Multi-stage contact model between two rough surfaces based on the improved equivalent contact method

Two-dimensional contact of asperities to multi-stage contact between curved fractal surfaces based on attitude angle

The accuracy and reliability of a measuring device is crucial to determine the quality of wood surface. This paper compares the surface quality of thermally modified spruce wood measured by two different methods. Spruce wood specimens were thermally modified at different temperatures (160, 180, and 210 °C) and then milled with a single-spindle milling machine operated at different combinations of processing parameters (cutting speed, rake angle, and feed rate). Surface quality (surface roughness and surface waviness) of the specimens were measured by laser as well as contact method. Higher values of surface roughness and waviness were obtained by the laser method compared with the contact method. Average surface roughness was 31% higher, while average waviness was 35% higher in laser method as compared with the contact method. Based on the surface quality obtained by laser method and energy consumption during milling, the optimum combination of parameters for milling of thermally modified spruce wood was ascertained. The best surface quality with lower energy consumption during machining was obtained in spruce wood thermally modified at 210 °C and processed at a cutting speed of 20 m/s, rake angel of 20°, and a feed rate of 4 m/min.

Multi-stage contact model between fractal rough surfaces based on ellipsoidal asperity deformation

Roughness measurements by optical interferometry and scanning tunneling microscopy on a magnetic thin-film rigid disk surface have shown that its surface is fractal in nature. This leads to a scale-dependence of statistical parameters such as r.m.s height, slope and curvature, which are extensively used in classical models of contact between rough surfaces. Based on the scale-independent fractal roughness parameters, a new model of contact between isotropic rough surfaces is developed. The model predicts that all contact spots of area smaller than a critical area are in plastic contact. When the load is increased, these plastically deformed spots join to form elastic spots. Using a power-law relation for the fractal size-distribution of contact spots, the model shows that for elastic deformation, the load P and the real area of contact Ar are related as P~Ar(3−D)/2, where D is the fractal dimension of a surface profile which lies between 1 and 2. This result explains the origins of the area exponent which has been the focus of a number of experimental and theoretical studies. For plastic loading, the load and area are linearly related. The size-distribution of spots also suggests that the number of contact spots contributing to a certain fraction of the real area of contact remains independent of load although the spot sizes increase with load. The model shows that the load-area relation and the fraction of the real area of contact in elastic and plastic deformation are quite sensitive to the fractal roughness parameters.

Dry friction damping structures are simple and can be used in big range of working temperature, therefore varied kinds of friction contact damping structures have been widely used in turbomachine blades to reduce the forced vibration and improve dynamic stability. However, the dynamic analysis of such structures is still a challenging engineering task because the dry friction damping is a dynamic contact problem with complex boundary condition and strong nonlinear characteristics. A three dimensional numerical model for friction contact has been proposed to investigate the contact kinematics in the contact surfaces between adjacent blade shrouds. Microslip effects taken into account with a discretization of the contact surface with a mesh of contact elements, by altering the number of contact node can consider the effects of the area of the contact surface on forced response of shroud blade. The complex movement in the shroud contact surfaces was described by tracking the trajectory of the relative motion of the contact node. The model can consider the differences between the static friction coefficient and dynamic friction coefficient. The model has the mathematically tractable characteristic and can be easily used, and conforms to the engineering need. In order to decrease time consuming for computing the forced response, a reduced method is employed to condense all nonlinear degrees of freedom (DOF) to the nonlinear DOF on the contact surfaces, hence, iterative procedure of solution is limited in nonlinear degrees of freedoms. An alternating frequency/time domain method (AFT) which takes the advantages of both the time domain method and the frequency domain method is introduced to predict nonlinear vibration of shrouded blade systems. The developed friction model and calculated method of dynamic equation are applied to calculate nonlinear vibration for a real steam turbine blade. The effect of parameters on resonant frequency and response of the blade are investigated and discussed.

An efficient multiregion model is extended with the single integral equation (SIE) method to calculate the EM scattering from a dielectric rough surface. In the multiregion model, the rough surface is divided into multiple regions depending on their positions along the rough surface as well as the energy distribution of the incident wave. Two intermediate regions are chosen as the domain region on which the method of moment (MoM) is adopted. The mutual couplings between different regions are considered approximately based on the magnetic and field integral equations, from which closed-form approximations for electric current on other regions are derived.

The authors wish to explain the similarity between some figures in the above paper (hereafter called the JPD paper) and in their other publication, Lee S, Jang Y H and Kim W 2008 Effects of nanosized contact spots on thermal contact resistance J. Appl. Phys.103 074308 (hereafter called the JAP paper), and to explain the differences between the two papers, which are not explicitly stated in the JPD paper.The main objective of the JAP paper is to calculate the thermal contact resistance of the nanosized contact spots in multiscale contact. During the process of multiscale analysis, the thermal conductivity varies, especially below the phonon mean free path. The JPD paper deals with the electrical contact resistance in the multiscale contact distribution with an assumption of constant electrical resistivity, which is known as a different kind of physics in a larger characteristic length scale.There are similar figures in the JPD paper and the JAP paper: figures 6, 7 and 8 in the JPD paper and figures 3, 4 and 5 in the JAP paper. Two research works were performed on the basis of a specific microcontact distribution. In the JAP paper, the scale of the contact distribution is in the range of the phonon mean free path of Si, which is a very small size of contact distribution. In the JPD paper, the scale of contact distribution is in the continuum scale, which is larger than the phonon mean free path. In addition, due to the characteristics of a fractal surface which repeatedly generates a similar shape of contact distribution in the different length scales, the shape of contact distribution looks similar, but the total sizes of domain in the JPD and JAP figures are different. The projected areas L × L of fractal surface of the JAP paper and JPD paper are 10 μm × 10 μm and 10 mm × 10 mm, respectively. The length scale is already stated in the JAP paper, but not in the JPD paper. Thus, we have to state that the figures were adapted from the JAP paper without clear attribution and that credit should be given to the original source of the images. Most significantly, the two most important features of the two works are based on totally different physics and the calculation methods for contact resistance.The text of section 4.3 of the JPD paper should be modified. The left column of page 5 and the first two lines of the right column should be replaced by the following text.The projected area of a self-affine fractal surface is plotted in figure 6. In order to find the microcontact spot distribution from the fractal surface, numerical simulations are applied to the model of multiscale rough surface. Several contact models are constructed according to the resolution of 1/24 to 1/28. Figure 7 shows a typical finite element model in which the rough elastic surface is in contact with a perfectly flat rigid surface. Due to the fine meshes in the contact interface, strong mesh gradations are required. The contact simulation enforcing the impenetrability constraint on the mating surfaces is performed by a commercial finite element package, Abaqus/HKS ([22] of the JPD paper). The resulting microcontact spot distributions for different resolution of the rough surface are obtained in figure 8. As reported by Borri-Brunetto et al ([23] of the JPD paper), the actual contact area decreases and the number of contact spots increases as the resolution of the discretization escalates.A more detailed description for the model can be obtained in the JAP paper.

Fatigue life analysis of aero-engine blades for abrasive belt grinding considering residual stress

When solving the problems involving inhomogeneous materials, the influence of the inhomogeneity upon contact behavior should be properly considered. This research proposes a fast and novel method, based on the equivalent inclusion method where inhomogeneity is replaced by an inclusion with properly chosen eigenstrains, to simulate contact partial slip of the interface involving inhomogeneous materials. The total stress and displacement fields represent the superposition of homogeneous solutions and perturbed solutions due to the chosen eigenstrains. In the present numerical simulation, the half space is meshed into a number of cuboids of the same size, where each cuboid is has a uniform eigenstrain. The stress and displacement fields due to eigenstrains are formulated by employing the recent half-space inclusion solutions derived by the authors and solved using a three-dimensional fast Fourier transform algorithm. The partial slip contact between an elastic ball and an elastic half space containing a cuboidal inhomogeneity was investigated.

The possibility of predicting the fatigue behavior of additively manufactured materials by means of microstructure- and defect-sensitive models is discussed in this paper. The effects of surface roughness, process-induced defects, and microstructure on the fatigue life of additively manufactured materials are presented, along with discussions on efforts to incorporate the subsequent effects of these features on fatigue performance using fracture mechanics approach, the multistage fatigue model, and numerical modeling and analysis. Such efforts in fatigue modeling are critical to evaluate the reliability of additive manufactured parts in order to further expand their industrial adoption.

The finite element method (FEM) of Monte Carlo simulations of random rough surface scattering is extended to penetrable rough surface scattering. The attraction of the method is the banded nature of the resulting matrix equation. The method yields a system of linear algebraic equations which is solved by a direct sparse symmetric matrix inversion. Convergence and accuracy of the method is demonstrated and established by varying various input parameters such as the number of evanescent waves, the number of sampling points and the surface lengths. Results with incident plane wave TE polarization are presented for both the mean reflected scattered intensity and the mean transmitted scattered intensity as a function of surface parameters such as RMS surface heights and correlation lengths. The numerical results are compared against the tapered wave integral equation (TWIE) method. The results of a tapered wave solution of the integral equation averaging over many realizations are in good numerical ag...

In this paper, an electro-thermal model is proposed for the first time to accurately investigate the self-heating effects in gate-all-around (GAA) silicon nanowire MOSFETs (SNWTs) for thermal-aware design optimization. The model is derived based on the equivalent thermal network method, in which the impacts of gate length dependence, nanowire diameter dependence and surface roughness on the nanowire channel thermal conductivity as well as the influence of unique GAA structure features on the heat dissipation are taken into account. The proposed model agrees well with the experimental results of SNWTs. Based on the model, the impacts of structure parameters on the current driving capabilities and heat dissipation of SNWTs are discussed. The developed electro-thermal model can be further applied to the thermal-aware design of SNWT-based circuits.

This article introduces a novel approach for predicting the electrical contact resistance (ECR) between two rough surfaces based on a combination of contact modeling with surface topography analysis. Firstly, asperities distributed on rough surfaces are simulated as parabolas. An asperity shoulder-shoulder contact model is developed, which is similar to the well-known Kogut-Etsion (KE) model but requires extended capability regarding different degrees of contact misalignment. On the basis of such a contact model, Holm's principle is then incorporated to create a new theoretical formulation revealing the constitutive relations between the ECR and the deformation patterns of microcontacts arising at the contact interface. Then, a watershed approach is employed to get the contact surface topographies with which an iterative computational strategy is then proposed to alleviate the programming and computing efforts for implementing the calculation of the total ECR at the contact interface. To verify the feasibility of the proposed method, aiming at one case, the KE-based model is reviewed and compared numerically to the new model. The comparison shows good agreement between the two models. A slight difference is that the suggested model gives a relative lower estimation on the ECR value, which is mainly attributed to the different judgment of the deformation mechanism.

The machining of free form surfaces is one of the most challenging problems in the field of metal cutting technology. The produced part and machining process should satisfy the working, accuracy, and financial requirements. The accuracy can describe dimensional, geometrical, and surface roughness parameters. In the current article, three of them are investigated in the case of the ball-end milling of a convex and concave cylindrical surface form 42CrMo4 steel alloy. The effect of the tool path direction is investigated and the other cutting parameters are constant. The surface roughness and the geometric error are measured by contact methods. Based on the results, the surface roughness, dimensional error, and the geometrical error mean different aspects of the accuracy, but they are not independent from each other. The investigated input parameters have a similar effect on them. The regression analyses result a very good liner regression for geometric errors and shows the importance of surface roughness.

In theoretical research pertaining to sealing, a contact model must be used to obtain the leakage channel. However, for elastoplastic contact, current numerical methods require a long calculation time. Hyperelastic contact is typically simplified to a linear elastic contact problem, which must be improved in terms of calculation accuracy. Based on the fast Fourier transform, a numerical method suitable for elastoplastic and hyperelastic frictionless contact that can be used for solving two-dimensional and three-dimensional (3D) contact problems is proposed herein. The nonlinear elastic contact problem is converted into a linear elastic contact problem considering residual deformation (or the equivalent residual deformation). Results from numerical simulations for elastic, elastoplastic, and hyperelastic contact between a hemisphere and a rigid plane are compared with those obtained using the finite element method to verify the accuracy of the numerical method. Compared with the existing elastoplastic contact numerical methods, the proposed method achieves a higher calculation efficiency while ensuring a certain calculation accuracy (i.e., the pressure error does not exceed 15%, whereas the calculation time does not exceed 10 min in a 64 × 64 grid). For hyperelastic contact, the proposed method reduces the dependence of the approximation result on the load, as in a linear elastic approximation. Finally, using the sealing application as an example, the contact and leakage rates between complicated 3D rough surfaces are calculated. Despite a certain error, the simplified numerical method yields a better approximation result than the linear elastic contact approximation. Additionally, the result can be used as fast solutions in engineering applications.