车辆动力学(5)- 行星齿轮传动建模分解
行星齿轮的三维建模与运动仿真
北京工业大学耿丹学院毕业设计(论文)基于Solidwork的行星齿轮的三维建模与运动仿真所在学院专业班级姓名学号指导老师年月日摘要行星齿轮减速器是一种至少有一个齿轮的几何轴线绕着固定位置转动圆周运动的传动，变速器通常和若干行星轮和传递载荷的作用，为了使功率分流。
渐开线行星齿轮传动具有以下优点：传动比大，结构紧凑，体积小、质量小，效率高，噪音低，运转平稳，因此被广泛应用于冶金，工程机械，起重，运输，航空，机床，电气机械及国防工业等部门，作为减速、变速或增速的齿轮传动装置NGW型行星齿轮传动机构的传动原理：当高速轴由电机驱动，带动太阳轮，然后带动行星轮转动，内齿圈固定，然后带动行星架输出运动的，在行星架上的行星轮既自转和公转，具有相同的结构。
二级，三级或多级传输。
NGW型行星齿轮传动机构主要由太阳齿轮，行星齿轮，内齿圈，行星架，命名为基本成分后，也被称为zk-h型行星齿轮传动机构。
本设计是基于行星齿轮结构设计的特点，和SolidWorks三维建模和运动仿真。
行星齿轮和各种类型的特性的比较，确定方案；其次根据输入功率，相应的输出转速，传动比的传动设计、总体结构设计；三维建模并最终完成了SolidWorks，和模型的装配，并完成了传动部分的运动仿真和运动分析。
关键词：行星齿轮减速器、运动仿真、装配、三维建模AbstractPlanetary gear reducer is driving a at least one gear geometric axis rotated around a circular motion of fixed position, the transmission is usually and planetary gear and transfer load, in order to make the power split. Involute planetary gear transmission has the following advantages: large transmission ratio, compact structure, small volume, small mass, high efficiency, low noise, smooth operation, so it is widely used in metallurgy, engineering machinery, lifting, transportation, aviation, machine tools, electrical machinery and defense industry and other departments, as gear reducer, gear or the growthThe transmission principle of NGW type planetary gear transmission mechanism: when the high-speed shaft driven by a motor, to drive the sun gear, and the planet wheel is driven to rotate, the inner gear ring is fixed, and then drives the planetary frame outputting motion, on the planet carrier planet wheel both rotation and revolution, has the same structure. The two level, three level or multilevel transmission. The NGW type planetary gear transmission mechanism mainly consists of a sun gear, planet gear, inner gear ring, a planetary frame, named after the basic components, also known as the ZK-H type planetary gear transmission mechanism.This design is the design of planetary gear structure based on SolidWorks, and 3D modeling and motion simulation. Comparison of characteristics of planetary gears, and various types of determination scheme; secondly according to the input power, the output speed of the overall design, transmission design, ratio; 3D modeling and finished SolidWorks, assembly and model, and the motion simulation and motion analysis of the transmission part.Keywords: planetary gear reducer, assembly, motion simulation, 3D modeling目录摘要 (1)Abstract (3)第1章绪论 (6)1.1 国内外的研究状况及其发展方向 (6)1.2 SOLIDWORKS行星齿轮的选题分析及设计内容 (7)1.3 主要的工作内容 (7)第2章 NGW型行星轮减速器方案确定 (9)2.1 机构简图的确定 (9)2.2 周转轮系部分的选择 (9)2.3 NGW型行星轮减速器方案确定 (9)2.4 行星轮系中各轮齿数的确定 (12)第3章 NGW型行星减速器结构设计 (14)3.1 基本参数要求与选择 (14)3.1.1 基本参数要求 (14)3.1.2 电动机的选择 (14)3.2 方案设计 (14)3.2.1 机构简图 (14)3.2.2 齿形及精度 (15)3.2.3 齿轮材料及性能 (15)3.3 齿轮的计算与校核 (16)3.3.1 配齿数 (16)3.3.2 初步计算齿轮主要参数 (16)3.3.3 按弯强度曲初算模数m (19)3.3.4 齿轮疲劳强度校核 (20)3.4 轴上部件的设计计算与校核 (26)3.4.1 轴的计算 (26)3.4.2 行星架设计 (31)3.5 键的选择与校核 (35)3.5.1 键的选择 (35)3.5.2 键的校核 (36)3.6 联轴器的选择 (37)3.7 箱体尺寸及附件的设计 (38)第4章 SOLIDWORKS的建模与运动仿真 (43)4.1 建模软件的介绍 (43)4.2 行星齿轮机构的建模 (43)4.2.1 对行星齿轮的建模 (43)4.2.2 行星齿轮其他部件的建模 (45)4.3 行星齿轮机构的虚拟装配 (47)4.4 装配体的实现 (58)4.5 减速机的运动仿真 (60)4.5.1 仿真一般步骤 (60)4.5.2 机构运动分析的任务和方法 (61)4.5.3 运动的生成 (62)4.5.4 运动分析 (62)总结 (64)参考文献 (65)致谢 (66)第1章绪论1.1 国内外的研究状况及其发展方向国内对行星齿轮传动比较深入的研究最早开始于20 世纪60 年代后期，20 世纪70 年代制定了NGW 型渐开线行星齿轮减速器标准系列JB1799-1976。
基于多体动力学的行星齿轮传动系统研究
基于多体动力学的行星齿轮传动系统研究行星齿轮传动系统是一种高效率、高精度的传动装置，广泛应用于机械工程和自动化领域。
在过去的几十年里，随着计算机技术的飞速发展，研究人员开始更深入地研究行星齿轮传动系统的动力学行为。
多体动力学是一种用于描述和分析系统中多个物体之间相互作用的数学模型。
本文将探讨如何利用多体动力学方法研究行星齿轮传动系统。
首先，行星齿轮传动系统由太阳齿轮、行星齿轮和内齿轮组成。
太阳齿轮位于行星轴的中心，内齿轮围绕太阳齿轮旋转，行星齿轮与太阳齿轮和内齿轮相连接。
传动比由齿轮的尺寸和齿数决定，控制了输出轴的旋转速度和力矩。
在多体动力学模型中，每个齿轮被建模为一个刚体，其运动由牛顿力学定律描述。
通过建立各个齿轮的运动方程，并考虑他们之间的接触和相互作用力，可以分析传动系统的动力学行为。
其中的关键问题是确定行星轮和内齿轮的轨迹和接触点，以及计算系统中的力和力矩。
在传动系统中，齿轮的接触问题是一个重要的研究方向。
行星齿轮传动系统的齿轮接触分析包括接触点位置确定和接触力计算两个方面。
接触点位置的确定需要考虑到齿轮的几何参数和初始位置，可以通过数值求解等方法得到。
接触力的计算涉及到齿轮之间的接触力和支撑力，并且需要考虑到张力、撞击和摩擦等因素。
此外，传动系统的动力学分析还需要考虑到诸如振动、噪声和寿命等方面的问题。
通过对行星齿轮传动系统的多体动力学模型进行仿真和分析，可以评估系统的性能和可靠性，并优化设计和参数选择。
例如，在避免共振、降低振动和噪声水平以及提高传动效率方面，多体动力学分析可以发挥重要作用。
综上所述，基于多体动力学的行星齿轮传动系统研究为我们深入理解传动机构的运行原理和行为提供了一个有效的方法。
通过对齿轮接触、力学行为和系统性能进行建模和仿真，我们可以更好地优化传动系统的设计和运行。
尽管研究中还存在许多问题和挑战，但多体动力学方法无疑将持续为行星齿轮传动系统的研究和应用提供重要支持。
车辆动力学行星齿轮传动建模分解课件
车辆动力学主要研究车辆行驶过程中的动态性能，包括牵引性能、制动
性能、操作稳定性和行驶平顺性等。
03
耦合关系的重要性Βιβλιοθήκη 行星齿轮传动与车辆动力学之间存在密切的耦合关系，行星齿轮传动的
性能直接影响车辆的动力学性能，因此需要对两者进行耦合建模以实现
更精确的仿真和分析。
行星齿轮传动与车辆动力学的耦合模型
1 2 3
耦合效应的实际意义
通过对耦合效应的分析，可以深入了解行星齿轮传动与车 辆动力学之间的相互关系和影响机制，为优化车辆设计和 性能提供理论支持和实践指点。
05
实例分析与应用
某型汽车行星齿轮传动的动力学分析
总结词
详细描述
该部分第一介绍了车辆动力学行星齿轮传动 的基本概念和原理，然后以某型汽车为例， 详细讲授了其行星齿轮传动的动力学分析过 程，包括模型建立、参数设置、结果分析等 。
总结词
该部分主要讲述了某型汽车的动力学仿真与优化过程。通过仿真分析，得到了该型汽车在不同工况下 的动力学特性，并针对不良工况进行了优化设计。
详细描述
在某型汽车的动力学仿真方面，采用了专业仿真软件对该型汽车进行了动力学仿真分析，得到了其在 不同工况下的动力学特性。在优化设计方面，根据仿真结果，针对不良工况进行了优化设计，包括改 变齿轮参数、调整悬挂系统等措施，最终提高了该型汽车的整体性能。
建立耦合模型的方法
通过将行星齿轮传动的运动方程与车辆动力学方 程进行耦合，建立行星齿轮传动与车辆动力学之 间的耦合模型。
耦合模型的基本组成
耦合模型包括行星齿轮传动的运动方程和车辆动 力学方程，其中涉及到的变量包括转速、转矩、 加速度等。
模型简化与假设
为了简化模型并使其更易于分析，通常需要对模 型进行假设和简化，例如假设传动系统为线性系 统，忽略阻尼等次要因素。
行星齿轮建模方法
行星齿轮建模方法全文共四篇示例，供读者参考第一篇示例：行星齿轮是一种常见的传动装置，广泛应用于机械制造领域。
行星齿轮具有结构紧凑、传动效率高、承载能力强等优点，因此在各种机械设备中被广泛应用。
行星齿轮的设计和制造是一项复杂的工程，需要掌握高级的建模技朧。
本文将介绍一种常用的行星齿轮建模方法，希望对从事机械设计和制造领域的工程师和技术人员有所帮助。
一、行星齿轮的结构和工作原理行星齿轮是一种特殊的齿轮传动装置，由太阳齿轮、行星齿轮和内齿圈组成。
太阳齿轮位于中心，行星齿轮围绕太阳齿轮旋转，内齿圈则是行星齿轮的外部。
当太阳齿轮转动时，行星齿轮和内齿圈也随之转动，实现了传动作用。
二、行星齿轮建模的基本步骤行星齿轮的建模是一项复杂的工程，需要通过计算机辅助设计软件来完成。
下面介绍一种常用的行星齿轮建模方法，包括以下基本步骤：1. 确定行星齿轮的传动比和结构参数：首先要确定行星齿轮的传动比，即行星齿轮和太阳齿轮的齿数比值。
然后确定行星齿轮的结构参数，包括齿轮的压力角、齿距等。
2. 绘制行星齿轮的三维模型：通过CAD软件绘制行星齿轮的三维模型，包括太阳齿轮、行星齿轮和内齿圈三部分。
在绘制过程中需要考虑行星齿轮的结构和尺寸参数。
通过调整模型的参数，优化行星齿轮的设计。
3. 完成齿轮的设计和生成齿条：根据行星齿轮的结构参数和传动比，设计行星齿轮的齿条。
可以采用齿轮设计软件来生成齿条，保证齿轮的准确性和精度。
4. 进行齿轮的强度分析：通过有限元分析软件对行星齿轮进行强度分析，评估其受力性能和承载能力。
根据分析结果优化行星齿轮的结构，提高其传动效率和稳定性。
5. 完善齿轮的制造工艺：根据行星齿轮的设计要求，制定相应的制造工艺流程。
确保齿轮的加工精度和表面质量，提高齿轮的使用寿命和可靠性。
三、行星齿轮建模的关键技术和注意事项1. 行星齿轮建模是一项复杂的工程，需要掌握高级的CAD软件技术和齿轮设计原理。
工程师和技术人员应该具备相关的专业知识和技能，熟练运用CAD软件进行建模和分析。
2K-H行星齿轮传动优化设计数学 建模与解算
2K-H行星齿轮传动优化设计数学建模与解算【摘要】本文针对2K-H行星齿轮传动进行优化设计，通过数学建模和解算方法，提出了一种有效的优化设计方案。
首先介绍了行星齿轮传动的基本原理，然后详细分析了2K-H行星齿轮传动的结构特点。
在数学建模方法部分，提出了如何利用数学模型来优化设计方案。
接着通过解算过程展示了优化设计的具体步骤。
在对设计优化结果进行评价，并总结了研究成果。
展望了未来研究方向，为行星齿轮传动的进一步优化提供了参考。
本研究对于提高行星齿轮传动的性能和效率具有重要意义，为相关领域的研究和发展提供了有益的启示。
【关键词】关键词：行星齿轮传动、2K-H行星齿轮传动、优化设计、数学建模、解算过程、设计评价、研究成果、未来展望。
1. 引言1.1 研究背景在实际应用中，2K-H行星齿轮传动的设计和优化仍然存在一些问题和挑战。
传统的设计方法往往过于依靠经验和试错，难以确保设计的最优性。
通过数学建模和优化设计，可以有效地提高2K-H行星齿轮传动的性能和效率。
本文旨在通过对2K-H行星齿轮传动的数学建模与解算进行深入研究，提出一种优化设计方案，并通过解算过程验证设计结果的有效性。
通过本研究，可以为2K-H行星齿轮传动的设计和应用提供理论基础和技术支撑。
部分将围绕行星齿轮传动的发展历程、2K-H行星齿轮传动的特点和存在的问题进行介绍和分析，为后续的研究工作奠定基础。
1.2 研究目的研究目的是通过对2K-H行星齿轮传动进行优化设计，提高其传动效率和工作性能。
具体目的包括：优化齿轮的结构参数，减小传动系统的摩擦损失和能量损失；提高传动系统的传动精度和稳定性，降低噪声和振动水平；提高传动系统的承载能力和寿命，增强其工作可靠性和耐久性。
通过数学建模和解算分析，寻找最佳的设计方案，使得2K-H行星齿轮传动在实际工程应用中能够发挥最佳效果，满足不同领域和行业的需求。
通过本研究的成果，为行星齿轮传动的设计优化提供新的思路和方法，推动行星齿轮传动技术的发展和应用，为相关领域的工程设计和制造提供技术支持和参考依据。
2K-H行星齿轮传动优化设计数学 建模与解算
2K-H行星齿轮传动优化设计数学建模与解算作者：史素华来源：《中阿科技论坛（中英阿文）》2019年第01期摘要：通过研究2K-H行星轮系的设计要求及分析各种约束条件，以最小体积为目标建立数学模型。
在确定设计变量，建立目标函数后，利用约束变尺度优化算法和Fortran语言编程进行最优化的求解。
关键词：行星齿轮传动;优化设计;m数学建模渐开线行星齿轮传动与普通定轴齿轮传动相比具有承载能力大、体积小、效率高、重量轻、传动比大、噪音小、可靠性高、寿命长、便于维修等优点，广泛应用于小汽车、重型载重汽车、工程车辆和飞机等的传动系中[1]。
研究指出，同一制造精度下，行星传动比起定轴线固定传动，载荷一般沿齿宽分布得较好[2]。
这是由于在行星传动中齿宽对直径的比值一般不超过0.7，而在普通减速器中却达到1.6，在个别情况下，例如在涡轮机减速器中则显著超过此值。
在同样条件下，行星传动的箱体重量比普通定轴齿轮传动的箱体其重量要小好几倍，因为行星传动箱体外廓尺寸比普通定轴齿轮传动的箱体要小得多。
设计行星传动时，正确选择齿轮参数的意义远比设计普通定轴传动的大。
齿轮参数选择不当时，不但可能丧失在外廓尺寸和重量方面的优点，甚至可能得到不利于使用的传动。
按最小体积为目标对行星齿轮机构进行最优化设计，不仅对缩小体积，而且对减小质量、节约材料及降低成本等都是很有实效的，这些对汽车及飞机这一类的产品尤其重要[3]。
现在就以这类产品中常采用的2K-H型行星齿轮机构作优化设计。
一、2K-H行星齿轮设计要求对于2K-H行星齿轮，如右图所示，要设计一个符合条件的行星齿轮传动，需要根据已知条件确定齿轮的几个参数：各齿轮的齿数z，模数m，齿宽b，如果将行星轮的个数也作为设计变量，则有四个参数。
根据机械设计知识，行星齿轮参数需要满足以下两种条件：一是几何设计条件就是在不考虑材料视齿轮为刚体的情况下齿轮正常传动的条件;二是齿轮的强度条件，行星齿轮作为一种机械构件，需要在确定材料的情况下对强度作一定的要求，保证齿轮到达预期寿命[4]。
运输车辆传动系统动力学建模与分析
运输车辆传动系统动力学建模与分析运输车辆是现代交通运输中发挥重要作用的关键工具。
为了保证运输车辆的安全性和稳定性，必须对其传动系统进行动力学建模和分析。
本文旨在探讨运输车辆传动系统的动力学特性，并提供一些分析方法和实用建议。
传动系统是运输车辆中的核心部件，它负责将发动机的动力传输到车轮，驱动车辆行驶。
传动系统由多个组成部分构成，包括发动机、离合器、变速器、传动轴、差速器和驱动轴等。
这些组成部分之间的协调运动至关重要，影响着整个车辆的动力性能和燃油经济性。
在进行动力学建模和分析之前，我们首先需要了解传动系统的基本工作原理。
当发动机输出动力时，离合器负责将动力传递给变速器。
变速器可以根据车辆的实际运行需求，选择合适的齿轮组合来改变车速和引擎转速。
传动轴则将变速器输出的动力传递给驱动轮，通过差速器使两个驱动轮能够以不同的转速旋转，以适应转弯和车辆行驶过程中的不平路面。
传动系统的动力学特性主要包括传动效率、扭矩变化和轴线变形等方面。
传动效率是指传动系统将发动机输出的动力转化为有效驱动车辆行驶所需的能量比例。
传动效率的高低直接影响着车辆的燃油经济性和动力性能。
因此，在传动系统设计和优化中，提高传动效率是一个重要的研究方向。
扭矩变化是传动系统动力学中的另一个重要参数。
由于传动系统中的不同组成部分有不同的质量和惯性特性，因此在传递动力的过程中会发生扭矩的变化。
这种扭矩变化会导致车辆在行驶过程中出现颠簸和振动，对驾驶员的操控稳定性造成影响。
因此，减小扭矩变化是提高车辆行驶平稳性的关键。
此外，传动系统的轴线变形也是值得关注的一个问题。
在高速行驶和重载情况下，传动轴和驱动轴可能发生一定的弯曲和变形，进而影响车辆的操控和行驶安全。
因此，在传动系统设计和优化中，需要考虑合适的材料和结构来减小轴线变形，并提高传动系统的可靠性和耐用性。
针对以上问题，研究人员提出了多种分析和优化方法。
例如，可以使用数学模型和仿真软件来模拟传动系统的运动规律和相关参数变化。
车辆动力学(4)-齿轮机构建模
二、行星齿轮机构模型
车辆传动应用的典型行星机构
（a）单星行星排 ，（b）复星行星排， （c、d）双星行星排 （e、f）锥齿差速器， （g、h）柱型差速器
二、行星齿轮机构模型
2. 行星机构转速方程
太阳轮s
齿圈r
行星机构三基本构件
行星架c
二、行星齿轮机构模型
2. 行星机构转速方程
rp c
s
行星齿轮传动转速分析
（1）单星行星排
每个行星轮 同时与两个中心轮相 啮合。结构最简单， 应用最广泛。
二、行星齿轮机构模型
（2）内外啮合双联排
行星轮为复 式双联齿轮。
二、行星齿轮机构模型
（3）外啮合双联排
行星轮为复 式双联齿轮。
二、行星齿轮机构模型
（4）内啮合双联排
行星轮为复 式双联齿轮。
二、行星齿轮机构模型
（5）内外啮合双星行星排
10 9
8
一、定轴齿轮机构模型
3. 轮齿和轴均按弹性体建模
动态传递误差x 静态误差e
θ1
J1
M1
r1
e km
cm
x ——啮合线上两齿轮的相对位移, x r11 r22
e —— 轮齿啮合综合误差 , e(t) eh cos(ht e )
传动误差: x e r11 r22 e
θ2
M2
J2
r2
一、定轴齿轮机构模型
3. 轮齿和轴均按弹性体建模
θ1
θ2
J1
M1
r1
e km
M2
J2
r2
cm
J11 J 22
M1 Fd r2
Fd r1 M
2
2011车辆动力学(4)- 齿轮机构建模
J2
θ2
θL
ML
k2 k = 2 i
* 2
Me
θe
Je
k1 c1
J*
k
* 2
c
* 2
* JL
c2 c = 2 i
* 2
* ML
一、定轴齿轮机构模型
一、定轴齿轮机构模型
3. 动态模型 θe
Me Je
J1
k1 c1
θ1
k2 c2 JL
km cm
J2
θ2
θL
ML
集中参数模型（4自由度）
&& & & J eθ e = M e − k1 (θ e − θ1 ) − c1 (θ e − θ1 ) && & & J1θ1 = k1 (θ e − θ1 ) + c1 (θ e − θ1 ) − Fd r1 && & & J 2θ 2 = Fd r2 − k2 (θ 2 − θ L ) − c2 (θ 2 − θ L ) J θ = k (θ − θ ) + c (θ − θ ) − M && & & L L 2 2 L 2 2 L L
2. 行星机构转速方程
r p c s
行星齿轮传动转速分析
如何转化？
熟悉的定轴齿轮传动
固定行星架
zr k= zs
行星排特性参数
ns − nc zr =− n r −nc zs
ns + knr − (1 + k )nc = 0
二、行星齿轮机构和转速、转矩关系式 行星齿轮机构和转速、
3. 行星机构转矩关系式
行星齿轮箱动力学建模及振动信号仿真
Vibration signal modeling of a planetary gear set for tooth crackdetectionXihui Liang,Ming J.Zuo ⇑,Mohammad R.HoseiniDepartment of Mechanical Engineering,University of Alberta,Edmonton,Alberta T6G 2G8,Canadaa r t i c l e i n f o Article history:Received 3May 2014Received in revised form 20October 2014Accepted 17November 2014Available online 26November 2014Keywords:Signal modeling Dynamic simulation Transmission path Tooth crackSidebandsa b s t r a c tIn a planetary gearbox,there are multiple vibration sources,and the transmission path ofvibration signals changes due to the rotation of the carrier.This study aims to model thevibration signals of a planetary gearbox and investigate the vibration properties in thehealthy condition and in the cracked tooth condition.A dynamic model is developed tosimulate the vibration source signals.A modified Hamming function is proposed to repre-sent the effect of the transmission path.By incorporating the effect of multiple vibrationsources and the effect of transmission path,resultant vibration signals of a planetarygearbox are obtained.Through analyzing the resultant vibration signals,some vibrationproperties of a planetary gearbox are revealed and the fault symptoms of sun gear toothcrack are identified and located.Finally,the proposed approach is experimentally verified.Ó2014Elsevier Ltd.All rights reserved.1.IntroductionThe vibration signals of a planetary gearbox are more complicated comparing with that of a fixed-shaft gearbox.For a planetary gear set,several sun-planet gear pairs and several ring-planet gear pairs mesh simultaneously.The vibration signals generated by each sun-planet gear pair are similar but with different phases [1].Similar comments apply to the ring-planet meshes.Due to the phase differences,some of the excitations are canceled or neutralized [2]while others are augmented.In general,vibration transducers,mounted on the housing of a gearbox or the housing of a bearing,are used to acquire vibration signals.Transmission paths of the vibration signals to a transducer change due to the revolution of the carrier.Multiple vibration sources and the effect of the transmission path will cause fault symptoms hard to be distinguished.Even though many signal processing methods have been proposed to detect gear faults [1–4],the improvements of these methods are still desired.The transducer signal is comprised of many sub signals,such as the vibrations of the sun gear,pla-net gear,ring gear,bearings and shafts.Unfortunately,there are no mature signal processing methods which can effectively denoise and separate these signals [5,6].If we can ‘‘open’’the black box,‘‘see’’all the sub-signals,and understand the gen-eration mechanisms of vibration signals,effective tools can be developed to detect gear faults.Mathematical models have been used by several researchers to investigate the vibration properties of a planetary gearbox[7,8].However,the mathematical models lack the connection with the physical parameters of a gearbox,like the mesh stiff-ness and damping.In addition,they can hardly model the process of the fault growth.Dynamic simulation is a better choice to investigate the vibration properties of a planetary gearbox.A dynamic model is more closely connected with the physical /10.1016/j.engfailanal.2014.11.0151350-6307/Ó2014Elsevier Ltd.All rights reserved.⇑Corresponding author.Tel.:+17804924466;fax:+17804922200.E-mail address:ming.zuo@ualberta.ca (M.J.Zuo).186X.Liang et al./Engineering Failure Analysis48(2015)185–200parameters of a planetary gearbox than the mathematical model.It can model the process of fault growth and the corre-sponding pared with experimental orfield systems,dynamic simulation models have the following advantages [9]:(1)environmental noises can be eliminated so that the changes in vibration signals caused by the faults can be identified easily;and(2)with a good dynamic simulation model,we can easily simulate different types and different levels of faults, and observe changes in the vibration signal due to the faults.A large range of dynamic models have been developed to simulate the behavior of planetary gears.Kahraman[10] proposed a nonlinear dynamic model to investigate the load sharing characteristics of a planetary gear set.Inalpolat and Kahraman[11]used the same model as Ref.[10]to predict modulation sidebands of a planetary gear set having manufac-turing errors.Lin and Parker[12]modified the model of Ref.[10]and investigated the free vibration properties of a planetary gear set.Cheng et al.[13]developed a pure torsional dynamic model to investigate the properties of a planetary gear set when a single pit was present on one tooth of the sun gear.Chaari et al.[14]used a similar model as Ref.[12]to investigate the effect of manufacturing errors on the dynamic behavior of planetary gears.The effects of tooth profile modification or manufacturing errors are not considered in this paper.Studies on the effect of manufacturing error are given in Refs. [11,14]while studies on the effect of tooth profile modification are given in Refs.[15–18].However,the investigation of the vibration properties of a planetary gearbox with cracked teeth is limited.Barszcz and Randall[19]applied spectra kurtosis to detect a ring gear tooth crack in the planetary gear of a wind turbine.Lewicki et al.[20]utilized vibration separation techniques to detect the tooth damage in the sun gear,planet gear and ring gear,respec-tively.Chen and Shao[21]investigated the vibration properties of a planetary gear set when there was a tooth root crack in the ring gear.Chaari et al.[22]applied the dynamic model developed in Ref.[14]to investigate the vibration properties of the sun gear and the carrier of a planetary gear set with tooth crack or a single pit on the sun gear.In their studies,the gear mesh stiffness was approximated as a square waveform which would generate unwanted frequency components in the dynamic response[23].Chen and Shao[24]studied the dynamic features of a planetary gear set when a tooth crack was under dif-ferent sizes and inclination angles.The displacement signals of the sun gear and the planet gear were investigated when a crack was present on the sun gear or the planet gear.But,Refs.[21,22,24]did not considered the effect of transmission path in their studies.In this study,we focus on cracks in the sun gear only considering the effect of transmission path.All the above mentioned dynamic models can be divided into two categories:fixed coordinate model and rotating coor-dinate model.In order to consider inertia effect caused by the rotation of the carrier,a rotating coordinate model is more convenient to use.The inertia force contains gyroscopic force and centrifugal force.Some previous studies[14,24]considered the gyroscopic force in their dynamic models;however,they did not consider the centrifugal force properly in the equilib-rium equations of planet gears.In this study,both the gyroscopic force and the centrifugal force will be considered.A few studies considered the effect of the transmission path in the vibration signal modeling.Inalpolat and Kahraman[7] expressed the resultant acceleration signal of a planetary gear set as follows:X NCw nðtÞF rpnðtÞð1:1ÞaðtÞ¼n¼1where C is a constant;N represents the number of planet gears;w n(t)denotes the effect of transmission path for the n-th planet gear which is a weighting Hanning function[7]with a time duration of T c/N;and F rpn(t)is the dynamic force of the n-th ring-planet mesh.Later,Inalpolat and Kahraman[11]improved the modeling considering the dynamic forces of both sun-planet meshes and ring-planet meshes.They used the same Hanning function as Ref.[7]to cover the effect of the transmission path.X NaðtÞ¼ðC s w nðtÞF spnðtÞþC r w nðtÞF rpnðtÞÞð1:2Þn¼1where C s and C r are constants facilitated to establish the relation between the gear mesh forces;and F spn(t)and F rpn(t)rep-resent the dynamic forces of the n-th sun-planet mesh and the n-th ring-planet mesh,respectively.However,the correctness of Eq.(1.2)is worth discussing.The line of force F spn(t)is the internal common tangent of the base circles of the sun gear and the n-th planet gear.While the line of force F rpn(t)is the internal common tangent of the base circles of the ring gear and the n-th planet gear.Since dynamic forces F spn(t)and F rpn(t)are not in the same direction,it is not proper to add weighted F spn(t)and weighted F rpn(t)together as two scalars.Feng and Zuo[8]investigated possible transmission paths of vibration signals in a planetary gearbox.In Fig.1,three transmission paths are illustrated from its origin to the transducer.According to their studies,the transducer perceived sig-nal arriving along paths2and3will have negligible amplitude.Therefore,only thefirst transmission path was considered in their studies,and the transmission path was modeled by a Hanning function with a time duration of T c.All the previous studies modeled the effect of transmission path using a Hanning function[7,8,11].They all assumed that as planet n approached the transducer location,its influence would increase,reaching its maximum when planet n was the closest to the transducer location,then,its influence would decrease to zero as the planet went away from the transducer. However,even if the planet n is in the farthest location from the transducer,its influence may not be zero.In this study,we propose an approach to overcome this shortcoming.In this paper,a planetary gear dynamic model is developed to simulate the vibration signals of each gear,including the sun gear,the planet gears,and the ring gear.In this dynamic model,both the gyroscopic force and the centrifugal force areconsidered,and more accurate physical parameters are adopted.The vibration signals are simulated in the perfect condition of a planetary gearbox and in the faulty condition when there is a cracked tooth in the sun gear.A mathematical model is proposed to represent the effect of the transmission path which can fit different planetary gearboxes by choosing proper model parameters.Incorporating the effect of the transmission path,the resultant signals of a planetary gearbox at the trans-ducer location are generated.The vibration signals are investigated both in the time domain and in the frequency domain,and fault symptoms are revealed which can be used to detect the severity of tooth crack.Finally,experimental verification of the proposed approach is performed.Preliminary results of the proposed approach were earlier documented in the technical report [25],and a shorter version of this journal paper is included in the conference proceedings of PHM 2014[26].2.Dynamic simulationIn this section,a lumped-parameter model is developed to simulate the vibration signals of each gear of a planetary gear set.This model is similar to that used by Lin and Parker [12]with three distinctions:(1)the planet deflections are described in the horizontal and vertical coordinates,(2)both the gyroscopic force and the centrifugal force (inertial force)are incor-porated,and (3)more accurate physical parameters are adopted.Whether gear deflections are described in horizontal and vertical coordinates,or radial and tangential coordinates,the gear dynamic behaviors will not be affected.However,the inertial forces may change the dynamic behavior of a gearbox in high speed applications from that at low speeds.Time-varying mesh stiffness is one of the main sources of vibration in a gear transmission system [27].In Ref.[12],the gear mesh stiffness was approximated by a square waveform.The square waveform reflects only the effect of the change in the tooth contact number,but ignores the effect of the change in the tooth contact position [28].In addition,the physical damp-ing was ignored in their model.In this study,more accurate physical parameters (mesh stiffness and physical damping)will be adopted in the simulation of vibration signals.2.1.Modeling of a planetary gear setFig.1shows a two-dimensional lumped-parameter model which is used in this study to simulate the vibration signals of a planetary gear set,which consists of one sun gear (s ),one ring gear (r ),one carrier (c )and N planet gears (p ).Each com-ponent has three degrees of freedom:transverse motions in the x -axis and y -axis,and rotation.The rotation coordinates h i ,i =s ,r ,c ,p 1,...,p N are the angular displacement.The sun gear,ring gear and carrier translations x j ,y j ,j =s ,r ,c and planet translations x pn ,y pn ,n =1,...,N ,are measured with respect to a rotating frame of reference fixed to the carrier with the origin o .The gear mesh interface is modeled as a spring-damper system.The directions of all the coordinates at the initial time (time zero)are shown in Fig.2.Since we are focusing on the effects of a growing crack on the vibration response of the mesh-ing gears,we have ignored the effects of transmission errors in the gears,the frictions between the gear teeth,and other practical phenomena such as backlash.The equations of motion of a planetary gear set are expressed as follows:Equations of motion for the sun gear:m s €x s þc sx _xs þk sx x s þX F spn cos w sn ¼m s x s X 2þ2m s _y s X þm s y s _X m s €ys þc sy _y s þk sy y s þX F spn sin w sn ¼m s y s X 2À2m s _xs X Àm s x s _X ðJ s =r s Þ€h s þX F spn ¼T i =r sð2:1ÞFig.1.Transmission paths [8].where F spn represents the dynamic force of the n -th sun-planet gear mesh:F spn ¼k spn d spn þc spn _d spnd spn ¼ðx s Àx pn Þcos w sn þðy s Ày pn Þsin w sn þr s h s þr pn h pn Àr c h c cos aw sn ¼p =2Àa þw nw n ¼2ðn À1Þp =n ;i ¼1;2;...;NEquations of motion for the ring gear:m r €x r þc rx _x r þk rx x r þX F rpn cos w rn ¼m r x r X 2þ2m r _y r X þm r y r _X m r €y r þc ry _y r þk ry y r þXF rpn sin w rn ¼m r y r X 2À2m r _x r X Àm r x r _X ðJ r =r r Þ€h r þðc rt =r r Þ_h r þðk rt =r r Þh r þX F rpn ¼0ð2:2Þwhere F spn represents the dynamic force of the n -th sun-planet gear mesh:F rpn ¼k rpn d rpn þc rpn _d rpnd rpn ¼ðx r Àx pn Þcos w rn þðy r Ày pn Þsin w rn þr r h r Àr pn h pn Àr c h c cos aw rn ¼p =2þa þw nEquations of motion for the planet gears:m pn €x pn þF cpnx ÀF spn cos w sn ÀF rpn cos w rn ¼m pn x pn X 2þ2m pn _y pn X þm pn y pn _X þm pn r c X 2cos w nm pn €y pn þF cpny ÀF spn sin w sn ÀF rpn sin w rn ¼m pn y pn X 2À2m pn _x pn X Àm pn x pn _X þm pn r c X 2sin w nðJ pn =r p Þ€h pn þF spn ÀF rpn ¼0ð2:3Þwhere F cpnx and F cpny describe the bearing forces between the carrier and the n -th planet in the x and y directions:F cpnx ¼k pnx ðx pn Àx c Þþc pnx ð_x pn À_x c ÞF cpnx ¼k pny ðy pn Ày c Þþc pny ð_y pn À_y c ÞEquations of motion for the carrier:m c €x c þc cx _x c þk cx x c ÀX F cpnx ¼m c x c X 2þ2m c _y c X þm c y c _X188X.Liang et al./Engineering Failure Analysis 48(2015)185–200m c€y cþc cy_y cþk cy y cÀXF cpny¼m c y c X2À2m c_x c XÀm c x c_XðJ c=r cÞ€h cþXF cpnx sin wnÀXF cpny cos wn¼T o=r cð2:4ÞAs a planet gear rotates around the center of the sun gear,the inertial force will be generated.The inertial force contains two items m pn x pn X2(gyroscopic force)and m pn r c X2(centrifugal force)which can be observed from the equations of transverse motions of planet gears in Eq.(2.3).x pn,which is the x-direction displacement of the n-th planet gear,is much smaller than r c which is the distance between centers of sun gear and planet gear.If cos w n takes a value near1,the item m pn r c X2cos w n will dominate the inertial force when the rotation speed of the carrier is large.On the other hand,if cos w n takes a small value near0,the item m pn r c X2sin w n will dominate the inertial force when the rotation speed of the carrier is large,but it is in the y-direction motion.Some previous studies[14,24]considered the gyroscopic force,but ignored the gyro-scopic force.In this study,both these two items are considered.A list of symbols used in this paper is provided at the end of this paper.2.2.Crack modeling and mesh stiffness evaluationGear tooth crack is one common failure mode in a gear transmission system.It may occur due to excessive service load, inappropriate operating conditions or simply fatigue[29].In the dynamic model described in Section2.1,the gear mesh interface is modeled as a spring-damper system.When a pair of spur gear meshes,the tooth contact number and the tooth mesh position change during meshing.It leads to a periodic variation in the gear mesh stiffness.When a crack happens in one gear tooth,the mesh stiffness will decrease and consequently the vibration properties of the gear system will change.In order to comprehensively understand the vibration properties of a planetary gear set,it is essential to evaluate the mesh stiffness effectively.According to the research by Belsak and Flasker[30],crack mostly initiates at the critical area of a gear tooth(area of the maximum principle stress),and the propagation paths are smooth,continuous,and in most cases,rather straight with only a slight curvature as shown in Fig.3.Liang et al.[28]simplified the crack growth path as a straight line starting from the crit-ical area of the tooth root.The same model as Ref.[28]will be used in this study.The method reported in Ref.[28]will be used directly to evaluate the mesh stiffness of a planetary gear set in the perfect and the cracked tooth condition.Potential energy method[28,31,32]will be applied to evaluate the mesh stiffness of a pair of sun-planet gear and a pair of ring-planet gear.The total potential energy of a pair of meshing gears is considered to be the summation of the Hertzian energy,bending energy,shear energy,and axial compressive energy.The total effective mesh stiffness can be calculated based on the Hertzian,bending,shear,and axial compressive mesh stiffness values.If there is a tooth crack,the bending stiffness and the shear stiffness will reduce due to the change in the tooth length and the tooth height caused by the crack[28],which leads to the decrease of the total mesh stiffness.While each of the sun-planet meshes (or ring-planet meshes)has the same shape of mesh stiffness variation,they are not in phase with each other[33].Incorpo-rating the mesh phasing relationships,the mesh stiffness of all sun-planet gear pairs and all ring-planet gear pairs can be calculated,thus,the mesh stiffness of a planetary gear set is obtained.In a planetary gearbox,sun gear teeth easily suffer damage because their multiplicity of meshes with the planet gears increases the potential for damage on the sun gear[2].Fig.4shows the mesh stiffness of a pair of sun-planet gears withCriticalareacentre lineTooth crack propagation path[30].X.Liang et al./Engineering Failure Analysis48(2015)185–200189190X.Liang et al./Engineering Failure Analysis48(2015)185–200Table1Physical parameters of a planetary gear set[28].Parameters Sun gear Planet gear Ring gearNumber of teeth193181Module(mm) 3.2 3.2 3.2Pressure angle20°20°20°Mass(kg)0.700 1.822 5.982Face width(m)0.03810.03810.0381 Young’s modulus(Pa) 2.068Â1011 2.068Â1011 2.068Â1011 Poisson’s ratio0.30.30.3Base circle radius(mm)28.346.2120.8Root circle radius(mm)26.245.2132.6Reduction ratio 5.263Bearing stiffness k sx=k sy=k rx=k ry=k cx=k cy=k pnx=k pny=1.0Â108N mBearing damping c sx=c sy=c rx=c ry=c cx=c cy=c pnx=c pny=1.5Â103Ns/mdifferent crack levels(perfect,0.78mm crack,2.34mm crack and3.90mm crack)on a sun gear tooth.The physical param-eters of this planetary gear set(one sun gear,onefixed ring gear and four equally spaced planet gears)are shown in Table1. As the growth of the crack,the mesh stiffness reduces gradually,which will cause the gearbox vibrating abnormally.Fig.5describes the mesh stiffness of four sun-planet gear pairs with the consideration of mesh phasing relationships of multiple gear pairs.The curves k sp1,k sp2,k sp3and k sp4represent the1st,2nd,3rd and4th pair of the sun-planet mesh stiffness, respectively.The mesh stiffness of ring-planet gears are assumed not to be affected by the tooth crack on the sun gear andthe stiffness equations of the ring-planet gears were derived in Ref.[28].The cracked tooth on the sun gear meshes with the four planet gears in turn,therefore,the mesh stiffness of the four pairs of sun-planet gears are all affected.The time intervals of the cracked tooth in meshing are labeled in Fig.4.The symbol c sn(n=1,2,3,4)is the relative phase between the n th sun-planet pair with respect to the1st sun-planet pair.The value of c s1,c s2,c s3and c s4are1,0.75,0.5and0.25,respectively[23]. The symbol h m denotes the mesh period.2.3.Numerical simulation of vibration signalsIn this section,vibration signals of each gear of a planetary gear set are numerically simulated using MATLAB ode15s sol-ver.Physical parameters of the planetary gear set are mainly listed in Table1.In addition,the mass of the carrier is10kg.A constant torque of450N m is applied to the sun gear.The rotation speed of the carrier is8.87r/min.The gear mesh damping coefficient c is calculated by the following equation[34]:c¼2fffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffikm1m212rð2:5Þwhere k denotes the time-varying mesh stiffness of a pair of gear;m1and m2represent the mass of the pinion and the gear of a pair of gears,respectively;f is a constant damping ratio which is set to be0.07in this study.Through this simulation,the displacement,velocity,and acceleration signals of the sun gear,planet gears,ring gear and carrier are all obtained.Fig.6shows displacement signals of the sun gear in three health conditions:perfect,0.78mm crack and3.90mm crack in one sun gear tooth.The sun gear has19teeth and Fig.6illustrates the signals in19mesh periods(T m).Within19meshes,the cracked tooth will mesh with the four planets in turn.The time duration of the cracked tooth in meshing can be calculated analytically[33].For the planetary gear set used in this paper,the time duration is4.75(19/4)T m which is labeled in Fig.6. When the cracked tooth is in meshing,the sun gear generates a bigger displacement(fault symptom).With the growth of the crack,the fault symptoms enlarge.However,the fault symptom may appear in the x-direction displacement or in the y-direction displacement,even we can see4uniformly spaced fault symptoms in the absolute displacement of the sun gear. In the3.90mm crack condition,we can observe clearly fault symptoms.However,when the crack length is0.78mm,the fault symptom(indicated by the arrows)is very week.That’s why it is hard to detect the fault symptom in the early stage of crack growth.Fig.7depicts the center locus of the sun gear in one revolution of the carrier in three health conditions:perfect,0.78mm crack and3.90mm crack in one tooth of the sun gear.For this sun gear,the crack length is3.90mm when the crack prop-agates to the tooth center line as indicated in Fig.3.To demonstrate the fault symptom when there is a small crack,the vibra-tion signals of0.78mm(3.90/5mm)crack are simulated.According to Table1,the ring gear has81teeth,thus in one revolution of the carrier,81gear meshes will occur.From Fig.7,we can see81spikes in the perfect condition which corre-spond to the81gear meshes.When there is a crack,some even bigger spikes(fault symptom)can be observed from Fig.7.In 81gear meshes,the cracked tooth is involved in meshing in17or18times(81/4.75).17bigger spikes are illustrated in the crack condition of Fig.7.However,when the crack length is0.78mm,the fault symptom is weak.X.Liang et al./Engineering Failure Analysis48(2015)185–200191192X.Liang et al./Engineering Failure Analysis48(2015)185–200From the displacement signals of the sun gear from Figs.6and7,we can see clear fault symptoms when there is a crack in a sun gear tooth.However,in real applications,it is very hard to acquire the vibration signals of the sun gear.Inside a plan-etary gearbox,there are multiple vibration sources,because several pairs of sun-planet gears and several pairs of ring-planet gear pairs mesh simultaneously.The vibration signals from these vibration sources will interfere with each other.In addition, due to the rotation of the carrier,the transmission paths of the vibration signals,from the vibration sources to a transducer, change.The effect of the multiple vibration sources and the effect of transmission path will lead to the complexity of the resultant vibration signals acquired by a transducer.To demonstrate the effects of inertial force(includes the gyroscopic force and the centrifugal force),we compared the dynamic responses of a planetary gearbox in two cases:with considering inertia force and without considering inertia force. When the carrier was running at8.87r/min(correspondingly,the sun gear was running at46.68r/min),the influence of the iner-tial force was negligible.The inertial force is not negligible when the rotation speed is large.Fig.8shows the Y-direction displace-ment of the sun gear when the carrier is running at950r/min(correspondingly,the sun gear is running at5000r/min).There is a 2.34mm crack in a sun gear tooth.The time duration of the X-axis is one revolution of the sun gear(19gear meshes).When the rotation speed of a gearbox is low,the inertial force is small and consequently its influence is very limited. However,with the speed increase of a gearbox,the influence of the inertial force becomes important[12].As shown in Fig.8,in the high speed,if the inertial force is incorporated in the dynamic model,the amplitude of gear vibration signal becomes small and the signal oscillation becomes slow.In addition,the fault symptom becomes weak when the inertial force is considered.Thus,it is essential to incorporate the inertial force especially in the high speed applications in order to pre-cisely reflect the real application,because in the real application,the inertial force exits and it never disappears.3.Modeling effect of transmission pathIn this study,the resultant vibration signal is considered to be the summation of weighted vibration of each planet gear as shown in Eq.(3.1).The planet gear meshes with the sun gear and the ring gear simultaneously.Therefore,the vibration of the planet gear contains both the information of sun-planet mesh and ring-planet mesh.The effect of the transmission path ismodeled as a modified Hamming function.The exponent expression in Eq.(3.1)can be used to increase or decrease the band-width of the Hamming function by choosing different a values.The value of a is determined by the properties of a gearbox,like its size,bearing characteristics,ring gear-housing interface and ring gear flexibility.A proper accounting of these effects would require a deformable-body dynamic model that can represent the transfer path between a given gear mesh and the point of measurement accurately [7].Fig.9illustrates the differences of Hanning function,Hamming function and modified Hamming function corresponding to different a values.The bandwidth is increased when a is positive,and decreased when a is negative.However,we need to see that a cannot take a very large positive value.If a is very large,the effect of vibration from the farthest planet (distance to the transducer)is amplified,even overweight the effect of vibration from the nearest planet.a ðt Þ¼X N n ¼1e a ðmod ðw c t þw n ;2p ÞÀp Þ2H n ðt Þa n ðt Þð3:1Þwhere H n (t )represents Hamming function for the n -th planet gear and a n (t )is the acceleration signal of the n -th planet gear.4.Properties of resultant vibration signalsIn this section,resultant vibration signals of a planetary gearbox are obtained and the vibration properties are investi-gated.Solving the dynamic equations in Section 2.1,we can get acceleration signals of each planet gear in the rotating carrier coordinate system.Applying the theory of acceleration in the rotating coordinate system [35],the absolute acceleration of each planet gear in the coordinate system fixed on the housing of a gearbox can be attained.In this study,only the vertical direction (y -direction)of the resultant acceleration signals is considered.The resultant acceleration signals of a planetary gearbox in the y -direction are expressed as the weighted summation of the y -direction acceleration signal of each planet gear.Fig.10shows the y -direction acceleration signals of a planetary gearbox at four different cases (the effect of transmission path is represented by a modified Hamming function with a =0.1,Hamming function,Hanning function and modified Hamming function with a =À1).We can see amplitude modulation in all the cases;however,the degree of the amplitude modulation is different.The amplitude modulation is strongest when the effect of the transmission path is represented by a modified Hamming function with a =À1.The second strongest one is in the case of Hanning function.The weakest one is in the case of modified Hamming function with a =0.1.In addition,we can observe that amplitudes of the vibration signals in the four cases are different.The signal amplitude is largest when the effect of the transmission path is represented by a modified Hamming function with a =0.1,while the signal amplitude is smallest when the effect of the transmission path is represented by a modified Hamming function with a =À1.The advantage of the modified Hamming function is capa-ble of representing the effect of different transmission paths while the Hanning function can represent only one specific transmission path.However,this study does not intend to propose a method to find the optimum value of a for a given planetary gearbox.The selection of a will be investigated in our future work.We have simply tried a few values of a which are 0.1,0and À1.0.Correspondingly the modified Hamming function has the values of 0.21,0.08and 0.03when the planet gear is in the farthest location from the transducer.The simulated resultant vibration signals for these a values are presented in Fig.10.Visually comparing the simulated vibration signals shown in Fig.10with the experimental vibration signal in the perfect condition of the gearbox shown in Fig.16,we believe that the simulated vibration signals match the experimental signals the best when aX.Liang et al./Engineering Failure Analysis 48(2015)185–200193。
车辆系统动力学结构模型
Z w2(t) Z 01(t)
Kh Z w1(t) P1(t)
22
第四章 车辆系统动力学模型
单自由度系统
x k c
23
单自由度系统振动方程
Fs
mx Fg Fs Fg mg Fc kx cx
mx cx kx mg
Fg
x ( Fg Fs ) / m
(2)
xn1 xn xn t (1/ 2 ) xn t 2 xn1t 2 xn1 xn (1 ) xn t xn1t
轴箱悬挂界面
空气弹簧节流孔 垂向减振器阻尼力 横向减振器阻尼力 抗蛇行减振器阻尼力 抗侧滚纽杆力矩 横向止挡力 牵引拉杆力 轴箱弹簧力 一系悬挂力 轴箱定位装置力 减振器阻尼力
法向力
轮轨界面 轮轨力 蠕滑力 蠕滑力矩
纵向、横向、垂向
纵向、横向、垂向 纵向、横向、垂向 36
四轴货车模型运动自由度
运 构件名称 纵向 车 体 摇枕 侧 架 轮 对 横向 垂向 侧滚 点头 摇头 动 形 式
(1000 9.81 104 19.58104 108 29.45108 ) / 1000 9.76
车辆系统垂向动力学模型
2lc
oc
ks mb2 Ib2 kp mw4 zw4 m w3 cp zb2 b2 zw 3 kp mw2 zw2 mw1 cs mb1 Ib1 cp
7
构架弹性化
8
车体弹性化
9
部件与弹簧装置系统模型化
车辆的轮对、转向架、车体结合的部位，实际 上有轴箱弹簧、空气弹簧、减振器等，但这些 部件的特性通常等效为弹簧与减振器。 空气弹簧除了有弹性作用外，还有具有减衰作 用，因此可视为弹簧与减振器的并列系统。 各主要联结部件可简单视为线性，在进行详细 解析中，要考虑松动与间隙的存在、弹簧的非 线性特性、减振器摩擦特性、可动部分的挡块 等非线性特性。
直齿行星齿轮传动动力学分析设计word版
XXXX学士学位论文直齿行星齿轮传动动力学分析作者:AAA指导教师：BB班级：CCC班2013年10月27日摘要：行星齿轮被广泛应用于船舶、飞机、汽车、重型机械等许多领域，它的振动和噪音一直以来都是普遍关注的问题。
为了减小其振动和噪音，动力学分析是必不可少的。
本文分析了行星齿轮动力学当中的一些关键性问题，提高了对于行星齿轮传动动态特性的理解。
本文在系杆随动参考坐标系下建立NGW型直齿行星齿轮传动的动力学模型。
把行星齿轮机构划分成几个相互关联的子系统，通过分析各构件间的相对位移关系利用牛顿第二定律推导出系统的运动微分方程。
应用仿真分析软件ADAMS对行星齿轮传动系统模型进行仿真模拟及运动学分析,并应用solidworks软件对行星齿轮传动系统进行三维实体参数化建模。
实现了用虚拟样机来代替实际样机进行验证设计,提高了设计质量和效率。
关键词：行星齿轮，动力学分析，ADAMS，仿真Abstract:Planetary gear noise and vibration are primary concerns in their applications in the transmissions of marine vessels, aircrafts, automobiles, and heavy machinery. Dynamic analysis is essential to the noise and vibration reduction.This work analytically investigates some critical issues and advances the understanding of planetary gear dynamics. This work Developed An analytical dynamic model of NGW spur planetary gear unit. In order to derive the displacement relationships between gears and carrier, divided the planetary gear mechanism into several sub systems. The governing differential equations were obtained by Newton's second law.ADAMS simulation analysis software for planetary gear drive system is applied to simulate and perform dynamic analysis. And solidworks software for planetary gear drive system to build three-dimensional solid parametric modeling is applied. With a virtual prototype instead of the actual prototype for the design verification, the design quality and efficiency is improved.Key word：planetary gear transmissions, dynamic analysis, ADAMS, simulation目录1 绪论 (1)1.1 本文研究的背景及意义 (1)1.2 行星齿轮传动的特点及其应用 (1)1.2.1 行星齿轮传动简介 (2)1.2.2 行星齿轮传动的特点 (2)1.2.3 行星齿轮传动的应用 (2)1.3 齿轮系统动力学概述 (4)1.3.1 动力学概述 (4)1.3.2 齿轮系统动力学研究的目标及内容 (4)1.4 行星齿轮传动动力学研究现状及展望 (5)1.4.1 行星齿轮传动动力学研究现状 (5)1.4.2 行星齿轮传动动力学研究展望 (6)1.5 论文研究的主要内容 (7)1.5.1 直齿行星齿轮传动动力学建模 (7)1.5.2 直齿行星齿轮传动固有特性分析 (8)1.5.3 直齿行星齿轮传动动响应分析 (8)1.6 初始数据 (9)2 直齿行星齿轮传动动力学建模 (10)2.1 数学模型 (10)2.2 动力学微分方程的推导 (11)2.2.1 变形协调条件的推导 (11)2.2.2 子构件运动微分方程的建立 (13)2.2.3 系统运动微分方程的建立 (17)3 相关设计参数的计算 (19)3.1 尺寸参数与质量参数的计算 (19)3.1.1 尺寸系数的计算 (19)3.1.2 质量参数的计算 (20)3.2 载荷计算 (20)3.3 刚度参数的计算 (24)3.3.1 轴承刚度系数的计算方法 (25)3.3.2 齿轮啮合综合刚度的计算方法 (27)3.3.3 刚度参数的计算结果 (31)3.4 轮齿啮合点的计算 (31)4 直齿行星齿轮传动固有特性分析 (32)4.1 ADAMS中动力学模型的建立 (32)4.2 利用ADAMS进行固有特性分析 (32)4.2.1 直齿行星齿轮传动系统的固有频率分析 (33)4.2.2 直齿行星齿轮传动系统的振型分析 (33)4.3 数学模型与仿真模型结果对比 (35)4.4 直齿行星齿轮传动固有特性分析的结论 (36)4.4.1 旋转模式 (36)4.4.2 平移模式 (36)4.4.3 行星模式 (37)5 直齿行星齿轮传动动响应分析 (38)5.1 直齿行星齿轮系统实体模型的建立 (38)5.2 ADAMS与solidworks之间的数据交换 (38)5.3 建立行星齿轮多体动力学模型 (38)5.3.1 ADAMS碰撞力的选择及定义 (39)5.3.2 碰撞参数的确定 (40)5.4 仿真计算 (41)5.4.1 输入输出转速仿真结果及分析 (41)5.4.2 接触力仿真结果及分析 (42)6 全文总结及展望 (47)6.1 全文总结 (47)6.2 展望 (47)致谢参考文献附录1 绪论1.1 本文研究的背景及意义随着科学技术的飞速发展，机械工业也发生着日新月异的变化，特别是近二三十年来机电一体化产品的广泛应用，在机械、航空、航天领域的机电系统正朝着高速、重载、大柔度、高精度和自动化的方向发展，使得人们对设备的动态性能提出了更高的要求。
应用滑动轴承的风电齿轮箱行星轮系动力学建模及解耦方法
[ ]
系耦合动力学模型;
YIN 等 １５ 、
YANG 等 １６ 采用
刚度 阻尼系数 描 述 行 星 轮 滑 动 轴 承 支 撑 的 不 对
称 性 和 相 互 作 用,建 立 了 齿 轮 系 统 动 力 学 模 型.
也有一 些 学 者 采 用 有 限 元 分 析 方 法,如 HAGEＧ
[
]
MANN 等 １７Ｇ１８ 基于 热 弹 流 体 动 力 学,研 究 了 结 构
星轮系动力学模型,对比了工况和轴承参数对模型计算精度与系统动态响应的影响,并通过试验加以验
证.研究结果表明,齿轮副动态啮合力波动会使滑动轴承刚度 阻尼系数和附加偏心修正力产生周期性
变化;在稳定和瞬态工况下,提出的模型可以很好地预测系统响应,尤其是行星轮振动响应;减小滑动轴
承宽径比与间隙、增大输入转矩可以改善系统均载性能.
i
ng;dynami
c
s
yge
ywo
收稿日期:
２０２３ １２ １４
基金项目:国家 重 点 研 发 计 划 (
２０２２YFB４２０１１００);重 庆 市 技 术
创新与应用发展专项重点 项 目(
CSTB２０２２TIADＧKPX００５１);国
家海上风力发电工程技术研究中心开放基金(HSFD２２００５)
０ 引言
保障多级传动系统实现增速或减速传动.基于滑
动轴承等效刚度 阻尼系数计算理论,学者们开展
行星轮系具有功率密度高、结构紧凑等优点,
被广泛应用 于 风 电 齿 轮 箱 中.在 行 星 轮 系 中,行
５９１
中国机械工程 第 ３５ 卷 第 ４ 期 ２０２４ 年 ４ 月
星轮常采用滚动 轴 承 进 行 支 撑,但 随 着 风 电 齿 轮
Workbench行星齿轮瞬态动力学分析(甲类精制)
然后我们就需要对模型添加约束和连接，主要包括有joints和frictionless contacts，添加完的效果如图。添加过程请看下面详述。
首先添加三个类似的运动副，都是需要Body-Ground形式。
第一个添加太阳轮的旋转副。revolute joint。Body-ground。
再添加三角架的旋转副。revolute joint。Body-ground。
再添加内齿圈的固定副。fixed joint。Body-ground。
接着添加一个Body-Body的旋转副，也就是三角板与行星轮之间的旋转连接。revolute。Body-Boby。
车辆系统动力学结构模型PPT课件
严格上说，构成车辆的各个要素都是质量分 布系统，模型化时常常将其近似为一个质量 集中的集中系统。
但在评价由车体的弹性振动而引起的乘坐舒 适度问题时，则须将车体作为一个分布质量 系统，来考虑其弯曲弹性振动问题。
三自由度系统振动方程
（7.3）
M c zc cs (zs zb ) ks (zs zb ) 0 M b zb cs (zs zb ) k s (zs zb ) c p (zb zw ) k p (zb zw ) 0
M w zw c p (zb zw ) k p (zb zw ) 0
23
（1） 速度与动量
刚体速度： v v0 刚体加速度： a a0 ( )
刚 体 的 角 速 度: x i y j z k
刚 体 的 速 度 矢 量: v vx i vy j vz k
x3
x2
(1.5x2
x1)t
14.72
104
(1.5
9.78
9.81)
104
19.58104
x3 (mg cx3 kx3) / m
(10009.81104 19.58104 108 29.45108) /1000 9.76
三自由度系统
Mc zc
Ks
Cs
Mb
Kp
Cp
zb
Mw
zw
19
车辆系统动力学结构模型
1
模型化总体原则
总体原则：根据不同研究目的，实行最适当的近 似化。 动力学研究目的多种多样，但无论从整体的简要 研究到局部的详细研究，都随着各自要求的精度 不同，模型化程度各不相同; 对能够做到何种程度的近似化判断时，首先必须 从力的传递、能量的传递和预计可能发生的现象 开始是极其重要的;
NW型直齿行星传动的动力学建模与固有特性分析
Ｎ Ｗ 型行星传动进行建模 的做法尚待完善． Ｇ 由于双 联行星轮结构 的引人 ， Ｗ 型行星传动的动力学特ｌ Ｎ 生 必然与 Ｎ Ｗ 型传动有所不 同． Ｇ 为明晰该类传动的动
通 讯作 者 ：张
俊 ，ｚａｇｊｎ ｊ． ｕ ｎ ｈｎ ｕ ＠ｔ ｅ ． ． ｕ ｄ ｃ
＿
天
津
大
学
学
Ａｂ ｔ ａ ｔ Ａｎ ａ ａ ｙ ｉａ ｒ ｎ ｌ ｔ ｎ ｌｒ ｔ ｔｏ ａ ・ ｏ ｐ ｉ ｇ ｄ ｎ ｍ ｉ ｏ ｅ ｓｄ ｖ ｌ ｐ ｄ ｔ ｖ ｌ ａ ｅ ｔ ｅ ｉ ｈ ｒ ｎ ｈ ｒ ｓｒ ｃ ： ｎ ｌ ｔｃ ｌ ａ ｓ ａ ｉ ａ －ｏ ａ ｉ ｎ ｌ ｕ ｌ ｙ ａ ｃｍ ｄ ｌ ｔ ｏ － ・ ｃ ｎ ｗａ ｅ ｅｏ ｅ ｅ ａｕ ｔ ｅ ｅ ｔｃ ａ － ｏ ｈ ｎ － ａ ｔ ｒｓｉ ｓｏ Ｗ ｐ ｒｐ ａ ｅ ａ ｙ ｇ ａ ｎ ｔ Ｂｙ ｄ ｒ ｎ ｈ ｉｐ ａ ｅ ｎ ｅ ａ ｉ ｎ ｈｉ ｓｂ ｔ ｅ ｎ ｇ ａ ｓ ａ ｄ ｃ ｒ ｉｒ ｔ ｅ ｃ ｅ ｉｔｃ ｆ Ｎ ｓ ｕ ｌ ｎ ｔ ｒ ｅ ｒｕ ｉ ． ｅ ｉ ｇ ｔ ｅ ｄ ｓ ｌ ｃ ｍｅ ｔｒ ｌ ｔ ｓ ｐ ｅｗ ｅ ｅ ｒ ｎ ａ ｒｅ ， ｈ ｖｉ ｏ ｇ ｖ ｒ ｉ ｇ ｄ ｆｅ ｅ ｔ ｌｅ ｕ ｔ ｎ ｒ ｂ ａ ｎ ｄ Ｔｈ ｏ ｕ ｉ ｎ ｔ ｓ ｏ ｉ ｔ ｄ ｅ ｇ ｎ ａ ｕ ｒ ｂｌｍ ｅ ｏ ｎ ｔ ａ ｅ ｕ ｎ ｏ ｅ ｎ ｎ ｉ ｒ ｎ ｉ ｑ ａ ｉ ｓｗｅ ｅ ｏ ｔ ｉ ｅ ． ｅ ｓ ｌ ｔ ｏ ａ ｓ ｃ ａ ｅ ｉ ｅ ｖ ｌ ｅ ｐ ｏ ｅ ｌ ｄ ｔ ａｕｒ ｌｆ ｑ ｅ — ａ ｏ ｏ
车辆动力学行星齿轮传动建模分解课件
对行星齿轮传动进行可靠性评估，包括寿命预测、失效模式分析等 ，以确定其可靠性和潜在的改进方向。
可靠性设计
在设计阶段就考虑可靠性要求，通过优化设计参数、改进制造工艺 等方式提高行星齿轮传动的可靠性。
可靠性分析方法
采用现代分析方法，如有限元分析、有限差分分析等，对行星齿轮传 动进行详细的分析和评估，以实现更精确的可靠性预测和优化。
通过车辆动力学分析，可以对车辆的 制动性能、行驶稳定性等进行评估， 为车辆安全性设计和改进提供依据。
动力系统匹配
通过对发动机、变速器和制动系统等 进行动力学分析，可以实现动力系统 的优化匹配，提高车辆的动力性和经 济性。
车辆动力学的发展趋势
01
多体动力学与有限元方法的结合
将多体动力学和有限元方法相结合，可以更精确地模拟和分析复杂车辆
行星轮的旋转运动
行星轮通过与内齿圈和太 阳轮的啮合，实现自身的 旋转运动。
行星架的旋转运动
行星架通过行星轮的旋转 运动，实现自身的旋转运 动。
太阳轮的旋转运动
太阳轮通过与行星轮的啮 合，实现自身的旋转运动 。
行星齿轮传动的效率与功率流
效率分析
行星齿轮传动的效率主要取决于齿轮的材料、加工精度、润滑条件和传动比等 因素。
行星齿轮传动在车辆控制系统设计中的应用
实现精确的扭矩控制
行星齿轮传动具有较好的扭矩分配能力，通过精确控制行星 齿轮的转速和转矩，可以实现精确的扭矩控制。
提高车辆动态响应速度
行星齿轮传动具有较快的响应速度，通过优化控制算法，可 以提高车辆的动态响应速度，提升驾驶体验。
05
行星齿轮传动的优化设计
行星齿轮传动的参数优化
02
行星齿轮传动的工作原理
浅谈汽车行星系机构的结构分析
浅谈汽车行星系机构的结构分析前言行星系结构传动具有传动比大、承载能力大、结构紧凑、传递运动平稳等诸多优点,被广泛应用在工程机械、钢铁行业、军事领域、汽车等各种工业领域。
工业用行星系主要是由太阳齿轮、行星齿轮、齿圈、齿圈支架、行星架等部件组成,内齿圈常与机体相连接,并与行星轮啮合以传递运动和动力。
本文以重型汽车轮边为NGW型五个直齿行星的传动为例,采用三维软件实体建模与ABAUQS软件建立完整的有限元模型。
针对行星传动中复杂结构及非承载部件,对有限元模型施加合适的约束以及适当的结构简化;根据重合度与齿间载荷分配系数,对主要承载轮齿施加分布载荷;利用ABAQUS有限元软件的接触分析功能,分析了整个行星系结构的受力情况以及变形情况。
1、有限元模型的建立和求解1.1行星系的系统参数太阳齿轮、五个行星齿轮和齿圈及齿圈支架均为渐开线直齿圆柱齿轮;齿圈与齿圈支架通过相互配合固定在一起,齿圈支架通过xxxx规格的花键固定在桥壳上,太阳轮上的运动和动力通过半轴输入,行星架(汽车驱动桥轮边的钟形毂)输出最后传递到轮胎上。
太阳轮、行星轮和齿圈的材料均采用20CrMnMoH的渗碳淬火钢。
为简化清晰表达行星结构。
1.2三维实体模型的建模轮边行星系动力传递主要是在齿轮结构系内完成,本文通过catia三维软件建立准确的三维模型;主要以表格内的零件以及行星销进行建模。
为了有限元分析能够准确反映出系统的受力状态,为了使用ABAQUS中的接触功能,齿轮在建模时需考虑一定的侧隙;侧隙的大小可以根据设计要求进行选定。
齿轮建模时需考虑齿轮的变位系数、齿形、修缘等细节,在齿轮方面的详细细节就不在赘述。
1.3有限元模型的建模catia生成的stp格式三维准确数模,导入ABAQUS有限元软件中生成有限元分析的模型,赋予模型材料属性,弹性模量E为2.06E5MPa/mm2,泊松比为0.3。
为减少计算成本,模型的网格划分采用abaqus中tetfree进行划分(单元类型为C3D10单元28216+62398+49550*5+xxxx)。
- 1、下载文档前请自行甄别文档内容的完整性，平台不提供额外的编辑、内容补充、找答案等附加服务。
- 2、"仅部分预览"的文档,不可在线预览部分如存在完整性等问题,可反馈申请退款(可完整预览的文档不适用该条件!)。
- 3、如文档侵犯您的权益，请联系客服反馈,我们会尽快为您处理(人工客服工作时间：9:00-18:30)。
M s : M r : M c 1: k : (1 k )
ns knr (1 k )nc 0
Jc0 =Jc +Nmp Rc 2
Jc—行星架转动惯量 mp—行星轮质量 N —行星轮个数
二、纯扭刚体动力学模型
例 4：
d s Js Mi M s dt d c J c0 Mc M f dt
S M F
P B
{D} {D}
Clutch B
Clutch D Output Carrier /Input Ring Inertia
R C R S C
Input Carrier /Output Ring Inertia 2 In Input Planetary Gear
1 Out
S
Input Sun Inertia
M s1 M i M r1 2.8M i M c1 3.8M i
二、纯扭刚体动力学模型
d s Js M s M se dt d r Jr M r M re dt dc Jc0 M c M ce dt
外力矩符号 根据外力矩 方向确定 内力矩符号 根据传递路 线确定
单行星排：
J ss Rs Fspj M se
j 1 N N
J rr Rr Frpj M rb
j 1
( J c J pj Rc2 mpj )c J pjpj Rs Fspj Rr Frpj M cf
j 1 j 1 j 1 j 1 j 1
M s : M r : M c 1: k : (1 k )
ns (1 k )nc 0
二、纯扭刚体动力学模型
例 5：
制动器C
制动器D
离合器B 离合器R 离合器A
输入
输出
4前1倒变速机构
二、纯扭刚体动力学模型
{B} {B}
P B
S M F
SlipB ModeB
SlipD ModeD
Output Sun Inertia
Output Planetary Gear
SlipC {R} {R}
B P S M F
SlipR ModeR
ModeC
S M F B P
OutSpeed {C} {C} {A} {B} {C} {D} {R} Clutch Pressures
5 5
v
Clutch R
ns nc zr n r nc zs
行星排特性参数
ns knr (1 k )nc 0
zs np ns nc zp
一、静力学模型
3. 行星传动转矩关系式
zr Rr z s Rs
k
1 Rc Rr Rs 2
(1 k ) Rs : Rr : Rc 1: k : 2
N
N
N
N
N
Jpjpj Jpjc Rpj Fspj Rpj Frpj 0
( j 1,2
N)
F为动态啮合力。根据需要选择线性的或者非线性的。
练习：行星传动动力学建模
Inventors:Raghavan
GM
2008，11，18
3自由度3排6前1倒
Fs : Fr : Fc 1:1: 2
M s : M r : M c 1: k : (1 k )
一、静力学模型
4. 静力学模型
M s : M r : M c 1: k : (1 k )
ns knr (1 k )nc 0
例1：汽车差速器
1 M1 M 2 M 0 2 n1 n2 2n0
第一章 第五节 行星传动系统建模
一、静力学模型（转速、转矩关系式）
二、纯扭刚体动力学模型
三、纯扭弹性体动力学模型
第二章 车辆传动系关键部件建模 一、静力学模型 1.行星轮系
r-齿圈
单星（内外啮合）行星排
c-行星架
一、静力学模型
2. 行星传动转速方程
r p c s
行星齿轮传动转速分析
相对行星架
zr k zs
Clutch C {A} {A}
P B S M F
SlipA ModeA
1 P
InSpeed
Clutch A
simulink仿真模型
Double -click to show Clutch日方程
d T T U V 单行星排：dt ( ) Qi (i 1, 2, i i i i ,3 N )
i K2=1.9 K1=2.8
o KR=1.9
ni k1n1 1 k 1 no 0 n1 1 kR no 0
转矩关系式 构件转矩平衡
iR ni / no 4.32
M s 2 2.8M i M r 2 5.32M i M c 2 -8.12M i
T Ts Tr Tc Tpj
N
Qi为非保守广义力
1 Ts J ss 2 2 1 Tr J r r 2 2
Tc
j 1
1 J c c 2 2 2 1 1 Tpj J pj pj c mpj Rc2 c 2 2 2
三、纯扭弹性动力学模型
一、静力学模型
例2：防滑差速器
防滑差速器：直接切断一路功率输出，使得功率从另 外的通路传递
1 M1 M 2 M 0 2
滑转一侧制动时转速关系为：
n1 0，n2 2n0
一、静力学模型
例3：行星变速机构转速和 转矩分析。1）分析倒档传 动比。2）分析倒档各元件 转矩。
C B2 B1 BR