 56.6 N lateral). In contrast, Approach B overpredicted contact force magnitude for both compartments (average RMSE = 323 N medial and 348 N lateral) and poorly matched contact force shape for the lateral compartment (average r = 0.90 medial and −0.10 lateral). Approach B had statistically higher lateral muscle forces and lateral optimal muscle fiber lengths but lower medial, central, and lateral normalized muscle fiber lengths compared to Approach A. These findings suggest that poorly calibrated model parameter values may be a major factor limiting the ability of neuromusculoskeletal models to predict knee contact and leg muscle forces accurately for walking.

Viscoelastic Contact of Nominally Flat Rough Surfaces

2005 ◽  
Author(s):  
K. Farhang ◽  
A. Lim
Keyword(s):  
Contact Force ◽  
Rough Surfaces ◽  
Tangential Force ◽  
Tangential Velocity ◽  
Surface Profile ◽  
Contact Forces ◽  
Profile Measurement ◽  
Tangential Contact ◽  
Corrective Factor ◽  
Percent Accuracy

Approximate closed-form equations are derived for normal and tangential contact forces of rough surfaces in dry friction. Using an extension of the Greenwood and Tripp model, in which the derivations permit asperity shoulder-to-shoulder contact and viscoelastic asperity behavior. Mathematical formulae are derived for normal and tangential components of the contact force that depend not only on the proximity of the two surfaces but also the rate of approach and relative sliding. A statistical approach is forwarded in which dependence of the asperity tangential contact force on relative tangential velocity of two asperities can be cast as a corrective factor in the mathematical description of tangential force. In this regard two corrective coefficients are derived: force directionality corrective coefficient and force-velocity directionality corrective coefficient. The results show that for a moderate to high load ranges the contact force can be analytically described to within 20 percent accuracy, well below the uncertainties due to surface profile measurement.

Predicting Fly-Height Modulation and Contact Forces in Ultra-Low Flying Head-Disk Interfaces Using a Tri-State Switching Dynamic Contact Model

2001 ◽  
Author(s):  
Sung-Chang Lee ◽  
Andreas A. Polycarpou
Keyword(s):  
Contact Force ◽  
Contact Stiffness ◽  
Dynamic Contact ◽  
Design Guidelines ◽  
Contact Forces ◽  
Contact Dynamics ◽  
Contact Model ◽  
Flying Height ◽  
Disk Contact ◽  
Fly Height

Abstract In order to achieve higher recording densities up to 1 Tbit/In2 using conventional recording technologies, the recording slider will need to “fly” within 5 nm or less from the rotating disk. In such ultra-low flying height regimes, intermittent head/disk contact is unavoidable. Head/disk contact can cause large vibrations of the recording slider in the normal and lateral (off-track) directions as well as damage the disk due to large dynamic contact forces. This paper describes a simple continuum mechanics-based model that includes the dynamics of a flying head/disk interface (HDI) as well as the contact dynamics. Specifically, a lumped parameter one degree-of-freedom, three state nonlinear dynamic model representing the normal dynamics of the HDI and an asperity-based contact model are developed. The effects of realistic (dynamic microwaviness) and harmonic input excitations, contact stiffness (surface roughness) and air-bearing force during contact on fly-height modulation (FHM) and contact force are investigated. Based on the tri-state model predictions, design guidelines for reduced FHM and dynamic contact force are suggested.

scholarly journals Catheter contact area strongly correlates with lesion area in radiofrequency cardiac ablation: an ex vivo porcine heart study

2021 ◽  
Author(s):  
Kriengsak Masnok ◽  
Nobuo Watanabe
Keyword(s):  
Contact Angle ◽  
Catheter Ablation ◽  
Contact Force ◽  
Contact Area ◽  
Radiofrequency Catheter Ablation ◽  
Contact Angles ◽  
Contact Forces ◽  
Ablation Lesion ◽  
Lesion Area ◽  
Lesion Depth

Abstract Purpose Our previous study confirmed that not only force but also the catheter contact angle substantially impacted the contact area and its morphology. Therefore, in this study, we aimed to further investigate the relationship between the catheter contact area and the dimensions of the ablation lesion area as a function of catheter contact angle and force in radiofrequency catheter ablation. Methods The radiofrequency catheter ablation test was performed for 5 contact angles and 8 contact forces at a fixed ablation time of 30 s. The initial impedance was 92.5 ± 2.5 Ω, the temperature during ablation was 30 °C, and the power was 30 W. The irrigation rate during ablation was set to 17 mL/min. Each experiment was repeated 6 times. Results The catheter contact area showed a strong correlation with the ablation lesion area (r = 0.8507). When the contact area was increased, the lesion area also increased linearly in a monotonic manner. The relationships between catheter contact force and ablation lesion area and between catheter contact force and ablation lesion depth are logarithmic functions in which increased contact force was associated with increased lesion area and depth. The catheter contact angle is also an important determinant of the lesion area. The lesion area progressively increased when the contact angle was decreased. In contrast, the lesion depth progressively increased when the contact angle was increased. Conclusions The catheter contact area was strongly correlated with the ablation lesion area. Additionally, catheter contact force and contact angle significantly impacted the dimensions of the lesion in radiofrequency catheter ablation procedures.

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