一种求解直齿圆柱齿轮啮合刚度的方法

在ＩＳＯ标准计算啮合刚度的基础上，用抛物线担合单齿副的啮合刚度，经过叠加求得直齿轮啮合刚度的数学表达式，并对刚度波动函数进行付立叶展开，使之在振动分析的应用中极为方便。     

基于多项式的等高齿锥齿轮时变啮合刚度建模

针对某型雷达装置的等高齿锥齿轮在啮合时的时变啮合刚度,提出一种多项式函数展开的时变啮合刚度新模型。通过转速、负载扭矩、阻尼因子系数分析,构建了多项式函数展开的时变啮合刚度模型,建立了等高齿锥齿轮的非线性动力学方程。将本文建立的时变啮合刚度模型与传统的多阶简谐波叠加形式的时变啮合刚度模型以及综合刚度参考数据模型进行分析对比,发现在小阻尼、重载工况下这种多项式形式的时变啮合刚度模型能更贴近于时变啮合刚度的实际特性,该模型为齿轮传动的减振、降噪、平稳传动等方面的动力学研究打下基础。     

含齿面分形啮合刚度的齿轮传动系统动力学

为研究考虑齿面分形特性的时变啮合刚度对齿轮-轴承系统的影响,用分形理论描述齿轮轮廓,采用Weber-Banaschek公式计算和分析不同分形维数D对齿轮时变啮合刚度的影响,将不同分形维数D下的刚度代入计及滑动轴承非线性油膜力、综合传递误差及齿侧间隙等因素的齿轮-轴承系统中,分析不同分形维数D下的刚度对系统动力学特性的影响.采用Runge-Kutta法求解系统动力学微分方程,得到系统响应的相图、Poincaré截面图、时域图、分岔图以及三维频谱图等.结果表明:随着分形维数D的增大,时变啮合刚度波动降低,系统趋于更加稳定的周期运动;相比含随机扰动的刚度,齿轮-轴承系统对于考虑齿面分形特性的齿轮啮合刚度的变化更加敏感,更能表现因齿廓变化导致的系统响应的变化;随着阻尼比的增大,系统会趋于相对稳定的单周期运动.     

基于ANSYS workbench齿轮啮合刚度计算及动力学仿真

为了解决在齿轮动力学仿真中啮合刚度的时变性问题,在三维建模软件Solidworks中,通过渐开线参数方程建立了直齿圆柱齿轮装配体模型,将模型导入ANSYS workbench的瞬态动力学模块,用准静态的方法求出了综合啮合刚度,考虑齿轮的惯性效应以及轮齿摩擦力进行齿轮动力学仿真.结果表明,实际情况下综合啮合刚度与理论重合度计算的综合啮合刚度是不同步的.轮齿在进入和退出双齿啮合时振动加剧,轮齿的交替啮合产生冲击力,单齿啮合比双齿啮合振动强烈.     

Forced oscillations with time-varying mesh stiffness and backlash in gear systems

A dynamic model to describe the torsional vibration behaviors of a spur gear system is presented in this paper.Differential equations of nonlinear dynamics for the gear system exhibiting combined nonlinearity influence such as time-varying mesh stiffness,backlash and dynamic transmission error(DTE) were obtained.The method of multiple scales was employed to solve the nonlinear differential equations with parametric excitation in gear systems,by which both the frequency-response curves of the primary resonance caused by internal excitation and the analytical periodic solutions of nonlinear differential equations were obtained.The nonlinear influence of stiffness variation,the damping and the internal excitation on the system response was shown by frequency-response curves.Compared with numerical examples,the approximate analytical solutions are in good agreement with exact solutions,which proves that the method of multiple scales is effective for solving nonlinear problems in gear systems.     

含弹性支撑的船用减速器箱体动态特性

为分析弹性支承对船用减速器动态特性的影响,提高其动态性能,综合考虑齿轮时变啮合刚度、齿轮偏心误差及啮合误差等因素的影响,依据各零件作用力传递关系,建立传动系统动力学模型,计算系统动态激励．采用有限元法构建齿轮箱稳态动响应分析模型,应用弹簧单元对其底部支撑进行模拟,依据自编制动响应求解流程,对齿轮箱在系统动激励作用下的稳态响应进行求解,得到齿轮箱节点振动加速度响应时域历程及其频谱．引入齿轮箱隔振系统频率比概念,分析支撑刚度对齿轮箱振动传递及倾斜变形的影响,发现当频率比为2～3时可达到较好的支撑效果,为齿轮箱的设计提供了理论依据．     

基于刚柔耦合动力学的齿轮传动系统动态特性

为得到齿轮轴系响应的动态特性,从柔体动力学基本理论出发,系统分析了刚柔耦合动力学模型的机理,建立了多级齿轮传动刚柔耦合的虚拟样机。此模型能综合考虑传动轴各方向上的柔性特征、湿式换档离合器动态特性以及齿轮时变啮合力对轴类零件动态响应的影响。仿真结果证明了通过虚拟样机技术获取载荷谱的可行性,可用于轴的疲劳寿命预测以及齿轮箱体的振动研究。     

变刚度轴承-碰摩转子机动飞行动力学响应

为研究机动飞行状态下高速滚动轴承-转子耦合系统非线性动力学特性,利用有限元方法建立爬升-俯冲机动飞行状态下含滚动轴承时变刚度的轴承-碰摩转子系统数学模型,并利用Newmark-β积分法对系统动力学方程进行求解. 模型中考虑了滚动轴承时变刚度与转子非线性动力学特性之间的相互影响,分析了转子偏心及滚动轴承径向间隙的影响. 求解模型得到了系统在不同状态下的时域图、频域图及分岔图等,并以此为依据对高速滚动轴承刚度的时变特性、轴承刚度与转子动力学状态的相互影响、轴承-转子系统非线性特性、机动飞行状态对系统的影响及含碰摩故障的转子系统在机动飞行状态下的动力学响应进行了分析. 研究结果表明:轴承刚度的时变特性与转子系统的动力学特性密切相关,是限制转子系统最高转速的因素之一;机动载荷会使转子系统产生复杂的非线性动力学特性,但当系统转速较低时,机动载荷的引入能一定程度上提高系统稳定性;随着碰摩刚度的增大,系统稳定运动区间减小.     

谐调盘片结构在干摩擦阻尼影响下的稳态响应研究

采用动柔度法建立一般的带有B-B型和B-G型两类干摩擦副的谐调盘片结构的动力学模型,并且应用谐波平衡原理进一步得到系统稳态周期响应幅值和相角的非线性代数方程组。最后,通过拟牛顿迭代算法对一个简化的谐调盘片结构数学模型进行数值仿真,给出其频响特性,着重分析干摩擦阻尼的影响作用。     

考虑摩擦的磨损和修形齿轮啮合刚度计算

研究齿面偏差对齿轮啮合刚度的影响,对准确获得齿轮系统动态特性具有重要意义。本文基于改进能量法,提出了一个求解考虑齿面摩擦的直齿轮啮合刚度的完整模型。该模型通过齿廓的参数方程,实现考虑齿轮加工刀具圆角半径和齿面偏差对齿轮单齿啮合刚度的影响;通过齿形误差带来的齿间间隙和轮齿加载变形量的关系,求解出双齿啮合区齿轮副总刚度。分析了磨损齿轮和修形齿轮的啮合刚度、齿间载荷分配系数和传递误差。结果表明：齿面非均匀磨损量会显著降低双齿啮合区刚度并降低重合度,轻载条件下尤为严重;修形齿轮载荷大于修形设计载荷值时,修形效果不明显,而载荷小于修形设计载荷值时,可能出现刚度不足、重合度减小和加载传动误差显著增大等问题。     

基于ANSYS的变速器齿轮有限元静力学分析

用有限元分析方法对变速器齿轮的静力学特性进行理论计算和研究。建立各齿轮的有限元模型,应用有限元分析软件ANSYS对模型进行分析计算,得出各齿轮的应力和应变,并对计算结果进行静态分析。     

基于刚-柔混合建模的时变结构动力学分析

为适应液压挖掘机高速、轻量化的要求，以具有时变固频特性的液压挖掘机工作装置为研究对象，提出了以角加速度判断时变结构的关键工况，利用刚性多体动力学和有限元方法对液压挖掘机在整个作业循环中的动力学特性进行建模和分析.分析了液压挖掘机工作装置在受力最大处的动态应力分布，并与传统刚性体模型的分析结果进行了比较.结果表明，刚 柔混合建模方法与刚性体建模方法相比，获得的位移和应力较小，反映出以往的设计偏于保守，为轻量化设计提供了依据.     

精确建模的双圆弧齿轮有限元分析

圆弧齿轮是凹形齿廓与凸形齿廓之间的啮合，具 有承载能力强、润滑性能好、加工方便等优点，广泛应 用于石油、煤炭、钢铁等行业.但在使用中，也暴露了其 噪音较高、动力性能较差的缺点，并阻碍了进一步的推 广应用.所以对其进行受力变形分析显得极为重要，而 精确建模却是进行     

基于能量分析的复阻尼模型结构抗震性能

由于当前动力分析中所使用的阻尼模型无法描述结构内未知的材料非线性能量耗散,基于应力相关复阻尼理论,推导出多自由度复阻尼系统的震动能量方程,研究了复阻尼模型的结构震动响应和材料能量耗散规律,计算了构件和结构的时变材料损耗因子.研究结果表明,在地震总输入能量中,材料阻尼耗能占很大比例,并随时间单调增加,结构的材料阻尼耗能及其变化率、动能、应变能均随着能量输入的增加而增加.通过对损耗因子的计算表明,与传统方法相比,采用时变形式而非常数形式的材料损耗因子能够更精细地体现材料阻尼效应.     

Effect of Tooth Profile Modification on Vibration of Power Split Gear Transmission System

Based on Newton''s second law, the bend-torsion-shaft coupling nonlinear dynamic model and equations of power split gear transmission system are established. According to the principle of tooth profile modification, the tooth profile modification is considered as time-varying gear backlash function acting along the line of action. Then the dynamic functions are solved by using Runge-Kutta numerical method. After analyzing the effect of tooth profile modification quantity(TPMQ) and relative tooth profile modification length(TPML) to the nonlinear dynamic characteristics of power split gear transmission, the following conclusions are drawn: ①The TPMQ of a certain stage transmission affects the vibration of its own stage more significantly than the other stage, and the coupling effect between two stages can be ignored usually in the modification design; ②If the first stage TPMLs are less than 0.3, the influence of the first stage TPMLs to the first stage transmission vibration is much more greatly than the influence of the second stage TPMLs to the first stage transmission vibration, or else both the first and second stage TPMLs affect the first stage transmission vibration largely. The same is true for the second stage TPMLs, and the cutoff value is 0.2; ③The TPMQ affects the vibration of power split gear transmission system more principally than the TPML, and should be top-priority in the modification design.     

Fault diagnosis of AMT gear shifting process based on semi-quantitative SDG model

In order to diagnose gear shifting process in automated manual transmission (AMT), a semi-quantitative signed directed graph (SDG) model is applied. Mathematical models are built by analysis of the power train dynamic and the gear shifting control process. The SDG model is built based on related priori knowledge. By calculating the fuzzy membership degree of each compatible passway and its possible fault source, we get the possibilities of failure for each possible fault source. We begin with the nodes with the maximum possibility of failure in order to find the failed part. The diagnosis example shows that it is feasible to use the semi-quantitative SDG model for fault diagnosis of the gear shifting process in AMT.     

叶片刚度对风力发电机组载荷的影响

为了研究受叶片刚度变化影响的载荷灵敏度问题,提出利用柔性多体动力方程对全耦合风机进行建模的方法,并考虑叶片旋转时产生的空气动力、重力及离心力作用对叶片进行模态分析,求解叶片的气动阻尼.运用Newmark法对风力发电机组叶片进行动态分析计算,得到总的动态响应载荷.以某3 MW风力发电机组为例,计算叶片在不同刚度下的载荷敏感度,仿真其在额定风速下的正常发电情况,获得其叶根、塔底、偏航轴承以及轮毂的载荷.仿真结果表明,叶片刚度降低导致叶根载荷减小,但是塔底、偏航轴承载荷增加;叶根XY、塔底Z、偏航轴承Y及轮毂Z方向载荷变化较为敏感.     

Numerical computation and analysis of unsteady viscous flow around autonomous underwater vehicle with propellers based on sliding mesh

The flexible transmission shaft and wheel propeller are combined as the kinetic source equipment, which realizes the multi-motion modes of the autonomous underwater vehicle (AUV) such as vectored thruster and wheeled movement. In order to study the interactional principle between the hull and the wheel propellers while the AUV navigating in water, the computational fluid dynamics (CFD) method is used to simulate numerically the unsteady viscous flow around AUV with propellers by using the Reynolds-averaged Navier-Stokes (RANS) equations, shear-stress transport (SST) k-w model and pressure with splitting of operators (PISO) algorithm based on sliding mesh. The hydrodynamic parameters of AUV with propellers such as resistance, pressure and velocity are got, which reflect well the real ambient flow field of AUV with propellers. Then, the semi-implicit method for pressure-linked equations (SIMPLE) algorithm is used to compute the steady viscous flow field of AUV hull and propellers, respectively. The computational results agree well with the experimental data, which shows that the numerical method has good accuracy in the prediction of hydrodynamic performance. The interaction between AUV hull and wheel propellers is predicted qualitatively and quantitatively by comparing the hydrodynamic parameters such as resistance, pressure and velocity with those from integral computation and partial computation of the viscous flow around AUV with propellers, which provides an effective reference to the study on noise and vibration of AUV hull and propellers in real environment. It also provides technical support for the design of new AUVs.     

斜齿轮三维弯曲有限元模型及应力分析

为了应用有限元法精确求解斜齿轮的弯曲应力,根据斜齿轮啮合原理,提出了斜齿轮啮合接触线确定方法.采用有限元ANSYS软件的参数化设计APDL语言,开发了自动完成斜齿轮三维弯曲有限元建模与应力分析程序模块.以某型货车变速器齿轮为研究对象,建立了相应的斜齿轮三维弯曲有限元模型,通过斜齿轮三维有限元分析与齿轮承载能力计算ISO标准结果比较,说明所建立的斜齿轮三维弯曲有限元模型不但可以准确反映斜齿轮的三维应力分布,而且可以精确求解斜齿轮不同啮合位置的齿根应力.