Optimal design of journal bearings

A new mathematical optimization technique, geometric programming, is used to optimize a number of journal bearing design problems. Though a few simplifying assumptions must be made in order to write the bearing design problem mathematically, no additional simplifying assumptions are required in order to apply geometric programming. Geometric programming is found to be a powerful technique for optimizing journal bearing design problems.     

An experimental investigation on dynamic analysis of high speed carbon–epoxy shaft in aerostatic conical journal bearings

Advanced composite materials are being increasingly used in aerospace and aircraft industry where high stiffness and strength to weight ratios are important. Most of the components usually designed are static components and often non-load bearing components. But focus by designers is now shifted to critically loaded structural components such as discs, blades, etc. In early stages composite shafts were operated in the sub critical region, therefore the research was directed towards the problem associated with their sub critical operation. However, the recent trend in design of high performance rotating machinery is towards higher operating speeds leading inevitably to supercritical operation of such shafts that gives rise to issues of vibration, stability and stress. As composite material like carbon–epoxy exhibits excellent properties for structures owing to high specific modulus, high damping and low thermal expansions and therefore composite shaft made of carbon–epoxy has been made for the high speed CNC grinding machines and the centrifuges. For the analysis purpose the one step composite shaft made of carbon–fibers in epoxy matrix has been manufactured with 16 layers having stacking angles [0°/90°/45°/−45°]_2s using filament winding process. The experimental set up has been designed to investigate static and dynamic analysis and performance characteristics of the carbon–epoxy shaft in aerostatic conical journal bearing at high speeds in the range of 10,000–65,000 rpm. The vibration spectrum analysis has been observed and studied for the same. Comparison of amplitude of vibration decides the maximum operational speed of the shaft with low vibration in aerostatic conical bearings.     

Nonlinear dynamic behavior and bifurcation analysis of a rigid rotor supported by a relatively short externally pressurized porous gas journal bearing system

Summary A numerical analysis of a rigid rotor supported by relatively short externally pressurized porous gas journal bearings is presented for nonlinear dynamic behavior and bifurcation. The compressible Reynolds' equation is solved by the finite differences method, and the successive over relaxation method and a time-dependent mathematical model for porous gas journal bearings are studied. A comparison of the results for the system state trajectory, Poincaré maps, power spectra, and bifurcation diagrams is made, and the dynamic behavior of the rotor center in the horizontal and vertical directions under different operating conditions is analyzed. The analysis shows the existence of a complex dynamic behavior comprising periodic and quasi-periodic response of the rotor center. This paper shows how the dynamic behavior of this type of system varies with changes in rotor mass and bearing number.     

Tribological failure analysis of journal bearings used in sugar mills

In present paper the premature failure of journal bearings encountered in sugar mills has been analyzed. The causes of bearing failure are identified by simulating the operating conditions and conducting controlled experiments on a fully automated Journal Bearing Test Rig with provisions for varied combination (i.e. load, speed, and lubricating oil) of operating conditions. The results of performance behavior (i.e. coefficient of friction, change in surface roughness and weight loss) of the bearings as observed in these experiments have been reported. The theoretical and experimental results indicate the existence of boundary lubrication conditions in sugar mill journal bearings. To mitigate the problem of relatively high wear, lubricating oil with boundary additives have been tried and results are reported.     

Optimum design of aramid-phenolic/glass-phenolic composite journal bearings

Composite journal bearings are increasingly employed in large journal bearings for marine applications because composite materials can eliminate the seizure problem between the journal and the bearing during the start and stop periods of journals. Recently, aramid/glass reinforced phenolic composite journal bearings have been employed rather than the asbestos-phenolic composite bearings due to the health hazard of asbestos. In this work, the mechanical properties of aramid/glass reinforced phenolic composite were measured in order to analyze the stress on the journal bearing using the finite element (FE) method. The failure modes of the aramid/glass reinforced phenolic composite journal bearings were observed. The modified dimensions of aramid/glass reinforced phenolic composite journal bearings and the optimum interference fit amount were suggested using the FE-analysis results.     

Adhesive joining of composite journal bearings to back-up metals

Composite journal bearings are becoming popular for marine applications because they eliminate the possibility of seizure to steel journals, which is a drawback of white metal bearings. However, a reliable joining method for composite bearings to steel housings is required. In this work, hybrid composite journal bearings composed of carbon/phenolic and glass/epoxy laminated composites were manufactured with different stacking sequences and adhesively bonded to steel housings. The effect of deformations of the composite bearings due to thermal residual stresses on the adhesive joint performance was estimated with respect to stacking sequence by finite element method, and compared to the experimental results. From the measured and experimental results, it was found that the outward radial deformation of the composite bearings was beneficial to the adhesively bonded joint strength of the hybrid composite journal bearing.     

Surface roughness effects in dynamically loaded short bearings

Summary In this paper, the stochastic theory developed by Christensen is applied to the analysis of dynamically loaded short rough bearings. Approximate polynomial in place of Gaussian is used to represent the roughness height. To make the analysis applicable in real lubrication situations, it is assumed that the surface roughness and the minimum film thickness are of the same order. Attention is focussed on cyclic squeeze films under sinusoidal loading. It is concluded that the load is increased in the longitudinal case as compared with the transverse case. This happens due to excessive side leakage in the latter case. The effect of roughness is much more pronounced at the time when the load reverses its direction in both longitudinal and transverse cases.List of symbols c radial clearance - D diameter of the journal - e eccentricity - E() expectation of () - f(h _s ) probability density function - h film thickness - h _n nominal film thickness - h _s asperity height - H _n dimensionless nominal film thickness - L ₀ bearing length in the axial direction - n revolutions per unit time - p hydrodynamic pressure - P ₀ unit loading - R radius of journal - S Sommerfeld number - t time - T dimensionless time - U tangential velocity of the journal - V ₀ normal velocity of the journal centre - angular velocity of the journal - _L frequency of applied load - _p frequency of oscillation - W load capacity - W _a mean amplitude of the load - W ₀,W _/2 load components along and perpendicular to the line of centres - eccentricity ratio (=e/c) - Newtonian viscosity - standard deviation of the asperity height distribution - dimensionless quantity (=/c) - attitude angle - angle between vertical line and load line - random variable     

考虑刚性转子非线性振动的圆柱滚子轴承动态特性研究

圆柱滚子轴承支承的转子系统由于赫兹接触力会使系统产生复杂的非线性振动,考虑圆柱滚子轴承的四个自由度推导了非线性轴承力,在此基础上建立了滚子轴承-刚性转子系统的四自由度非线性振动方程,使用Newmark-β法和Newton-Laphson法求解方程。给出了考虑刚性转子非线性振动计算滚子轴承动态特性的方法,分析了非线性振动对滚子轴承动态性能的影响,在滚子轴承转子实验台上测试了轴承的动态性能。结果表明,在转子系统的非周期振动范围,滚子轴承的保持架打滑率、刚度等动态特性会出现较大的变化,可能会引起轴承失效。考虑转子系统非线性振动,使得滚子轴承动态特性的预测结果准确度有较大提高。     

Nonlinear dynamic analysis of a flexible rotor supported by micropolar fluid film journal bearings

The bifurcation and chaos of dynamic response of a rotor–bearing system with nonlinear suspension are investigated on the basis of assumptions of the micropolar lubricant together with short bearing approximation. The dynamics of the rotor center and bearing center are studied. The spatial displacements in the horizontal and vertical directions are considered for various non-dimensional speed ratios. The dynamic equations are solved using the Runge–Kutta method. The analysis methods employed in this study is inclusive of the dynamic trajectories of the rotor center and bearing center, Poincaré maps and bifurcation diagrams. The maximum Lyapunov exponent analysis is also used to identify the onset of chaotic motion. The numerical results show that the stability of the system varies with the non-dimensional speed ratios. Specifically, it is found that the dynamic behaviors of the system include periodic, quasi-periodic and chaotic motions. Thus it is concluded that the bearing and rotor center trajectory had undesirable vibrations. Understanding the dynamic behaviors of these parameters provides theoretical and practical ideas for controlling rotor–bearing systems and optimizing their operation.     

固定瓦-可倾瓦组合径向轴承—柔性转子系统非线性运动分析

摘要：本文针对流体润滑中具有Reynolds边界条件的非定常Reynolds方程,运用Castelli法求解Reynolds方程,生成了单块轴瓦坐标系下的非线性油膜力数据库。根据固定瓦-可倾瓦组合滑动轴承的结构特点,对单瓦库进行检索、插值和拼装,获得了固定瓦-可倾瓦组合径向滑动轴承的非线性油膜力。针对柔性转子-组合滑动轴承系统,运用自适应步长Runge-Kutta法和Poincaré映射计算了不同支点比下的轴颈的非线性运动轨迹。数值结果表明,转子系统表现出周期解,倍周期解和准周期解等非线性现象,支点比为0.6时的系统性能略优于支点比为0.5时的系统性能。     

The mechanical behaviour of PEEK short fibre composites

Short glass (GF) and carbon fibre (CF) reinforced poly-ether-ether-ketone (PEEK) composites were prepared by injection moulding and then microstructurally characterized. Their mechanical behaviour was determined by two different methods: a classical unidirectional tensile test and an immersion ultrasonic technique. The reinforcing effect of fibres is discussed in the context of the theory of reinforcement of Bowyer and Bader. Interfacial shear strength and critical fibre length at break are calculated for both PEEK/GF and PEEK/CF composites. Examinations of fracture surfaces of uniaxial tensile specimens revealed a higher adhesion of carbon fibres to PEEK matrix in regards to the adhesion concerning glass fibre-PEEK interfaces, which is in agreement with the results provided by the model. Compatibility of ultrasonic and tensile results is reported.     

The fracture behaviour of short glass fibre-reinforced polyoxymethylene

This paper describes an examination of the fracture behaviour of hydrostatically extruded polyoxymethylene. Unfilled and glass-filled extrudates were tested, both with a nominal draw ratio of 8, the highest obtainable for this material using the extrusion process. The compact tension geometry was used for the fracture tests. Samples were loaded perpendicular and parallel to the extrusion direction and tests were carried out at +20 and −50°C. The glass-filled extrudate showed a significant improvement in fracture behaviour compared with the unfilled extrudate, with an increase in the fracture toughness and stable rather than unstable crack propagation. Most interestingly, the crack propagation was still stable at − 50°C.     

Analysis of finite journal bearings with longitudinal and transversal rough surfaces

This paper represents a numerical iterative scheme for calculation of finite 360° journal bearings with longitudinal and transversal rough surfaces. A modified Christensen's Reynolds type equation is solved numerically under isothermal boundary condition. The Reynold's boundary condition assuming that the pressure and its derivative vanish near the point of location of the minimum film thickness is used in an iterative scheme to find out this location. Results of the analysis show the great influence of surface roughness on the bearing behaviour, especially when the bearing operates at its hydrodynamic limit.     

Torsional load transfer from a rigid shaft to an elastic plane with a slit

A plane elastostatic problem for an elastic wedge loaded by a concentrated moment at its apex provides an example of violation of the Saint-Venant principle for apex angles 2 larger than . Considering the problem for a truncated wedge, Neuber demonstrated the method of construction of an applicable solution for any apex angles in the range 22, despite the failure of the Saint-Venant principle. In the present paper the particularly important case of the truncated-wedge problem is examined. The truncated wedge degenerates into a slitted elastic plane, while a rigid circular shaft, acted upon by a torsional moment, is inserted into the plane. The analytical solution of the mixed boundary-value problem is obtained. Numerical results turn out to be in complete agreement with Neuber's results for the slitted elastic plane.     

Wear behaviors of Polytetrafluoroethylene and glass fiber reinforced Polyamide 66 journal bearings

In this study, the effect of sliding velocity, bearing pressure and temperature on friction and wear of PA66 (Polyamide 66), PA66 + 18% PTFE (Polyamide 66 + 18% Polytetrafluoroethylene) and PA66 + 20% GFR + 25% PTFE (Polyamide 66 + 20% glass fiber + 25% Polytetrafluoroethylene) journal bearings were examined at ambient conditions. The results of experiments are presented in graphics which proves that friction coefficients, contact temperatures and wear rates are affected by forming film, increasing temperature, pressure and velocities depending on GFR and PTFE mechanical properties. There are many factors and their widely fluctuation characters on the polymer friction and wear behaviors. The best wear behavior was seen at the PA66 + 20% GFR + 25% PTFE journal bearing.     

Thermoelastic contact of a rotating shaft with a rigid bush in conditions of bush wear and stick-slip movements

The nonlinear problem of thermoelastic contact of a rotating shaft with a rigid bush fixed to the base elastically (springs) is investigated using both Laplace transform and perturbation methods. A friction coefficient is assumed to be a nonlinear function of a relative velocity. The solution to the problem is reduced to the system of nonlinear differential and integral equations. Zones of steady-state solution stability and friction self-excited oscillations existence are established. The numerical analysis is carried out and some important conclusions are given.     

Corrosion fatigue short crack growth behaviour in a high strength steel

The influence of an aggressive environment (0.6 M, aerated NaCl solution) on short fatigue crack initiation and growth behaviour has been studied. The study involved three major test series, namely: air fatigue, corrosion fatigue, and intermittent air fatigue/corrosion fatigue. The above tests carried out under fully reversed torsional loading conditions at a frequency of 5 Hz, showed that it was the non-metallic inclusions which took part in crack initiation resulting from debonding at metal matrix/inclusion interface and pitting of inclusions in both air and corrosove environments, respectively. Short fatigue crack growth results in these two environments obtained by using plastic replication technique, indicated a large effect of microstructure i.e. prior austenite grain boundaries. The stage/stages at which the environmental contribution was dominant has been discussed by considering the results achieved from intermittent tests. However, the mechanisms involved in corrosion fatigue short crack growth have also been described in the light of results obtained from futher investigations carried out by conducting corrosion fatigue tests under applied cathodic potential conditions and tests on hydrogen pre-charged specimens under air fatigue and uniaxial tension conditions.     

基于混合均质模型的气液两相流润滑动静压轴承性能分析

依据所建立的从全液体状态经混和介质状态,直至全气体状态的连续汽化流体属性模型,联合广义雷诺方程及全能量方程,从理论上对处在连续变化低温介质条件下的径向动静压轴承的静动特性进行研究。研究结果表明,由于两相流条件下的流体压缩性发生了极大变化,因而使得处在该条件下的轴承性能不再满足全液体或全气体介质润滑下的轴承性能规律。