多支承轴系轴承受力与刚度的有限元迭代计算方法

为了准确计算多支承轴系中每一个轴承的受力与刚度,分析预紧力对轴承刚度的影响,提出了一种基于有限元分析的迭代计算方法.该方法考虑了主轴受载后轴承受力与刚度的相互影响关系,在轴系和单轴承的有限元模型中利用受力-变形-刚度关系式进行迭代求解,以此寻找轴承受载后的平衡状态.通过与典型数值计算结果的比较可以看出,所提方法解算出了每一个轴承的受力和刚度,解决了多支承轴系的超静定问题和支承-轴承受力分配问题.通过轴承受载变形实验同时验证了方法的正确性.

风电齿轮箱高速轴多支承轴系耦合振动研究

风电齿轮箱高速轴轴承的振动是造成风电机组安全隐患的重要因素,而轴系的耦合作用会对轴承振动产生重要影响。以某750 kW风电齿轮箱高速轴多支撑轴系为研究对象,基于中心差分法提出一种用于分析多支承轴系耦合振动的建模方法,并通过MATLAB进行了模拟计算。结果表明:耦合模型比非耦合模型轴承振动幅度小;不同轴承的接触力不同,且载荷作用点越靠近轴承接触力越大;当载荷作用点在靠近单轴承的一侧时,会出现接触力远大于另一侧的双轴承的情况。

Fault diagnosis method of AC motor rolling bearing based on heterogeneous data fusion of current and infrared image

In order to improve the accuracy of rolling bearing fault diagnosis when the motor is running under non-stationary conditions,an AC motor rolling bearing fault diagnosis method was proposed based on heterogeneous data fusion of current and infrared images.Firstly,VMD was used to decompose the motor current signal and extract the low-frequency component of the bearing fault signal.On this basis,the current signal was transformed into a two-dimensional graph suitable for convolutional neural network,and the data set was classified by convolutional neural network and softmax classifier.Secondly,the infrared image was segmented and the fault features were extracted,so as to calculate the similarity with the infrared image of the fault bearing in the library,and further the sigmod classifier was used to classify the data.Finally,a decision-level fusion method was introduced to fuse the current signal with the infrared image signal diagnosis result according to the weight,and the motor bearing fault diagnosis result was obtained.Through experimental verification,the proposed fault diagnosis method could be used for the fault diagnosis of motor bearing outer ring under the condition of load variation,and the accuracy of fault diagnosis can reach 98.85%.

载荷状况对机床三支承主轴疲劳寿命的影响

载荷状况和支承形式对轴的疲劳寿命具有重要影响.以机床三支承轴为研究对象,建立三支承主轴组件的有限元模型,应用基于临界面法的FS和SWT多轴疲劳寿命预测模型,通过计算应力应变估算疲劳寿命.结果表明:三支承轴在低速重载下的疲劳寿命随着载荷的增加而降低,破坏位置位于齿轮和轴配合处,在计算转速附近,破坏位置改变到前支承处,在计算转速之后轴的疲劳寿命又随着载荷的增加而降低,降低速度也随之变缓.三支承轴的疲劳寿命随着轴承位移的增大随之降低,在中间支承处的轴承位移影响最大,其次是后支承处,最小是前支承处.

挤压油膜阻尼器参数搭配研究

对影响同心式挤压油膜阻尼器件能的三个主要参数，即弹性支座的刚度S，油膜半径间隙C和转子系统的不平衡量Q进行了分析。先将三个参数中的两个按通常的设计数据范围固定．变化第三个，然后再将三个参数中的一个固定，搭配变化其余两个，来观察影响挤压油膜阻尼器幅频特性和外传力的情况．得到六个范例。分析每一范例．便提供了如何搭配这三个参数，才能获得挤压油膜阻尼器的最佳性能的方法。

GRADE-LIFE PROGNOSTIC MODEL OF AIRCRAFT ENGINE BEARING

Research on practical and verifiable prediction methods for the service life of bearings plays a critical role in improving the reliability and safety of aircraft engines. The concept of grade-life （GL） is introduced to de- scribe the service life of bearings. A GL prognostic model for aircraft engine bearings is proposed based on sup- port vector machine （SVM） and fuzzy logic inference. Firstly, the mathematical model is discussed to predict the physics-based GL （PGL）. Then, the diagnostic estimation model based on SVM is presented in detail to predict the empirical GL （EPL）. Thirdly, a fuzzy logic inference is adopted to fuse two GL predicted results. Finally, the GL prognostic model is verified by the run-to-failure data acquired from an accelerated life test of an aircraft bearing. The results show that the model provides a more practical and reliable prediction for the service life of bearings.

Estimation of the Forces on Rubbing Rotor-Bearing System

It*ss very important to identify the load on rotor bearing system. Based on load identification in time domain, a new method combined with transfer matrix method is applied in rubbing rotor bearing system to estimate the force on rubbing rotor for the first time. Avoiding calculating the modal parameters, the outside excitation force on multi point and the distribute of internal forces on rubbing rotor bearing system can be identified by this way at the same time. Finally, the simulation is made on partial lateral rubbing rotor bearing system. For the faulty of rotor/stator rub, the point where rubbing occurs and the change of impact forces can be detected by this method in order to improve the accuracy of rotor/stator rub faulty diagnosis.

Dynamic characteristics of high speed angular-contact ceramic ball bearing

The dynamic characteristics of a high speed angular-contact ceramic ball bearing are studied and compared with that of the steel ball bearing. According to rolling bearing analysis theory, the bearing dynamic equations are established and are solved based on Hook-Jeeves's optimization theory on the computer. The results show that the bearing dynamic characteristics mainly depend on the rotational speed and ball material property at high speed. The bearing stiffness, initially decreases obviously and then increases with the increase of rotational speed. The ceramic ball bearing gains significant advantages over the steel ball bearing in high speed applications, such as lower contact stress, smaller deformation, less altering amount of contact angle, decreasing extent of variation of axial and radial stiffness and higher performance stability.

Dynamic Simulation Study of Friction and Lubrication on ICE Bearings

Friction and lubrication simulation analysis of internal combustion engine bearings are studied. A series of software implementary precepts for mathematical modeling, to analytic calculating and realizing simulation outcome are brought forward. As a dynamic simulating technique is introduced into the process of engine bearing design, simulation models of the oil film are built and the emulational analysis of the shaft center track is carried out. A software program package “Engine Bearing Friction and Lubrication Dynamic Simulation System” is developed to realize the real time simulation of the working status of bearing during the design process. Through developing virtualized products, the defects of the product design can be found in time and improve the products at once. Thus the purpose of predicting and controlling the cost, quality and design period of the products can be achieved.

THERMOHYDRODYNAMIC LUBRICATION ANALYSIS ON EQUILIBRIUM POSITION AND DYNAMIC COEFFICIENT OF JOURNAL BEARING

The finite element method （FEM） is introduced to calculate the oil film pressure and temperature distribution of a journal bearing. The perturbation is performed directly on the finite element equation. Consequently, the Jacobian matrices of the oil film forces are concisely obtained. The equilibrium position of the bearing with a given static load is found by the Newton-Raphson method. As byproducts, dynamic coefficients are obtained simultaneously without any extra computing time. From the numerical results, it is concluded that the effects of film temperature on stiffness coefficients are bigger than those on damping coefficients. With the increase of rotational speed, the load capacity and the stiffness coefficients of the journal bearing are increased when the eccentricity is small, while decreased when the eccentricity is big.

异极式永磁偏置径向磁轴承的建模与实验

为了满足储能飞轮系统、卫星动量轮等对高空间利用率的需求,提出了一种异极式永磁偏置径向磁轴承的拓扑结构。通过在槽口放置平行充磁的永磁体获得紧凑的结构,同时永磁磁路和电励磁磁路耦合距离较短,有利于获取高解耦特性。该文首先采用磁力线法,分别获取考虑齿槽效应、转子偏心的永磁磁场、电励磁磁场的气隙磁通密度分布,建立了磁路模型;然后根据磁路模型求解位移刚度和电流刚度,建立磁轴承的数学模型;与有限元仿真进行对比,证明所建立的磁场模型能够准确计算气隙磁通密度分布。设计、制造一台实验样机并进行相关实验,实验结果验证了磁路模型及有限元仿真的可靠性。

REDUCING VIBRATION WITH FRICTION-DAMPING IN HIGH-SPEED ROTOR SYSTEM

To reduce the excessive vibration of a high-speed rotor system at the critical speed, a friction damper with a flexible support structure is introduced. The mechanism of vibration reduction and support characteristics are analyzed and a friction damper is designed. The effect on an unbalanced response is studied. Results show that the stiffness factor and the friction-damping factor of the damper are related to the cone angle and the friction factor of the inner-ring when adopting a proper structure. By changing these parameters and the Z-directional stiffness of the outer-ring, the stiffness and the damping characteristic of the damper can be varied. Introducing a friction damper into the support can reduce the stiffness and increase the damping of the support, thus decreasing the critical speed to avoid the operating speed, suppress the resonant response of a rotor system, and attenuate vibration forces to the outside.

COMPENSATION CONTROL OF REAL-TIME UNBALANCE FORCE FOR ACTIVE MAGNETIC BEARING SYSTEM

Aiming at the stability and others properties of active magnetic bearing （AMB） system influenced by the periodic unbalance stimulation synchronous with rotor rotational speed, a new real-time adaptive feed-forward unbalance force compensation scheme is proposed based on variable step-size least mean square（LMS） algorithm as the feed-forward compensation controller. The controller can provide some suitable sinusoidal signals to com- pensate the feedback unbalance response signals synchronous with the rotary frequency, then reduce the fluctua- tion of the control currents and weaken the active control of AMB system. The variable step-size proportional to the rotational frequency is deduced by analyzing the principle of normal LMS algorithm and its deficiency in the application of real-time filtering of AMB system. Experimental results show that the new method can implement real-time unbalance force compensation in a wide frequency band, reduce the effect of unbalance stimulant force on the housing of AMB system, and provide convenience to improve rotational speed.

COUPLED DYNAMIC CHARACTERISTICS AND CONTROL OF ROTOR-CONICAL MAGNETIC BEARING SYSTEM

The coupled dynamic characteristics of the conical electromagnetic bearing are presented and their definitions are given. On the basis of the analyses of the characteristics, the dynamic model of five degrees of freedom (five-DOF) rotor-conical electromagnetic bearing system is made, and the influence of the coupled characteristics on the system optimal controller is analyzed.

A fatigue life prediction method of rolling bearing under elliptical contact elastohydrodynamic lubrication

In order to more accurately predict the contact fatigue life of rolling bearing, a prediction method of fatigue life of rolling bearing is proposed based on elastohydrodynamic lubrication （EHL）, the 3-paameter Weibull distribution ad fatigue strength. First,the contact stress considering elliptical EHL is obtained by mapping film pressure onto the Hertz zone. Then,the basic strength model of rolling bearing based on the 3-parameter Weibull distribution is deduced by the series connection reliability theory. Considering the effect of the type of stress, variation of shape and fuctuation of load, the mathematical models of the 尸 -tS-TV curve of the minimum life and the characteristic life for rolling bearing are established, respectively, and thus the prediction model of fatigue life of rolling bearing based on the 3-paameter Weibull distribution and fatigue strength is further deduced. Finally, the contact fatigue life obtained by the proposed method ad the latest international standard （IS0281： 2007） about the fatigue life prediction of rolling bearing are compared with those obtained by the statistical method. Results show that the proposed prediction method is effective and its relative error is smaier than that of the latest international standard （IS0281： 2007） with reliability R 〉 0. 93.

Study on Adaptive Shape Optimization

Aim To introduce a new method of adaptive shape optimization (ASOP) based on three-dimensional structure boundary strength and optimize an engine bearing cap with the method. Methods Using the normal substance's property of thermal expansion and cooling shrinkage,the load which is proportional to the difference between the nodes' stress and their respective objective stress were applied to the corresponding variable nodes on the boundary.The thermal load made the nodes whose stress is greater than their objective stress expand along the boundary's normal direction and the nodes whose stress is less than objec- tive stress shrink in the opposite direction , This process would repeat until the stress on the boundary nodes was converge to the objective stress. Results The satisfied results have been obtained when optimizing an engine bearing cap.The mass of the bearing cap is reduced to 55 percent of the total. Conclusion ASOP is an efficient,practical and reliable method which is suitable for optimizing the shape of the continuous structures.

Computer Aided Analysis of the Performances of a Tilting Pad Gas Journal Bearing

Tilting pad gas journal bearing is one of the most widely used types of aerodynamic bearings due to its inherent excellent stability in high speed applications.A practical method for analyzing and calculating the per- formances of such bearings is presented as well as its rotordynamics based on the computer aided technique.The method of calculation and the philosophy of programming with a microcomputer for the computer aided analysis are highlighted.

Analysis of dynamic characteristics of self-aligning ball bearing

A dynamics model of the self-aligning ball bearing is proposed based on the Jones-Harris method （JHM）, and a computer program is developed to solve the equations by using the Newton-Raphson method. A parametric analysis of the centrifugal force and the gyroscopic moment, the contact loads, the contact angles, the radial deformation and the radial stiffness is carried out. The analytical results show that the applied loads and the rotational speed are two main factors that can influence the distributions of the contact loads and values of the contact angles. The centrifugal force and the gyroscopic moment increase with the increase in the rotational speed, resulting in the decrease of the inner raceway contact load and the increase of the outer raceway contact load. The outer raceway contact angle increases under the centrifugal force; on the contrary, the inner raceway contact angle decreases. Furthermore, the differences between the inner and the outer contact angles increase with the increase in the rotational speed. The higher rotational speed results in the decrease in radial stiffness for the self-aligning ball bearing, and the raceway curvature coefficient, to some extent, also influences the radial stiffness.

EFFECTS OF MANUFACTURING ERRORS ON GAS LUBRICATED JOURNAL BEARING WITH COMPLIANT SURFACE

A theoretical study has been performed to investigate the influence of manufacturing errors on the bearing housing of a gas lubricated journal bearing with compliant surface I in particular on the bearing load capacity. A gas film thickness distribution is presented, in which errors o f both circumferential and axial bearing housing are considered. The influence of the errors on bearing performance is compared between rigid and compliant surface bearings. It was shown that the compliant surface bearings are less sensitive to the manufacturing errors than the rigid surface bearings. Thelefore, the cost of compliant surface bearing could be reduced by setting a larger manufacturing error tolerance.

Improved finite difference method for pressure distribution of aerostatic bearing

An improved finite difference method （FDM）is described to solve existing problems such as low efficiency and poor convergence performance in the traditional method adopted to derive the pressure distribution of aerostatic bearings. A detailed theoretical analysis of the pressure distribution of the orifice-compensated aerostatic journal bearing is presented. The nonlinear dimensionless Reynolds equation of the aerostatic journal bearing is solved by the finite difference method. Based on the principle of flow equilibrium, a new iterative algorithm named the variable step size successive approximation method is presented to adjust the pressure at the orifice in the iterative process and enhance the efficiency and convergence performance of the algorithm. A general program is developed to analyze the pressure distribution of the aerostatic journal bearing by Matlab tool. The results show that the improved finite difference method is highly effective, reliable, stable, and convergent. Even when very thin gas film thicknesses （less than 2 Win）are considered, the improved calculation method still yields a result and converges fast.