Contact Deformation Research Articles

Dynamics Modeling and Analysis of Rolling Bearings Variable Stiffness System with Local Faults

By analyzing the support of load-carrying rolling elements when the rolling elements fall into the fault position, the dynamics model of a rolling bearing variable stiffness system with local faults is proposed, considering the retention factor of the contact deformation. Then, this paper researches the change of effective contact stiffness, contact deformation, contact force, and the total effective stiffness of the rolling elements. The results show that the contact stiffness of the rolling elements abruptly decreases when the rolling elements fall into the fault position. The contact deformation and contact force of the load-carrying rolling elements in the load zone increase, rebalancing the external radial load while causing a sudden reduction in the total effective stiffness, resulting in the vibration of the system. When different rolling elements fall into the outer ring fault position, the change in total effective stiffness and the system response are equal in magnitude. Additionally, there is a significant outer race fault characteristic frequency accompanied by frequency multiplication in the fault characteristic spectrums. When different rolling elements fall into the inner race fault position, the total effective stiffness is modulated by the inner race rotation and varies dramatically, resulting in the amplitude of the system time domain vibration response also being modulated by the inner race rotation and varying dramatically. Additionally, there is a significant inner race rotational frequency accompanied by frequency multiplication, an inner race fault characteristic frequency accompanied by frequency multiplication, and a side frequency in the fault characteristic spectrums. The research can provide some reference for the effective diagnosis of the rolling bearing fault.

Influence of the concentration and dispersiveness of the epoxy-gravel composite filler on the resistance to contact deformation during the penetration of a solid spherical body

The nature and degree of resistance to contact deformation of epoxy-gravel composites during the penetration of a solid spherical body are considered depending on the concentration of components and the fineness of the filler. Keywords: epoxy composition, gravel component, composite, contact deformation, filler, concentration, dispersiveness.mihalchenkov.alexandr@yandex.ru

Research on the Influence of the Closing Amount of Electrical Connector Contacts on Fretting Wear under a Vibration Environment

As a key component for transmitting electrical signals, the electrical contact performance of electrical connectors is directly affected by the closing amount of the socket. It is urgent to explore the relationship between contact resistance and the closing amount of cylindrical groove electric connectors, as well as the range of the closing amount when their comprehensive performance is optimal in vibration environments. Based on Hertz contact theory, the long- and short-axis parameters of the contact elliptical surface were obtained using the Boussinesq solution and the contact deformation coordination equation. An electrical contact resistance (ECR) theoretical model was obtained using Holm’s electric contact theory and the GW contact model. According to the ECR and long- and short-axis parameters of the contact elliptical surface and the theoretical model of contact resistance, an ECR model based on changes in the initial closing amount (deflection) of the socket spring was established by introducing the cantilever beam model of the socket spring. Then, the failure mechanism of fretting wear and the change mechanism of the ECR of the electrical connectors under a vibration environment were analyzed using the sinusoidal vibration test of electric connectors. The optimal range of the initial closing amount of the cylindrical-groove-closing-type electrical connector socket spring was determined, providing a reference for the reliability designs of electrical connectors.

Improved SNS-PFEM framework with dual mortar method to model geotechnical large deformation contact problems

This work proposes an improved stable node-based strain smoothing particle finite element method (SNS-PFEM) with the dual mortar method to model the geotechnical large deformation contact problems. The proposed SNS-PFEM framework requires only basic length parameters for constructing stabilization terms, thus yielding a simpler implementation and less computational cost than the existing methods. Based on this framework, an efficient dual mortar contact algorithm is introduced for finite frictional sliding analysis, utilizing the segment-to-segment discretization and dual Lagrange multiplier method. The resulting stiffness matrix is well-conditioned and positive-defined, leading to higher accuracy and less computational cost than penalty-type methods. Furthermore, a dynamic mesh adjustment technique is proposed to ensure high mesh quality throughout the large deformation process. Since all variables are stored on the node in our SNS-PFEM framework, the process of mesh adjustment is both straightforward and computationally efficient. The precision and robustness of our methods are validated through three classical benchmarks and two representative geotechnical problems. Results show that the proposed SNS-PFEM framework effectively eliminates the over-soft issue seen with the NS-PFEM; the dual mortar method offers an accurate, and efficient performance for nonlinear contact analysis; and the dynamic mesh adjustment technology is effective in preventing mesh quality degradation during large deformations.

Planarization profile modeling using pad bulk deformation and real contact area analysis of macro-scale device pattern

In general, the shape of the polished pattern is not flat but has a rounded curved profile. Unlike micro-patterns that have similar scales to pad asperities, macro-patterns have a very large scale compared to asperities, so bulk deformation must also be considered. To derive the pad bulk deformation, real contact area (RCA) measurements were performed in this study. Based on the preceding contact model, a semi-empirical model for RCA and bulk deformation was derived. After including the constructed pad bulk deformation function in the existing Greenwood–Williamson model, a new model that can derive the material removal rate profile according to the position in the pattern was presented. Unlike the general upper and lower removal rate behavior, this model shows a unique behavior. At the beginning of polishing, the edge shows a higher removal rate than the center, but after a specific step height, the center has a higher removal rate due to the curved shape. Analysis was performed for comparison between the proposed model equation and the experimental value. When the polishing profile in the 10 mm pattern was compared with the previous model and the proposed model, respectively, the existing model did not predict the removal rate distribution according to the position in the pattern. However, this model has the advantage of predicting both over-polishing at the edge of the pattern and high removal rate at the bottom. In addition, it was confirmed through simulation that the 4 mm and 2 mm patterns had excellent matching properties.

Molecular dynamics study of graphene-coated reinforced tribomechanical properties: Hard versus soft substrates

As a two-dimensional material, graphene film is a good solid lubricant candidate for improving the tribomechanical performance of micro-and nano-electromechanical systems. Graphene has a significant impact on protecting the top layer of a substrate from wear and reducing friction. However, the frictional behavior has been found to vary when coating graphene onto different substrates. In the present study, using molecular dynamics (MD) simulations, graphene was deposited as a monolayer coating on the substrate sliding against the diamond tip, which revealed not only significant improvement in tribological behavior by reducing both friction and contact deformation volume, but also notably demonstrated the difference between hard and soft substrate coating with graphene. Under 58.5nN loading, the optimal antifriction effect of graphene coating on Au substrate was 94.2%, with a higher friction indicating a greater indentation depth and greater contact deformation. The contact deformation volume can be used as a standard to measure the surface friction of graphene. Unlike hard Si substrates, monolayer graphene coatings are prone to rupture at 200 nN loads. At low loads, the single graphene coating has the best anti-friction effect on the soft gold substrate, and at higher loads, the graphene on the hard silicon substrate is not prone to rupture, providing continuous and stable lubrication. The study also revealed a tunable toughening mechanism of graphene layers. The mechanism entails a reduction in the volume of substrate contact deformation with the progressive addition of graphene layers. This finding has the potential to enhance the tribological performance of the graphene-coated substrate.

Influences of upsetting on the propagation characteristic of the elastic wave in the countersunk head riveted joints

The countersunk head riveted joints (CHRJ) have extensive use in the aerospace and marine industry. When testing the CHRJ with ultrasonic technology, the signal near the initial pulse cannot be used to detect near-surface defects due to the blind zone of the ultrasonic testing (UT). Moreover, the presence of clutters between the first and second bottom echoes can significantly affect the effectiveness of the UT. Therefore, it is crucial to investigate the propagation characteristic of ultrasonic waves in the CHRJ. The relationship between the interface stiffness and the upsetting length was obtained because of the multi-interface feature of the CHRJ. The propagation characteristic of ultrasonic waves in the CHRJ was investigated using the finite element simulation based on the spring model of the imperfect interface. The simulation results showed that shank echoes would generate at the surface of the rivet shank when the elastic wave propagates in the shank of the CHRJ. The shank echoes would propagate obliquely downward and reflect repeatedly on the surface of the rivet shank. Furthermore, the amplitude of the first shank echo would decrease with the increase of the upsetting length due to the increase of contact stress and deformation. To verify the simulation results, the experiments were carried out using the piezoelectric ultrasonic transducer, and the experimental results matched well with the simulation results. This paper can provide a reference for the ultrasonic testing of defects in the CHRJ.

Contact Area and Deformation of Escherichia coli Cells Adhered on a Cationic Surface.

When bacteria adhere to surfaces, the chemical and mechanical character of the cell-substrate interface guides cell function and the development of microcolonies and biofilms. Alternately on bactericidal surfaces, intimate contact is critical to biofilm prevention. The direct study of the buried cell-substrate interfaces at the heart of these behaviors is hindered by the small bacterial cell size and inaccessibility of the contact region. Here, we present a total internal reflectance fluorescence depletion approach to measure the size of the cell-substrate contact region and quantify the gap separation and curvature near the contact zone, providing an assessment of the shapes of the near-surface undersides of adhered bacterial cells. Resolution of the gap height is about 10%, down to a few nanometers at contact. Using 1 and 2 μm silica spheres as calibration standards we report that, for flagella-free Escherichia coli (E. coli) adhering on a cationic poly-l-lysine layer, the cell-surface contact and apparent cell deformation vary with adsorbed cell configuration. Most cells adhere by their ends, achieving small contact areas of 0.15 μm2, corresponding to about 1-2% of the cell's surface. The altered Gaussian curvatures of end-adhered cells suggest the flattening of the envelope within the small contact region. When cells adhere by their sides, the contact area is larger, in the range 0.3-1.1 μm2 and comprising up to ∼12% of the cell's total surface. A region of sharper curvature, greater than that of the cells' original spherocylindrical shape, borders the flat contact region in cases of side-on or end-on cell adhesion, suggesting envelope stress. From the measured curvatures, precise stress distributions over the cell surface could be calculated in future studies that incorporate knowledge of envelope moduli. Overall the small contact areas of end-adhered cells may be a limiting factor for antimicrobial surfaces that kill on contact rather than releasing bactericide.

Modelling elastoplastic frictional collisions of ellipsoidal granules with collisional-SPH

The Collisional-SPH method models the combined evolution of deformation and frictional contact forces in elastoplastic granular collisions. However, there are many applications in which the granules are not spherical. In this paper, CSPH is extended to model an impact of an ellipsoidal granule on a flat deformable substrate. The CSPH spring-stiffness formulation is developed to account for the contact area eccentricity. Validation for different granule orientations and aspect-ratios are presented. The combined effect of substrate deformation and non-spherical granule shape on the contact-zone mechanics is investigated for different granule orientations and aspect ratios. It is found that the granule’s orientation and aspect ratio influences the interdependence between substrate deformation and contact-force distribution and should be accounted for in collision models.

Method of predicting valve seal leakage considering deflection of the spool

The small angular deflection of the spool under the action of non-equilibrium force is a main reason for valve seal failure. In the present study, a prediction model of the valve seal leakage was established considering the sectional shape and channel height of the leakage channel. The effect of spool deflection on the leakage rate was analyzed quantitatively from the results of three-dimensional finite element mechanical analysis. The microscale leakage channel of a contact deformation surface was then generated through the reconstruction of the rough surface with nanoscale precision, deterministic rough-peak contact analysis, and lattice leakage theory. The results showed that the spool deflection was the key factor affecting the leakage rate. The leakage rate was measured on a self-built experimental platform, and the experimental results verified the accuracy of the theoretical calculations.

Rail and wheel health management

Rail and wheel health management is investigated with focus on deterioration phenomena in the wheel/rail contact interface – plastic deformation, wear, and rolling contact fatigue (RCF). How operational conditions affect deterioration, and how they can be included in wheel/rail health predictions is linked to a more in-depth description of deterioration mechanisms. Here means of measuring, quantifying, and predicting deterioration is in focus. This discussion provides the basis for the outline of a rail and wheel health management framework. As discussed in the paper, the proposed framework is well in line with the requirements in the ISO 55000 standard for asset management.

Theoretical Analysis on Postbuckled Large Deformation and Subsequent Contact in a Spring-hinged Beam with Changing Length

Theoretical Analysis on Postbuckled Large Deformation and Subsequent Contact in a Spring-hinged Beam with Changing Length

Semi-analytical loaded tooth contact analysis method for spiral bevel gears

Loaded tooth contact analysis (LTCA) is an important tool for analyzing the meshing of spiral bevel gears. This paper presents a semi-analytical LTCA method, where the analytical formulas are used to calculate the tooth deformation and contact force, with partial coefficients corrected by finite element analysis (FEA) results. Based on Tredgold's Approximation, the tooth is sliced, of which the flank is determined by simulating the manufacturing process. In order to calculated the potential contact curves of a real gear pair, an optimization model is established to find the points more likely to be in contact within the range of contact curves obtained by the help of roll angle surfaces. The compliance of tooth is modeled as a combination of two contributions, where the deformation of cantilever beam under load is used to determine the global deformation, and the local contact deformation is obtained by Hertz line contact assumption. A contact judgement strategy is proposed to detect the contact of the slices at ends of contact curves, and the correction coefficients are introduced in the tooth deformation to consider the coupling effect among slices. In the end, a numerical instance of LTCA under different load torques is provided, which demonstrates the accuracy and efficiency of the presented LTCA method by comparisons with results of FEA. This method can be easily modified to analyze other gear pairs and has the ability to be extended to simulate the gears with local defects or cracks.

Influence of microgeometry in the point contact zone of rest friction on fatigue life for friction bearing units

A comprehensive methodology has been developed to assess the maximum contact stresses and deformations in the point contact zone and the maximum tangential stresses, including their position in the subsurface zone in depth and in the rolling direction when the microgeometry of the rest contact.

Contact of Rough Surfaces: An Incremental Model Accounting for Strain Gradient Plasticity

In the contact of rough surfaces, most contact patches are at the scale of micrometers, and thus, their contact deformation can be dominated by the size-dependent plasticity. In this paper, we propose a new strategy to analyze the role of strain gradient plasticity in the contact response between a realistic rough surface and a rigid plane, which modifies the incremental contact model based on the mechanism-based gradient plasticity (MSGP) theory. For several different rough surfaces with their topography measured experimentally, the relations between applied load and real contact area are derived in a simple but effective way. It is found that strain gradient plasticity significantly increases the level of mean contact pressure. The hardening effect caused by strain gradient plasticity weakens somewhat as the contact area increases. Compared with previous methods, the present model might be more efficient and of wider application.

Modeling contact deformation of bare and coated rough metal bodies

The effect of the presence of a passivation layer on a metal rough surface during contact loading is investigated by means of dislocation dynamics simulations. The metal body is modeled as an FCC single crystal with a self-affine rough surface that is either bare, or covered by a thin coating, impenetrable to dislocations. This analysis permits to isolate the effect of surface roughening driven by dislocation motion: when the surface is bare the dislocations can glide out, leaving crystallographic steps at the surface that modify the local roughness; when the surface is passivated, dislocations are stopped by the interface.

A multi-asperity adhesive contact model for catheter and vascular artery contact in endovascular surgery.

Contact behaviors of medical devices, such as guidewires and catheters, are critical in endovascular surgeries. In this work, a new method to predict adhesive contact force between catheter and vascular artery is presented. Multi-asperity adhesion on the surface of vascular artery, deformation of asperity and deformation of vascular substrate are all considered. The single asperity behavior is described with Johnson-Kendall-Roberts (JKR) contact model. The multi-asperity behavior is based on Greenwood-Williamson (GW) asperity model. Vascular substrate is considered as elastic bulk substrate and its deformation is determined with Hertzian pressure from asperity on a circular region on the elastic half space. The model shows that the deformation of vascular substrate accounts for the majority of the total contact deformation and significantly affects the predicted contact force. The model is verified with published experimental data. The comparison shows that the model produces very accurate prediction of contact force between catheter and vascular artery when the contact force is compressive. Parametric analysis based on asperity topography is carried out. The analysis shows that the diameter of the circular region of the interface between asperity and vascular substrate has more significant effect on the estimation of contact force than the radius of asperity. Further validation of prediction accuracy of the model under experiment is needed.

Equivalent numerical method and sensitivity analysis of microparameters for micropore compression stage of cemented tailings backfill

The discrete element method has been widely used to study the mechanical properties of rock and cemented tailings backfill (CTB). The high matching degree of mechanical properties between numerical simulation and experiment is the precondition of accurate numerical simulation research. However, as the discrete element method’s particle system cannot characterize pore structure of rock and CTB, it cannot simulate the micropore compression stage (MPCS) of laboratory test. Therefore, the traditional discrete element method cannot accurately simulate the whole process of stress − strain curve of rock and CTB. To solve this problem, in this study, the variation law of the porosity and pore radius of CTB samples’ MPCS were first explored using nuclear magnetic resonance and computed tomography scanning tests. Based on the findings, the equivalent cell model of CTB is proposed. The relative deformation of cells can equivalently characterize the compressive deformation of pores in CTBs. Thus, the initial effective modulus, E0, the progressive coefficient of the effective modulus, k, and cycle steps, b, were introduced to improve the soft-bond model (SBM) in a particle flow code (PFC). This improvement changes the contact structure between particles and makes the contact deformation between particles more consistent with the deformation behavior of micropores in laboratory test. A numerical method for the nonlinear deformation of MPCS is established in PFC. Finally, the parameter sensitivity of the softening factor, softening tensile strength factor, friction coefficient, E0, k, and b in the improved SBM was analyzed. The variation law of samples’ macromechanical parameters with different microparameters is obtained. The results provide a basis for a more accurate study of the mechanical behavior of rock and CTB based on the discrete element method.

Continuous deformation analysis and contact force estimation for pneumatic bending actuators interacting with environment

Soft bending actuators show high adaptability for applications such as rehabilitation or grasping. Although constant curvature assumption has been extensively used for free motion modeling, these actuators do not bend circularly when interacting with the environment. In such situation, conventional bending sensors cannot provide useful information on their shape. In this paper, the Finite Rigid Elements approach is utilized to model the behavior of a soft pneumatic bending actuator in free motion and contact. With this method, the variable curvature configuration under different external loads can be modeled. Then, the contact force between the actuator and an object located in a specific position is estimated utilizing the Gradient Descent optimization method. Experimental results verified the combinatorial proposed approach for both force estimation and structure deformation.

Modeling and analysis of load distribution ratio and meshing stiffness for orthogonal spur-face gear drive under point contact

Analytical models of load distribution ratio (LDR) and meshing stiffness for orthogonal spur-face gear drive under point contact are established to provide the parameter basis for dynamics studies in this paper. Meshing point tracks and contact line ranges on tooth surfaces are strictly divided according to the point contact ratio. Local contact stiffness at meshing point is calculated based on Hertz contact theory and calculation approaches of global tooth stiffness under line and point contact are proposed and compared. Then, models of LDR and meshing stiffness are constructed and analyzed. The results show that the global tooth stiffness decreases after considering point contact on the basis of line contact. LDR is significantly affected by the error on tooth surface. The meshing stiffness increases with the increase in meshing force. The contact deformation accounts for a high proportion in the total deformation. It expands the existing modeling methods to cover line and point contact, and lays the foundation of studies for orthogonal spur-face gear drive.