结合面切向接触阻尼三维分形模型

基于分形理论,考虑摩擦因素的影响,应用描述三维粗糙表面形貌的W-M函数,推导了结合面切向阻尼能耗和切向等效黏性阻尼三维分形模型.使用Matlab软件进行仿真分析,结果显示:结合面的切向阻尼能耗随着法向总载荷、摩擦因数的增大而减小,随着材料塑性指数、切法向载荷比、分形粗糙度参数的增大而增大;结合面的切向接触阻尼能耗和分形维数之间的关系比较复杂;结合面的切向接触等效黏性阻尼随着摩擦因数、分形粗糙度参数的增大而减小,随着法向总载荷、切法向载荷比、材料塑性指数的增大而增大;结合面的切向接触等效黏性阻尼随着分形维数增大先增大后减小,在分形维数等于2.7附近时取最大值;当分形维数等于2.1～2.5时,结合面的切向接触等效黏性阻尼和法向总载荷呈现明显的非线性关系;当分形维数2.5～2.9时,结合面的切向接触等效黏性阻尼和法向总载荷趋于线性关系.     

从单自由度系统衰减响应分离与辨识粘性与干摩擦混合阻尼的方法

针对正压力随位移成正比的干摩擦与粘性混合阻尼单自由度振子,从其位移自由振动响应导出了分离和辨识粘性阻尼比与干摩擦阻尼因子的理论公式,并通过数值仿真例子对公式进行了验证。结果表明,在无测量噪声条件下,本文所提出的公式是理论上的精确表达式。其数值仿真例子的参数估计结果精度非常高,完全能够满足科学研究与工程实际的需要。     

考虑摩擦的球面切向接触刚度分形模型研究

为准确且方便地计算两球面的切向接触刚度（TCS）,在前期对两球面接触分形模型研究的基础上,通过引入考虑摩擦因素的弹塑性变形临界面积计算公式,并基于接触面切向刚度基本理论,建立了考虑摩擦因素的两球面切向接触刚度的分形模型。对模型进行了仿真分析,结果表明：切向接触刚度与法向载荷成正比关系;摩擦因数与切向接触刚度的关系因分形维数的变化而呈现出不同的规律;受到分形维数变化的影响,切向接触刚度随接触面材料特性参数和分形粗糙度幅值的增大而增大;在一定工况下,切向接触刚度在分形维数取1.5时达到最大,且当分形维数在1.5左右时,其值增大最快;球面内接触比外接触时的切向刚度大;随着曲率半径的增大,切向刚度增大。研究结果为后续开展高副结合面（如轴承等）润滑及动力学分析提供了理论基础。     

干摩擦阻尼叶片周期振动响应的解析计算

研究一个描述干摩擦阻尼器叶片振动的质量-弹簧-阻尼器振动系统。阻尼器摩擦力由黏滞模型描述,由接触面滑动或黏滞状态决定。将滞后摩擦力分为四个阶段,从而得到各个阶段上的线性振动系统,给出求干摩擦阻尼叶片周期响应的解析公式。计算表明,阻尼端压力取适当值时,阻尼器会处于最优的摩擦接触状态,获得较好减振效果。同时引入阻尼器处对叶片还起到调频作用,也可以起到使激振频率避开共振频率的作用,减小振动幅值。     

由振动引起的螺栓连接预紧力松脱的数学模型

引入一种数学模型以研究螺纹连接在横向振动作用下引起的松脱.此横向振动激励会引起螺纹接触面间的滑动以及螺栓头与支撑表面之间的滑动.式中包括剪切力、支撑力以及螺纹摩擦阻力矩,它们均与振动速度相关,当所施加横向振动激励足够大时,螺纹连接会出现松脱现象.本文研究了螺栓预紧力、支撑力及螺纹摩擦系数、横向振动激励以及螺栓头下部弯矩...     

金属橡胶材料干摩擦阻尼的产生机理及力学模型

金属橡胶材料干摩擦阻尼、非线性刚度的产生机理是一个较为复杂的问题,其内部存在大量的干摩擦接触,通过螺旋型金属丝相互摩擦接触来损耗振动能量。干摩擦阻尼与物体表面的微观结构密切相关,从微观角度分析了金属橡胶材料干摩擦阻尼的产生机理,欲准确地揭示干摩擦阻尼的减振规律,还必须正确的提出描述干摩擦规律的数学模型。由于金属橡胶客观存在不光滑的非线性泛函本构关系,使得含有干摩擦环节的金属橡胶结构的响应计算问题非常困难。介绍了关于两固体接触表面间的干摩擦问题的四种数学模型,即Sgn摩擦模型、滞迟模型、动态系统中干摩擦力的数值计算模型、三次非线性粘性阻尼双线性滞迟模型,这四种模型为后人在该领域的继续研究奠定了坚实的理论基础。     

法向加-卸载过程中弹塑性微凸体侧向接触能耗研究

针对法向加-卸载作用下双粗糙表面上微凸体接触阻尼能耗问题,提出弹性、弹塑性、塑性微凸体侧向接触能耗计算方法。基于微凸体接触球形假设,根据微凸体侧向接触受力分析,将其分解为垂直于微凸体接触点公切面的法向分力和沿该面的切向分力。采用HERTZ,ETSION理论,分别建立了加-卸载过程中微凸体发生弹性、弹塑性、塑性变形时,法向分力与变形之间关系;依据CATTANEO-MINDLIN黏着-滑移理论,BKE模型,ERITEN模型理论,建立了加-卸载过程中三个变形阶段的切向分力与位移之间关系。利用法向分力-变形和切向分力-位移之间的关系,求得微凸体在法向、切向分力共同作用下产生的应变能耗以及摩擦能耗,进而求得微凸体侧向微观接触在三个阶段下的能耗。研究表明,微凸体侧向接触时耗能包括应变耗能和摩擦耗能,且法向变形量越大,应变耗能、摩擦耗能越大;接触角度越大,应变耗能越大,摩擦耗能越小。     

转子--轴承系统受轴向摩擦时的振动

研究轴向摩擦对单跨双盘转子-轴承系统横向振动的影响。盘与静子在不同位置发生轴向接触时，对盘的轴向压力由作用于两个轴端的力代替，轨迹切向摩擦力用单参数干摩擦力模型计算。数值模拟发现，轴颈位置、轨迹大小变化与轴向摩擦位置、程度和转速都有关系，因此表现为振动不稳定。另外，频谱中还包含倍频成分，且可能有比较复杂的运动形式如概周期运动、混沌等。     

滑动摩擦振动噪声的非线性显式动力学分析

利用有限元软件ABAQUS/Explicit(显式动态求解器)对球-平面接触条件下的滑动摩擦振动噪声进行了数值模拟分析。对比试验结果,探讨了摩擦噪声的发生机制,并分析了摩擦噪声发生时接触界面的运动特性。结果表明,摩擦噪声主要是由摩擦系统的自激振动引起的,法向振动与切向振动的耦合是系统产生自激振动和摩擦噪声的一个重要因素。当摩擦系统发生自激振动时,从面节点与主面的接触并不是连续不变的,两者在相对运动的过程中具有黏着-滑动-分离-黏着的特性。     

复杂接触运动下非线性摩擦力的求解

提出了复杂接触运动下求解接触非线性摩擦力的数值轨迹跟踪方法,利用该方法对几种复杂接触运动下的非线性摩擦力进行了计算。计算结果表明:数值方法在分析二维接触椭圆运动时可以得到更准确的结果;计算接触面摩擦力时不能忽略法向运动与切向运动之间的相位差,该相位差对接触状态的转变、摩擦力的大小以及迟滞回线的形状都有很大的影响;对于接触面的三维运动,必须同时考虑法向运动与接触面内两个方向切向运动之间的耦合;数值轨迹跟踪方法可以方便地求解一维、二维以及三维接触运动下的非线性摩擦力,为求解带干摩擦阻尼结构的动态响应提供了一种实用算法。     

Mechanism of energy dissipation in mechanical system with dry friction

Determination of the energy dissipative mechanism in a mechanical system composed of two elastic structures in dry contact is presented. The analysis is based on the measurement of displacement ratio of the contacting elastic structures as a function of frequency due to light impulse excitation at a single point on any of the two elastic structures. The theoretical analysis depends on a very simple model of a two-degree-of-freedom system where two solid friction models are adopted in the analysis of the mathematical model. Several experiments are presented to illustrate the dominant friction mechanism of contacting surfaces within the micro slip regime in a frequency range of oscillation up to 400 Hz. It was shown experimentally that the solid friction model behaves in a way that is described as structural (hysteretic) damping. In other words, the energy dissipated due to dry friction during micro slip regime does not depend on the relative velocity between the two contacting surfaces but it is proportional to their relative displacements. The determination of the contact stiffness and damping loss factor in addition to their variation with the applied normal load was also shown.     

Development of a new method for joint damping identification in a bolted lap joint

Mechanical joints have considerable effects on dynamic behaviour of machine tools; thus, joint damping identification is important in studying the dynamics of mechanical structures. Due to the difficulties in analysis of microslip friction, the experimental prediction of microslip joint dynamics is of great importance. In this study, a new experimental approach is proposed to determine the damping of bolted lap joints. Because of the complex nature of the mechanical joints, the lap joint is isolated through the addition of a mechanical resonator, which consists of a lumped mass and spring, to the bolted structure. The frequency response function (FRF) of this system is used for joint damping identification. This approach is used for bolted structures under both translational and torsional excitations and overcomes difficulties associated with slip boundaries identification in the joint interface. The method is verified by comparing the obtained results with those of the hysteresis loop approach.     

Solution of ill-posed problems for identification of the dynamic parameters of bolted joints

The measured frequency response functions (FRFs) are directly used to identify the bolted joint properties. However, the noise effect and the matrix inverse operations create ill-posed problems, and a small noise level may cause the identified result to be faulty. A sensitivity method is developed to avoid the ill-posed problems for identification of the dynamic parameters of bolted joints in this paper. To calculate the sensitivity of stiffness and damping for bolted joints, the sensitive values are used to determine the frequency ranges before the identification. Then, the equivalent stiffness and damping of bolted joints are identified by FRFs method in this range. All results of simulation and experiment show that the proposed method can improve significantly the identification accuracy. Additionally, the sensitivity method can be used to avoid an ill-posed problem by eliminating ill-posed FRFs in some frequency range before identification.     

Surface contact stress-based nonlinear virtual material method for dynamic analysis of bolted joint of machine tool

The components of machine tools are mainly fixed and connected by bolts. The performance of the assembly can be affected by the dynamic characteristics of the bolted joints. This paper presents a nonlinear virtual material method based on surface contact stress to describe the bolted joint for accurate dynamic performance analysis of the bolted assembly. Fractal geometry theory is used to describe the surface topography. The elastic modulus and shear modulus of one micro-contact are derived based on fractal contact theory. The equivalent elastic modulus, Poisson ratio, and density of the bolted joint can be obtained through the weighted mean method. In order to obtain the stress distribution, the contact surface is assumed flat in the macro-scale, and the uneven distribution of contact stress can be obtained by the finite element method (FEM). The contact surface can be divided into several sections, and the parameters of a virtual material layer can be determined based on the mean contact stress. Both theoretical and experimental results for a bolted joint are obtained for a box-shaped specimen under equal pre-tightening force and bending moment effect. The results show that the theoretical mode shapes are in good agreement with the experimental mode shapes. The relative errors between the theoretical and experimental natural frequencies are less than 4.41%, which indicates that the present nonlinear virtual material method is appropriate for the bolted joint in modeling CNC machine tools.     

含间隙连杆机构非线性行为研究

分析了间隙铰接触的特点，指出线性弹簧阻尼模型不能满足接触边界条件并产生力突变；采用符合接触边界条件的非线性弹簧阻尼模型描述碰撞分离过程，建立了含间隙曲柄摇杆机构的动力学模型，对含间隙机构的非线性特性进行了分析和讨论，说明含间隙机构动力学行为中存在混沌现象。     

磁流变发动机悬置的参数化建模与辨识

研究频变、磁变效应下的磁流变悬置的力学模型建立问题。以某磁流变悬置为例,根据Bingham模型,将悬置恢复力分为库仑阻尼力、弹性恢复力,黏性阻尼力三部分;通过分析各部分力与频率、磁场的相关性分析,提出一种改进的多项式Bingham参数化模型。该模型以外部电流、外载频率为变量,通过推导外部位移激励的能量耗散、储存关系,提出该多项式模型中九个待识别参数的辨识方法。设计了试验方案,并通过真实试验测试各种工况下该挤压式磁流变悬置的恢复力-位移关系,根据所提方法,得到在不同工况下的磁流变悬置的恢复力随电流、外载频率变化的关系。对比试验结果表明,该参数化模型在动刚度、滞后角以及滞回曲线上能良好地反映悬置的宽频段动力学特性。     

Generic element formulation for modelling bolted lap joints

Joints have significant effects on the dynamic response of the assembled structures due to existence of two non-linear mechanisms in their interface, namely slipping and slapping. These mechanisms affect the structural response by adding considerable damping into the structure and lowering the natural frequencies due to the stiffness softening. Neglecting these effects in modelling of joints produces errors in predictions of the structure responses. In this paper, a non-linear generic element formulation is developed for modelling bolted lap joints. The generic element is formed by satisfying all conditions that are known for a joint interface and hence providing a non-linear parametric formulation for the families of allowable joint models. Dynamic response of the developed model for the assembled structure including the generic joint interface element is obtained using the incremental harmonic balance (IHB) method. The generic parameters of the joint are identified by minimising the difference between the model response obtained from IHB method and the observed behaviour of the structure. The procedure is demonstrated by modelling an actual structure containing a single lap bolted joint in the middle. The frequency responses of the structure around the first two resonance frequencies are measured by exciting the structure using a sinusoidal force at each individual frequency. The measured responses are compared with the predictions of the model containing a parametric generic joint element. The parameters of the joint interface model are successfully identified by minimising the difference between the measured responses and the model predictions.     

An analytical model of dissipated viscous and hysteretic energy due to interaction forces in a pneumatic tire: Theory and experiments

When in use, a tire dissipates energy according to various mechanisms: rolling resistance, viscosity, hysteresis, friction energy, etc. This dissipation of energy contributes to influencing tire temperature, contact conditions and the resulting friction coefficient.This research project deals with viscoelastic and hysteretic mechanisms, and presents an explicit expression of the energy dissipated by tire-road interactions caused by these mechanisms. It is based on the Dahl model with regard to the hysteretic force together with a spring and a frequency variable damping coefficient with regard to the viscoelastic one. The energy expression found in this way can be used in tire thermal models to determine one of the heat flows needed to estimate the contact temperature and to find out the actual friction coefficient to be used in real time tire-road interaction models.Experimental tests were carried out, for longitudinal interaction only, in order to evaluate the effectiveness of the proposed expression by identifying the parameters and validating the results.     

A model for micro-slip between flat surfaces based on deformation of ellipsoidal elastic bodies

Micro-slip is a phenomenon that occurs between contacting surfaces when a frictional load, less than that necessary to produce macro-slip, is applied to the contacting surfaces. A model is presented for micro-slip between a flat smooth surface and a flat rough surface. The rough surface is covered with uniformly distributed ellipsoidal elastic bodies. The results from two test cases show that anisotropy of the contacting surfaces influences the tangential stiffness at zero displacement, the length of the micro-slip zone and the energy dissipated in the contact.     

TRIBOS: A Performance Evaluation Tool for Traction-Transmitting Partial EHD Contacts

The details are given of a computer model for performing a state-of-the-art tribological assessment of the performance of a lubricated concentrated rolling/sliding/spinning/contact comprising general anisotropic rough surfaces. The name chosen for this program is TRIBOS.

It computes: 1. The contact ellipse dimensions and area

2. The elastohydrodynamic (EHD) film thickness both at the plateau and at the constriction that forms at the rear of a lubricated concentrated contact under fully flooded (un-starved) and isothermal lubricant inlet conditions

3. The apportionment of the applied load between the asperities and the lubricant film

4. The magnitude and direction of the tractive force transmitted between the contacting bodies by the combined effects of (a) shearing of the fluid film and (b) coulomb friction between contacting asperities

5. The mean number of asperity contacts and the real contact area, i.e. the total contact area of the elastically deformed asperities

6. A film thickness correction factor accounting for lubricant starvation in the contact inlet

7. A film thickness correction factor accounting for a viscosity decrease of the inlet oil due to fluid heating

8. An index of surface fatigue behavior

The program is a synthesis of computational tools from the current literature for the computation of fluid film thickness and traction, and a general asperity simulation model for the elastic contact of anisotropic rough surfaces. In the example given, it is used to perform a comparative evaluation of the performance of 18 combinations of 9 surface roughnesses and 2 lubricants in a traction drive contact.