Contact Stiffness Research Articles

Investigating the time- and space- dependent mechanical, physical and chemical properties of aged polyethylene gas pipes using nanoindentation tests

Macroscopic tensile tests are conventionally used to obtain mechanical properties of aged polyethylene (PE) gas pipes, but cannot characterize the inhomogeneous aging behavior of the specimens caused by diffusion-limited oxidation (DLO). Nanoindentation test procedures have, therefore, been adopted to obtain time- and space-dependent mechanical properties of small-sized PE pipe samples, especially, creep properties directly from two types of the PE pipes in accelerated aging and natural conditions. The results indicate that the energy-based method to calculate the initial contact stiffness is not only suitable for cementitious materials and rocks, but also for PE materials. The combination of nanoindentation creep test and generalized Kelvin model can extract detailed parameters that are more representative of the differences in material deformation. The change of crystallinity with aging times probably leading to the difference of mechanical properties was revealed by physical and chemical properties obtained by the DSC and FITR technique. In addition, the correlation between nanoindentation results and structural information also indicates crystallinity plays a dominant role on mechanical performances of the PE pipe. This method using nanoindentation can significantly promote the accuracy of mechanical properties characterization and possess well fitness for PE pipes in accelerated aging conditions or in-service.

Processing of Co-base/C-nanotubes compound coatings on D2 steel using plasma transferred by arc: Tribological and mechanical performance

In this study, compound coatings consisting of Co-based nanostructured filler metals (FM-Stellite 6) and carbon nanotubes (CNTs) were deposited on D2 steel using the plasma transferred by arc (PTA) technique. The coatings were prepared and analyzed in two steps. First, FM-Stellite 6 was mixed with 0.1 and 0.3 wt% CNTs at 120 °C for 72 h to prepare a Co-based xerogel using Pechini's method and then sintered at 1200 °C for 30 min. High-resolution transmission electron microscopy revealed the growth of bar-shaped solids on the surface of the nanostructured FM with 0.3 wt% CNTs (FM-3CNT) as well as Co particle growth inside the CNTs. In the second step, PTA was used to deposit the coating by replying with and without the FM-CNT. Raman spectroscopy indicated that Co3O4 spinel and MW-CNTs were formed on the compound coatings prepared using 0.1 and 0.3 wt% CNTs. A compound coating prepared from 0.3 wt% CNTs (COAT-3CNT) showed excellent tribological performance owing to its low volumetric wear (0.22 mm3) arising from the combination of self-lubrication and high elastic modulus (123.62 GPa) with a low dissipation energy (39.00 %), which contributed to the high contact stiffness (210 N/m). Likewise, the COAT-3CNT coating underwent a decrease in the secondary-dendrite-arm spacing (SDAS) of 6.81 μm owing to dendritic refinement as a result of the high solidification rate.

A Novel Three-Dimensional Fractal Model for the Normal Contact Stiffness of Mechanical Interface Based on Axisymmetric Cosinusoidal Asperity

A novel three-dimensional fractal model for normal contact stiffness is proposed in this paper. First of all, a hypothetical surface based on axisymmetric cosinusoidal asperity is established. Then, based on the hypothetical surface, the analytical expressions for the contact stiffness and contact load are derived by combining the three-dimensional fractal theory with the contact mechanics theory. In addition, the simulation results of the presented model and the Pan model are compared with the experimental results. The comparison results show that the maximum relative error of the Pan model is 29.58%, while the maximum relative error of the presented model is 4.35%. Ultimately, the influence of different fractal parameters on contact stiffness is discussed. Under the same contact load, the normal contact stiffness first increases and then decreases with the increase of the fractal dimension D, while the normal contact stiffness monotonically decreases with the increase of scale coefficient G. The results are explained from the perspective of the shape of the asperity. This study provides a novel model for the calculation of normal contact stiffness, which provides a model basis for the study of contact properties for the mechanical interface.

Analytical Model of Hydraulic Fracturing for Low Permeability Hot Dry Rock Reservoirs and DEM Simulation Base on Fluid-Solid Coupling

The formation of a rich underground-seam network is the key problem in the development of low-permeability hot dry rock (HDR) resources. Considering the lack of macroscopic continuum theory to study hydraulic fracturing having preset fracture-interface element, the particle-flow method of micro-mechanical discrete-element theory is introduced to simulate the mechanical behavior of hydraulic fracturing for HDR low permeability reservoirs. The reservoir is simulated as a round particle; the fracturing fluid movement is described by the seepage field equation, and rock movement is described by the displacement field equation. Finally, the particle-flow numerical model of hydraulic fracturing for HDR low permeability reservoirs is established under the condition of fluid-solid coupling: the model contains two parts (rock and fracture). Based on the parallel-bond model, a definition of micro-fractures of hydraulic fracturing is given. The relation between the fracturing effect and influence parameters is discussed. The results show that the fracture-initiation pressure is proportional to the magnitude of minimum horizontal stress, particle normal-contact stiffness, and particle normal- and tangential-connection strengths; the pressure is also independent of maximal horizontal stress and tangential contact stiffness. At the same time, the formation temperature of dry hot rock will reduce the strength of the rock, so particle-flow numerical models of hydraulic fracturing in different temperatures are discussed. Results show that fracture length and width show a trend of increase before decrease with the increase of injection pressure, an inverse relationship with minimums horizontal principal stress, and a positive relationship with HDR reservoir permeability.

A fault diagnosis method based on stiffness evaluation model for full ceramic ball bearings containing subsurface cracks

Most of the surface macroscopic faults of ceramic bearings are caused by the extended evolution of early subsurface cracks in mesoscopic and microscopic levels. Because of the greater contact stiffness and brittle failure mechanism of ceramic materials, the dynamic response becomes more sensitive, especially in the early failure stage with subsurface cracks. To evaluate the non-negligible effect for the cumulative expansion of subsurface cracks on the contact stiffness, this paper proposes a stiffness evaluation method based on the combination of theory and experiment. Combined with fracture mechanics, the quantified weakening effect of subsurface cracks on stiffness is substituted into the dynamics model to establish the stiffness evaluation model. Then the mapping relationship between the subsurface crack groups and the dynamic response is obtained. The results show that the different degrees of early subsurface crack failures in different directions have a significant effect on the magnitude of contact stiffness and the area of action. The model not only effectively evaluates the weakening effect on the contact stiffness of ceramic bearings when early subsurface failures occur, but also promotes the stiffness evaluation models of key components using ceramic materials.

Experimental analysis of Wellbore cement-steel bond mechanics and characterization

Portland cement is commonly used in everything from general construction to fluid barriers in environmental and petroleum structures. Wellbore integrity finite element models have shown that the bond strength between cement to steel is a weak point, but the failure mechanism is not well understood. Bond strength of cement to steel has been modeled using traction separation law which includes the bond strength, critical energy, and contact stiffness associated with the bond. However, experimental measurements only focus on the bond strength resulting in an incomplete analysis of the failure. A novel experimental methodology was developed to measure the tensile bond strength, critical energy, and contact stiffness of neat cement to steel bonds cured at atmospheric conditions for two days. Strain rates of 0.1 mm/min, 1.0 mm/min, and 10 mm/min were tested. The results showed that the 0.1 mm/min strain rate is too slow for bond testing since two of the bonding parameters experience relaxation during testing and result in low values. The 1.0 and 10 mm/min strain rates do not have statistical significance with respect to the bonding parameters. From the direct tensile tests of neat cement to steel, the bond strength is 0.61 MPa, the critical energy is 204.2 J/m2, and the contact stiffness is 1.00 E+09 N/m3.

Evaluating route to impact convergence of the harmonic balance method for piecewise-smooth systems

In this work, we investigate the applicability of the harmonic balance method (HBM) to predict periodic solutions of a single degree-of-freedom forced Duffing oscillator with freeplay nonlinearity. By studying the route to impact, which refers to a parametric study as the contact stiffness increases from soft to hard, the convergence behavior of the HBM can be understood in terms of the strength of the non-smooth forcing term. HBM results are compared to time-integration results to facilitate an evaluation of the accuracy of nonlinear periodic responses. An additional contribution of this study is to perform convergence and stability analysis specifically for isolas generated by the non-smooth nonlinearity. Residual error analysis is used to determine the approximate number of harmonics required to get results accurate to a given error tolerance. Hill’s method and Floquet theory are employed to compute the stability of periodic solutions and identify the types of bifurcations in the system.

A simulation method for dynamic force and vibrations of a roller bearing in the planetary gears considering the roller profile

The roller profile shape can change the fatigue life and vibrations for planet roller bearing (PRB), as well as the impact between the rollers and cage. In this study, an analytical study of the dynamic forces and vibrations of a PRB considering the roller profile. To avoid the stress concentration at the roller ends, the roller modification method is proposed to improve the dynamic forces. The contact stiffness and load-deformation exponent of the roller-race interaction for four different roller modification types are achieved. A PRB dynamic model is established to discuss the effects of roller modification types on the dynamic forces and vibrations for PRB. Computation results of those four roller modification types are compared to the results of the PRB with the cylindrical roller type. It includes that the roller profile shape can greatly change the contact forces between the rollers and races, as well as the impact forces between the rollers and cage. The roller profile shapes can also influence the vibrations of PRBs.

Forced Servoing of a Series Elastic Actuator Based on Link-Side Acceleration Measurement

Joint stiffness of an elastic-joint robot can be changed according to joint stiffness requirements. A series elastic actuator (SEA) can reduce the contact stiffness between the body and the environment or human, which can further ensure interactive operation in a human–machine-compatible environment. However, the introduction of the SEA improves the complexity of the robot dynamics model. In this paper, we propose a control schema based on link-side acceleration measurement to eliminate the overshoot and vibration in the transient process of force control. An extended Kalman filter (EKF) algorithm that fuses photoelectric encoders and accelerometers is first presented based on the link-side acceleration measurement. Following this, based on the external torque estimation, the vibration reduction control algorithm is designed. The simulation model is built, and the algorithm design and simulation of position control and force control are carried out and finally tested on the real robot platform. The effectiveness of the control algorithm is proved. The experimental results show that the dynamic response of the external force estimation is about 2 ms faster than that of the force sensor, and the error between the estimated external torque and the real external torque is within ±0.16 N·m.

Modelling and stability analysis of a high-speed train braking system

The stability of a braking system is crucial for the steady and safe operation of trains. To investigate the dynamic behaviors and stability of a train braking system as influenced by key parameters, a numerical model integrating mode-coupling, negative friction–velocity slope (NFVS), and stick–slip theories was established. Additionally, the wheelset connected with the braking system was contained in the model considering that mode-coupling and stick–slip characteristics were affected by system structures. Based on this model, the influence and mechanism of stiffness, damping, and NFVS characteristics on mode-coupling of the braking system were revealed. The results showed that when the tangential and normal contact stiffness values of the pad were close, the system experienced mode-coupling instability and vibrations in these two directions were coupled. When the tangential and normal damping values of the pad were unequal, the energy dissipation in the two directions became different and the system instability was enhanced. Additionally, the system complex eigenvalues always had positive real parts and the dynamic behaviors were more complicated by considering NFVS at relatively low speeds. This is because NFVS characteristics can be equivalent to negative damping values, which cause the difference in tangential and normal damping values and continuously input energy into the braking system, then weakening the system stability.

Variable-Coefficient Dynamic Modeling Method for a Ball Screw Feed System in the No-Extra-Load Running State

In a ball screw feed system of high-speed/high-acceleration machine tools, large frictional and inertial forces may change the real contact state of the kinematic joints, resulting in changes in the contact and transmission stiffnesses and, hence, changes in the dynamic characteristics of the system. In this study, a variable–coefficient dynamic modeling method for a ball screw feed system is proposed, considering the influence of changes in the no-extra-load running states, such as position, speed, and acceleration. Based on Timoshenko beam elements with two nodes and four DOFs, an equivalent dynamic model of a ball screw feed system is established using the hybrid element method. The expression for the equivalent axial stiffness of individual kinematic joints is derived, considering the influence of the feed speed/acceleration under the no-extra-load running state of the system. In addition, the stiffness and mass of the screw shafts on both sides of the screw nut are calculated, considering the influence of the system’s feed position. Hence, we obtain the total stiffness and mass of the system in the no-extra-load running state and analyze the natural frequency. Finally, we conduct validation experiments on a ball screw feed system of a large gantry-type machine tool with different no-extra-load running states.

Flexoelectricity at fractal rough surfaces

This study quantifies the role of surface roughness on interfacial flexoelectricity under normal compression and oscillation by examining a series of 3D-printed surfaces with diverse roughness features. For incipient contact, the measured flexoelectric charge is found to follow a power-law dependence on normal compression load, with the exponent positively correlated with the fractal dimension. The value of this power-law exponent is similar to that for contact stiffness. The underlying mechanism for this coincidence is elucidated by contact analyses based on geometric truncations of surface structures. Contact micromechanics show that the interfacial flexoelectric charge will increasingly concentrate on large microcontacts as the compression continues. A rougher surface with higher fractal dimension tends to demonstrate less heterogeneity for flexoelectric polarizations over microcontacts. This study provides systematic experimental measurements and comprehensive explanations for interfacial flexoelectricity and establishes quantitative links to multi-scale surface structures, shedding light on novel approaches for contact evaluation and flexoelectricity enhancement.

Study on the method for detecting contact state of bolted joint surface based on laser ultrasonic

The contact state of the bolt joint surface has an important influence on the contact stiffness, damping, and other properties of the equipment. To obtain the contact state of the bolt joint surface, the method to detect the contact state of the bolt joint surface based on laser ultrasonic technology is proposed in this paper. The reflectivity under different working conditions is obtained by the reflection amplitude of the longitudinal wave before and after bolt tightening. The relationship between reflectivity and bolt torque is studied. The results show methods proposed in this paper can effectively detect the contact state of the bolt joint surface, and it provides a basis for the study of the mechanical properties of the contact surface.

Slow dynamics in a single bead with mechanical conditioning and transient heating

The ultrasonically-measured contact stiffness of an aluminum bead confined between two slabs diminishes on mechanical conditioning, and then recovers like log(t) after the conditioning ceases. Here that structure is evaluated for its response to transient heating and cooling, with and without accompanying conditioning vibrations. It is found that, under heating or cooling alone, stiffness changes are mostly consistent with temperature dependent material moduli; there is little or no slow dynamics. Hybrid tests in which vibration conditioning is followed by heating or cooling lead to recoveries that begin like log(t) and then become more complex. On subtracting the known response to heating or cooling alone we discern the influence of higher or lower temperatures on slow dynamic recovery from vibrations. It is found that heating accelerates the initial log(t) recovery, but by an amount more than predicted by an Arrhenius model of thermally activated barrier penetrations. Transient cooling has no discernable effect, in contrast to the Arrhenius prediction that it inhibits recovery. [Supported by the DOE, DE-SC0021056].

Investigation of Lateral Stability of UHPC Beams Supported by Bearing Pads Considering the Nonlinear Lift-Off Effect

Ultrahigh-performance concrete (UHPC) is an advanced cement-based material with a compressive strength greater than 150 MPa. The application of UHPC on prestressed girders allows the design of very long spans with thin sections. However, the increased slenderness, low lateral flexural stiffness, flexible supports, and beam imperfections make lateral instability critical. Therefore, this paper presents an analytical prediction of precast beams’ behaviors considering the nonlinear contact interaction with the bearing pads. The nonlinear geometric theory for the slender element is coupled with the nonlinear contact mechanism developed between the beam and pad through the energy approach. The proposed solutions are compared with the equations available in the literature that consider the linear stiffness contact interaction. Changes in the limit load of up to 84% were a result of the lift-off effect (contact interaction). From the results, the UHPC is highly sensitive to lateral instability, giving a maximum load/dead weight ratio of up to 1.08 where the common technical recommendation is greater than four.

An Analytical Model for the Normal Contact Stiffness of Mechanical Joint Surfaces Based on Parabolic Cylindrical Asperities.

The analytical results of normal contact stiffness for mechanical joint surfaces are quite different from the experimental data. So, this paper proposes an analytical model based on parabolic cylindrical asperity that considers the micro-topography of machined surfaces and how they were made. First, the topography of a machined surface was considered. Then, the parabolic cylindrical asperity and Gaussian distribution were used to create a hypothetical surface that better matches the real topography. Second, based on the hypothetical surface, the relationship between indentation depth and contact force in the elastic, elastoplastic, and plastic deformation intervals of the asperity was recalculated, and the theoretical analytical model of normal contact stiffness was obtained. Finally, an experimental test platform was then constructed, and the numerical simulation results were compared with the experimental results. At the same time, the numerical simulation results of the proposed model, the J. A. Greenwood and J. B. P. Williamson (GW) model, the W. R. Chang, I. Etsion, and D. B. Bogy (CEB) model, and the L. Kogut and I. Etsion (KE) model were compared with the experimental results. The results show that when roughness is Sa 1.6 μm, the maximum relative errors are 2.56%, 157.9%, 134%, and 90.3%, respectively. When roughness is Sa 3.2 μm, the maximum relative errors are 2.92%, 152.4%, 108.4%, and 75.1%, respectively. When roughness is Sa 4.5 μm, the maximum relative errors are 2.89%, 158.07%, 68.4%, and 46.13%, respectively. When roughness is Sa 5.8 μm, the maximum relative errors are 2.89%, 201.57%, 110.26%, and 73.18%, respectively. The comparison results demonstrate that the suggested model is accurate. This new method for examining the contact characteristics of mechanical joint surfaces uses the proposed model in conjunction with a micro-topography examination of an actual machined surface.

Effects of nonlinear behaviour of linear ball guideway on chatter frequency of lathe machine tool

Linear ball guideways (LBGs) have several advantages for the precise positioning control of machine tools. However, the ball-groove contact behaviour leads to poor dynamic compliance, which induces a significant nonlinear behaviour of the guideway and a poor chatter stability. The nonlinearity complicates the chatter prediction due to the dependence of the contact stiffness. This approach aims to offer an industrially orientated method of estimation of chatter stability for structures based on LBG. Consequently, the present study first employs Hertzian contact theory to describe the ball-groove contact behaviour in the LBG of a lathe machine. Two static models are presented, both predict the LBG stiffness under different cutting loads. The first model describes is simplified, ignores the effects of the contact force on the deformation of the guideway components, even with that limitation depicts the main behaviour of the system. The second model is more precise and adopts a dynamic substructuring cosimulation method to incorporate the effects of structural deformation into the analysis. For both models, a linearisation approach is employed to analyse the dynamic behaviour of the system under static loading and define the dynamic compliance. The chatter frequencies of the LBG are estimated using the second model and are shown to be in good agreement with the experimental results. In general, the results of the analysis show that fundamental shifts in the frequency response of the LBG occur under specific values of the cutting force and gravity load. In other words, the results confirm that this method provides sufficient estimation of nonlinear behaviour of machine tool based on the LBG.

Theoretical Investigations on Tribological Properties of Air Foil Thrust Bearings during Start-Up Process

During the start-up process, air foil thrust bearings (AFTBs) come into contact and are prone to localized overheating and even failure. Frequent starts and stops are the major sources of wear. In this study, a transient mixed lubrication model considering the air rarefaction effect is established. In the model, asperity contact between the top foil of the air foil thrust bearing (AFTB) and the rotor surface is considered using a deterministic approach, and the deformation of the foil structure is considered using the elastic-aerodynamic coupling. The influences of bearing compliance, external load, acceleration time and contact stiffness on the tribological properties during the start-up process are investigated. The results show that the lift-off speed increases with the increase of the bearing compliance and of the external load. Specifically, the lift-off speed of AFTBs increases from 1950 rpm to 5325 rpm when the bearing compliance increases linearly from 0.2 to 1.0. When the external load increases from 10 N to 80 N, the lift-off speed is increased by approximately 30 times, from 450 rpm to 13,575 rpm. Furthermore, a decrease in the acceleration time of the rotor generates a decrease in the lift-off time and an increase in the contact stiffness of the bearing leads to a decrease in the lift-off speed of the bearing. By exploring the effects of the bearing parameters and working conditions on the tribological performance of AFTBs during start-up, the results presented in this study can provide theoretical support for improving start-up performance and designing high-reliability and long-life AFTBs.

Numerical and Experimental Investigation on Bending Behavior for High-Performance Fiber Yarns Considering Probability Distribution of Fiber Strength

The performance of fiber-reinforced composite materials is significantly influenced by the mechanical properties of the yarns. Predictive simulations of the mechanical response of yarns are, thus, necessary for fiber-reinforced composite materials. This paper developed a novel experiment equipment and approach to characterize the bending behavior of yarns, which was also analyzed by characterization parameters, bending load, bending stiffness, and realistic contact area. Inspired by the digital element approach, an improved modeling methodology with the probability distribution was employed to establish the geometry model of yarns and simulated bending behavior of yarns by defining the crimp strain of fibers in the yarn and the effective elastic modulus of yarns as random variables. The accuracy of the developed model was confirmed by the experimental approach. More bending behavior of yarns, including the twisted and plied yarns, was predicted by numerical simulation. Additionally, models revealed that twist level and number of plies affect yarn bending properties, which need to be adopted as sufficient conditions for the mechanical analysis of fiber-reinforced composite materials. This efficient experiment and modeling method is meaningful to be developed in further virtual weaving research.

Development of a Contact Force Model Suited for Spherical Contact Event

The stiffness coefficient suited for a spherical contact body is developed by means of a contact semi-angle based on Steuermann’s theory. The new static contact force model is close to the results of FEM when the index of the polynomial is equal to 2. The strain energy is derived according to the contact stiffness coefficient. Taylor expansion is used in the dissipated energy integration process to obtain a more accurate hysteresis damping factor. The new dynamic contact force model consists of the new stiffness coefficient and new hysteresis damping factor, which is suitable for the spherical-contact event with a high coefficient of restitution.