在微粗糙平面上滚动的Chaplygin球的稳定性

本文利用文献[1]的结果,继续讨论 Chaplygin 球在微粗糙平面上滚动的稳定性。严格证明了在粘性和库仓两种磨擦条件下球绕最大惯量主轴滚动的一致稳定性,和在粘性摩擦条件及球的最大与中间主惯量矩十分接近的前提下球绕最小惯量主轴滚动的不稳定性。     

微粗糙平面上翻身陀螺的稳定性

本文讨论微粗糙平面上翻身陀螺绕直立的极轴永久转动的稳定性。应用关于部分变量的稳定性定理,导出在粘性和库仑两种摩擦条件下的解析形式稳定性判据。该判据用永久转动角速度的大小而不是进动角速度的大小作为判别准则,较为合理。     

A comprehensive study on the behavior of a rigid block on an oscillating ground with friction,elastic and viscous forces

This paper investigates the behavior of a non-linear mechanical model where a block is driven by an oscillating ground through Coulomb friction, a linear viscous damper and a linear spring. The governing equation is solved analytically for different partial configurations: friction only, friction with viscous damping, friction with a linear restoring force, and for the complete model. Using dimensionless groups, the analysis of the block motion provides a comprehensive set of information on the motion regime (stick, stick-slip or permanent sliding), on the dominant energies or forces, on the resonance and on the amplification of the ground oscillation by the system. The limit between the stick-slip regime and the permanent slipping regime is found either analytically or numerically. It is also shown that there exists a set of parameters for which the friction force, the viscous dissipative force and the elastic restoring force are equal.     

粗糙平面上陀螺的稳定性

本文用摄动法讨论微粗糙平面上轴对称陀螺绕直立的极轴或赤道轴永久转动的稳定性。作为摄动因素的摩擦力是滑动速度的任意非线性函数。导出的解析形式稳定性判据与Contensou-Magnus线性理论一致,但摒弃了线性摩擦假定,指出刚体在接触点处滑动速度的方向是影响陀螺旋转稳定性的主要因素,并给出明确的物理解释。     

A shock tube research facility for high-resolution measurements of compressible turbulence

A new shock tube facility with a 30.5 cm (1 ft) inside diameter is currently in operation that allows for high-spatial-resolution measurements of compressible turbulence. Small scales of turbulence behave very differently from large scales when they interact with shock or expansion waves. Highly resolved measurements can provide new information on the interaction at small scales. Another notable characteristic of the present facility is the ability to control the flow velocity behind the reflected shock through the porosity of the reflecting wall. Tests showed good flow quality with sufficiently long observation times. Measurements of piecewise average skin friction over short segments of the tube indicated strong viscous effects very close to the diaphragm where the shock is developing. The skin friction and the shock propagation speed virtually remained constant inside the working section of the shock tube in all investigated flow cases, even in low Mach number cases where viscous effects are stronger. The experimental results are compared with numerical simulations, including the effects of the reflecting porous wall and viscous effects.     

Non-linear dynamic analysis of the ultra-short micro gas journal bearing-rotor systems considering viscous friction effects

Due to the micro-fabrication limitations and the low thickness of the silicon wafer, the length-to-diameter ratio (L/D) of the gas journal bearings in Power MEMS is about one order lower than that of the conventional bearings, which suggests that the viscous friction force in the micro-bearing is comparable to the load capacity. The effects of viscous friction force on non-linear dynamic characteristics of the ultra-short micro-bearing-rotor system are studied in this paper. The molecular gas-film lubrication model, which valid for arbitrary Knudsen numbers, is systematically coupled with the rotor kinetic equations and solved simultaneously to investigate the non-linear dynamic behavior of the system. The center orbits, phase portraits, Poincaré maps, and FFT spectra of the system response at different L/D ratio, rotor mass, and bearing number, and the corresponding bifurcation diagrams for cases of ignoring and considering viscous friction force are inspected and compared. The results indicate that, if the viscous friction force is not taken into account in the case of low L/D ratio, the low-frequency large-amplitude self-excited whirl motion will be predicted as the increase of the rotor mass and the bearing number. However, when the viscous friction force is included in the non-linear dynamic model, the rotor motion becomes more stable under the same conditions, as the synchronous motion with smaller amplitude prevails.     

液粘离合器摩擦特性及热负荷特性研究

本文针对新型液粘离合器的摩擦系数和热负荷进行试验研究,其中摩擦系数是液粘离合器特性的核心衡量指标,通过摩擦学理论研究,确定液粘离合器的摩擦状态,找到适用的试验方法对其进行了测试计算,根据结果进行分析,得出液粘离合器在不同转速差、不同入口油温以及不同正压力的摩滑状态时摩擦系数的变化趋势,并得到不同转速差对摩擦系数的影响公式;应用润滑油流量和摩擦功率损失计算液粘离合器的热平衡温度,并通过试验对摩擦片的热负荷进行了研究,对比分析液粘离合器热量散失的方式,发现液粘离合器摩擦片摩滑状态的热负荷计算公式有待改进;针对摩擦片轴向温度分布不平衡,制定了润滑流量的匹配结构优化方案.     

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.     

Viscosity-stratified flow in a Hele–Shaw cell

A hierarchy of mathematical models describing viscosity-stratified flow in a Hele-Shaw cell is constructed. Numerical modelling of jet flow and development of viscous fingers with the influence of inertia and friction is carried out. One-dimensional multi-layer flows are studied. In the framework of three-layer flow the interpretation of the Saffman–Taylor instability is given. A kinematic-wave model of viscous fingering taking into account friction between the fluid layers is proposed. Comparison with calculations on the basis of two-dimensional equations shows that this model allows to determine the propagation velocity of the viscous fingers.     

Friction Drag Variation via Spanwise Transversal Surface Waves

The introduction of spanwise velocity is a promising technique to effect the near-wall turbulent flow field to influence friction drag. However, the essential physical mechanism which significantly reduces friction drag has not been understood, yet. It is the objective of this numerical study to improve the fundamental knowledge on the drag reduction mechanism. The investigation is based on spanwise traveling transversal surface waves which are applied to modify the near-wall flow field and to influence friction drag. Two actuation configurations are analyzed in detail. Compared with an unactuated flat plate boundary layer simulation the first wave setup, which represents a low frequency wave at an amplitude larger than the viscous sublayer, leads to a reduced wall-shear stress resulting in friction drag reduction of up to 9%. The second wave setup, which possesses a higher frequency and an amplitude in the range of the viscous sublayer, yields an increase of friction drag of about 8%. Unlike previous investigations which focus on excitation setups to lower friction drag, the comparison of the two wave setups in this study allows to identify the effects which on the one hand, lead to drag reduction and on the other hand, result in drag increase. That is, due to the pronounced differences the major effects determining the friction distribution are more evident. The two key features for drag reduction are the damping of the wall-normal vorticity fluctuations above the entire surface and the decrease of turbulence production. Furthermore, the effect of rearranging streamwise vorticity, which has been stated to be responsible for drag reduction, is found to occur at increasing and decreasing drag, i.e., it is not the effect that lowers the friction drag.