Contact Stiffness Research Articles

Synthesis and Evaluation of Engineering Properties of Polymer-Coated Glass Beads.

Modern construction projects are often challenging, which has increased the demand for innovative materials that ensure improved safety, durability, and functionality. To explore the potential of enhancing soil material functionality, this study synthesized polyurethane on the surface of glass beads and evaluated their mechanical properties. The synthesis of polymer proceeded according to a predetermined procedure, where the polymerization was confirmed through analysis of chemical structure by Fourier transform infrared spectroscopy (FT-IR) and microstructure observation by a scanning electron microscope (SEM) after complete synthesis. The constrained modulus (M) and the maximum shear modulus (Gmax) of mixtures with synthesized materials were examined by using an oedometer cell equipped with bender elements under a zero lateral strain condition. Both M and Gmax decreased with an increase in the contents of polymerized particles due to a decrease in the number of interparticle contacts and contact stiffness induced by the surface modification. The adhesion property of the polymer induced a stress-dependent change in M but was observed to have little effect on Gmax. Compared to the behavior of the rubber-sand mixtures, polymerized particles show the advantage of a smaller reduction of M.

The effect of contact compliance of sliding pair on friction force reduction at longitudinal tangential vibrations

The main purpose of this work was to experimentally test the impact of modification to the tangential contact stiffness of the friction pair, caused by changing the kind of material, roughness of the contact surfaces and surface pressures, on the level of friction force reduction in the sliding motion, under the influence of high-frequency longitudinal tangential vibrations introduced into the contact area. The tests were carried out on an original test stand for three kinds of friction pair materials, such as: steel C45, cast iron GGG40 and polytetrafluoroethylene PTFE – Teflon, working in homogeneous connections: steel – steel, cast iron – cast iron and Teflon – Teflon and in mixed connections: steel – Teflon, steel – cast iron and cast iron – Teflon. For each friction pair, at defined values of normal pressures, the compliance characteristics of the contact in the tangential direction were determined. On their basis, as a function of normal pressures, values of the tangential contact stiffness coefficient were calculated. Then, also as a function of normal pressures, experimental tests were carried out on changes in the friction force in sliding motion occurring in the contact under the influence of longitudinal tangential vibrations. The tests were carried out for different speeds of the drive, with fixed vibration parameters, such as amplitude and frequency. On the basis of obtained results of the dependence of contact compliance on the kind of material of the friction pair, contact surface roughness and surface pressures, as well as on the dependence of friction force changes under the influence of tangential vibrations on the same factors, the relationship between the level of friction force reduction under the influence of these vibrations and contact compliance was examined.

Multiscale characterization and contact performance analysis of machining surfaces

Accurately characterizing the surface topography of parts is crucial to improve the surface measurement accuracy and analyze the surface contact performance. A method is proposed to separate the morphological characteristics of the actual machined surface based on the layer-by-layer error reconstruction method and the signal-to-noise ratio method during the wavelet transform process, so as to evaluate the contact performance of the different joint surfaces. First, the actual machined surface morphological features are separated by using the wavelet transform method, the layer-by-layer error reconstruction method, and the signal-to-noise ratio method. Second, the reconstructed three-dimensional surface contact model is established by the reverse modeling engineering method. Third, the finite element method is used to analyze the impact of processing methods and surface roughness on contact surface parameters. The result demonstrates that the simplified and efficient three-dimensional reconstructed surface is achieved based on the real machining surface in contrast to other existing approaches. The surface roughness has a more significant influence on contact performance. The contact deformation increases with the increase of surface roughness, while the curves of average contact stress, contact stiffness, and contact area have the opposite trend.

Load-induced local phase transformation and modulus of shape memory alloys under spherical indentation by finite element method

Shape memory alloys are a unique class of materials that are capable of large reversible deformations under external stimuli such as stress or temperature. The present study examines the phase transformations and mechanical responses of NiTi and NiTiHf shape memory alloys under the loading of a spherical indenter by using a finite element model. It is found that the indentation unloading curves exhibit distinct changes in slopes due to the reversible phase transformations in the SMAs. The normalized contact stiffness (F/S2) of the SMAs varies with the indentation load (depth) as opposed to being constant for conventional single-phase materials. The load-induced phase transformation that occurred under the spherical indenter was simulated numerically. It is observed that the phase transformation phenomenon in the SMA induced by an indentation load is distinctly different from that induced by a uniaxial load. A pointed indenter produces a localized deformation, resulting in a stress (load) gradient in the specimen. As a result, the transformation of phases in SMAs induced by an indenter can only be partially completed. The overall modulus of the SMAs varies continuously with the indentation load (depth) as the average volumetric fraction of the martensite phase varies. For NiTi (Ea > Em), the modulus decreases with the depth, while for NiTiHf (Ea < Em), the modulus increases with the depth. The predicted young modules during indentation modeling agree well with experimental results. Finally, the phase transformation of the SMAs under the indenter is not affected by the post-yield behavior of the materials.

On Boussinesq's Problem for a Power-Law Graded Elastic Half-Space on Elliptical and General Contact Domains.

The indentation of a power-law graded elastic half-space by a rigid counter body is considered in the framework of linear elasticity. Poisson's ratio is assumed to be constant over the half-space. For indenters with an ellipsoidal power-law shape, an exact contact solution is derived, based on the generalizations of Galin's theorem and Barber's extremal principle for the inhomogeneous half-space. As a special case, the elliptical Hertzian contact is revisited. Generally, elastic grading with a positive grading exponent reduces the contact eccentricity. Fabrikant's approximation for the pressure distribution under a flat punch of arbitrary planform is generalized for power-law graded elastic media and compared with rigorous numerical calculations based on the boundary element method (BEM). Very good agreement between the analytical asymptotic solution and the numerical simulation is obtained for the contact stiffness and the contact pressure distribution. A recently published approximate analytic solution for the indentation of a homogeneous half-space by a counter body, whose shape slightly deviates from axial symmetry but is otherwise arbitrary, is generalized for the power-law graded half-space. The approximate procedure for the elliptical Hertzian contact exhibits the same asymptotic behavior as the exact solution. The approximate analytic solution for the indentation by a pyramid with square planform is in very good agreement with a BEM-based numerical solution of the same problem.

Inner-paddled atomic force microscopy cantilever for rapid mechanical mapping

Mechanical characterization methods at the nanoscale are of critical importance for many fields including nanomaterials, micro/nano devices and nanomechanics. As a key tool in nanotechnology, atomic force microscopy (AFM) is widely used due to its high-resolution topography imaging capabilities, and is also recognized as a useful platform for nanoscale mechanical characterization. Contact-resonance AFM, which modulates the tip-sample contact with ultrasonic frequencies and then analyzes the cantilever’s resonance responses, is an important AFM method for viscoelastic characterization. However, contact-resonance AFM requires the cantilever’s contact-resonance frequency and quality factor values to quantify the elastic modulus and loss tangent of the sample. This requires time-consuming frequency sweep, which makes a quantitative scanning impractical, therefore only single-point quantitative measurement and qualitative single-frequency scanning are usually applied. To address this issue, here we present an AFM cantilever design with an integrated inner-paddle substructure, which provides an eigenmode whose resonance keeps consistent, but whose resonance amplitude varies with varying contact stiffness. With this probe, it is hoped to quantify the elastic properties of the sample with fast single-frequency amplitude imaging.

Nonlinear excitation and mesh characteristics model for spiral bevel gears

Accurate and rapid calculation of nonlinear excitation (NE) and loaded mesh characteristics (LMC) of gear pairs is a key to achieving rapid iterative optimization of gear system designs. Therefore, an analytical model (AM) was proposed for the accurate and numerically efficient calculation of NE and LMC for application to spiral bevel gears (SBG). First, a tooth contact analysis of an SBG was completed using Coons surface technology and mesh theory to determine the contact path and unloaded transmission error (UTE). Thus, an AM for the principal and relative normal curvatures of the SBG was derived using the Euler's formula. Based on the traditional calculation method for a Hertz contact ellipse, the relation between the relative curvatures was introduced to derive the formulas for the major and minor axes using the Muller's method, which could improve the programmability and avoid numerical instability of the program. Then, analytical models for the contact ellipse and pressure distribution on the contact tooth surfaces were derived using the Hertz model and geometric theory. Subsequently, based on a single tooth LMC, infinitesimal method, elasticity, and series stiffness model, a single mesh stiffness (SMS) model for SBGs was developed, which incorporates transverse tooth stiffness, transverse gear foundation stiffness, axial tooth stiffness, axial gear foundation stiffness, and Hertz nonlinear contact stiffness. Based on the SMS and UTE, compliance and load matrices were established, and the time-varying mesh stiffness, loaded transmission error, mesh force, and multi-tooth LMC models of the SBG were determined. Finally, the proposed method was validated against nonlinear FE simulations using examples. Compared to FE simulations, the proposed method requires significantly less computational effort and can be further extended to optimization or system analysis problems.

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.

Dynamic characteristics of a spur gear pair under the coupled effects of angular misalignment fault and tooth modification

Angular misalignment is a common fault in gearbox manufacturing and installation, which directly affects the meshing characteristics of the gear pair. Tooth axial modification is considered to be a useful way to suppress angular misalignment. However, accurate determination of contact characteristics, e.g., contact stiffness and friction, caused by the coupled effects of angular misalignment and tooth modification is difficult. To settle this problem, this article put forward a method on the strength of the slice coupling and nonlinear Hertzian contact calculation. With the proposed model, the meshing errors caused by angular misalignment and tooth axial modification are derived. Then the influence of nonlinear Hertzian contact and friction on time-varying mesh stiffness (TVMS) is considered in each sliced tooth. In addition, an iterative computation method is proposed to calculate the proposed analytical model. Further, a dynamic model is developed to study the influences of angular misalignment and tooth axial modification on gear dynamic characteristics. Finally, the analytic model is validated by an experimental setup for a spur gear pair with ideal installation, misalignment and tooth axial modification. Results show that the proposed model is effective and efficient for predicting the dynamic response of the spur gear pair under the coupled effects of angular misalignment and tooth modification.

Nano to macro-mechanical properties of laser directed energy deposited CoCrNi medium entropy alloy

The CoCrNi Medium Entropy Alloy is a popular subset of the Cantor alloy due to its superior cryogenic and elevated temperature properties. This study reports the successful deployment of a laser-based near-net shaping technique known as laser directed energy deposition (LDED) to fabricate the CoCrNi MEA. The effect of laser power and scan speed on track geometry is studied in detail. The bulk deposition is performed using a parametric combination yielding regular defect-free tracks with an aspect ratio greater than five and a maximum deposition rate. The EBSD analysis revealed a strong < 001 > cubic texture along the build direction, due to the thermal gradient in that direction. Across both the scan and build directions, the cellular and columnar substructure is observed. Solid solution strengthening and dislocation strengthening contribute 39 % and 42 % to yield strength. The nanoindentation analysis revealed hardness, reduced modulus, and elastic modulus of 6.32 ± 0.32 GPa, 222.08 ± 5.72 GPa, and 250.62 ± 8.25 GPa, respectively. The contact stiffness, reduced modulus, and hardness showed a positive linear relationship with strain rate. The strain rate sensitivity of MEA is in the range of 0.030–0.042, which is higher than that of conventional fcc metals. It is attributed to the higher lattice frictional stresses and different atomic-level structures of MEA than conventional fcc metals. Furthermore, chemical short-range ordering and a stronger peierls barrier resulted in a lower activation volume of the order of ∼100b3. The present study provides a detailed understanding of the effect of process parameters on melt-pool geometry, microstructure evolution, as well as the influence of strain rate on nanomechanical properties.

Parameter identification of contact model for tank saddle ring system based on genetic algorithm and BP neural network

This paper is devoted to present an experimental identification method of tank saddle ring system parameters based on BP neural network algorithm and genetic algorithm. The contact parameters in mechanical system cannot be obtained directly through measurement, and it is inevitable that there will be errors between the parameters estimated by engineering experience and the real value. In this paper, a 6-degree-of-freedom swing experimental device of tank turret is built, the excitation source is 1Hz sine function, the contact stiffness and contact damping coefficient are identified by constructing error functions based on simulation results and data of four laser displacement sensors distributed around the saddle ring, by the combination of BP neural network and genetic algorithm. Then, the sensor data in the test results and simulation results are compared to further verify the accuracy of the turret model and parameter identification method.

Skidding characteristics of urban rail vehicle axle-box bearings considering surface waviness on races

As one of the core transmission components, axle-box bearings have been widely applied in urban rail vehicles and played a crucial role in their safe and stable operation. No matter in the starting and stopping stage or stable operation stage of the vehicle, the skidding phenomenon in axle-box bearings exists and impacts their own dynamic characteristics. Furthermore, as one of the main shape errors of the bearing surface, waviness may cause fluctuations for skidding characteristics of axle-box bearings. This study investigates the skidding dynamic analysis of axle-box bearings, taking into account race surface waviness. Firstly, a dynamics model for double-row cylindrical roller bearings is established, considering the cage flexibility and friction forces between different components. Then, this model is coupled with a three-dimension vehicle–track model, allowing for more precise dynamic simulation of axle-box bearings under actual running conditions. Furthermore, an excitation related to race surface waviness is added to the coupling model through time-varying displacement and contact stiffness. At last, the influence of race surface waviness on skidding characteristics of axle-box bearings is analyzed. The effectiveness of the proposed model is validated through theoretical analysis and field tests. Simulation results demonstrate that race surface waviness can impact the cage and roller slip ratio of axle-box bearings. Overall, this study provides valuable insights into the skidding dynamic analysis of axle-box bearings, highlighting the importance of considering race surface waviness in designing and maintaining axle-box bearings.

The Truncated Cone Effect in AFM Nanoindentation on Soft Materials

Background: Atomic Force Microscopy (AFM) nanoindentation is the principal method for the characterization of soft materials at the nanoscale. In most cases, pyramidal tips are used and approximated to perfect cones. However, the extended use of the AFM tip may alter its sharpness. Objective: In many cases, a truncated cone shape is appropriate for tip modeling. In this technical note, the equation that relates the force with the indentation depth when indenting an elastic halfspace using a truncated cone is derived. Methods: The nanoindentation equation for a truncated cone tip is derived using the fundamental differential equation that relates the sample’s contact stiffness with Young’s modulus. Results: When fitting Sneddon’s equation (which is valid for a perfect cone) on data obtained using a truncated cone-shaped AFM tip, the results show a ‘pseudo-softening’ behavior. Conclusion: The AFM tip's sharpness in nanoindentation experiments is a crucial parameter for obtaining the correct mechanical patterns of unknown samples.

DYNAMIC ANALYSIS OF A HELICOPTER BLADE WITH DAHL FRICTION IN A VERTICAL HINGE

A one-dimensional model of a helicopter main rotor blade in the plane of rotation with a vertical hinge (VSH) is considered. The friction in the VH corresponds to the Dahl model. The resonant frequency, free oscillations and phase trajectories of the model are analyzed depending on the value of the contact stiffness of Dahl friction.

Relation Between Interface Geometry and Tensile Shear Strength of Ultrasonically Welded Joints

The reliable use of ultrasonic metal welding requires a thorough understanding of the relevant bonding mechanisms. This article presents an approach to systematically investigate the relation between the mechanical properties and the interface of selected Al/Cu and Al/GFRP joints. The hypothesis is that the microstructure and tensile shear strength of the specimen can be related to their interface properties presented by contact stiffness and damage initiation traction. For this purpose, the mentioned hybrid material systems were ultrasonically welded using specific parameters to achieve defined levels of mechanical joint strengths. Micro sections and fracture surfaces were characterized to identify the interface geometry at certain strength levels. The main findings were different shares of bonded areas in the interface and characteristic micro geometries. Microscale finite element models of representative samples were developed to determine the stress and deformation behavior in the interface under tensile shear load and to compare the influence of the interface geometry on contact conditions to a simplified model. The simulations provide information about the influence of different damage initiation tractions and geometrical characteristics in the joints’ interfaces, as well as their contribution to the overall joint strength. For prospective industrial applications, they can serve as basis for further development of a contact model on component scale.

Magneto-controlled friction behaviors of magnetorheological elastomers with cosine-shaped surface structure

This study investigated the friction behaviors of magnetorheological elastomers (MREs) with cosine-shaped surface structures under the magnetic field. First, a magneto-controlled friction model for such MREs was proposed, and the friction coefficient was determined using the friction binomial theory and magnetic dipole theory. Then, the effects of the amplitude and wavelength, and magnetic field on the friction coefficient were analyzed. Finally, MRE-glass sliding friction behaviors were investigated by using the newly established test rig. It was found that the contact stiffness and friction coefficient of the MREs decreased with increasing amplitude and decreasing wavelength, respectively, which was consistent with the theoretical model. Moreover, the variation rate of the friction coefficient was up to 41% under magnetic field regulation.

Monitoring Wear of a Deep Groove Ball Bearing Using Ultrasonic Reflection

Abstract Wear changes the contact state and contact stiffness of the interface between the ball and the outer raceway under the operation of a deep groove ball bearing, resulting in the change of reflection coefficient of the interface. This paper describes a method based on ultrasonic reflection to assess the wear status of rolling element bearings. A deep groove ball bearing wear test was performed and the reflected pulses were collected with a linear ultrasonic probe mounted on the bearing outer ring. The results show as the wear intensity first increases and then decreases from running-in stage to steady wear period, the reflection coefficient of the interface between the outer raceway and ball shows the expected opposite trend. In addition, the ultrasonic measurement of wear state was verified by oil debris monitoring using on-line visual ferrography.

The Effects Analysis of Contact Stiffness of Double-Row Tapered Roller Bearing under Composite Loads

Double-row tapered roller bearings have been widely used in various equipment recently due to their compact structure and ability to withstand large loads. The dynamic stiffness is composed of contact stiffness, oil film stiffness and support stiffness, and the contact stiffness has the most significant influence on the dynamic performance of the bearing. There are few studies on the contact stiffness of double-row tapered roller bearings. Firstly, the contact mechanics calculation model of double-row tapered roller bearing under composite loads has been established. On this basis, the influence of load distribution of double-row tapered roller bearing is analyzed, and the calculation model of contact stiffness of double-row tapered roller bearing is obtained according to the relationship between overall stiffness and local stiffness of bearing. Based on the established stiffness model, the influence of different working conditions on the contact stiffness of the bearing is simulated and analyzed, and the effects of radial load, axial load, bending moment load, speed, preload, and deflection angle on the contact stiffness of double row tapered roller bearings have been revealed. Finally, by comparing the results with Adams simulation results, the error is within 8%, which verifies the validity and accuracy of the proposed model and method. The research content of this paper provides theoretical support for the design of double-row tapered roller bearings and the identification of bearing performance parameters under complex loads.

INTEGRATED CALCULATION AND EXPERIMENTAL TECHNOLOGY FOR ANALYSIS OF CONTACT INTERACTION WITH ACCOUNT OF ELASTIC INTERMEDIATE LAYER

The work delivers solution to a relevant scientific problem of solid mechanics. It consists in developing theoretical basis for computational and experimental research of contact interaction of complex-shaped bodies with account for micromechanical models of roughness and other intermediate or surface layers. New methods and models have been developed for the analysis of contact interaction of complex-shaped bodies with account for the micromechanical properties of surface and intermediate layers characterized by nonlinear local contact stiffness. The developed methods and models as well as the numerical analysis tools have been applied to a series of model and applied problems. The deformation behaviour of novel materials with network microstructures of one-dimensional elements has been determined. Macroscopical properties of these materials have been evaluated based on the special microscopic models and the homogenization methods. Regularities in contact distribution and its dependence on geometrical and physical factors have been determined for various complexshaped bodies. New design solutions for machine elements that improve their strength and durability have been justified. The developed methods and analysis tools have been introduced into the design of new engineering products. Their implementation resulted in improved technical characteristics of protection, structural and functional elements of transport vehicles of special purpose, gear transmissions, technical equipment, hydrovolumetric drives and so on. The conducted computational and experimental studies showed good agreement with the real response of network materials and the observed behavior of interacting elastic bodies with intermediate contact layer. Keywords: solid mechanics, complex-shaped body, contact interaction, contact pressure, intermediate layer

The Sensitivity of Micro—Macro Mechanical Behaviour of Sand to the Inter-Particle Properties

Sand is a particulate material but is treated as a continuum solid in some engineering analyses. This approach is proven to be acceptable when dealing with geotechnical structures, provided an adequate factor of safety is applied so that there is no risk of failure. However, the continuum approach does not account for the effect of interparticle forces on the micro–macro behaviour of sand. Sand could be modelled as a particulate material using the discrete element method (DEM), taking into account its discrete nature. This paper shows how the microscopic contact properties between the idealised sand particles influence the macro-mechanical behaviour, highlighting the development of the fabric as the soil approaches failure. Thirty DEM biaxial tests were performed to study the sensitivity of the macro–micro mechanical properties of sand to the inter-particle properties of an idealised sand particle. The conditions of these simulations were the same (e.g., particle size distribution, number of particles, porosity after radius enlargement, boundary conditions, and rate of loading). The sensitivity of the pre-peak, peak, and post-peak behaviour of these simulations to the inter-particle properties of an idealised sand particle was studied. Two extra DEM biaxial tests under different confining pressures were performed to verify the cohesionless nature of the synthetic material used for this study. Since a two-dimensional DEM is used for this study, a detailed approach to interpret the results assuming either a plane strain or a plane stress situation was discussed. This study highlighted the critical inter-particle properties and the range over which these influence macro-mechanical behaviour. The results show that Young’s modulus is mainly dependent on the normal contact stiffness, and peak stress and the angle of internal friction are greatly dependent on the inter-particle coefficient of friction, while Poisson’s ratio and volumetric behaviour of particulate sand are dictated mainly by shear contact stiffness. A set of relationships were established between inter-particle properties and macro-machinal parameters such as Young’s modulus, Poisson’s ratio, and angle of internal friction. The elastoplastic parameters obtained from these tests are qualitatively in agreement with the typical medium and dense sand behaviour.