Chaotic motions of a rigid rotor in short journal bearings

In the present paper the conditions that give rise to chaotic motions in a rigid rotor on short journal bearings are investigated and determined. A suitable symmetry was given to the rotor, to the supporting system, to the acting system of forces and to the system of initial conditions, in order to restrict the motions of the rotor to translatory whirl. For an assigned distance between the supports, the ratio between the transverse and the polar mass moments of the rotor was selected conveniently small, with the aim of avoiding conical instability. Since the theoretical analysis of a system's chaotic motions can only be carried out by means of numerical investigation, the procedure here adopted by the authors consists of numerical integration of the rotor's equations of motion, with trial and error regarding the three parameters that characterise the theoretical model of the system: m, the half non-dimensional mass of the rotor, , the modified Sommerfeld number relating to the lubricated bearings, and , the dimensionless value of rotor unbalance. In the rotor's equations of motion, the forces due to the lubricating film are written under the assumption of isothermal and laminar flow in short bearings. The number of numerical trials needed to find the system's chaotic responses has been greatly reduced by recognition of the fact that chaotic motions become possible when the value of the dimensionless static eccentricity % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbnL2yY9% 2CVzgDGmvyUnhitvMCPzgarmWu51MyVXgaruWqVvNCPvMCG4uz3bqe% fqvATv2CG4uz3bIuV1wyUbqee0evGueE0jxyaibaieYlf9irVeeu0d% Xdh9vqqj-hEeeu0xXdbba9frFf0-OqFfea0dXdd9vqaq-JfrVkFHe9% pgea0dXdar-Jb9hs0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaaca% qabeaadaabauaaaOqaaiabew7aLnaaBaaaleaacaWGZbaabeaaaaa!4046!\[\varepsilon _s \] is greater than 0.4. In these conditions, non-periodic motions can be obtained even when rotor unbalance values are not particularly high (=0.05), whereas higher values (>0.4) make the rotor motion periodic and synchronous with the driving rotation. The present investigation has also identified the route that leads an assigned rotor to chaos when its angular speed is varied with prefixed values of the dimensionless unbalance . The theoretical results obtained have then been compared with experimental data. Both the theoretical and the experimental data have pointed out that in the circumstances investigated chaotic motions deserve more attention, from a technical point of view, than is normally ascribed to behaviours of this sort. This is mainly because such behaviours are usually considered of scarce practical significance owing to the typically bounded nature of chaotic evolution. The present analysis has shown that when the rotor exhibits chaotic motions, the centres of the journals describe orbits that alternate between small and large in an unpredictable and disordered manner. In these conditions the thickness of the lubricating film can assume values that are extremely low and such as to compromise the efficiency of the bearings, whereas the rotor is affected by inertia forces that are so high as to determine severe vibrations of the supports.Nomenclature C radial clearance of bearing (m) - D diameter of bearing (m) - e dimensional eccentricity of journal (m) - e _s value of e corresponding to the static position of the journal - E dimensional static unbalance of rotor (m) - f _x, f _y =F _x/(P), F _y/(P): non-dimensional components of fluid film force - F _x, F _y dimensional components of fluid film force (N) - g acceleration of gravity (m/s²) - L axial length of bearing (m) - m % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbnL2yY9% 2CVzgDGmvyUnhitvMCPzgarmWu51MyVXgaruWqVvNCPvMCG4uz3bqe% fqvATv2CG4uz3bIuV1wyUbqee0evGueE0jxyaibaieYlf9irVeeu0d% Xdh9vqqj-hEeeu0xXdbba9frFf0-OqFfea0dXdd9vqaq-JfrVkFHe9% pgea0dXdar-Jb9hs0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaaca% qabeaadaabauaaaOqaaiabg2da9maalaaabaGaeqyYdC3aaWbaaSqa% beaacaaIYaaaaaGcbaGaeqyYdC3aa0baaSqaaGabciaa-bdaaeaaca% WFYaaaaaaakiabg2da9maalaaabaGaeqyYdC3aaWbaaSqabeaacaaI% YaaaaOGaam4qaaqaaiabeo8aZjaadEgaaaaaaa!4C14!\[ = \frac{{\omega ^2 }}{{\omega _0^2 }} = \frac{{\omega ^2 C}}{{\sigma g}}\]: half non-dimensional mass of rotor - M half mass of rotor (kg) - n angular speed of rotor (in r.p.m.=60/2) - t time     

圆形刚性夹杂双周期分布的反平面问题

研究含双周期分布的圆形刚性夹杂在无穷远受纵向剪切的弹性平面问题，遵循复合材料中各夹杂相互影响的重要条件。采用复变函数方法。构造相应模型的复应力函数。通过坐标变换，同时满足夹杂边界位移条件，再利用围线积分将求争方程组化为线性代数方程组。导出了圆形刚性夹杂双周期分布的界面应力解析表达式。算例给出了界面应力最大值与夹杂间距的变化规律。求出了刚性夹杂的合理间距问题，本文发展的分析方法为研究夹杂材料的细观机理探索了一条有效的分析途径。     

Studying the Suitability of Nineteen Lignins as Partial Polyol Replacement in Rigid Polyurethane/Polyisocyanurate Foam

In this study, nineteen unmodified lignins from various sources (hardwood, softwood, wheat straw, and corn stover) and isolation processes (kraft, soda, organosolv, sulfite, and enzymatic hydrolysis) were used to replace 30 wt.% of petroleum-based polyol in rigid polyurethane/polyisocyanurate (PUR/PIR) foam formulations. Lignin samples were characterized by measuring their ash content, hydroxyl content (Phosphorus Nuclear Magnetic Resonance Spectroscopy), impurities (Inductively Coupled Plasma), and pH. After foam formulation, properties of lignin-based foams were evaluated and compared with a control foam (with no lignin) via cell morphology, closed-cell content, compression strength, apparent density, thermal conductivity, and color analysis. Lignin-based foams passed all measured standard specifications required by ASTM International C1029-15 for type 1 rigid insulation foams, except for three foams. These three foams had poor compressive strengths, significantly larger cell sizes, darker color, lower closed-cell contents, and slower foaming times. The foam made with corn stover enzymatic hydrolysis lignin showed no significant difference from the control foam in terms of compressive strength and outperformed all other lignin-based foams due to its higher aliphatic and p-hydroxyphenyl hydroxyl contents. Lignin-based foams that passed all required performance testing were made with lignins having higher pH, potassium, sodium, calcium, magnesium, and aliphatic/p-hydroxyphenyl hydroxyl group contents than those that failed.     

医用硬性内窥镜畸变的评定基础和方法

建立医用硬性内窥镜畸变的评定基础和方法,用视轴对称的球面Z视场为模型来模拟体腔凹面特征,以建立内窥镜物像共轭的分析基础;运用光学原理并结合ISO9039:1994“光学和光学仪器光学系统质量评价———畸变的测定”的定义原则,并根据理论畸变的临床要求确定畸变定义;采用主光线追迹原理推导不同球面Z形状的畸变换算通式。创立了医用硬性内窥镜以单位相对畸变表述的定义和表达式,并导出变换视场面的畸变换算通用公式和测试方法。本文建立的畸变评定基础和方法适用于医用硬性内窥镜的标准应用。     

液态金属熔池中气泡-液体两相湍流的数值模拟研究

应用欧拉-欧拉双流体模型,以及分别描述气泡和液体湍流的两相湍流模型,描述液态金属中气体射流发泡过程的两相流动及气泡分布。与实验结果的对比表明,本模型的预测能力优于前人未考虑气相湍流的模型。考查了液体物性和气泡尺寸对流场特性的影响,结果发现,液体密度越低,气泡尺寸越小,气泡分布就越均匀。     

Effect of multiple H‐bonding on the properties of polyimides containing the rigid rod groups

To investigate the influence of hydrogen bonding on the properties of polyimides (PIs) containing rigid rod‐like groups, five symmetrical diamines containing benzimidazole, benzoxazole, and hydroxy group were synthesized, and then a series of PIs were prepared. Results showed that hydroxyl‐containing poly(benzoxazole imide)s possess higher glass transition temperature (T_g) and dimensional stabilities than their corresponding poly(benzoxazole imide)s. Moreover, the corresponding poly(benzimidazole imide)s presented the best performances, such as the highest T_g, the highest char yield and the highest dimensional stabilities. The influence of hydrogen bonding of benzimidazole on the properties of PIs was stronger than that of hydroxyl groups. Hydroxyl‐containing poly(benzoxazole imide)s were formed in crosslinking structures after heat treatment at 400 °C. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2016 , 54, 570–581     

Effect of Temperature on Henry's Constant in Simple Mixtures

Abstract

The molecular theory of dense fluids is progressing rapidly and its extension to mixtures is well underway. The purpose of this note is to call attention to a possibly serious difficulty in comparing experimental Henry's constants with those calculated from theory. The difficulty arises because whereas theorists choose temperature and density as independent variables, experimental equilibrium measurements on mixtures are often made along the saturation line where (at fixed composition) temperature and density are not both independent variables. Unless Henry's constants are defined with care, the effect of temperature on Henry's constants calculated from molecular theory may be qualitatively different from that observed.     

Synthesis of poly(isopropenylphenoxy propylene carbonate) and its facile side‐chain functionalization into hydroxy‐polyurethanes

4‐Isopropenyl phenol ( 4‐IPP ) is a versatile dual functional intermediate that can be prepared readily from bisphenol‐A ( BPA ). Through etherification with epichlorohydrin to the phenolic group of 4‐IPP , it can be converted into 4‐isopropenyl phenyl glycidyl ether ( IPGE ). On further reaction with carbon dioxide in the presence of tetra‐n‐butyl ammonium bromide ( TBAB ) as the catalyst, IPGE was transformed into 4‐isopropenylphenoxy propylene carbonate ( IPPC ) in 90% yield. Cationic polymerization of IPPC with strong acid such as trifluoromethanesulfonic acid or boron trifluoride diethyl etherate as the catalyst at ?40 °C gave a linear poly(isopropenylphenoxy propylene carbonate), poly( IPPC ), with multicyclic carbonate groups substituted uniformly at the side‐chains of the polymer. The cyclic carbonate groups of poly( IPPC ) were further reacted with different aliphatic amines and diamines resulting in formation of polymers with hydroxy‐polyurethane on side‐chains. Syntheses, characterizations of poly( IPPC ) and its conversion into hydroxy‐polyurethane crosslinked polymers were presented. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2016 , 54, 802–808     

Geometric lattice actions, entropy and fundamental groups

Let be a lattice in a noncompact simple Lie Group G, where . Suppose acts analytically and ergodically on a compact manifold M preserving a unimodular rigid geometric structure (e.g. a connection and a volume). We show that either the action is isometric or there exists a "large image" linear representation of . Under an additional assumption on the dynamics of the action, we associate to a virtual arithmetic quotient of full entropy. Received: December 14, 2000