Interfacial Contact Stiffness Research Articles

An improved contact parameter model with elastoplastic behavior for bolted joint interfaces

In this study, considering the elastoplastic behavior of contacting asperities on micro-scale and the contact pressure distribution of bolted joint interfaces on macro-scale, an improved contact stiffness model is presented. Firstly, the bolted T-stub joint is chosen as the object of study, and the distribution of normal contact load over the interface under preload conditions is studied. Then, combining the continuity, smoothness and monotonicity of the constitutive relations of normal contact load-deformation in three different regimes of plastic- elastoplastic-elastic of contacting asperities, the contact stiffness of individual asperity is analytically derived. Meanwhile, the relation between the distribution of contact stiffness and the distribution of normal contact load for bolted joint interfaces is determined based on fractal theory. The presented model overcomes the shortcomings of the contact stiffness without elastoplastic behavior obtained from the MB model and reveals the inhomogeneous distribution features of interfacial contact stiffness in bolted joints. Finally, the finite element (FE) analysis for flange-bolted joints incorporating the proposed model and the relevant experimental verification are performed. The results show that the average error of the first 4-order natural frequencies between the FE results and the experimental ones is only 0.72%, and the predicted results in frequency-domain are consistent with the measured ones, which illustrates that the proposed model can be used in interface modeling of jointed structures.

On the Electric Contact Resistance

When an electric current flow across an interface between two contacting solids a change in the electric potential occur over the interface. One part of the electric contact resistance is due to the constrictions at asperity contact regions. Barber has shown that the constriction resistance can be related to the interfacial contact stiffness. I discuss the relation between the classical (approximate) Holm theory for the constriction resistance and the (exact) theory involving the contact stiffness.Graphical

Contact characteristic parameters modeling for the assembled structure with bolted joints

Considering the non-uniformly distributed contact pressure, this study presents a new contact characteristic parameters (contact stiffness and damping) model for bolted joint interfaces. Firstly, to transform the contact pressure distribution into normal contact load distribution, the contact pressure distribution and its mathematical representation of single-bolted joint are studied. Subsequently, the relationships among contact stiffness distribution, contact damping distribution and normal contact load distribution are determined based on the improved MB model. It is found that the interfacial contact stiffness and damping exhibit significant inhomogeneous distributions. The proposed model overcomes the shortcomings of homogeneous distributions of contact stiffness and damping in bolted joints derived from previous models. In addition, the effects of bolt preload, tangential-to-normal contact load ratio and friction coefficient on the contact stiffness and damping are discussed in detail. Finally, the finite element (FE) analysis for beam lap structure with bolted joints incorporating the proposed model and the relevant experimental are performed to verify the validity of the modeling method. The results indicate that the proposed model can significantly improve the modeling accuracy of bolted joints.

Effect of joint interfacial contact stiffness on structural dynamics of ultra-precision machine tool

The contact stiffness of the joint interface significantly affects the dynamic characteristics of a machine tool structure. Herein, an improved theoretical model is proposed to calculate the joint interfacial contact stiffness. This model is established based on fractal theory. To mitigate the plastic and elastic contact problems, the Stronge contact model is adopted to express the contact force in the plastic regime innovatively, whereas the elastic contact force is interpreted using Hertz theory; the domain extension factor is compensated to revise the microcontact size distribution. Furthermore, the rotational contact stiffness is first derived, which renders the contact model more comprehensive. A representative test structure is designed, and the contact model is validated by comparing the simulated contact stiffness with experimental results. The transfer matrix method for multibody systems is incorporated with fractal contact model to establish a dynamic model of an ultra-precision machine tool; this ensures that the dynamic characteristics of the machine tool can be predicted more precisely. Experiments involving a vibration response test and a modal test demonstrate the feasibility of the fractal contact and dynamic models. Based on these two models, the effect of the interfacial contact stiffness on the structural dynamics is investigated. As the preloads at two joints loosen by 15%, the maximum vibration displacements increase by 1.74% and 2.90%, respectively, indicating that the joint interface between the column and lathe bed is more sensitive. The procedure presented herein will facilitate the design and optimization of the complex structures.

An improved virtual material based acoustic model for contact stiffness measurement of rough interface using ultrasound technique

In this work, an improved acoustic model based on virtual material is proposed to provide an accurate measurement of interfacial contact stiffness using ultrasound. The rough interface is assumed to be a thin layer of virtual material to incorporate the effect of ultrasound attenuation at the interface. The derived acoustic model shows that the developed contact stiffness expression is a refinement of the general spring model by considering the interfacial property and is related to the material properties of the virtual material thin layer. The analytical solutions of the material parameters for the virtual material are further deduced based on the statistical micro-contact theory. It reveals that the surface roughness parameters of the contact interface and the material property of the contact body are other information required to improve the measurement accuracy of contact stiffness, in addition to the ultrasonic measurement parameters in the original spring model. The accuracy of the developed acoustic model for contact stiffness measurement is verified by comparison with the spring model and the statistical contact models.

Study on the normal contact stiffness of the fractal rough surface in mixed lubrication

In this paper, an elastic interface model is developed to theoretically analyze the contact stiffness of a mixed lubrication surface where the solid and the lubricant contacts have to-be-determined contributions to the whole contact stiffness. The interfacial contact stiffness is composed of the solid contact stiffness and the lubricant contact stiffness, in which the two components are associated with each other via the equivalent thickness of lubricant. Based on the combination of two widely acknowledged ultrasonic measurement models and the Taylor approximating equation, the derivation of the lubricant contact stiffness is mostly affected by the material properties and the equivalent thickness of lubricant, and the equivalent thickness is determined by the solid contact properties under the mixed lubrication condition. Results of the mathematical analysis show that the contact stiffness of the mixed lubrication surface is larger than that of the dry rough surface due to the presence of lubricant. The interfacial contact stiffness of the mixed lubrication is obviously affected by the surface topography and the lubricant property. The proportions of contact stiffness contributed from the solid part and the lubricant part are varying with the contact area and the surface topography. Model predictions are compared with experiment results to verify the accuracy of proposed model. The analysis of the interfacial contact stiffness involved in mixed lubrication provides a theoretical basis for the performance prediction of machine tools, and might be useful to elucidate the contact properties by ultrasonic pulse probing in real engineering applications.

Interfacial contact stiffness of fractal rough surfaces

In this work we describe a theoretical model that predicts the interfacial contact stiffness of fractal rough surfaces by considering the effects of elastic and plastic deformations of the fractal asperities. We also develop an original test rig that simulates dovetail joints for turbo machinery blades, which can fine tune the normal contact load existing between the contacting surfaces of the blade root. The interfacial contact stiffness is obtained through an inverse identification method in which finite element simulations are fitted to the experimental results. Excellent agreement is observed between the contact stiffness predicted by the theoretical model and by the analogous experimental results. We demonstrate that the contact stiffness is a power law function of the normal contact load with an exponent α within the whole range of fractal dimension D(1 < D < 2). We also show that for 1 < D < 1.5 the Pohrt-Popov behavior (α = 1/(3 − D)) is valid, however for 1.5 < D < 2, the exponent α is different and equal to 2(D − 1)/D. The diversity between the model developed in the work and the Pohrt-Popov one is explained in detail.

Non-linear Behavior of Normal Contact Stiffness of Tunnel Surface and Supporting System of Tunnel Boring Machines

The interfacial contact stiffness between the supporting system of tunnel boring machines(TBM) and the tunnel surfaces is closely related to the mechanical behavior of rocks and the morphology of tunnel surfaces. The mathematical model based on the fractal theory is employed to study the relation between the roughness and fractal parameters of three dimensional tunnel surfaces. The coarse surfaces are established by using the projecting method according to the characteristics of tunnel surfaces. Many parameters such as the roughness of the tunnel surfaces, the mechanical behavior of rocks, the number of the supporting boots and composite geologic structures are taken into consideration to obtain the correlation between the normal contact stiffness and the loads. The results show that the increases of the fractal dimension, the elastic modulus, the normal loads and the number of support boots cause the increase of the interfacial contact stiffness. The contact stiffness of the double supporting systems is twice of that of the single one subjected to the same load. The normal stiffness is minimal when the ratios of the soft and hard rocks in the composite geologic structures are approximately identical. The increasing of the ratio of soft rocks in the contacting area causes the increase of the contact stiffness. However, the variation of the contact stiffness is not obvious when the proportions of two kinds of rocks on the contacting area are changed.

An Investigation Into Using Magnetically Attached Piezoelectric Elements for Vibration Control

A novel vibration control method utilizing magnetically mounted piezoelectric elements is described. Piezoelectric elements are bonded to permanent magnets, termed here as control mounts, which are attached to the surface of a steel beam through their magnetic attraction. The magnetic-piezoelectric control mounts are an alternative to traditional epoxy attachment methods for piezoelectric elements which allows for easy in-the-field reconfiguration. In model and laboratory measurements, the beam is driven through base excitation and the resonant shunt technique is utilized to demonstrate the attenuation characteristics of two magnetic-piezoelectric control mounts. The coupled system is discretized using a Galerkin finite element model that incorporates the tangential and vertical contact stiffnesses of the beam-magnet interface. The vibration reduction provided by the control mounts using a single magnet are compared to those designed with a magnetic array that alternates the magnetic dipoles along the length of the mount. Even though each design uses the same magnet thickness, the alternating magnetic configuration's interfacial contact stiffness is over 1.5 and 4 times larger in the tangential and vertical directions, respectively, than that of the single magnet, resulting in increased vibration reduction. Measured and simulated results show that the magnetic-piezoelectric control mounts reduced the beam's tip velocity by as much as 3.0 dB and 3.1 dB, respectively. The design tradeoffs that occur when replacing the traditional epoxy layer with a magnet are also presented along with some methods that could improve the vibration reduction performance of the control mounts. This analysis shows that the control mounts attenuate significant vibration despite having an imperfect bond with the beam, thus providing a viable and adaptable alternative to traditional piezoelectric attachment methods.

Ultrasonic assessment of rough surface contact between solids from elastoplastic loading–unloading hysteresis cycle

An ultrasonic method to characterize the elastoplastic contact between two rough surfaces is presented. Ultrasonic experiments are performed on three different interfaces formed by aluminum surfaces with different levels of roughness. The frequency-dependent ultrasonic reflection coefficient from the interface is measured during loading and unloading cycles as a function of pressure, from which the ultrasonic interfacial contact stiffness is reconstructed by the least-squares inversion procedure. It is shown that one should distinguish between the ultrasonic (dynamic) interfacial stiffness and static interfacial stiffness for rough surfaces in elastoplastic contact (they are identical for purely elastic contact). It is shown that ultrasonic stiffness is associated with local unloading stiffness. An elastoplastic micromechanical model is used to describe the plasticity-induced hysteresis in the ultrasonically measured interfacial stiffness during loading–unloading cycles. The topographic parameters of the interface contact are reconstructed by matching the model-predicted results with the experimentally determined ultrasonic stiffness. Using these parameters the real area of contact, which is not directly measurable, is predicted during loading–unloading cycles using the model.