A ray method of solving problems connected with a shock interaction

This sheet deals with analysis of the oblique impact system, which is composed of the golf-ball and club. The impact system is modeled by both a nonlinear spring and a nonlinear dashpot using Hertz's contact theory. This model is applied to the oblique impact system of ball. The characteristics of the oblique impact were obtained by using this model. In previous studies,the validity of the normal model was confirmed, validity of tangential model was not confiemed. Therefore, reconsider the tangential model. The result is improved accuracy of the model. Also.examined the characteristics of oblique impacts of changes in coefficient of friction from experiments and analysis.

This sheet deals with characteristics of the oblique impact system, which is composed of the ball and flat surface. The impact system is modeled by both a nonlinear spring and a nonlinear dashpot using Hertz's contact theory. This model is applied to the oblique impact system of ball. The characteristics of the oblique impact were obtained by using this model. The results show that the spin rate increased in proportion to the angle of incidence and impact velocity. Also, in the case of increase the tangential stiffness, the spin rate was decreased and the angel of reflection was increased.

The ball-on-ring (BOR) test is an effective technique used to characterize the biaxial fracture strength of brittle materials. In particular, damages induced by wafer backgrinding process can be evaluated using the BOR test. It is difficult to measure directly the radius of contact area between the loading ball and a specimen, which is needed for stress determination by an analytic solution. In this study, parametric finite element analyses were performed to compare with known closed-form solutions. It was found that the effect of small loading area must not be ignored and that the radius of contact could be precisely determined using Hertz's contact theory. This can serve as a guideline to accurately obtain the fracture strength of a BOR specimen.

In this paper, photoelastic experimental hybrid method using external traction free boundary condition and using the relative equation of two stress functions in contact problems are developed. Their validities are confirmed through experiments and discussions Hertz's contact theory and two photoelastic experimental hybrid methods explained above are applied to the stress analysis of O-ring under 10% or 20% squeeze rate. Among them, the photoelastic experimental hybrid method using the relative equation of two stress functions in contact problems is most effective. When squeeze rates of O-ring are 20%, Maximum of absolute σ_x is greater than maximum of absolute σ_y by little. But they are almost equal to each other. Maximums of absolute τ_<xy> are 1/5 of absolute σ_x when squeeze rate of O-ring is 20%.

Our sense of touch is spatially focused and has a far lower bandwidth in comparison with visual sense that has the largest bandwidth. While most haptic studies utilize point interactions, resulting in a conflict between this low information bandwidth and relative complexity of virtual scene. In this paper, we investigate a novel multi-resolution force evaluation scheme of hybrid virtual models in a unified haptic interaction framework. Force contact model of tool-object interaction based on Hertz's contact theory is integrated in our work. Physical properties with different object materials expressed by Poisson's Ratio and Young's Modulus are involved to investigate most realistic perception during multi-resolution haptic interaction. The hierarchical impostor representation of surface and volumetric models are constructed, and the optimal performance based on cost and benefit evaluation at run time is employed to meet both the visual and hapic perceptual qualities. During this multi-resolution haptic interaction, our scheme adaptively determines the rendering mode using graphics and haptics impostors represented in the virtual environments. Our experimental results have demonstrated the satisfactory performance of proposed multi-resolution haptic interaction framework applicable for hybrid virtual models.

An effective method for calculating elasto-plastic contact pressure and contact patch size under elliptical, circular and line contact conditions

In industrial plants and pressurized equipment, leakage control and prevention are key tasks in preventive maintenance programs. The most critical element in these types of equipment is the seals. Several types of seals are used and the most popular are flat seals and O-rings. Two conditions affect the proper functioning of the seals: the mounting configuration and the initial loading parameters during operation. In this work, the analysis of the mechanical and leakage behaviour of the O-ring seal, when installed either in a cylindrical concave groove or in a rectangular one, is presented. Two finite element models were developed with Ansys software to study the behaviour of the assemblies in both cases when the clamping load is applied and when the assembly is pressurized. The results of the numerical models are compared to the analytical approach based on Hertz's contact theory. This study shows that the use of a cylindrical concave groove for mounting elastomeric O-rings can improve sealing in pressurized systems.

This sheet deals with characteristics of the oblique impact system, which is composed of the golf ball and elastic supported clubface. The impact system is modeled by both a nonlinear spring and a nonlinear dashpot using Hertz's contact theory. This model is applied to the oblique impact system of golf ball and elastic supported clubface. The characteristics of the oblique impact were obtained by using this model. The results show that the spin rate increased in proportion to the angle of incidence and impact velocity and a coefficient of friction. Also, in the case of increase the tangential stiffness, the spin rate was decreased.

We report on the results of extensive computer simulation of the effect of deformation on the morphology of a porous medium and its fluid flow properties. The porous medium is represented by packings of spherical particles. Both random and regular as well as dense and nondense packings are used. A quasistatic model based on Hertz's contact theory is used to model the mechanical deformation of the packings, while the evolution of the permeability with the deformation is computed by the lattice-Boltzmann approach. The evolution of the pore-size and pore-length distributions, the porosity, the particles' contacts, the permeability, and the distribution of the stresses that the fluid exerts in the pore space are all studied in detail. The distribution of the pores' lengths, the porosity, and the particles' connectivity change strongly with the application of an external strain to the porous media, whereas the pore-size distribution is not affected as strongly. The permeability of the porous media strongly reduces even when the applied strain is small. When the permeabilities and porosities of the random packings are normalized with respect to their predeformation values, they all collapse onto a single curve, independent of the particle-size distribution. The porosity reduces as a power law with the external strain. The fluid stresses in the pore space follow roughly a log-normal distribution, both before and after deformation.

The aim of the article is to review the literature devoted to the solution of wave dynamics problems resulting in the propagation of nonstationary surfaces (volume waves) or lines (surface waves) of strong and weak discontinuities. In so doing one-term and multiple-term ray expansions, which are truncated power series with variable coefficients, are used. Jumps in all kinds of order of the time-derivatives of the functions to be desired serve as the coefficients. With their help the solutions are constructed behind the wave fronts up to the boundary of the wave motion domain. If the domains of the wave motion existence are extended, then the truncated ray series approximating the solution are not always uniformly valid over these domains. In this article, the methods for regularization of the truncated ray series are discussed, and in particular a new method which has been called by the authors as the method of “forward-area regularization”. These methods have gained recently wide application to solve the boundary-value problems connected with the wave propagation in bars, beams, plates, shells, 3D bodies, as well as with the dynamic contact interaction. In so doing, linear and nonlinear elastic, isotropic and anisotropic, thermoelastic, elastoplastic, and elastoviscoplastic media are used.

The head-on colliding process of binary liquid droplets at low velocity: High-speed photography experiments and modeling

For determining die strength, there are a couple of tests available in the literature, such as three-point and four-point bending, ball breaker, ball-on-the-ring, ring-on-the-ring, and recently proposed ball-on-elastic- pad (BoEP) and ball-on-the-hole (BoH) tests. It's well known that the test data reduction with theoretical formulations is more convenient and useful than that with numerical simulation results. However, those theoretical formulations have to be validated either by numerical simulation or experiments, before their applications. The objective of this study is to reevaluate and thus improve the existing BoEP and BoH tests for die strength using Hertzian contact theory, plate theories and finite element method (FEM). In this paper, the FEM analysis with ¿contact element¿ successfully has been verified with Hertzian contact theory and further proved that Hertzian contact theory can be employed to estimate the contact area for calculating die strength in both methods. The results indicate that the consistency between the theoretical formulation and FEM simulation for both tests exist only at the relatively large radius of ball and high applied loading, because the feasibility of the theoretical formulations requires large contact radius(> 0.06 mm) or area. For the BoEP test, the elastic moduli of elastic pad and ball have no obvious effect on the difference of maximum die stress between theoretical and FEM results. The theoretical solutions associated with contact radius determined by Hertzian contact theory are successfully proved for improving BoEP and BoH tests for die strength determination, and for better accuracy of die strength the ball with radius ranging from 2 mm to 4 mm is suggested.

A new effective mesh stiffness calculation method with accurate contact deformation model for spur and helical gear pairs

A uniform asymptotics of the surface Love modes for a special case of anisotropy (tranverse isotropy) of an elastic media is obtained. In constructing the asymptotics of surface waves, the space-time (ST) ray method is employed. The wave field of each Love mode is represented as the sum of the ST caustic expansion involving the Airy functions with a real eikonal and two correction terms that are ST ray solutions, which in fact are inhomogeneous waves with complex eikonals. The eikonals and coefficients of the caustic and ray series are sought in the form of expansions in powers of two variables. The first variable is the distance from the surface, whereas the other characterizes the proximity of the caustic of a ray field to the boundary surface. Thanks to the specific structure of the elasticity tensor for a transversely isotropic medium, the boundary surface is necessarily a plane. A recursion process of computation of higher terms of the asymptotic expansion allows one to trace the conversion of the formulas obtained to the known ray solutions for isotropic elastic media. Relations between the elasticity parameters of a medium are obtained that ensure the existence of SH Love waves in a transversely isotropic medium and that are consistent with the conditions of the positiveness of the elastic energy of deformation. Bibliography: 6 titles.

The power series solution is a cheap and effective method to solve nonlinear problems, like the Duffing-van der Pol oscillator, the Volterra population model and the nonlinear boundary value problems. A novel power series method by considering the multiple scales $R_k$ in the power term $(t/R_k)^k$ is developed, which are derived explicitly to reduce the ill-conditioned behavior in the data interpolation. In the method a huge value times a tiny value is avoided, such that we can decrease the numerical instability and which is the main reason to cause the failure of the conventional power series method. The multiple scales derived from an integral can be used in the power series expansion, which provide very accurate numerical solutions of the problems considered in this paper.