几种数值算法在弹道微分方程组解算中的仿真与比较（英文）

本文简述了数值分析的应用范围,介绍了微分方程几种不同的数值解法,及其在弹道解算中的应用。在简化弹丸弹道动力学微分方程的基础上,通过Mablab软件编写欧拉法、梯形法、经典四阶龙格库塔法程序,计算动力学微分方程组近似解及各种方法的局部截断误差和计算时间。通过对结果的分析比较,明确了几种经典解法在弹道解算中的优劣,为弹道解算方法的选择提供了依据。     

捷联惯导系统姿态解算的实现

提出了捷联惯性导航系统姿态解算模块的一种实现方法。基于DSP的硬件平台和四元数的数学平台,设计了捷联惯性导航系统的姿态解算模块。介绍了捷联惯性导航系统的工作原理和姿态解算的基本算法,并给出了四元数法的四阶龙格—库塔数值解法。设计了姿态解算模块的硬件电路和软件实现程序。实验测试结果表明,在增量角小于5°的情况下,四阶龙格—库塔法进行姿态解算,误差小于0.0053％,能够满足捷联惯性导航系统的精度要求;应用TMS320C6713B进行硬件电路设计,每次解算时间小于36µs,能够满足捷联惯性导航的实时性的要求。     

捷联惯导系统姿态解算模块的实现

提出了一种实现捷联惯性导航系统姿态解算模块的方法。基于DSP的硬件平台和四元数的数学平台,设计了捷联惯性导航系统的姿态解算模块。介绍了捷联惯性导航系统的工作原理和姿态解算的基本算法,并给出了四元数法的四阶龙格一库塔数值解法。设计了姿态解算模块的硬件电路和软件实现程序。实验测试结果表明,在增量角〈5°的情况下,用四阶龙格一库塔法进行姿态解算,误差〈0．0053％;应用TMS320C6713B进行硬件电路设计,每次解算时间〈36μs,能够满足捷联惯性导航系统对精度和速度的要求。     

基于四元数法的捷联式惯性导航系统的姿态解算

载体的姿态解算算法是实现捷联式惯性导航系统精确导航的核心技术之一。分析了欧拉法、方向余弦法、四元数法求解姿态矩阵的优缺点,采用四元数法与方向余弦法两种解算方法分别计算载体姿态,两种方法的计算结果之差与理论真值比较以得到解算的相对误差,从而验证了四元数法的正确性和有效性。最后,指出提高采样频率和采用高阶计算算法能进一步减小姿态解算误差。数字化仿真与转台试验结果表明,本文提出的载体姿态解算法的理论数值相对误差为10^-10％,测试实验相对误差为10^3％,计算时间为36μs,具有良好的实时性。     

基于四元数法的捷联式惯性导航系统姿态解算研究

为实现捷联式惯性导航系统的精确导航,载体的姿态解算算法是核心技术之一。首先分析了欧拉法、方向余弦法、四元数法求解姿态矩阵的优缺点,根据四元数法与方向余弦法两种解算方法分别进行计算,两种方法的计算结果之差与理论真值比较以得到解算的相对误差,从而验证了四元数法的正确性和有效性,最后提出提高采样频率和采用高阶计算算法能进一步减小姿态解算误差。数字化仿真与转台试验结果表明,根据本文所述算法进行载体姿态解算的误差很小,具有良好的实时性,为捷联式惯性导航技术的工程实践提供了依据。     

皮带驱动机构的1/3次亚谐共振分析

应用拉格朗日方程,得到皮带驱动机构的非线性振动微分方程,根据非线性振动的多尺度解法,得到系统满足1/3次亚谐共振情况的一次近似解以及对应的定常解,并对其进行数值计算,分析带的长度和横截面积、外激力、谐调值、系统阻尼等对系统的影响,揭示一些新的动力学现象.     

基于小波变换的偏微分方程求解

偏微分方程在计算流体力学和许多化工过程建模中有广泛的应用.当在空间位置出现突变时,偏微分方程的经典解法如有限元法和加权残差法等无法保证解的精度和收敛性.在此基于内插小波变换,研究了改善偏微分方程求解精度的方法.     

岸边集装箱起重机上部结构非线性耦合动力分析方法

根据哈密顿原理推导出岸边集装箱起重机大梁-小车-吊重系统的耦合振动偏微分方程.采用有限元方法求出复杂边界条件下梁的模态.把所得模态参数代入耦合振动偏微分方程中,将复杂的偏微分方程转化为变系数非线性常微分方程组,用Runge-Kutta方法获得方程的数值解.通过数值算例验证了该方法的有效性,为工程中常见的刚柔耦合振动问题提供了一种简便的计算方法.     

基于四元数的机械海流计姿态解算

流向是海流测量中不可或缺的信息之一,可以通过解算海流仪姿态角的方式获得流向。目前,采用欧拉角微分方程式和方向余弦法计算姿态都存在着奇点或者计算量过大的问题。文章利用四元数的方法求解姿态变换矩阵,采用四元数四则运算组合简化计算过程,并基于6轴处理组件MPU6050和磁阻传感器HMC5883L设计电路和编程,最后在实验的基础上对算法可行性进行了验证。     

基准不重合时工序尺寸及公差的计算方法

基准不重合时工序尺寸及公差的确定.需要通过尺寸链的解算才能获得.介绍了这种类型的尺寸链的解法和步骤.     

基于惯量伪速度的机械多体系统高效率动力学建模

对于多个体组成的复杂大型多体系统,传统动力学建模方法推导过程费时费力,通过形位参数建立的二阶微分方程组冗长、繁多并且计算量大难以求解。伪速度从运动的本质出发,引入速度级独立变量代替广义坐标,拓宽了独立变量的选取范围,得到了形式简洁的可积分的一阶微分方程组。笔者通过旋量递推与惯量伪速度结合,研究了高效率的建模方法,对两类伪速度进行区分,并阐述了惯量伪速度的物理含义,并得到了伪速度建模的优点。得到的对角化一阶动力学方程形式简洁,直接面向计算机编程实现,易于设计解耦控制或非交互控制,并把建模过程应用于Puma560机器人中。     

螺杆成型立铣刀廓形计算方法研究

应用微分几何原理,通过分析刀具、工件的接触特性计算螺杆的成型立铣刀廓形方程,对方程的求解方法进行讨论提出利用弦割法求解超越方程,并对迭代区间提出合理、有效的计算方法。应用本文方法编写计算程序,经实际应用效果良好。     

Two new methods for computer forming of dynamic equations of active mechanismsZwei neue methoden für das aufstellen der dynamischen gleichungen aktiver mechanismen mitteks rechner teil 2

Two new methods for setting dynamic equations of active spatial mechanisms are considered in this part of paper. The first section of this part presents a new version of the method based on Appel's equations. In contrast to the version of Popov and associates, this procedure may be applied to solving both problems: the calculation of accelerations and also the calculation of driving forces. The second section presents a procedure for forming dynamic equations via Lagrange's second-order equations; this procedure is fully adapted to iterative procedures for forming these models on a computer.     

Approximate Solutions of Primary Resonance for Forced Duffing Equation by Means of the Homotopy Analysis Method

Nonlinear dynamic equation is a common engineering model.There is not precise analytical solution for most of nonlinear differential equations.These nonlinear differential equations should be solved by using approximate methods.Classical perturbation methods such as LP method,KBM method,multi-scale method and the averaging method on weakly nonlinear vibration system is effective,while the strongly nonlinear system is difficult to apply.Approximate solutions of primary resonance for forced Duffing equation is investigated by means of homotopy analysis method (HAM).Different from other approximate computational method,the HAM is totally independent of small physical parameters,and thus is suitable for most nonlinear problems.The HAM provides a great freedom to choose base functions of solution series,so that a nonlinear problem may be approximated more effectively.The HAM provides us a simple way to adjust and control the convergence region of the series solution by means of an auxiliary parameter and the auxiliary function.Therefore,HAM not only may solve the weakly non-linear problems but also may be suitable for the strong non-linear problem.Through the approximate solution of forced Duffing equation with cubic non-linearity,the HAM and fourth order Runge-Kutta method of numerical solution were compared,the results show that the HAM not only can solve the steady state solution,but also can calculate the unsteady state solution,and has the good computational accuracy.     

Approximate solution of the differential equations of motion of inertial-pulsed transmissions

Approximate methods of solving the nonlinear differential equations of motion of inertial-pulsed transmissions based on a pulsed mechanism are compared. These methods take account of the nonuniform driveshaft rotation and the dynamic characteristics of the motor. Analysis of the solutions reveals the best method for dynamic study of the given transmissions.     

Determination of thermal state of sliding bearing with fluid lubrication

The load-carrying capacity of sliding bearing operating in the fluid lubrication mode is determined on the basis of the solution of the differential equations of motion and continuity of the lubricant filling the clearance between the journal and bushing. The method is developed for the heat calculation of the sliding bearing on the basis of the hydrodynamic lubrication theory.     

齿轮系统非线性动力学微分方程的渐进法

利用渐进法研究了一类考虑时变啮合刚度和间隙的齿轮系统的非线性动力学微分方程,建立了这类模型的解的统一形式。通过计算表明,渐进法具有良好的通用性,尤其适用于求解大型非线性微分方程组。最后给出了渐进法的计算结果,并且验证能与数值计算结果很好地吻合。     

A new process damping model for chatter vibration

This paper presents a new analytical process damping model (PDM) and calculation of Process Damping Ratios (PDR) for chatter vibration for low cutting speeds in turning operations. In this study a two degree of freedom complex dynamic model of turning with orthogonal cutting system is considered. The complex dynamic system consists of dynamic cutting system force model which is based on the shear angle (φ) oscillations and the penetration forces which are caused by the tool flank contact with the wavy surface. Depending on PDR, the dynamic equations of the cutting system are described by a new mathematical model. Variation and quantity of PDR are predicted by reverse running analytical calculation procedure of traditional Stability Lobe Diagrams (SLD). Developed mathematical model is performed theoretically for turning operations in this study and simulation results are verified experimentally by cutting tests.     

基于CFD的可倾瓦轴承静动特性研究

目前对于可倾瓦轴承的静动特性研究方法,主要是先研究单块瓦片的特性,再通过瓦片子系统的叠加得到轴承整体特性,在计算中忽略了瓦间间隙及瓦块相互之间的流场影响。用瓦块独立计算模型模拟理论计算中只考虑轴瓦与轴颈间隙流场的情况,整体计算模型考虑轴承瓦间间隙的影响,在Fluent软件中计算两种模型的静动特性参数,并进行对比和分析。计算结果表明,瓦间间隙对轴承流场的影响不能忽略,尤其是在涉及温度场计算时,瓦块独立计算模型计算的结果与整体模型计算结果相差很大。     

机械加工定位误差的计算

给出了合成法、几何定义法和微分法三种定位误差的分析计算方法,阐述了定位误差计算的特点,并以典型的不同工序尺寸的实例,分析了定位误差对零件加工质量、工艺性和生产成本分析的影响.