机床基础理论讲座——第三讲 机床动态特性(下)

四、动态特性计算与优化设计 分析和解决机床中的振动问题,除用试验的方法外,还需要掌握计算的方法。六十年代以后,随着电子计算技术的发展,出现了一些新的动态特性计算方法,主要有传递矩阵法、有限元法和机械阻抗法。 1.传递矩阵法 传递矩阵法应用于计算,可以简化为梁的零、部件。它是把线性弹性系统分为几段,用矩阵表示每段的特性,再利用矩阵乘法得出表示整个系统特性的矩阵,代入边界条件,即可求出系统的固有频率和振型,掌握阻尼值时,也可以准确地求出振幅和动柔度。这种方法的基本思想是把一个本来具有分布参数的系统,近似处理为由一些集…     

环板式针摆行星传动输入轴系振动特性的研究

采用有限元和传递矩阵两种方法对环板式针摆行星传动轴系的振动特性进行了分析.利用ANSYS软件建立了环板式针摆行星传动输入轴系动力学分析模型.分析计算了输入轴系的固有频率和振型.通过传递矩阵法计算了输入轴系的固有频率.传递矩阵数值计算结果与有限元分析结果基本吻合,说明输入轴系固有频率的计算值是基本正确的.电机的额定转速要避开输入轴系的低阶固有频率值,以免发生共振,固有频率分析为动态特性分析奠定了基础.     

配气台管路系统气固耦合振动特性分析

针对配气台管路振动问题,采用传递矩阵法和有限元模态分析法,建立管道系统振动频率的计算模型。运用MATLAB,ANSYS和AMESim软件分析计算,得到气柱固有频率、结构固有频率及扰动频率三者之间的关系,确定配气台管路振动的原因,并提出有效的解决措施。研究表明:由于扰动频率与管路内气柱低阶固有频率相近,激发配气台管路剧烈共振,通过增加阻尼孔板和增加管路支撑,改变了管路内气柱固有频率和结构固有频率,有效的解决了配气台管路共振问题。     

大间隙环流中刚支转子系统振动特性研究

基于Myklestad传递矩阵法．建立了大间隙环流中转子系统的运动方程，采用数值方法分析转子系统的振动特性。数值计算结果表明，由于大间隙环流的流固耦合作用，使转子系统的固有频率、阻尼临界转速、稳定性和不平衡响应均发生了不同程度的变化。数值计算结果与已有的解析分析和实验结果有较好的一致性。     

采用频响函数法计算复杂管道系统的气相固有频率

介绍了计算有阻尼复杂管道系统的气柱固有频率的频响函数法，应用该方法可克服传递矩阵法计算时产生漏根等不足之处，并使实际系统的模型简化更趋合理。通过计算和试验表明，这是一种有效，可靠的方法，所编程序具有工程应用价值。     

基于传递矩阵法的碳纤维复合材料传动轴模态分析

以某汽车传动轴为参考对象设计出碳纤维复合材料(CFRP)传动轴铺层方案,采用传递矩阵法(TMM),把CFRP传动轴离散为若干个盘轴单元,建立集中质量圆盘左右截面的点传递矩阵,建立轴段的场传递矩阵,进而构建整根轴的传递矩阵。根据传动轴两端自由的边界条件,推导出其转子频率方程,利用MATLAB编程求解出CFRP传动轴的一阶临界转速及其对应的振型,并与传统的经验公式及有限元仿真软件Abaqus计算出的结果作比较。结果表明,对于传动轴一阶弯曲固有频率,传递矩阵法相比于有限元仿真计算误差为1.6%,一阶振型的最大偏差为0.015。表明传递矩阵法能较精确的计算CFRP传动轴的固有频率以及对应的模态振型。     

利用行星架附加阻尼的行星齿轮系统减振研究

在建立２Ｋ－ Ｈ 型行星齿轮系统动态分析数学模型的基础上,用复模态理论和矩阵摄动方法讨论了行星架附加粘性阻尼的阻尼灵敏度分析,并用Ｆｏｕｒｉｅｒ 级数法求解了系统的动态响应。提出了一种粘性阻尼线性系统的动态分析和减振设计的有效方法。通过算例给出了模态固有频率、阻尼灵敏度和动态响应的计算结果,得出了对工程应用有价值的结论。     

大型烟气脱硫系统搅拌轴系固有频率计算

介绍了用传递矩阵法、Rayleigh能量法和ANSYS软件计算搅拌轴系的固有频率.传递矩阵法计算比较繁琐,而ANSYS有限元法计算相对简捷且准确度较高,值得推广使用.     

用传递矩阵计算分支管路固有频率的方法

本文用传递矩阵法编程计算分支管路的固有频率,并通过实验进行了验证。此计算方法是计算液压管系固有频率的有效方法。     

大间隙环流中复杂轴承-转子系统振动特性研究

基于Myklestad传递矩阵法建立了大间隙环流中动压滑动轴承-转子系统的运动方程，用迭代方法确定了轴承．转子系统的静态平衡工作点，采用数值方法分析轴承-转子系统的振动特性。数值计算结果表明：大间隙环流使轴承-转子系统的固有频率、阻尼临界转速和稳定性均发生了不同程度的变化。大间隙环流不仅与轴承．转子系统发生了动态固耦合，而且也发生了静态固耦合。     

Critical speeds and the response of a tensioned beam on an elastic foundation to repetitive moving loads

A finite-length tensioned beam on a damped elastic foundation is acted upon by an infinite series of equally spaced and steadily moving concentrated transverse loads. The deflection response of the beam is obtained by an expansion in terms of the normal modes of vibration. Numerical results are determined for various values of the load-spacing, beam tension, foundation stiffness and damping, and for a range of load-speeds. It is found that the critical velocities for repetitive loading exist at significantly lower speeds than would be expected based upon the well-known critical speed for a single moving load. An interpretation in terms of forced vibration response is given.     

Dynamic analysis of a rig shafting vibration based on finite element

In recently, finite elements method (FEM) has been used most popular for analysis of stress, vibration, heat flow and many other phenomena. Taking a rig shafting as an example, this paper studies the lateral vibration of the rig shafting with multi-degree-of-freedom by using FEM. The FEM model is created and the eigenvalues and eigenvectors are calculated and analyzed to find natural frequencies, critical speeds, mode shapes and unbalance responses. Then critical and mode shapes are determined. Finally, responses of unbalance force are analyzed in case of undamped and damped system, and peaks of response are compared.     

Prediction and assignment of latent roots of damped asymmetric systems by structural modifications

This paper studies the latent roots of damped asymmetric systems in which the stiffness matrix is asymmetrical. The asymmetric terms are due to ‘external’ loads and are represented by a parameter or parameters. The latent roots of such asymmetric systems are complex and the real parts become positive at some critical values of the parameter(s) (critical points). The work reported in this paper consists of two parts. The first part presents a method for predicting the latent roots of the damped asymmetric system from the receptance of the damped symmetric system. The second part presents an inverse method for assigning latent roots by means of mass, stiffness and damping modifications to the damped asymmetric system again based on the receptance of the unmodified damped symmetric system. The simulated numerical examples of a friction-induced vibration problem show the complexity in assigning stable latent roots for damped asymmetric systems. It is found that it is quite difficult to assign the real parts of latent roots to stabilise the originally unstable asymmetric system and sometimes there is no solution to the modification that is intended to assign certain latent roots.     

Transient Response Investigations of Short Journal Bearing Systems with Flexible Rotors and Damped Flexible Pedestals

This paper is a continuation of the earlier works of the authors on the problem of transient response of a journal during acceleration and deceleration periods. The paper first establishes a theoretical analysis for the transient response of a short journal bearing system with a flexible rotor and damped flexible pedestals. The transient response analysis is then used to assess the linearized system stability chart and determine the journal motion during stopping and starting periods. The paper also includes some detailed results for the limiting speeds of short bearings.     

Buckling and dynamic stability of spinning pre-twisted beams under compressive axial loads

The equations of motion of a spinning pre-twisted beam under compressive axial loads are formulated using Euler beam theory and the assumed mode method. The equations of motion are first transformed to the standard form of an eigenvalue problem for determining the critical buckling loads for various combinations of prescribed spinning speeds, aspect ratio of the cross-section and pre-twist angle of the beam. The equations of motion are then transformed to the form of another eigenvalue problem for determining the critical spinning speeds. Both the critical spinning speeds and critical buckling loads are found to exhibit similar trends of variation and curve veering phenomenon with respect to changes in the aspect ratio of the cross-section. For a spinning pre-twisted beam under axial compressive loads, the critical spinning speeds corresponding to divergent behaviours are found to be no longer the dividing points for separating the speed zones into stable and unstable regions, contrary to the stability behaviour of a nonpre-twisted beam which have distinct regions of stable and unstable spinning speed zones separated by critical spinning speeds.     

磁流变液阻尼器-柔性转子系统振动特性与控制的再研究

对先前提出的理论分析模型进行适当改进，用新模型对支承在磁流变液阻尼器上的单盘悬臂柔性转子系统的振动特性和控制技术进行再研究。研究表明，随着磁流变液阻尼器的库仑阻尼力的增大，系统在无阻尼临界转速处振幅明显下降，但在两阶临界转速之间的一定转速区振幅增加；同时，随着库仑阻尼力的增加，阻尼器轴承处的振幅在几乎所有转速时都被减小，甚至在某些转速区间该轴承被“锁住”，而且轴承能够振动的区间越来越窄。这说明转子系统从一个弹性支承系统逐步转化为一个准刚性支承系统，阻尼器支承的有效刚度越来越大，使得一阶有阻尼临界转速逐渐提高，并逐渐接近刚支临界转速。根据这些特性，提出通过开关控制抑止转子通过两阶临界转速过程中的振动，并使转子振幅在全转速区达到最小。仿真结果表明，系统能平稳通过两阶临界转速。     

风洞悬臂杆结构主动减振系统的研究

风洞测试时悬臂杆振动会影响测试数据的准确性,为了抑制悬臂杆振动,设计了基于压电驱动器的主动减振系统,提出了将人工神经网络与传统比例积分微分(proportion integration differentiation, 简称PID)相结合的智能控制算法,实现了控制参数在线实时调整。对该控制系统的减振性能分别进行了地面试验和风洞试验,并与采用传统PID控制的试验结果进行对比。结果表明,神经网络PID控制下的振动收敛时间比传统PID缩短了50%,而且在不同风速和攻角下,悬臂杆系统的1阶模态振动均得到了有效衰减（衰减幅度>19 dB）,表现出良好的鲁棒性。     

叠片联轴器联结的转子系统扭转振动计算和动力修改分析

由联轴器联结的多跨转子－轴承系统,整个系的扭转振动临界转速较低,为避免在工作转速范围内,常需要计算和进行结构修改。本文基于结构动力修改,提出了了修改的思路和方法。     

阻尼矢量图法设计输入整形器抑制柔性机械臂的残留振荡

输入整形技术的研究源于抑制小阻尼伺服系统振荡模态的残留振荡,其能以简单的开环控制实现系统的快速定位,因而在抑制高精度定位系统的残留振荡方面得到了广泛应用。本文提出了一种新的输入整形器的分析设计方法———阻尼矢量图,即将无阻尼系统的矢量图法推广应用于有阻尼系统,为有阻尼系统提供了一种输入整形器的图形化分析与设计方法,其运用简便、直观,且能在图上直接对输入整形器的鲁棒性进行分析,将其应用于柔性机械臂的残留振荡控制中,仿真结果验证了按此方法设计的输入整形器确能抑制残留振荡。     

DDM Rotordynamic design sensitivity analysis of an APU turbogenerator having a spline shaft connection

An eigenvalue design sensitivity formulation of a general nonsymmetric-matrix rotor-bearing system is devised, using the DDM (direct differential method). Then, investigations on the design sensitivities of critical speeds are carried out for an APU turbogenerator with a spline shaft connection. Results show that the dependence of the rate of change of the critical speed on the stiffness changes of bearing models of spline shaft connection points is negligible, and thereby their modeling uncertainty does not present any problem. And the passing critical speeds up to the 4th critical speed are not sensitive to the design stiffness coefficients of four main bearings. Further, the dependence of the rate of change of the critical speed on the shaft-element length changes shows quantitatively that the spline shaft has some limited influence on the 4th critical speed but no influence on the 1st to 3rd critical speeds. With no adverse effect from the spline shaft, the APU system achieves a critical speed separation margin of more than 40% at a rated speed of 60,000 rpm.