329 ゴルフボールとクラブとの衝突特性 : クラブフェイスの特性とスピンの関係(スポーツにおける打撃(2))

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.

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.

Problems connected with a shock interaction of a thin elastic cylindrical bar and an elastic sphere with an Uflyand-Mindlin plate of a finite size are considered. In enumerated problems, an impact process is accompanied by material local deformations and propagation of wave surfaces of a strong or weak discontinuity in elastic bodies coming in contact. The local deformations are taken into account in terms of the Hertz's contact theory, but the dynamic deformations behind the fronts of incident and reflected waves are determined by means of truncated power series with variable coefficients (what is known as ray series). These two types of deformations are mated on the contact region boundary. As the truncated ray series, as a rule, are not uniformly applicable in the whole region of the wave solution existence, then for their improvement the method of “forward-area” regularization is used which is based on a combination of the recurrent equations of the ray method with the method of multiple scales. The method of power series (ray method) allows one to find the main characteristics of the impact theory in an analytical form.

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.

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 record of impact‐induced shock heating in meteorites is an important key for understanding the collisional history of the solar system. Material strength is important for impact heating, but the effect of impact angle and impact velocity on shear heating remains poorly understood. Here, we report three‐dimensional oblique impact simulations, which confirm the enhanced heating due to material strength and explore the effects of impact angle and impact velocity. We find that oblique impacts with an impact angle that is steeper than 45‐degrees produce a similar amount of heated mass as vertical impacts. On the other hand, grazing impacts produce less heated mass and smaller heated regions compared to impacts at steeper angles. We derive an empirical formula of the heated mass, as a function of the impact angle and velocity. This formula can be used to estimate the impact conditions (velocity and angle) that occurred and caused Ar loss in the meteoritic parent bodies. Furthermore, our results indicate that grazing impacts at higher impact velocities could generate a similar amount of heated material as vertical impacts at lower velocities. As the heated material produced by grazing impacts has experienced lower pressure than the material heated by vertical impacts, our results imply that grazing impacts may produce weakly shock‐heated meteorites.

Scaling of oblique impacts in frictional targets: Implications for crater size and formation mechanisms

In this work, the normal (0°) and oblique (30° and 45°) ballistic impact behavior of glass fiber-reinforced aluminum laminates (fiber metal laminate, FMLs) impacted by a rigid cylindrical projectile (with a flat nose) has been investigated from an experimental point of view. The ballistic impact tests were conducted on the FMLs using a one-stage gas gun at different impact angels, i.e. 0°, 30° and 45°. A high-speed camera was used to capture and record the experimental images and data during the impacting process. Different failure patterns were observed in the FMLs under oblique and normal impact, with the differences concentrated on the initial crack (in the back surface) and plugging damage (in both the front and back surface). The angular change in direction of the projectile during perforation was only observed during oblique impact tests while the maximum value of the angular change was observed when the impact velocity was close to its ballistic limit velocity. In addition, the angular change decreases with increasing impact velocity and is almost constant when the value of [Formula: see text] reaches a critical value. It can also be observed from the impact test results (both normal and oblique impacts) that FMLs exhibited the lowest ballistic limit velocity when the impact angle was close to 30°. In particular, normal impact shows a higher ballistic limit velocity than that of oblique impact while the ballistic limit velocity at impact angle 45° is slightly higher than that at 30°.

The vocal folds are subject to repeated collision during phonation. The resulting contact pressure is often considered to play an important role in vocal fold injury, and has been measured in many experimental studies. In this study, vocal fold contact pattern and contact pressure during phonation were numerically investigated and compared to Hertzian contact theory. The results show that vocal fold contact in general occurs within a horizontal strip on medial surface, first appearing at the inferior medial surface and propagating upward. Because of the localized and traveling nature of vocal fold contact, sensors of a finite size may significantly underestimate the peak vocal fold contact pressure (by about as large as 80% for a sensor diameter of 2 mm), particularly for vocal folds of low transverse stiffness or thick medial surface. In general, the contact pressure increases with the size and curvature of the contact area, as predicted from Hertzian contact theory, indicating the possibility of estimating vocal fold contact pressure from medial surface kinematics. However, deviations from Hertzian theory were also observed, which need to be taken into consideration in estimating vocal fold contact pressure.

Ultra-high molecular weight polyethylene (UHMWPE) was modified on purpose to enhance the wear resistance. The modification was done either by crosslinking the amorphous region of the surface using difunctional monomers or by crosslinking the bulk in the melt state using peroxide. The changes in thermal and tensile properties indicated that the modifications were effected. The volumetric wear rate, determined on a pin-on-disk wear tester, was suppressed by the modifications. The correlation between the tensile properties and the wear rates was sought. Any single tensile property or tensile rupture energy did not correlate well with the observed wear rate. Instead, the ratio of maximum contact stress calculated by the Hertz's contact theory to yield stress appeared to correlate well with volumetric wear rate.

This paper presents an analytical model to investigate the nonlinear dynamic analysis of high speed ball bearings due to ball waviness and unbalanced rotor. The Hertzian contact theory is applied to calculate the elastic deflection and nonlinear contact force, while the rotor has translational and angular motions. In the analytical formulation, the contacts between rolling elements and inner/outer races are considered as nonlinear springs. A nonlinear damping formula, correlating the contact damping force with the equivalent contact stiffness and contact deformation rate is used in the derivation. The numerical integration technique Newmark-β with Newton-Raphson method is used to solve the nonlinear differential equations iteratively. The results are presented in the form of FFTs. The formulation predicts the discrete spectra with specific frequency components for each order of ball waviness. Numerical results obtained from the simulation are validated with respect to those of prior results. Due to an unbalanced rotor, the system is bi-periodically excited. In the vibration spectrum, the peak amplitude of vibrations appears at the wave passage frequency (Nwωroll), rotational frequency (X) and interaction between wave passage and rotational frequencies.