均匀细杆在光滑圆锥曲线壁内的稳定平衡分析

圆锥曲线到焦点与准线的距离比值为常值即离心率e.细杆置于光滑的圆锥曲线内壁,属于定常理想约束,其重心最低时稳定平衡.在极坐标下证明,细杆过焦点则为稳定平衡,其重心轨迹为离心率相同的圆锥曲线,只是缩小e/2且顶点移动至原曲线焦点;若细杆短于2ep而不能通过焦点,则在水平位置稳定平衡.     

抛物线壁内细杆的摩擦平衡分析

细杆在抛物线壁内支承,平衡特性与杆长、倾角和摩擦因子相关.细杆在自身重力作用下可发生焦点下方的顺时针运动,焦点上方的逆时针运动以及两端同时下滑.基于端部支撑力达到摩擦锥边界的条件,可确定细杆状态为不平衡、稳定或不稳定的平衡和摩擦平衡.平衡集为具有宽度的叉式分岔.     

质点在斜面上的二维运动

质点在斜面上受到大小恒定的下滑力和摩擦力而运动,但后者方向随速度而变化。摩擦因子与斜面坡度比值即等效摩擦因子λ> 1 时质点最终在斜面上停止;0:5 λ≤6 1 时质点不会停止但水平方向运动距离存在限界,而λ≤0:5 时水平方向也可运动至无穷远。相同等效摩擦因子下质点运动轨迹的曲线簇具有包络线。     

鸡蛋在水滴上的直立及水中的稳定平衡

蛋壳没有显著的接触变形,水洗干燥之后难以在坚硬光洁的平面上直立;但依赖两三颗细小盐粒或者水膜的辅助支承即可实现大端直立.蛋在液体中姿态与浮力有关,可在水中以小端直立.与刚体、浮体相同,潜体在重力、浮力和支承力作用下处于稳定平衡时势能达到极小值.     

考虑摩擦时刚性直杆倾倒的运动分析

为了探究考虑摩擦时均质刚性直杆倾倒的全过程,利用理论分析和数值计算的方法,详细分析了在不同摩擦因数下刚性直杆倾倒的三种运动过程,得到了倾倒时的动力学方程及其解答,并推导了杆触地端位移的表达式,通过数值计算的方法绘出了杆触地端最终位移与摩擦因数的关系曲线,并通过实验验证了部分结论.     

含对称间隙的摩擦振子非线性动力学分析

建立了两自由度含对称间隙的干摩擦碰撞振动系统的动力学模型,分析了系统运动中存在的滑动、黏着及碰撞,分别给出其判断方法和衔接准则,推导出各阶段系统的解析解,并采用数值迭代方法求解和分析了系统的复杂动力学行为,同时分析干摩擦对系统动力学性能的影响.结果表明,系统存在叉式分叉,系统由对称周期运动变为反对称周期运动,进而通过Hopf分叉或周期倍化分叉通向混沌.在参数变化范围较大的情况下,系统存在类型丰富的周期运动、拟周期运动以及混沌;系统存在对称运动、反对称运动对、黏滑碰撞运动以及由初始条件决定的共存吸引子.     

冰排与斜面结构作用时的破断长度分析

研究了冰排与斜面结构的相互作用过程．文中将冰排分为在斜面附近脱离水面部分和较远处漂浮于水面部分两个区域,建立了冰排因弯曲而发生破断的数学模型,根据弯矩分布分析了冰排可能的破断位置,从而得到冰排与斜面结构相互作用时的破断长度解析表达式．结果表明,冰排破断长度既不是冰厚的固定倍数,也不与冰排特征长度直接相关．计算结果与前人实验结果吻合较好,可以为近海冰区抗冰结构的设计提供参考．     

蜗杆传动用摩擦副材料在滑动干摩擦条件下的摩擦磨损性能研究

采用MG-200型摩擦磨损试验机评价了ZQSn12-2锡青铜、ZZnAl27Cu2锌合金、S16MnCr合金钢和20CrMnTi合金钢等几种蜗杆传动用材料在干摩擦滑动条件下的摩擦磨损性能,采用扫描电子显微镜观察了其磨损表面形貌,并分析了蜗杆副材料的摩擦磨损机理.结果表明,ZQSn12-2和S16MnCr组成的摩擦副的磨损轻微,磨损率较低,其磨损表面仅出现细小的擦伤痕迹,在蜗杆传动中具有推广价值.     

烧结Fe3Al金属间化合物基摩擦材料的摩擦磨损性能研究

采用热压烧结方法制备了不同成分的Fe3Al金属间化合物基摩擦材料,考察了其物相、力学性能、抗氧化性及干摩擦磨损性能.结果表明,Fe3Al金属间化合物基摩擦材料密度低、强度高、抗氧化性好、摩擦系数稳定、高温耐磨性好;其在不同摩擦阶段的磨损机制存在差异,主要磨损机制包括磨粒磨损、塑性变形、裂纹萌生与扩展、微区脆性剥落及氧化磨损等.     

轴向冲击载荷作用下直杆弹性动态屈曲的研究

本文利用分叉的概念,从应力波理论出发,把轴向冲击载荷作用下直杆的弹性动态屈曲问题化为特征值问题,从而导出直杆动态屈曲的临界分叉准则。同时,本文对一端固支直杆受轴向冲击时的弹性屈曲问题进行了实验研究,测到的临界屈曲时间和理论预计值基本符合,证实了理论模型的合理性.理论和实验两方面的结果都表明,直杆受轴向冲击载荷作用时的屈曲现象发生在波动过程的前期,因此在处理这类问题时考虑波动效应是必要的。     

Attractivity of Equilibrium Sets of Systems with Dry Friction

The dynamics of mechanical systems with dry friction elements, modelledby set-valued force laws, can be described by differential inclusions.An equilibrium set of such a differential inclusion corresponds to astationary mode for which the friction elements are sticking. Theattractivity properties of the equilibrium set are of major importancefor the overall dynamic behaviour of this type of systems. Conditionsfor the attractivity of the equilibrium set of MDOF mechanical systemswith multiple friction elements are presented. These results areobtained by application of a generalisation of LaSalle's principle fordifferential inclusions of Filippov-type. Besides passive systems, alsosystems with negative viscous damping are considered. For such systems,only local attractivity of the equilibrium set can be assured undercertain conditions. Moreover, an estimate for the region of attractionis given for these cases. The effectiveness of the results isillustrated by means of both 1DOF and MDOF examples.     

The Effect of Chemical Equilibrium on the Formation of Stable Stratification

The formation of a stable stratification, rather than a uniformly mixed state, is shown to depend critically on the equation of state (EOS) or mixing rule for the density as a function of the solution constitution. For instance, ideal solutions can form any stable stratification at hydrostatic equilibrium, although molecular diffusion will eventually make the concentration of solute uniform. Several other types of EOS are considered at hydrostatic equilibrium, resulting in two and three layer stratifications. In the presence of convective mixing, however, the EOS serves only as a guide, since the dynamics of, for example, turbulent dispersion, significantly alter the formation of stratifications. The case of recirculating flows, however, can be simply treated and results in two layer stratifications for an EOS which is superjacent to the ideal solution. The example of stratification formation in a Burt separator is given.     

端部切向载荷作用下的压杆失稳分析及其应用

细直杆件在压应力作用下会产生横向屈曲即失稳．直杆撞击刚性平面或拉断卸载后将形成压缩波，因承载压缩载荷的长度增加可以引起失稳．冲击速度转换的压应力沿着杆件切线方向，该处弯矩和剪力为零；而众多文献设定的失稳段固支边界条件并不准确．基于精确的杆件变形曲率方程得到端部载荷指向杆件中固定点时的受压失稳条件，得到其极限状态即载荷沿杆端切向作用时失稳长度相当于两端简支的1.5 倍．对于钢丝绳拉断形成的冲击失稳，载荷恒定而长度增加，可以产生高阶屈曲即在侧向出现多次曲折，并基于尼龙-橡胶带的模拟试验给出了定性说明．     

Selecting the Coefficients of Sliding Friction in the Problem on Frictional Interaction of Three Solids

The choice of the coefficients of sliding friction in the static equilibrium problem for a system of three solids with friction at two points is discussed. This system simulates the mechanism of gravitational seismic isolation of a solid. It is shown that the coefficients of friction must be identical at both points of frictional contact irrespective of the type of the material and surface finish. A formula for the balanced coefficient of friction is derived based on experimental data     

Equilibrium of a Prestressed Strip Reinforced with Elastic Plates

The contact problem for a prestressed elastic strip reinforced with equally spaced elastic plates is considered. The Fourier integral transform is used to construct an influence function of a unit concentrated force acting on the infinite elastic strip with one edge constrained. The transmission of forces from the thin elastic plates to the prestressed strip is analyzed. On the assumption that the beam bending model and the uniaxial stress model are valid for an elastic plate subjected to both vertical and horizontal forces, the problem is mathematically formulated as a system of integro-differential equations for unknown contact stresses. This system is reduced to an infinite system of algebraic equations solved by the reduction method. The effect of the initial stresses on the distribution of contact forces in the strip under tension and compression is studied     

炭纤维对纸基摩擦材料摩擦磨损性能的影响

研制了几种炭纤维增强纸基摩擦材料,采用热分析仪和惯量摩擦试验机研究了炭纤维含量同摩擦材料的耐热性能和摩擦磨损性能的相关性.结果表明:炭纤维含量对摩擦材料的耐热性能、动摩擦系数、静摩擦系数和磨损率有较大影响;随着炭纤维含量增加,摩擦材料的起始分解温度升高,热分解速率减慢,动摩擦系数呈增大趋势,静摩擦系数和磨损率呈现减小趋势;当炭纤维含量超过5%时,动摩擦系数达到0.13左右且保持恒定;当炭纤维含量超过10%时,静摩擦系数降至0.15左右且保持恒定,纸基摩擦材料的体积磨损率小于4.5×10-8cm3/J.     

非组分黏接剂对纸基摩擦材料摩擦磨损性能的影响

为了研究黏接剂对纸基摩擦材料摩擦磨损性能的影响,以改性酚醛树脂作为黏接剂,通过高精度天平测定涂胶量,由平板硫化机固定黏接压力得到不同涂胶量的试样.利用光学显微镜观察黏接剂的渗透情况,通过惯量摩擦试验机研究涂胶量对纸基摩擦材料摩擦磨损性能的影响.试验结果表明:随着单位面积涂胶最的增加,黏接剂渗入摩擦材料的深度逐渐增大,对于厚度不大于1.0 mm的纸基摩擦材料,黏接剂可渗透材料并影响其摩擦磨损性能.随着渗透至摩擦面胶量的增加,摩擦材料的制动平稳性逐渐变差,动摩擦系数降低,静摩擦系数升高,磨损率先减小后增大.     

石墨含量对纸基摩擦材料摩擦磨损性能的影响

采用湿法工艺制备不同石墨含量的纸基摩擦材料,通过惯量试验方法研究石墨含量对纸基摩擦材料的力矩曲线及动、静摩擦系数和磨损率的影响规律;利用扫描电子显微镜观察磨损表面形貌并分析其磨损机理.结果表明:随着石墨含量增加,摩擦力矩曲线尾部翘起程度减小,趋于平整;动、静摩擦系数降低,磨损率减小;不含石墨的纸基摩擦材料的磨损表面分布着尺寸较大磨粒且出现微裂纹;随着石墨含量增加,摩擦表面形成了润滑性能良好的固体润滑膜,从而降低了材料的磨损率.     

Dynamic Study of a Structure with Flexion-Torsion Coupling in the Presence of Dry Friction

In aero engines, blade vibrations are frequently reduced by centrifugal flyweights, which exert a dry friction force per unit length under blade platforms. The response of this system to a periodic load has been analysed experimentally and theoretically. From a model having mode shapes similar to those of a blade, and a dry friction link per unit length, we show that the presence of the dry friction link is very effective in reducing vibrations for a range of excitation loads. The theoretical analysis is based on the Craig and Bampton mode synthesis, the rigid movement of the platform in its plane and the replacing of the linear dry friction link by several discrete parallel systems. Direct integration of the equations of motion is carried out by using the Newmark method. The comparison with experimental results is good. This method can easily be extended to more complex structures and shows that the dry friction link is effective when stick-slip occurs in the contact zone by limiting the energy provided to the system.     

Disk in a groove with friction: An analysis of static equilibrium and indeterminacy

This note studies the statics of a rigid disk placed in a V-shaped groove with frictional walls and subjected to gravity and a torque. The two-dimensional equilibrium problem is formulated in terms of the angles that contact forces form with the normal to the walls. This approach leads to a single trigonometric equation in two variables whose domain is determined by Coulomb's law of friction. The properties of solutions (existence, uniqueness, or indeterminacy) as functions of groove angle, friction coefficient and applied torque are derived by a simple geometric representation. The results modify some of the conclusions by other authors on the same problem.