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.     

栓接结合部在动载荷下的能量耗散特性

研究栓接结合部在动载荷下的能量耗散特性,对描述机械系统复杂力学行为具有重要的理论和实际意义。利用Bouc-Wen模型模拟栓接结合部的迟滞非线性特性,提出在动载荷下系统能量耗散计算方法和参数辨识方法。为验证所提方法的正确性,利用Mindlin模型所仿真出的非线性迟滞曲线作为栓接结合部所获得的试验数据,对Bouc-Wen模型进行参数辨识,并采用力控制方式分析Bouc-Wen模型中各个参数对系统能量耗散特性的影响规律。结果表明:随着量纲一切向力的增加量纲一能量耗散随之非线性递增;参数A、δ、γ和n对能量耗散的影响与其灵敏度相关,灵敏度越大则能量耗散的递增速率也越大;能量耗散随着参数A、γ和n的增加而增加,但参数δ则反之;栓接结合部能量耗散不仅与Bouc-Wen模型中的参数相关,而且与系统激励频率和振幅非线性相关;量纲一切向力与量纲一能量耗散之间关系可表示为η=aΓb的函数形式。     

Identification of bolted lap joints parameters in assembled structures

Bolted lap joints have significant influence on the dynamical behaviour of the assembled structures due to creation of strong local flexibility and damping. In modelling the dynamical behaviour of assembled structures the joint interface model must be represented accurately. A nonlinear model for bolted lap joints and interfaces is proposed capable of representing the dominant physics involved in the joint such as micro/macro-slip. The joint interface is modelled using a combination of linear and nonlinear springs and a damper to simulate the damping effects of the joint. An estimate of the response of the structure with a nonlinear model for the bolted joint under external excitations is obtained using the method of multiple scales. The parameters of the model, i.e. the spring constants and the damper coefficient, are functions of normal and tangential stresses at the joint interface and are identified by minimizing the difference between the model predictions and the experimentally measured data.     

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.     

螺栓结合部切向动力学行为辨识方法

首先,以螺栓结合部切向动力学特性为研究对象,基于频响函数的子结构综合法为理论主线,建立结合部切向动力学行为辨识基本方程,推导其切向动刚度Za的理论表达式;其次,联合奇异值分解与最小二乘法,优化辨识结合部切向等效刚度ka与阻尼ca,由此建立螺栓结合部切向动力学数值模型;最后,利用该模型计算结构测点频响函数,进而将其与实测值进行对比。结果表明,二者吻合程度较高,且特征峰对应频率误差分别为1.38%,1.51%和0.84%,验证了所提方法能有效辨识螺栓结合部切向动力学行为,所得等效动力学参数精度较高,可为机械系统整机精准建模提供理论参考与数据支撑。     

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.     

基于改进自适应遗传算法的固定结合面动态特性参数优化识别

针对固定结合面传统建模方法精度较低和结合面的动态特性参数难以确定的问题,改进了基于弹簧阻尼单元的建模方法,提出了基于实验模态分析和改进自适应遗传算法的固定结合面动态特性参数的优化识别方法。该方法以有限元计算的理论固有频率和阻尼比与其对应实验模态分析结果的相对误差最小为目标函数,使用改进的自适应遗传算法优化识别固定结合面的刚度和阻尼参数。以自行设计制作的固定结合面模型为研究对象进行了建模、实验、参数识别等分析,分析结果表明：所提出的方法是正确的、有效的,参数识别误差在5%以内,达到了较高的识别精度。     

机械结合部动态特性的等效参数研究

为提高机械结构数值分析时结合部动态特性参数的应用简便性,提出一种基于等效参数的机械结合部动态特性分析方法。在通过实验获得具有通用性的结合部单位面积上的法向动态刚度和切向动态刚度的基础上,将单位面积上的结合部等效为各向同性连续介质,基于GW接触模型建立单位面积上的结合部微观形貌和结合部动态刚度变化关系式,根据离散单元应力波传播条件研究结合部单位面积上的法向动态刚度和切向动态刚度之间内在联系,推导出结合部动态特性的等效参数-单位面积上的弹性模量和泊松比,并以螺栓连接的两钢板为对象进行数值分析,将计算结果和试验测量结果进行比较,以验证结合部动态特性等效参数的可行性和准确性,为深入研究机械结合部问题奠定基础。     

Experimental modal test of the spiral bevel gear wheel using the PolyMAX method

To verify the effectiveness and correctness of free modal analysis results from a Spiral bevel gear (SBG) wheel by using Finite element method (FEM), an experimental platform was constructed through the free-hanging support of the SBG wheel. The experiment used the hammer knock percussion for excitation and a three-directional acceleration sensor as signal acquisition equipment and utilized the LMS modal analysis module. The geometric model of the SBG wheel was constructed using an eight-node octagon instead of the SBG wheel outer contour. The experiment then extracted the modal parameters of the wheel using the PolyMAX method and obtained the first- and second-order natural frequencies, damping ratios, and mode shapes of the SBG wheel at 0-7 kHz during the experimental modal test. The results of the experimental test were compared with those of the FEM free modal analysis. The first- and second-order natural frequency error rates by FEM were 0.25 % and 0.45 %, respectively. The experimental modal test result verified the rationality of the model by FEM, thus showing that the result of modal analysis by FEM is reliable and providing a basis for the dynamic characteristic analysis of SBG.     

Effects of joint on dynamics of space deployable structure

Joints are necessary components in large space deployable truss structures which have significant effects on dynamic behavior of these joint dominated structures.Previous researches usually analyzed effects of one or fewer joint characters on dynamics of jointed structures.Effects of joint stiffness,damping,location,number,clearance and contact stiffness on dynamics of jointed structures are systematically analyzed.Cantilever beam model containing linear joints is developed based on finite element method,influence of joint on natural frequencies and mode shapes of the jointed system are analyzed.Analytical results show that frequencies of jointed system decrease dramatically when peak mode shapes occur at joint locations,and there are cusp shapes present in mode shapes.System frequencies increase with joint damping increasing,there are different joint damping to achieve maximum system damping for different joint stiffness.Joint nonlinear force-displacement is described by describing function method,one-DOF model containing nonlinear joints is established to analyze joints freeplay and hysteresis nonlinearities.Analysis results show that nonlinear effects of freeplay and hysteresis make dynamic responses switch from one resonance frequency to another frequency when amplitude exceed demarcation values.Joint contact stiffness determine degree of system nonlinearity,while exciting force level,clearance and slipping force affect amplitude of dynamic response.Dynamic responses of joint dominated deployable truss structure under different sinusoidal exciting force levels are tested.The test results show obvious nonlinear behaviors contributed by joints,dynamic response shifts to lower frequency and higher amplitude as exciting force increasing.The test results are further compared with analytical results,and joint nonlinearity tested is coincident with hysteresis nonlinearity.Analysis method of joint effects on dynamic characteristics of jointed system is proposed,which can be used in optimal design of joint parameters     

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.     

试验台约束对滑动轴承动特性识别精度的影响

在滑动轴承的动特性测试中,试验台参数对动特性测试精度有重要的影响。以某倒置式轴承动特性试验台为研究对象,基于轴承动力学正反问题,提出滑动轴承动特性系数识别精度的仿真评估方法,分析不同激振频率时试验台约束参数对轴承动特性系数识别精度的影响规律,并对激振频率和约束参数的取值范围进行优选。结果表明：在较低激振频率的条件下,当约束刚度和约束阻尼取值较小时,动特性系数的识别精度受测试误差的影响不大,随着约束刚度和约束阻尼取值增大到一定值,动特性系数的识别精度受测试误差的影响迅速增大。针对研究的试验台,选择激振频率在30~300 Hz之间,选择试验台约束刚度小于试验轴承刚度的0.3%,试验台约束阻尼小于试验轴承阻尼的7%时,能够保证较好的轴承动特性系数的测试精度。     

基于模型修正的螺栓结合部虚拟材料参数识别及应用

针对螺栓结合部虚拟材料模型建模及参数识别问题,基于结合部显著影响整体结构动力学性能这一特性,提出基于模型修正的虚拟材料动力学模型参数识别方法。针对参数识别中修正方程的病态问题,根据虚拟材料相关参数及结构各阶模态频率相互之间的影响度,构造修正方程的左右加权函数以减轻其病态程度,并通过仿真算例验证参数识别方法的有效性。探讨平板螺栓连接及哑铃状结构用于虚拟材料参数识别的有效性及抗噪性,加工哑铃结构的实验零件,辨识螺栓结合部虚拟材料模型的参数。基于机床螺栓结构的常用工况,建立虚拟材料模型参数库,并在CKX5680数控机床上验证参数库的有效性。结果表明：采用模型修正技术可以准确地识别无噪声时的虚拟材料参数;采用哑铃结构实验试件在有噪声情况下,螺栓结合部虚拟材料参数识别误差小于8%;采用虚拟材料模型模拟螺栓结合部的建模误差小于5.6%。     

结合面切向动态特性参数的改进Levy法识别及验证研究

对Levy法进行了改进,通过对阻尼比的迭代实现结合面动态特性参数的识别。实验表明,该方法对刚度和阻尼比都有较高的识别精度,其中对阻尼比的精确识别是该方法最大的优点。同时研究了基于ANSYS的结合面动态特性参数的验证方法,并通过将改进的Levy法识别得到的参数代入到ANSYS验证模型中,计算得到的结合面固有频率与实测频率误差小于6%,峰值误差为50%左右,说明了识别参数的有效性以及验证方法的可靠性。     

Analysis and modeling for flexible joint interfaces under micro and macro scale

The flexible joint interfaces with random topography are re-constructed by data point cloud obtained by experimental measurements and a contact model between two rough random surfaces is established. Contact analysis is conducted by FEM considering the elasto-plastic constitution of the material. An exponential relationship model between normal pressure and normal deformation of the joint interfaces is presented by least-square method, and furthermore, the normal contact stiffness expressions of unit area of the joint interfaces are deduced. In order to use micro-scale model to deal with large scale practical engineering interfaces, a cantilever structure connected by bolted joint is taken as a macro scale example, and its dynamic model is established with the pressure distribution on the interface and real contact area obtained by simulations and experiments. Modal test experiments are conducted, and the first three natural frequencies and frequency response functions are obtained to validate the model.     

Improvement of measurement techniques for damping induced by micro-sliding

This paper deals with the damping caused by friction in joints. A new test bench is presented and justified by comparisons made with devices described in the literature. The purpose of this academic bench is to measure the damping induced by partial slip and friction in a planar joint. Moreover, allows uncoupling normal static and dynamic tangential forces. A new method for so-called stopped-sine excitation was developed. It allows more precise monitoring of the evolution of the vibration frequency and damping of non-linear modes. This method is associated with piezoelectric exciters for greater efficiency when stopping excitation. A large number of experimental results are presented and discussed. They are used to characterize the damping induced by micro-sliding in the bonds.     

DYNAMIC CHARACTERISTIC ANALYSIS OF PRECISE LONG STROKE LINEAR MOTOR WITH AIR-BEARING IN OPTICAL LITHOGRAPHY

Dynamic characteristic is presented by identifying the model and the dynamic parameters of a precise long stroke linear motor （PLSLM） with the air-bearing in optical lithography. The PLSLM is supported by air-bearing on the stator, and is driven by on-board two large linear motors in a cross-configuration. Firstly, a model of the PLSLM is established by finite element method （FEM）. Secondly, based on the model, the natural frequencies and model shapes are discusse＆ And the contribution of each active mode is evaluated by computing the modal participation factors （MPF）, which indicates the major vibration direction. Furthermore, by the experimental modal analysis, the experimental results are in agreement with simulation results, which it is sure that the FEM is reasonable. What＇s more, comparing with the effects on the frequency due to the air-bearing stiffness, the relations of the natural frequencies with the air-bearing stiffness are found. It is found that the frequency response curve is fluctuant with the air-bearing stiffness in each direction. Finally, it is conclusion that the natural frequency of the PLSLM is largely affected by the air-bearing stiffness variety. This research is contributed to the dynamic characteristics resulted from the air-beating stiffness. Further work will include better optimization on the dynamic parameter in the controller design through the control algorithm for the precise long stroke motor.     

高耸塔式结构动力特性设计与测试

为了满足上置设备工作需要,高耸塔式结构基频要大于某一给定数值。通过对结构基频计算公式和结构变形曲线分析,增大结构基频应以降低结构顶部质量和提高结构底部刚度为主的频率调整基本原则。基于空间有限元理论,通过模态分析获得了结构的频率和振型。利用环境激励下结构振动模态参数识别方法对雷达塔进行动力检测。采用模态识别法求出结构的前三阶频率、振型和阻尼值。引入模态置信因子和标准化模态差准则,对计算振型数据和实测振型数据进行分析比较,以验证有限元计算的准确性。该研究成果为深入研究高耸塔式结构频率调整、准确预测结构的动力响应提供可靠依据。     

Y-24手持式凿岩机模态分析

凿岩机动态特性对其工作性能有着重要影响。应用DASP测试系统通过实验模态的方法,对Y-24手持式凿岩机进行参数识别,获得其固有频率、阻尼和振型,结果表明凿岩机冲击频率27Hz低于其一阶固有频率37.6Hz,避免共振;隔振材料降低了手柄振动量,减少对人体的危害,这为Y-24手持式凿岩机结构设计提供了依据。     

Direct identification of non-proportional modal damping matrix for lumped mass system using modal parameters

Several damping materials have been employed to reduce the vibration of marine structures. In this paper, a new method of identifying system matrices for non-proportional damping structures using modal parameters is proposed. This method has two advantages. First, the mass and stiffness matrices do not need to be calculated using the FEM, so errors due to the inaccuracy of these matrices can be reduced. Second, various indirect methods can be used to identify modal parameters such as natural frequencies, modal damping ratios and mode shapes. Three case studies of lumped mass systems with non-proportional damping are carried out to verify the performance of the proposed method in this study.