Contact Stiffness Research Articles

Experimental and Numerical Investigation of the Fracture Behavior of Extruded Wood-Plastic Composites under Bending.

The ability of wood-plastic composites (WPCs) to withstand various loads and resist plastic failure is attracting more and more interest due to the global increase in demand for WPCs by over 6 million tons per year. Among the most important and innovative research methods are those based on fracture mechanics-their results enable material designers to optimize the structures of these hybrid polymer composites at the nano, micro and macro levels, and they allow engineers to more accurately evaluate and select functional, sustainable, long-lasting and safe product designs. In this study, standard single-edge notched bending (SENB) tests were used to analyze the fracture toughness of two different extruded WPCs along the longitudinal (L) and transverse (T) directions of extrusion. In addition to their resistance to crack propagation, critical fracture criteria, initial contact stiffness, fracture parameters and fracture surfaces, the mechanical properties of these composites were also investigated. The results showed that WPC-A coded composites withstood higher loads until failure in both directions compared to WPC-B. Despite the larger data spread, both types of composites were more resistant to crack propagation in the T direction. Mode II of crack propagation was clearly visible, while mode III was not as pronounced. The experimental results and the numerical finite element (FE) model developed up to 58% of the maximum load correlated well, and the obtained deformation curves were best approximated using cubic equations (R2 > 0.99). The shear stress zone and its location, as well as the distribution of the equivalent stresses, had a major influence on crack propagation in the fracture process zone (FZP).

A lubrication contact stiffness model considering asperity interactions

In practical engineering applications, most connection interfaces require lubrication. The contact stiffness of the lubrication interface can affect the static and dynamic characteristics of the interface, thus affecting the performance of the mechanical system, such as vibration, fatigue, and wear characteristics. Therefore, the measurement of lubrication contact stiffness is very important for the analysis and optimization of mechanical system performance. However, measuring the stiffness of the lubrication interface is a significant challenge. In this paper, a mixed lubrication contact stiffness model considering asperity interactions is proposed, which assumes the lubrication rough interface as an equivalent thin layer. The proposed model was compared with the lubrication contact model that does not consider the asperity interactions. Based on the microscopic contact behavior of the contact interface, the relationship between the mechanical parameters of the virtual thin layer and the contact pressure was analyzed. Finally, the predicted results of interface stiffness are verified by published theoretical and experimental results. The results show that the proposed model can more reasonably describe the actual contact behavior of the rough lubrication interface and give the variation law of the mechanical parameters of the virtual thin layer.

Normal Contact Model of Fractal Surfaces Considering Friction and Asperity Interactions

Friction as well as asperity interactions have significant influence on the contact area and force of rough surfaces. In this work, a single-asperity, elastoplastic contact model, considering friction, is established by means of continuum mechanics and power-exponential functions. Then, the deformation of the asperity interactions is modeled by the displacement of the average line for asperity height. Using fractal theory, the actual deformation and contact stiffness of an asperity are derived, which take the friction and asperity interactions into account. Furthermore, the actual contact area and normal stiffness models for fractal surfaces are developed, accounting for friction and asperity interactions. The accuracy of the developed models is confirmed by using published experimental results. The developed models are closer to experimental results than the reported fractal contact models. Finally, the effects of the friction coefficient and surface morphology parameters on contact characteristics are discussed.

New deterministic model for calculating mesh stiffness and damping of rough-surface gears considering elastic–plastic contact and energy-dissipation mechanism

For a long time, meshing parameter calculations and dynamic modeling of gear systems have assumed smooth tooth surfaces, disregarding the impact of actual three-dimensional (3D) microscopic topography. Based on elastic–plastic contact and energy-dissipation mechanisms, this work developed a comprehensive deterministic model that integrates 3D rough surface modeling, reconstruction, and contact analysis, for calculating the time-varying mesh stiffness (TVMS) and mesh damping (TVMD) of deterministic rough-surface gears. Distinct from fractal and statistical models, the deterministic model analyzes deterministic, real 3D rough surfaces rather than simple surfaces defined by a few parameters. Utilizing stochastic process theory, different-topography surfaces are obtained using height and spatial features and reconstructed employing watershed algorithm and ellipsoidal asperity fitting. Subsequently, a deterministic elastic–plastic contact model based on equivalent rough curved-surface contact is constructed, emphasizing local contact states and energy dissipation for calculating contact stiffness (CS) and damping (CD) of gears. Accordingly, a meshing characteristics analysis model is established for calculating TVMS, TVMD, and load sharing ratio (LSR). Experimental validation and comparisons with several statistical and gear contact models demonstrate the effectiveness, reliability, and superiority of the proposed deterministic model. Multi-parameter impact analysis reveals small Sq (meaning low roughness Sa) and Ssk and high load correlate with increased CS and TVMS, while CD and TVMD depend on their interaction and hardness. Overall, by bridging the micro-surface topography and macro-meshing parameters, our model provides essential insights for the design and manufacturing of high-performance gear to reduce vibration and noise.

Effective characterization for the dynamic indentation and plastic parameters acquisition of metals

As a fundamental test technique for the mechanical properties of materials, indentation shows broad application prospects. Compared to the well-studied quasi-static indentation, relatively few and incomplete studies on the dynamic indentation test and characterization have been performed. In this work, a dynamic indentation test technique based on the split Hopkinson pressure bar system is developed, and the corresponding “three-wave method” is proposed to effectively acquire the time-resolved dynamic indentation load and depth. Systematic indentation tests under different loading rates and indenter cone angles are conducted on typical metal materials such as Cu, α-Fe, and α-Ti. Based on the dynamic indentation contact stiffness analysis and indentation theory the indentation hardness under different loading conditions are determined. A procedure for plastic parameter inversion of metal materials, including strain hardening and strain rate strengthening terms based on dynamic indentation, is provided. The effectiveness is verified by the traditional compression test results, providing a new method for characterizing the dynamic mechanical properties of metal materials.

Lateral force controlled impact tribometer characterizing transient friction: Effect of contact pressure

A new Lateral Force Impact Tribometer (LFIT) is designed to quantify the dynamic friction of synthetic seat belt and D Ring Polymer (DRP) under transient conditions during the initial sliding period. LFIT simulates the sliding between two bodies subjected to a sudden lateral force applied, resulting in relative motion. Transient friction under suddenly applied initial acceleration conditions is obtained from the displacement response. LFIT overcomes stiffness concerns of most displacement-controlled tribometers in which the sensors and actuators influence the contact stiffness, nature of asperity interaction, and frictional characteristics. The displacement vs. time response showed the variation in displacement during the initial 0.3 mm sliding distance. LFIT is modelled as a spring-mass-Coulomb damper system applied for transient analysis. The effect of contact pressure on the transient Coefficient of Friction (CoF) is studied in the present work. This paper perhaps presents the first report that enables the capture of the friction transition within 10 ms from the start of sliding.

A stiffness model for EHL contact on smooth/rough surfaces and its application in mesh stiffness calculation of the planetary gear set

A method for calculating time-varying mesh stiffness (TVMS) is proposed by developing a stiffness model for elastohydrodynamic lubrication (EHL) contact and integrating it into three-dimensional loaded tooth contact analysis (3D-LTCA). To enhance the accuracy and efficiency of the calculation, three projects have been implemented: Firstly, the contact deformation is modified, and the average slope is employed for calculating contact stiffness. Secondly, the lubricant film and EHL contact deformation are introduced into the deformation compatibility equations. Finally, the polynomial chaos expansion (PCE) surrogate model is employed to enhance computational efficiency. The proposed method is used to calculate TVMS of the planetary gear set, and the influence of speed, torque, and rough surface are analyzed. The results show that the previous method underestimating the TVMS of planet-ring gear pair in double-teeth meshing area under fluid lubrication, while the proposed method effectively addresses the issue. The different effects of the torque and speed on TVMS under mixed and fluid lubrication also have been revealed, emphasizing the significance of surface topography in gear meshing characteristics.

Investigations on the modal vibration caused by bolted joint interface contact in the rotor-AMBs systems: Modelling and experimentation

Rotor-active magnetic bearings (rotor-AMBs) systems nowadays have been widely used in fluid machinery and the impeller and the shaft are commonly connected by bolted joint. However, when a certain pre-tightening force is applied to the bolted joint and the interface contact between the shaft and the impeller is formed, causing flexible modal vibrations when rotor is levitated. The mechanism of this modal vibration needs to be revealed to ensure stable operation of the machine. In traditional modelling, the effect of the interface contact is equated to an additional stiffness matrix by massless spring units, whose certain contact stiffness is uniformly distributed over the interface. Particularly, the calculation of contact stiffness and the effect of AMBs are neglected, resulting in the inaccurate response compared to experiments. Based on traditional modelling, we consider that there is partial separation in the contact interface due to the AMBs supporting and a novel additional stiffness matrix related to contact status is proposed by calculating the real-time contact area. The contact stiffness is calculated by microscopic contact model based on fractal theory and surface topography measurement. Finally, numerical simulation shows that the interface contact influences the system robustness and the unstable mode is excited. The increase of pre-tightening torque and contact radius both will increase the steady vibration amplitude, with the former being the major contributor. Moreover, the influence and order of the vibration are quantitatively validated by the experiments.

Influence of soundboard modelling approaches on piano string vibration.

This work explores the influence of the dynamics of the piano soundboard on string vibration and on the force acting between the vibrating string and the bridge. Four different soundboard representations of different complexities are considered: (i) a finite element model that considers the complete dynamic behavior of the soundboard at the connection point with the string within the frequency range of interest, (ii) a reduced modal model containing only five modes, (iii) a Kelvin-Voigt system characterized by an equivalent stiffness and damping, and (iv) a rigid soundboard represented by a simply supported boundary condition. The connection between the string and the soundboard is modelled by coupling a simply supported stiff string model with the different representations of the soundboard through a contact stiffness. As well as directly accounting for the string-soundboard coupling, this approach also includes the duplex scaling segment. The latter can be left to vibrate freely or muted with a continuous distribution of dampers. Although the simplest soundboard representation is not dissimilar from the other more complex models, the dynamics of the soundboard affect the decay time of the note, the force transmitted to it, and the vibration of the radiating surface of the soundboard.

Progressive damage analysis of embedment of metal washer into timber

ABSTRACT Metal washers are widely used in joints of timber structures. Thick washers embed fully into timber, whereas thin washers partially embed into timber due to their bending deformation. For thick washers, physical models have been proposed to estimate the stiffness and strength of timber. However, for thin washers, these estimation methods are insufficient. The objective of this study is to propose a finite-element analysis (FEA)-based approach to predict the stiffness and strength of wood during washer embedding, as well as forecast plasticity and damage behaviours of timber, regardless of the washer size. The FEA used a constitutive model with plastic and damage criteria for timber. In the FEA, an explicit dynamic solution method was used to prevent solution divergence. The FEA reproduced the embedment load–displacement relation and damage behaviours of three species. In addition, the FEA predicted the initial stiffness, second stiffness, and yield load with error margins of 12%, 16%, and 7%, respectively. The influences of the loading speed and mesh fineness on the FEA were investigated numerically to validate the results. In addition, parametric studies on contact stiffness and damage constants were conducted to understand the influences of material constants on the embedment behaviours of FE models.

К РАСЧЕТУ ПЛИТНЫХ АЭРОДРОМНЫХ ПОКРЫТИЙ ПРИ ИХ ВЗАИМОДЕЙСТВИИ С ИНЕРЦИОННОЙ НАГРУЗКОЙ ПРИ ДВИЖЕНИИ В РЕЖИМЕ ТОРМОЖЕНИЯ.

The method of calculating plates under the action of inertial loads during their movement with variable velocity is considered. The problem of the interaction of the airfield surface with the aircraft load is solved, at the moment of its movement, in braking mode, when landing on the surface in the form of an extended rectangular freely operable plate lying on an elastic base. When taking into account the nonlinear contacts of the chassis wheels with the plate, piecewise linear characteristics of contact stiffness are used. The vertical dynamics of the spatial model of the aircraft during the run is modeled by a system of rigid bodies with elastic-viscous bonds. To construct the methodology, the methods proposed earlier by the author of the article are used: a step-by-step method for solving problems of the relentless dynamics of structures and a method for calculating structures for the action of inertial and mobile force loads (the method of nodal accelerations).

Analysis of friction-induced vibration and wear characteristics during high-speed train friction braking process

This study explored the evolution of friction-induced vibration (FIV) and wear in high-speed train friction braking through experiments, theoretical analysis, and numerical simulation. Experimental tests revealed that vibration behavior transitions from high-frequency modes at high speeds to low-frequency stick-slip at lower speeds. Theoretical analysis indicated that brake disc speed, coefficient of friction (COF), and contact stiffness affect system stability. Specifically, the system experiences high-frequency vibrations at high speeds due to mode coupling, and the friction block surface primarily undergoes abrasive wear mechanisms. At lower speeds, the system demonstrates low-frequency stick-slip vibrations induced by the combined effects of mode coupling and negative friction velocity slope (NFVS) characteristics, and the friction block surface mainly experiences adhesive wear mechanisms.

Contact stiffness of the multi-indenter contact interface

Mechanical contact plays a pivotal role in both industrial and daily life applications. Contact stiffness of a multi-indenter contact interface fundamentally determines force–deformation relations. However, the understanding of the overall contact stiffness from the historical perspective is limited owing to inherent difficulties in precisely characterizing the interaction in multi-indenter contacts. In this study, the mechanical strong interaction among indenters is pinpointed. A theoretical model for accurately determining the contact stiffness of multi-indenter contact interface is developed. The physical mechanism of the contact stiffness of multi-indenter contact interface is revealed. The theoretical model is solidly validated by experiment and simulation. More importantly, the present theoretical model can predict the contact stiffness of contact interfaces with complex and irregular configurations, which may be filled up with indenters of hierarchical structures. The critical load is determined to guarantee the finished product rate during transfer printing. This is experimentally evidenced by the transfer printing of silicon wafers with complexly customized patterns. The present study provides a profound guidance for various engineering applications such as fabrication and integration of micro- and nano-electronic chips as well as electronic devices.

Modeling and contact analysis for spur gear pair with modification and localized crack failure

The modified teeth are deliberately manufactured to mitigate the stress concentration generated by offset components, which makes equipment more susceptible to localized failures. Therefore, this paper presents a model aimed at investigating the meshing characteristic of gear pair with modification and crack failure. In this model, the tooth deformation and force transmission are determined based on slice coupling theory. The torsional deformation of teeth produced by eccentric load distribution is considered and complemented to the calculation method. Finally, the approach is proven through the experimental tests and FE model. The result shows that when the equipment is operated in misalignment condition, eccentric load distribution, and stress concentration at tooth edge are generated, the meshing stiffness will be reduced drastically, which can be suppressed by appropriate modification, and the rapid decline of meshing stiffness is weakened by increasing the effective contact length. Although the contact stiffness would be further reduced by the crack failure and the tooth surface deformation is increased, it seems to alleviate the stress concentration and eccentric load effectively.

Synergizing Structural Stiffness Regulation with Compliance Contact Stiffness: Bioinspired Soft Stimuli‐Responsive Materials Design for Soft Machines

Stiffness regulation strategies endow soft machines with stronger functionality to cope with diverse application requirements, for example manipulating heavy items by improving structural stiffness. However, most programmable stiffness strategies usually struggle to preserve the inherent compliant interaction capabilities following an enhancement in structural stiffness. In this study, inspired by the musculocutaneous system, we propose a soft stimuli‐responsive material (SRM) by combining shape memory alloy into compliant materials. By characterizing the mechanical performance, the flexural modulus increases from 6.6 to 142.4 MPa under the action of active stimuli, crossing two orders of magnitude, while Young's modulus stays at 2.2 MPa during programming structural stiffness. This comparative result indicates that our SRMs can keep a lower contact stiffness for compliant interaction although structural stiffness increases. Then, we develop three diverse soft machines to show the application potential of this smart material, such as robotic grippers, wearable devices, and deployable mechanisms. By applying our materials, these machines possess stronger load‐bearing capabilities. Meanwhile, these demonstrations also illustrate the efficacy of this paradigm in regulating the structural stiffness of soft machines while maintaining their compliant interaction capabilities.

A simplified spherical roller bearing model and its application in the wind turbine main bearing system finite element modeling

Different from most bearing design guidelines, deformation of bearing rings and supporting structures usually influences the bearing performance significantly. Finite element analysis (FEA) can be used in bearing system design considering the structure deformation, but the contact region between rolling elements and raceways modeling is very complex and usually causes non-convergent problems. As to a spherical roller bearing (SRB), the model must also consider both its misalignment ability and roller contact stiffness. This paper presents a simplified SRB model considering the angular misalignment ability. In order to define the SRB roller raceway load deformation relationship, a lamina model is developed. And this simplified model is validated by solid roller model of a bearing sector. A wind turbine main bearing system is analyzed using the developed SRB model. Load distribution considering the system deformation and angular misalignment are discussed. With the help of fine meshed solid elements roller raceway contact model, the raceway contact pressure and subsurface stress distribution can also be obtained.

Modal characteristics of blade-disk including rough interfaces and geometric deviations

The inaccurate prediction of vibrations in blade-disk structures leads to frequent occurrences of failures in rotating machinery, such as air-engines. Existing methods often empirically treat the contact parameters of interfaces as globally constant and rarely consider manufacturing and assembly deviations, resulting in a deviation of prediction models from reality. This work presents a model for complex assembly structures that includes non-uniform distributions of normal contact stiffness and tangential friction coefficients at rough interfaces, while also introducing experimentally measured geometric deviations to enhance alignment with real-world conditions. Taking fir-tree blade-disk structure as an example, the accuracy of the proposed method is comprehensively verified by four measurement experiments and one modal experiment. Subsequently, the combined influence of rough interfaces and three experimentally measured geometric deviations on the overall modal characteristics of blade-disk structure are investigated, and their influencing mechanisms are revealed. The results indicate that ignoring the interface roughness and geometric deviations may significantly affect the prediction accuracy of the modal characteristics. The proposed method has great potential in the field of predicting the modal characteristics for complex assembly structures and optimizing the design of their machining and assembly processes.

Spherical Indentation and Implementation of S3/P for yield stress determination of brittle materials

A mathematically transparent and robust experimental method has been developed to estimate the yield stress of brittle materials through the analysis of depth-sensing spherical indentation. Employing Hertzian contact mechanics, an elastically invariant ratio based on the simple equation S3/P=6REr2, (where S and P are contact stiffness and indentation load, respectively) has been derived that enables more accurate and confident determination of the transition from elastic to inelastic deformation; a transition that the yield stress dictates and represents. Using two diamond spheres with radii of 3.2 and 8.6 μm, the indentation test method and analyses are applied to two vitreous silicates: Corning's HPFS 7980® fused silica and Vitro's Starphire® soda-lime silicate. The estimated yield strengths are 8.15 GPa ± 2.5 % for the fused silica and 6.1 GPa ± 3.3 % for the soda-lime silicate, and both were independent of indenter radius. Verification of this new experimental method is demonstrated with an as-drawn titanium by showing equivalence of measured yield stress by its spherical indentation and that from uniaxial compression testing. This method will enable easier and more confident estimation of yield stress in brittle materials - a property that historically has been elusive to measure for these materials using common laboratory mechanical test methods.

Nonlinear vibration characteristics of an aeroengine cantilever flexible rotor considering interference fit and unbalance

Aeroengine power turbine rotor is a typical nonlinear rotor system, in which the interference connection between long shaft and short shaft has a prominent influence on the coupling vibration of the system, especially at high speed, the nonlinear stiffness change of interference contact is more obvious. Therefore, the paper considers the change of the contact characteristics of the long shaft and the short shaft of the turbine rotor, and the nonlinear restoring force of the bearing to analyze the dynamic characteristics of the rotor. Firstly, according to the theory of elasticity, the contact parameters under different speed states are calculated, the contact stiffness model under interference fit is established, and the relationship between contact stiffness and speed is analyzed. Secondly, according to the Hertz contact theory, a bearing nonlinear restoring force model considering time-varying characteristics is established. Finally, the dynamic model of the bearing-flexible rotor coupling considering interference contact is established. The influence of contact parameters and unbalance parameters on the nonlinear vibration characteristics of the rotor is analyzed by amplitude-frequency curve, bifurcation diagram, time-domain waveform, spectrum diagram, trajectory diagram and Poincaré diagram. In addition, the simulation results are compared with the experiment results of the rotor test rig to verify the accuracy of the established dynamic model. By analyzing the influence of different parameters such as interference magnitude, unbalance position, unbalance magnitude and unbalance couple on the nonlinear vibration of the rotor, the basis for the design and vibration control of the cantilever turbine rotor is provided.

Research on the Impact of Non-Uniform and Frequency-Dependent Normal Contact Stiffness on the Vibrational Response of Plate Structures

Mechanical interfaces are prevalent in industries like aerospace and maritime, where the normal contact stiffness on these surfaces is a crucial component of the overall stiffness of mechanical structures. From the perspective of structural mechanics, normal contact stiffness significantly affects the dynamic response of mechanical structures and must be considered in mechanical design and simulation analysis. Essentially, the mechanical interface represents a typical type of nonlinear contact, characterized by both its non-uniform distribution and its frequency-dependent properties under external excitations. A plate structure was designed to study the distribution and frequency-dependent characteristics of normal contact stiffness on the mechanical interface. Experiments validated that the normal contact stiffness not only significantly increases the fundamental frequency of the plate but also alters its mode shapes. To replicate the experimental results in simulations, the BUSH elements were used to model the normal contact stiffness within the plate structure, arranging it non-uniformly and setting it to vary with frequency according to the plate’s mode shapes and frequency response. This method accurately replicated the plate’s mode shapes and response curves within the 0–1000 Hz range in simulations.