含非理想空间棱柱铰的多体系统接触分析

传统的接触分析方法通过物体间的相对运动确定接触位置. 将这种方法用于多体系统中铰内的接触分析时, 无论铰内间隙是否十分微小都必须解除铰的运动学约束, 从而导致求解效率和求解精度方面的诸多弊端. 基于铰约束反力与铰内接触力之间的力系等效关系, 以及铰内可能接触点运动之间内在的运动学关系, 以矩形截面的棱柱铰为例, 提出了一种对空间棱柱铰进行摩擦接触分析的方法, 可在不解除铰的运动学约束的前提下得到铰内接触模式和接触力. 数值算例验证了方法的可行性.      

考虑滚道波纹度的推力球轴承油膜的测量与计算

使用能够模拟推力球轴承工作的光干涉油膜测量系统,在静态时基于Hertz接触理论测量得到了该轴承座圈滚道的波纹度变化,并测量了轴承工作一周的油膜变化情况.依据试验参数进行了钢球与玻璃盘接触以及钢球与座圈滚道接触的弹性流体动压润滑（EHL）数值分析.试验和理论分析均较好地验证了表面波纹度对润滑状态的影响,发现推力球轴承运动时油膜的变化和滚道的表面波纹度密切相关.     

预紧方式对弹流润滑下角接触球轴承内部力学特性的影响

油膜厚度预测在评估弹流润滑(EHL)下角接触球轴承的性能和耐久性方面发挥着重要的作用. 耦合拟静力学理论和自旋下椭圆接触弹流模型,以干接触角接触球轴承拟静力学分析方法为基础,建立了定压和定位预紧方式下考虑弹流润滑和钢球自旋运动的角接触球轴承的拟静力学分析模型. 采用快速傅里叶变换(FFT)计算椭圆接触的弹性变形,运用Gauss-Seidel迭代方法求解Reynolds方程,得到自旋弹流模型的完全数值解,将其代入轴承拟静力学模型中迭代,得到轴承内部接触载荷、三维接触压力及三维膜厚分布. 对采用不同预紧方式的SKF7210型角接触球轴承进行分析,结果表明:富油润滑下,当轴承转速从0增大到15 000 r/min时,定压预紧时内圈轴向位移减小17.83%,而定位预紧时内圈承受的轴向载荷增大23.17%;定压预紧方式下球与内外滚道间膜厚均略大于定位预紧. 此外,不同预紧方式下,外圈上的中心膜厚大于内圈10%. 与干接触相比,定压下考虑弹流润滑内圈上接触载荷略大0.64%.      

RV减速器主支撑角接触球轴承混合润滑分析

针对RV减速器角接触球轴承承受预紧力、轴向力和径向力等联合外载荷作用的工况,分析得出了内、外圈滚道接触界面的接触区几何参数和接触载荷.在此基础上,综合考虑了角接触球轴承的接触区宏观几何、接触载荷、真实表面粗糙度、瞬态效应等因素,建立了角接触球轴承混合润滑数学模型,分析了在不同工况下角接触轴承的润滑状况及表面以下应力分布.结果表明:随着载荷的不断增加,钢球与内圈沟道之间的油膜厚度会不断减少,导致干接触面积迅速扩大,接触点表面以下最大应力增大;转速的增加会使油膜变厚,干接触面积缩小.该结果对角接触球轴承的实际工程应用具有重要借鉴意义.     

含摩擦滑移铰平面多刚体系统动力学的数值算法

基于LuGre摩擦模型和线性互补问题(LCP)的数值算法,给出了具有双边约束含摩擦滑移铰平面多体系统动力学的数值算法.首先,根据滑移铰的特点,当间隙充分小时,将其视为双边约束,给出了滑移铰中滑道作用于滑块上的法向接触力的互补关系;LuGre摩擦模型能有效地描述机械系统中的黏滞与滑移运动,将该模型用于描述滑块与滑道间的摩擦力.其次,结合Baumgarte约束稳定化方法,应用第一类Lagrange方程,建立了该多体系统的动力学方程,给出了Lagrange乘子与滑移铰中作用于滑块上的法向接触力的关系式.然后,将滑块与滑道间多种接触状态的判断以及作用于滑块上的法向接触力的计算转换为线性互补问题的求解,并用常微分方程的数值算法求解该多体系统的动力学方程.最后,通过数值仿真算例揭示了滑移铰中滑块的黏滞与滑移现象,以及滑块在滑道内的多种接触状态;另外,在文中分别采用Coulomb干摩擦模型和LuGre摩擦模型,对算例中的某些工况进行了数值仿真,并且分别用本文方法得到的数值仿真结果与已有方法得到的数值仿真结果对比,表明了本文给出的方法的有效性.      

含摩擦滑移铰平面多刚体系统动力学的数值算法

基于LuGre摩擦模型和线性互补问题(LCP)的数值算法,给出了具有双边约束含摩擦滑移铰平面多体系统动力学的数值算法.首先,根据滑移铰的特点,当间隙充分小时,将其视为双边约束,给出了滑移铰中滑道作用于滑块上的法向接触力的互补关系;LuGre摩擦模型能有效地描述机械系统中的黏滞与滑移运动,将该模型用于描述滑块与滑道间的摩擦力.其次,结合Baumgarte约束稳定化方法,应用第一类Lagrange方程,建立了该多体系统的动力学方程,给出了Lagrange乘子与滑移铰中作用于滑块上的法向接触力的关系式.然后,将滑块与滑道间多种接触状态的判断以及作用于滑块上的法向接触力的计算转换为线性互补问题的求解,并用常微分方程的数值算法求解该多体系统的动力学方程.最后,通过数值仿真算例揭示了滑移铰中滑块的黏滞与滑移现象,以及滑块在滑道内的多种接触状态;另外,在文中分别采用Coulomb干摩擦模型和LuGre摩擦模型,对算例中的某些工况进行了数值仿真,并且分别用本文方法得到的数值仿真结果与已有方法得到的数值仿真结果对比,表明了本文给出的方法的有效性.     

牵引模式下球环点接触高速弹流润滑行为机理分析

基于球环点接触高速膜厚测量系统采用PAO6基础润滑油进行了高速弹流润滑试验研究,采用玻璃环转动带动钢球旋转的牵引方式,模拟轴承外圈与钢球的润滑接触状态.试验结果显示高速下试验测得的中心膜厚值严重偏离经典弹流理论的预测.基于高速热弹流润滑模型分析了高速下膜厚降低并偏离经典弹流理论预测的原因,计算结果表明钢球与玻璃环之间的运动不是纯滚动,存在滑滚比,并通过测量钢球转速加以验证;进而结合数值计算结果中接触区温度的变化,探讨了高速弹流润滑膜厚行为机理,高速时较大滑滚比的存在使得卷吸速度远低于纯滚动理论值是膜厚下降的主要原因,由此而产生的热效应使得润滑油黏度下降,膜厚进一步减小.     

内圈离心位移对高速角接触球轴承刚度的影响

以弹性力学理论、滚动轴承动力学和沟道控制理论为基础,计算了角接触球轴承内圈在离心力作用下的径向位移,给出了计及内圈离心位移影响时,高速角接触球轴承滚动体与内、外圈的接触刚度与轴承整体的径向刚度、轴向刚度、角刚度的计算方法和相应程序。对7012/CD轴承的计算结果表明,轴承内圈外径的离心位移随转速增加而增大,在高速条件下其值较大,不容忽视;轴承内圈离心位移对内圈接触刚度和轴承径向刚度影响较大,导致内圈接触刚度和轴承径向刚度相对增大;对外圈的接触刚度、轴承轴向刚度和角刚度的影响很小;随着转速的增加与内圈离心位移的增大,对轴承内圈接触刚度与轴承径向刚度的影响会更加明显。因此,为使高速角接触球轴承的刚度分析更加精确、更加接近实际,必须考虑内圈离心位移的影响。     

安装方向对角接触球轴承保持架动态特性的影响

利用二次开发后的有限元软件MSC Patran/Ls-dyna实现角接触球轴承的参数化建模与动态性能分析. 通过与试验以及文献结果进行对比,验证了建立的有限元模型的正确性及仿真结果的可靠性. 在此基础上研究了角接触球轴承不同安装方向对保持架动态特性的影响. 结果表明:由于重力作用,保持架水平安装较竖直安装时更易形成圆形的质心轨迹. 低速工况下,保持架竖直安装时最大应力发生在过梁位置,水平安装时最大应力发生在侧梁位置. 高速工况下,保持架在两种安装方向的最大应力均发生在过梁位置. 不同转速下保持架在轴承竖直安装时最大应力值均更大.      

多体动力学程序切断铰的处理方法

多体系统动力学从非树系统派生出树系统的计算需要进行切断铰的处理。切断铰约束方程的形成是进行多体系统程序编写时的重要部分,其处理过程复杂,需要一定的技巧。本文引入了约束正交补轴的概念,详细介绍了几种典型(旋转铰、万向节、棱柱铰、旋转棱柱组合铰)切断铰位移约束方程、速度约束方程、加速度约束方程的形成方法,并给出了详细的程序化过程,该方法适用于任何类型的切断铰。最后给出相应算例,结果表明本文的方法能快速、正确地形成切断铰约束方程。     

RESEARCH ON MODELING AND NUMERICAL METHOD OF FREE STANDING BODY ON PLANAR RIGID MULTIBODY DYNAMICS

采用非光滑多体系统动力学的方法研究浮放物体与基础平台组成的多体系统,建立其非光滑接触的动力学方程与数值算法.浮放物体由主体部分和支撑腿组成,其间通过含黏弹性阻力偶的转动铰连接.支撑腿与基础平台间的接触力简化为接触点的法向接触力和摩擦力,采用扩展的赫兹接触力模型描述接触点的法向接触力,采用库伦干摩擦模型描述其摩擦力.采用笛卡尔坐标系下的位形坐标作为系统的广义坐标.首先,将基础平台运动看作非定常约束,用第一类拉格朗日方程建立系统的动力学方程,并采用鲍姆加藤约束稳定化的方法解决违约问题.随后给出基于事件驱动法和线性互补方法的数值算法.当相对切向速度为零时,构造静滑动摩擦力的正负余量和正、负向加速度的互补关系,从而将接触点黏滞——滑移切换的判断以及静滑动摩擦力的计算转化为线性互补问题进行求解,并采用Lemke算法求解线性互补问题.最后,通过数值仿真选择合适的步长;通过仿真结果说明浮放物体运动中存在的黏滞-滑移切换现象以及基础平台运动、质心位置对浮放物体运动的影响.     

含摩擦与碰撞平面多刚体系统动力学线性互补算法

基于接触力学理论和线性互补问题的算法, 给出了一种含接触、碰撞以及库伦干摩擦, 同时具有理想定常约束(铰链约束) 和非定常约束(驱动约束) 的平面多刚体系统动力学的建模与数值计算方法. 将系统中的每个物体视为刚体, 但考虑物体接触点的局部变形, 将物体间的法向接触力表示成嵌入量与嵌入速度的非线性函数,其切向摩擦力采用库伦干摩擦模型. 利用摩擦余量和接触点的切向加速度等概念, 给出了摩擦定律的互补关系式; 并利用事件驱动法, 将接触点的黏滞-滑移状态切换的判断及黏滞状态下摩擦力的计算问题转化成线性互补问题的求解. 利用第一类拉格朗日方程和鲍姆加藤约束稳定化方法建立了系统的动力学方程, 由此可降低约束的漂移, 并可求解该系统的运动、法向接触力和切向摩擦力, 还可以求解理想铰链约束力和驱动约束力. 最后以一个类似夯机的平面多刚体系统为例, 分析了其动力学特性, 并说明了相关算法的有效性.      

Development of a planar multibody model of the human knee joint

The aim of this work is to develop a dynamic model for the biological human knee joint. The model is formulated in the framework of multibody systems methodologies, as a system of two bodies, the femur and the tibia. For the purpose of describing the formulation, the relative motion of the tibia with respect to the femur is considered. Due to their higher stiffness compared to that of the articular cartilages, the femur and tibia are considered as rigid bodies. The femur and tibia cartilages are considered to be deformable structures with specific material characteristics. The rotation and gliding motions of the tibia relative to the femur cannot be modeled with any conventional kinematic joint, but rather in terms of the action of the knee ligaments and potential contact between the bones. Based on medical imaging techniques, the femur and tibia profiles in the sagittal plane are extracted and used to define the interface geometric conditions for contact. When a contact is detected, a continuous nonlinear contact force law is applied which calculates the contact forces developed at the interface as a function of the relative indentation between the two bodies. The four basic cruciate and collateral ligaments present in the knee are also taken into account in the proposed knee joint model, which are modeled as nonlinear elastic springs. The forces produced in the ligaments, together with the contact forces, are introduced into the system’s equations of motion as external forces. In addition, an external force is applied on the center of mass of the tibia, in order to actuate the system mimicking a normal gait motion. Finally, numerical results obtained from computational simulations are used to address the assumptions and procedures adopted in this study.     

解三维摩擦接触问题的一个二阶锥线性互补法

针对三维摩擦接触问题的求解,给出了一种基于参变量变分原理的二阶锥线性互补法. 首先,基于三维Coulomb摩擦锥在数学表述上属于二阶锥的事实,利用二阶锥规划对偶理论,建立了三维Coulomb摩擦接触条件的参变量二阶锥线性互补模型,它是二维Coulomb摩擦接触条件参变量线性互补模型在三维情形下的自然推广;随后,利用参变量变分原理与有限元方法,建立了求解三维摩擦接触问题的二阶锥线性互补法. 较之于将三维Coulomb摩擦锥进行显式线性化的线性互补法,该方法无需对三维Coulomb摩擦锥进行线性化,因而在保证精度的前提下所解问题的规模要小很多. 最后通过算例展示了该方法的特点.      

Modeling and analysis of rigid multibody systems with driving constraints and frictional translation joints

An approach is proposed for modeling and anal- yses of rigid multibody systems with frictional translation joints and driving constraints. The geometric constraints of translational joints with small clearance are treated as bilat- eral constraints by neglecting the impact between sliders and guides. Firstly, the normal forces acting on sliders, the driv- ing constraint forces （or moments） and the constraint forces of smooth revolute joints are all described by complementary conditions. The frictional contacts are characterized by a set- valued force law of Coulomb＇s dry friction. Combined with the theory of the horizontal linear complementarity problem （HLCP）, an event-driven scheme is used to detect the transi- tions of the contact situation between sliders and guides, and the stick-slip transitions of sliders, respectively. And then, all constraint forces in the system can be computed easily. Secondly, the dynamic equations of multibody systems are written at the acceleration-force level by the Lagrange multiplier technique, and the Baumgarte stabilization method is used to reduce the constraint drift. Finally, a numerical example is given to show some non-smooth dynamical behaviors of the studied system. The obtained results validate the feasibility of algorithm and the effect of constraint stabilization.     

A numerical analysis of partial slip problems under Hertzian contacts

In this study the tangential partial slip problems in Hertzian contact regions are treated by a numerical technique. The tangential loading may include tangential forces in the contact plane and a twisting moment normal to the contact plane. The Coulomb’s law of friction and the property that the direction of friction must oppose the relative motion lead to nonlinear equations. The Newton-Raphson method is utilized to solve these nonlinear equations. Numerical results for tangential tractions and sizes of stick and slip zones may be determined, and they agree with existing analytical results for circular contacts.     

An approach for calculating the dynamic load of deep groove ball bearing joints in planar multibody systems

This study is focused on dynamic modeling of planar multibody systems with multiple deep groove ball bearing joints, in which the radial clearance, contact deformation, and bearing kinematics are included. By using the approach presented, the variation of the joint reaction force and the dynamic load on each ball element in bearings can be simulated. The deep groove ball bearing joints are modeled by introducing a nonlinear force system, which takes into account the contact elastic deformations between the ball elements and the raceways. The contact force is calculated by the Hertzian contact deformation theory that accounts for the geometrical and material properties of the contacting bodies. A planar slider-crank mechanism with two deep groove ball bearing joints is chosen as an example to demonstrate the application of the methodologies presented in this paper. In this model, one bearing locates at the joint between the ground and crank, while the other one locates at the joint between the crank and connecting rod. By numerical calculation, the dynamic load distribution characteristics of bearings under real mechanism movement conditions are simulated. From the results, it can be concluded that the dynamic load on each rolling element varies differently and belongs to a variable load with the change of mechanism configuration. Load characteristic analysis is the foundation of developing research on the fatigue life and reliability of bearings. This study will provide a key mechanical support for the performance evaluation, dynamic design, and geometrical parameter optimization of the joint rolling element bearings.     

Nonlinear dynamics of mistuned bladed disks with ring dampers

In turbomachinery applications, rotating bladed disks (blisks) are often subject to high levels of dynamic loading, such as traveling wave excitations, which result in large response amplitudes at resonance. To prevent premature high cycle fatigue, various dry friction dampers are designed for blisk systems to reduce the forced responses. Ring dampers are located in the disk, underneath the blades, and are held in contact with the blisk by centrifugal loading. Energy is dissipated by nonlinear friction forces when relative motions between the ring damper and the blisk take place. To investigate the dynamic responses of blisk–damper systems in the presence of the nonlinear frictional contacts, conventional methods based on numerical time integration are not suitable since they are computationally expensive. This paper presents a reduced-order modeling technique to efficiently capture the nonlinear dynamic responses of the blisk–damper systems. Craig–Bampton component mode synthesis (CB-CMS) serves as the first model reduction step. A novel mode basis that mimics the contact behavior under sliding and sticking conditions is developed to further reduce the CB-CMS model while maintaining its accuracy. The resulting reduced nonlinear equations of motion are solved by a hybrid frequency/time domain (HFT) method. In the HFT method, the contact status and friction forces are determined in the time domain by a three-dimensional contact model at each contact point, whereas the reduced equations of motion are solved in the frequency domain according to a harmonic balance formulation. Moreover, to investigate the effects of blade mistuning, which can lead to drastic increase of forced responses, an extension of the reduced-order models (ROMs) is developed based on component mode mistuning. Forced responses computed by the proposed ROMs are validated for both tuned and mistuned systems. A statistical analysis is performed to study the effectiveness of ring dampers under random blade mistuning patterns.