Analytic study on structural behavior of the string bed in a tennis racket

The structural behavior of string bed of tennis rackets was investigated subjected to transverse force perpendicular to the string bed. The mathematical model developed for the string bed was implemented into a computer programming code. This code was used to conduct extensive parametric studies on the structural behavior of the string bed for various parameters, including string tension, axial rigidity of the string, string spacing and head size. The analysis results showed that while the transverse stiffness of the string bed is proportional to the string tension, the transverse stiffness of the string bed is inversely proportional to string spacing and head size. In addition, the axial rigidity of the string significantly amplifies the transverse stiffness of the string bed for relatively large transverse deflection of the string bed.     

网球自动发射器的研制

针对网球训练项目中的技术要求和存在的问题,提出了设计网球自动发射器的想法;介绍了网球自动发射器的基本结构;阐述了网球自动发射器实现发球频率、力量、角度的调整以及实现球的旋转等工作原理;并对该科研产品的性能特点进行了合理的分析.     

乒乓球偏心检测方法

在充分尊重现行国际乒乓球联合会制定的新T3标准的前提下, 提出了一种基于气流中悬浮和机器视觉的乒乓球偏心的检测方法. 该方法通过多次有序摄取处于悬浮旋转状态的乒乓球图像, 以不同截面圆最小二乘拟合圆圆心点集的最小包容圆直径作为评价乒乓球偏心程度的基本参数. 实验结果表明, 拟合圆圆心点集的最小包容圆直径能有效反应乒乓球的偏心程度. 该方法为乒乓球偏心的在线检测提供了技术基础.     

Effects of string tension and impact location on tennis playing

Finite element impact simulations were performed to observe the vibration of a tennis racket and its strings, as well as the effects of string tension and impact location on a player’s hand and his chances of getting an injury. Studies using the finite element method [FEM] revealed that decreasing the string tension lowers the coefficient of restitution. The ratio of speed to angle change increases with a decrease in string tension. Moreover, the resultant force on the player’s hand is stronger if the tennis ball hits the dead spot than if it hits the sweet spot. For instance, as a tennis ball hits the dead spot with a speed of 10.05m/s, an angle of 15°, and a string tension of 222N, the player’s hand feels a maximum resultant force of almost 424N, which is 1.61 times higher than if the ball hits the sweet spot, at t=0.081 and t=0.0149. Moreover, the force exerted on the player’s hand if the ball hits either the best-bounce spot or the off-center spot is 1.4 times higher than if the ball hits the sweet spot.     

Development and validation of a nonlinear dynamic impact model for a notch impact

The International Journal of Advanced Manufacturing Technology - Finite element simulations are being more and more applied when studying the crash-worthiness of vehicles during impact. This paper...     

Load-displacement relationship model and measurement of deep groove ball bearing and 4-point contact ball bearing

Journal of Mechanical Science and Technology - This paper established geometric coordination equations of deep groove ball bearings (DGBB) and 4-point ball bearings (4PBB) in which the contact...     

Nonlinear model identification of a frictional contact support

Accurate predictions of a structure dynamics require precise modeling of its boundary conditions including any nonlinear effects. This paper investigates the behavior of frictional supports that are examples of boundary conditions exhibiting nonlinear effects, such as stiction and slip phenomena, depending on the structure vibration amplitudes. The dependency of restoring forces in a frictional contact to the vibration amplitude level is identified in this study using experimental observations. In an experimental case study measured responses of a beam fixed at one end and frictionally supported at the other end were expanded using corresponding nonlinear normal modes of the structure and a reduced order model of the continuous system containing dominant nonlinear effects of the contact was obtained. The obtained discrete model constitutes bases for identification of restoring forces in the contact interface using force state mapping. The identified nonlinear restoring forces are then employed to specify parameters of a predictive contact model for the boundary support. The obtained contact model is capable of predicting damping and softening effects due to micro/macro-slippage and accurately regenerates the experimental results at various response levels.     

The nonlinear and ball pass effects of a ball bearing on rotor vibration

A ball bearing is generally assumed as a linear spring in rotor dynamic analysis. In real case, the force equilibrium of the bearing is changed as the relative position, of each ball with respect to the direction of radial force. So, the stiffness of the bearing is also changed and is a function of time and position. In this study, the nonlinear characteristics of a ball bearing are considered in analyzing the vibration response of a rotating shaft due to an unbalance force. A finite element method is used to analyze the vibration characteristics of a rotor-bearing system and a direct numerical integration is performed to calculate the transient response of the rotor system. The responses are converted to the frequency domain and the effects of the parametric excitation due to a ball bearing are examined. The test rig for the investigation of the effect of a ball bearing on the rotor vibration is set up and the results are compared with those of numerical calculation. The calculation results show that the amplitudes of the nonlinear model are larger than those of the linear one. The frequencies of the calculations can be matched to the measured frequencies.     

采用弹性连接降低滚珠丝杠副中滚珠对返向器的冲击

建立了滚珠丝杠副中返向器与螺母弹性连接时滚珠与返向器碰撞的模型,推导了连接刚度处于两种极限状态下最大碰撞力的公式,讨论了连接刚度对碰撞力的影响.研究表明,连接刚度较大时,滚珠对返向器的碰撞力也较大,连接刚度对碰撞力的影响程度受滚珠与返向器质量比的影响,该质量比较大时,连接刚度对碰撞力的影响比较明显.振动和噪声的测试结果表明,在返向器与螺母之间采用弹性连接可以有效降低滚珠对返向器的冲击,提高滚珠丝杠副的性能.     

A model for coulomb torque hysteresis in ball bearings

The frictional torque resisting rotation of an angular contact ball bearingg builds up from rest to its steady value through a small but finite angle of rotation. A similar transient torque is observed when the direction of rotation is reversed so that, in a bearing which undergoes oscillating rotations of small amplitude, the resistance torque traces out a hysteresis loop with angle of rotation. Following Dahl [AFO 4695-67-C-D158, Aerospace Corp. (1968)], the shape of the loop is expressed in terms of two parameters: (i) the initial and reversal gradient s and (ii) the steady-state torqueT_s. Theoretical expressions are derived for both s and T_s. s depends upon the elasticity of the bearing materials but not upon the frictional conditions at the contact interface whereas the opposite applies to T_s. Both depend upon the geometry of the bearing, particularly the conformity between the ball and race. Good correlation has been found between theoretical predictions and experiments carried out on three bearings of significantly different geometry.     

球体镀铬对圆弧槽强度及其使用寿命的影响

分析了阀杆对低强度钢或铜合金球体圆弧槽剪切破坏的原因。提出了球体及其圆弧槽的镀铬工艺方法，并进行了球体镀铬后的耐磨性试验。     

Nonlinear impact of traction rod on the dynamics of a high-speed rail vehicle carbody

Journal of Mechanical Science and Technology - This paper focuses on the bogie-carbody nonlinear dynamic interaction of a Shinkansen high-speed rail vehicle. The Euler-Bernoulli beam model is used...     

伺服系统中滚珠丝杠的温度场模型

分析了伺服系统中丝杠螺母的热特性规律,并对丝杠温度场进行了简化建模,以快速准确地预测丝杠温度分布及变化.简化模型能较好地预测丝杠温升过程,但稳态误差较大;通过引进时间修正系数修正了该简化模型,修正后的模型能较好地预测丝杠的稳态温度,但对温度上升过程的预测误差较大;鉴于两个模型的特点,基于分段建模的思想,建立了丝杠温度场...     

基于ANSYS/LS-DYNA的电源适配器外壳耐钢球撞击性的分析

钢球撞击试验是电源适配器安全规范测试中重要的一个测试,主要目的是模拟不明外物对其造成的伤害是否对使用者的安全构成威胁。介绍了GB 4943对资讯类电子产品钢球撞击试验,并寻求使用LS/DYNA对笔记本电源适配器的外壳厚度对抗钢球冲击进行仿真分析。建立在127×66×15 mm外壳基础上的仿真结果显示,厚度为1.1 mm、1.5 mm、1.7 mm、2.0 mm的正面撞击,钢球在撞击5 ms后,除了1.1 mm厚度外,返回的速度逐渐增大,从而对产品的破坏也随之减小,破坏程度可以通过带失效模式的材料模型进行仿真显示。可以通过LS/DYNA来仿真此类试验,且单纯撞击外壳时对仿真建立的外壳厚度2.0 mm是比较保险的。     

Nonlinear thermodynamic model of boundary friction

Melting of an ultrathin lubricant film confined between two atomically flat surfaces is studied. An excess volume parameter is introduced, the value of which is related to the presence of defects and inhomogeneities in the lubricant. Via minimization of the free energy, the Landau-Khalatnikov kinetic equation is obtained for this parameter. The kinetic equation is also used for relaxation of elastic strains, which in its explicit form contains the relative shear velocity of the rubbing surfaces. With the numerical solution of these equations, a phase diagram with domains corresponding to the sliding and dry stationary friction regimes is built at a fixed shear velocity. A simple tribological system is used to demonstrate that in the dynamic case, three friction regimes can occur, namely, dry, stick-slip, and sliding friction. It is shown that a lubricant can melt when the shear velocity exceeds a critical value and with elevation of its temperature. The dependence of the dynamic friction force on the pressure applied to the surfaces, the temperature of the lubricant, and the shear velocity is considered. It is shown that growth of pressure leads to the forced ordering and solidification of the lubricant.     

Nonlinear model predictive control of a Hammerstein Weiner model based experimental managed pressure drilling setup

Design and implementation of a nonlinear model predictive controller (NMPC) on a pilot scale managed pressure drilling (MPD) setup is demonstrated. The goal of the controller is to maintain constant bottomhole pressure (BHP) and mitigate kick during reservoir influx scenario. Under normal condition, the controller tracks bottomhole pressure to a predefined setpoint. A Hammerstein Weiner nonlinear model has been used for pressure prediction, and genetic optimization algorithm for calculating optimal control input. During reservoir influx the controller switches to flow control mode to balance the pump flow and choke flow. After kick mitigation the controller switches back to pressure regulation mode by revising the setpoint pressure to estimated reservoir pressure. The NMPC controller delivered good performance over PI controller during normal operation, pump failure, and gas kick cases where flow demand changes frequently.     

Liquid drop impact on solid surface with application to water drop erosion on turbine blades,Part I: Nonlinear wave model and solution of one-dimensional impact

Water drop erosion is regarded as one of the most serious reliability concerns in the wet steam stage of a steam turbine. The most challenging aspect of this problem involves the fundamental solution of the transient pressure field in the liquid drop and stress field in the metal substrate, which are coupled with each other. We solve the fundamental problem of high-speed liquid–solid impact both analytically and numerically. In Part I of this paper, the governing equations based on a nonlinear wave model for liquid are derived. Analytical and approximate solutions of one-dimensional liquid–solid impact are given for both linear and nonlinear models, which provide critical insights into the water drop erosion problem. Both continuous and pulsant impacts on rigid and elastic substrates are analyzed in detail. During continuous impact, the maximum impact pressure is always higher than the water hammer pressure. Upon pulsant impact and at a particular instant related with the impact duration, the maximum tensile stress appears at a certain depth below the solid surface, which can be readily related with the erosion rate. In Part II of this paper, two-dimensional (axisymmetric) liquid–solid impact is solved numerically, from which the most dangerous impact load/duration time and the most likely crack positions are deduced. Based on our recent solution of the water drop impact statistics (associated with the fluid flow in the blade channel), a comprehensive numerical study of the water drop erosion (fatigue) on a turbine blade is carried out.     

Nonlinear finite element analysis of composite shell under impact

Large deflection dynamic responses of laminated composite cylindrical shells under impact are analyzed by the geometrically nonlinear finite element method based on a generalized Sander’s shell theory with the first order transverse shear deformation and the von-Karman large deflection assumption. A modified indentation law with inelastic indentation is employed for the contact force. The nonlinear finite element equations of motion of shell and an impactor along with the contact laws are solved numerically using Newmark’s time marching integration scheme in conjunction with Akay type successive iteration in each step. The ply failure region of the laminated shell is estimated using the Tsai-Wu quadratic interaction criteria. Numerical results, including the contact force histories, deflections and strains are presented and compared with the ones by linear analysis. The effect of the radius of curvature on the composite shell behaviors is investigated and discussed.