微型面包车差速器设计【含CAD图纸+文档】

喜欢这个资料需要的话就充值下载吧。资源目录里展示的全都有预览可以查看的噢，下载就有,请放心下载，原稿可自行编辑修改=【QQ：11970985 可咨询交流】=喜欢就充值下载吧。资源目录里展示的全都有，下载后全都有,请放心下载，原稿可自行编辑修改=【QQ：197216396 可咨询交流】= 英文：Dynamic tooth loads of planetary gear sets having toothprofile wearC. Yuksel a, A. Kahraman b,*a The University of Toledo, Toledo, OH 43606, USAb Department of Mechanical Engineering, The Ohio State University, Room 255, 650 AckermanRoad,Columbus, OH 43202, USAReceived 25 June 2003; received in revised form 12 January 2004; accepted 10 February 2004 AbstractA computational model of a planetary gear set is employed to study the influence of surface wear on thedynamic behavior of a typical planetary gear set. The overall computational scheme combines a wear modelthat defines geometric description of contacting gear tooth surfaces having wear and a deformable-bodydynamic model of a planetary gear set. The wear model employ s a quasi-static gear contact model tocompute contact pressures and Archa rds wear model to determine the wear depth distributions. The wornsurfaces are input into the dynamic model to quantify the impact of wear on gear tooth and mesh dynamicforces. The results on a planetary gear set having a fixed planet carrier indicates that the dynamic behavioris nonlinear due to tooth separations in its resonance regions. The results for worn gear surfaces indicatethat surface wear has a signicant inuence in off-resonance speed ranges while its influence diminishes nearresonance peaks primarily due to tooth separations. 2004 Elsevier Ltd. All rights reserved. Keywords: Planetary gear sets; Gear dynamics; Gear wear 1. Introduction Planetary gear sets, also known as Epicyclic gear drives, are commonly used in a large number ofautomotive, aerospace and industrial applications. They posses numerous advantages over parallel-axis gear trains including compactness of design, availability of multiple speed reduction ratios, and less demanding bearing requirements. Most common examples of planetary gear sets can be foundin automatic transmissions, gas turbines, jet engines, and helicopter drive trains. A typical simple planetary gear set consists of a sun gear, a ring gear and a number of identical planet gears meshing both with the sun and ring gears. A common carrier holds the planets in place.Dynamic analysis of planetary gears is essential for eliminating noise and vibration problems of the products they are used in. The dynamic forces at the sun-planet and ring-planet meshes are the main sources of such problems. Although planetary gear sets have generally more favorable noise and vibration characteristics compared to parallel-axis gear systems, planetary gear set noise still remains to be a major problem. The dynamic gear mesh loads that are much larger than the static loads are transmitted to the supporting structures, in most cases, increasing gear noise. Larger dynamic loads also shorten the fatigue life of the components of the planetary gear set including gears and bearings. Surface wear is considered one of the major failure modes in gear systems. In case of planetary gear sets, experimental data has shown that especially the sun gear meshes might experience significant surface wear when run under typical operating conditions. While wear is a function of a large number of parameters, sliding distance and contact pressure were shown to be most significant parameters influencing gear wear. Wear of tooth profiles results in a unique surface geometry that alters the gear mesh excitations in the form of kinematic motion errors, enhancing the dynamic effects. Modeling of planetary gear set dynamics received significant attention for the last 30 years. A number of studies proposed lumped-parameter models to predict free and forced vibration characteristics of planetary gear sets. These models assumed rigid gear wheels, connected to each other by springs representing the flexibility of the meshing teeth. In these studies, nonlinear effects due to gear backlash and time-varying parameters due to gear mesh stiffness fluctuations were neglected. The corresponding Eigen value solution of the linear equations of motion resulted in natural modes. Modal summation technique was typically used to find the forced response due to external gear mesh displacement excitations defined to represent motion transmission errors. These lumped-parameter models vary in degrees of freedom included, from purely torsional models to two or three-dimensional transverse-torsional models. While these models served well in describing the dynamic behavior of planetary gear sets qualitatively, they lacked certain critical features. First, the gear mesh models were quite simplistic with a critical assumption that complex gear mesh contact interaction can be represented by a simple model formed by a linear spring and a damper. These models demand that the values of the gear mesh stiffness and damping, as well as the kinematic motion transmission error excitation, mustbe known in advance. It is also assumed that these parameter values determined quasi-statically remain unchanged under dynamic conditions. In addition, gear rim deflections and Hertzian contact deformations are also neglected. Another group of recent models used more sophisticated finite element-based gear contact mechanics models. These computational models address all of the shortcomings of the lumped-parameter models since the gear mesh conditions are modeled as individual nonlinear contact problems. The need for externally defined gear mesh parameters is eliminated with these models. In addition, rim deflection and spline support conditionsare modeled accurately . These models are also capable of including the influence of the tooth profile variations in the form of intentional profile modifications, manufacturing errors or wear on the dynamic behavior of the system. The study of wear of gear contact is becoming one of the emerging areas in gear technology. A number of recent gear wear modeling effortsform a solid foundation for more accurate, larger system analyses. All of these models use Archards wear model in conjunction with a gear contact model and relative sliding calculations. These studies focused on prediction of wear of either spur or helical gear pairs in aparallel-axis configuration. The tooth contact pressures were computed in these models using either simplified Hertzian contact or boundary element formulations under quasi-static conditions. Sliding distance calculations were carried out kinematically by using the involute geometry and Archards wear model was used with an empirical wear coefficient to compute the surface wear depth distribution. A number of studies investigated the influence of wear on gear dynamics response . Among them, Kuang and Lin simulated the tooth profile wear process by the model proposed by Ref. and predicted the variations of the dynamic loads and the corresponding frequency spectra as a function of wear for a single spur gear pair. Wojnarowski and Onishchenko performed analytical and experimental investigations of the influence of the tooth deformation and wear on spur gear dynamics. They stated that the change in the profiles of the teeth due to wear must be taken into account when dealing with the durability of the gear transmissions as well. These previous models considered surface wear effects for only a single spur gear pair, avoiding multi-mesh gear systems such as the planetary gear sets. They focused on only external gears and used lumped-parameter dynamic models excluding nonlinear and time-varying effects. 1.1 Objectives and scope As none of the previous studies on planetary gear set dynamics took into account the effect of wear, this study is intended to describe to the influence of gear tooth surface wear on dynamic behavior of planetary gears. A deformable-body dynamic model similar to the one proposed earlier will be used to investigate the influence of tooth surface wear on the dynamic behavior of planetary gear sets. The main objective here is to quantify the influence of surface wear on dynamic behavior of planetary gear sets. A planetary gear set formed by spur gears will be considered. A wear prediction model will be proposed to predict the gear surface wear distribution under quasi-static conditions. Different amounts of wear depths will then be introduced in the dynamic model to quantify the differences in dynamic behavior from the baseline behavior representing a gear set having no wear. Several complex dynamic phenomena exhibited by the planetary gear set including nonlinear behavior such as jump discontinuities and tooth separations will be demonstrated. The influence of surface wear on such behavior will also be described.2 Computational model This study relies on two previously developed models for investigation of the effect of surface wear on the dynamics of planetary systems. First, a wear model developed by Bajpai et al. will be used to determine the tooth surface wear profiles after different wear cycles. This model uses quasi-static finite elements-based gear contact model for prediction of the gear contact pressures and employs Archards wear model to predict wear of contacting tooth surfaces. Predicted tooth surface wear will then be applied to a deformable-body planetary gear dynamic model similar to the one proposed by Kahraman et al. to quantify the impact of gear surface wear on the dynamic behavior of planetary gear sets. 2.1 Wear prediction model For the local point on one of the contact gear surfaces, the induction wear equation can be expressed: Where k is the experimentally determined wear coefficient, h is the cumulative wear depth, P is the contact pressure, and s is the contact pressure between the sliding distance at the point of interest. Where all the parameters except the contact pressure and the sliding distance are calculated by k. These include many materials, heat treatment, surface roughness and lubrication related parameters. Although the wear model can be improved by explicitly describing additional parameters in the formula. It was proved that the work was not good enough for the purpose of the project.2.2 Deformable-body dynamics model Worn surface profiles predicted by the wear model are used in a dynamic model to quantify the changes in dynamic behavior. A commercial gear contact mechanics software package is used to develop the dynamic model of the planetary gear set. The model uses finite element (FE) method to compute relative deformations and stresses for points away from the contact zones and semi analytical techniques for the points within the contact zones, is employed . The semi analytical FE approach does not require a highly refined mesh at the contacting tooth surfaces, reducing the computational effort while conventional FE models require a refined mesh at gear tooth region, limiting the model to static analysis only. Therefore, the model used here allows a more accurate and comprehensive study of planetary gear dynamics than the conventional FE models . The gears have complex shapes that an be best modeled by the FE method. The tooth surfaces are modeled by a large number of coordinate nodes, representing the involute shape and surface modifications making it possible to incorporate worn profiles .The width of the contact zone in typical gear applications is two orders of magnitude smaller than the dimensions of the gear teeth themselves, requiring a very fine mesh inside the contact zone.The location of the contact zone changes as the gears enter and exit the mesh. When conventional .FE models are used, besides having an extremely refined mesh, re-meshing is necessary for every contact position. The model used here avoids this problem since deformations near or at the contact zone predicted by using a semi-analytical formulation are matched with the deformations away from the contact predicted by using FE method. The model attaches a reference frame to each individual component and the finite element computations are done for each individual component separately. The mesh stiffness and mesh contact forces, comprising the dynamic excitation for the system, are evaluated internally at each time step . Contact conditions are handled as essentially linear inequality constraints whose convergence is ensured by a revised Simplex solver. A contact analysis determines the contact stresses and deformations of the gears at each time step. The elastic deformations of the gears are much smaller and must be superposed on the rigid body motions. By choosing a gear coordinate frame that follows the rigid body motion, the FE displacement vector xfi for gear i can be represented by a linear system of differential equations. The equations for each gear are assembled into the entire planetary gear system to obtain the overall matrix equation of motion. For the solution of the above equation, the contact mechanics model employs a timediscretization scheme based on Newmark method as used successfully in previous studies . 3 Results and discussion An example spur-type planetary system representative of typical gear sets in automatic transmission systems is considered here. Design parameters of the example system are listed in Table 1 and dynamic model is shown in Fig. 2. The sun gear is the input, the internal gear is the output, and the carrier is held stationary. A constant torque of 25 Nm/mm face width (FW) is applied to the input member. The system has four equally spaced planets that are not allowed to float radially. In order to avoid added complexity of ring gear bending modes , the outside diameter of the internal gear is chosen as rigid throughout this study while radial planet bearing flexibilities are included. Dynamic analysis of the model shown in Fig. 2 took a significant computational time. The simulation must be carried out for a reasonably long period to surpass the transient region. For each analysis, first a speed ramp up was simulated for a complete input revolution to pass through the transients, followed by a more refined analysis at the desired speed to cover two complete input revolutions. The steady state response is extracted from the last stage of the analysis. Whenthe input speed is increased by a small increment, as it is the case in an actual speed sweep, the last point of the steady state motion from the previous speed increment was considered as the initial condition followed by a rapid ramp-up and a refined steady state simulation. Dynamic analyses were performed within an input speed range up to Xin 15; 000 rpm, with a speed increment between 50 and 250 rpm. In each analysis, individual tooth loads at the sun and ring gear meshes of the planet gears were considered the output parameters. The time increment is adjusted at each analysis such that there are nearly 120 data points per tooth mesh cycle that was found to be a sufficient resolution to capture high frequency dynamic effects on tooth loads. Total gear mesh force time histories were obtained by adding all tooth forces at a given mesh and the corresponding frequency spectrum was obtained by using a fast Fourier transform (FFT) routine.In predicting the wear depth, a wear coefficient value of k 1018 m2/N was used in this analysis. This value was determined experimentally by Bajpai et al. using a similar automatic transmission final drive planetary gear set formed by case carburized shaved external gears and shaped internal gears. Bajpai, et.al. also pointed out that the wear at thering-planet meshes is simply negligible compared to those measured at the sun-planet meshes. In the power flow configuration considered, a sun gear tooth that mates with four planets will experience four wear cycles per input revolution, while a ring tooth goes through only 4Zs=Zr 434=70 1:94 wear cycles for the example system. Therefore, given this kinematic condition and previous experimental observations , wear at the ring-planet mesh was neglected in this study all together for the sake of simplicity.4 Conclusions In this study, a computational model of a planetary gear set was employed to study thei nfluence of surface wear in the dynamic behavior of a typical automotive automatic transmission planetary gear set. The overall computational scheme combines a gear wear prediction model that gives geometric description of contacting tooth surfaces having wear and a deformable-body dynamic model of a planetary gear set. The wear model employs a quasi-static gear contact mechanics model to compute contact pressures and Archards wear model to determine the wear depth distributions. The worn surfaces were input into the dynamic model to quantify the impact of wear on gear tooth and mesh dynamic forces. It was shown that a planetary gear set is inherently nonlinear, and exhibits softening type nonlinear behavior near its resonance peaks, characterized by sudden jumps of dynamic gear mesh force amplitudes. A sun gear experiences the largest amount of wear, compared to other gears in the system as the maximum wear locations are in the dedendum of the sun gear. It is also observed that the tooth surface wear influences the fundamental harmonic of the gear mesh forces the most. While this influence is evident in both resonance and off-resonance regions of the forced response, the impact of wear is limited in the resonance regions dictated by higher harmonics. It is also concluded that wear has a negligible influence on the nonlinear behavior as nearly the same type of tooth separations were observed with or without surface wear. 翻译： 行星齿轮装置动态载荷的齿廓磨损C. Yuksel, A. Kahrama托莱多大学, 托莱多, OH 43606, 美国 机械工程系,俄亥俄州立大学, 255号, 650 艾克曼路, 哥伦布, OH 43202, 美国 2003年6月25号初稿2004年1月14号修订稿2004年2月10号发表 摘要 以一个行星齿轮装置的计算机模型为研究对象,研究表面磨损对典型的行星齿轮装置动态行为的影响。整体的计算机模型的定义包括齿面接触磨损的几何描述和可变动载荷系统的行星齿轮组。模型采用准静态过程的磨损齿轮接触模型接触压力的计算和Archard磨损模型来确定磨损深度分布。表面的磨损程度作为动态模型的输入量,用来定量研究了影响齿的磨损和啮合动态的力量。结果表明对于有一个固定行星架的行星齿轮组，动态行为的非线性是由于轮齿在共振区域的分散导致的。结果表明齿面的疲劳损坏在非共振速度区表面的缺陷起主要作用，在非共振区时轮齿的分散性起决定性作用。 关键词：行星齿轮；齿轮动力学；齿轮磨损 1 简介行星齿轮组，也被称为行星齿轮传动装置，通常大量的用在汽车，航空航天和工业领域。他们拥有了平行轴齿轮系众多优点，包括紧凑的设计，多种减速比可用性和不高的承载要求。行星齿轮组最常见的例子可以发现在自动变速器，燃气涡轮机，喷气发动机，直升机传动系统。一个典型的简单行星齿轮组由一个太阳轮齿圈和几个相同的行星齿轮都与太阳轮和环形齿轮啮合。一个共同的载体固定位置的行星。行星齿轮的动态分析，为消除他们在产品应用中的噪音和振动问题有很重要的作用。在太阳轮和行星轮的动力特性是这些问题的主要来源。虽然行星齿轮组相比平行轴齿轮系统一般都更有小的噪音和振动特性，但是行星齿轮组噪音仍然是一个主要问题。动态齿轮啮合载荷远大于静载荷传递到支撑结构，在大多数情况下增加齿轮噪声。较大的动载荷也能缩短包括齿轮和轴承在内的行星齿轮组件的疲劳寿命。 表面磨损是齿轮系统失效的主要形式之一。在行星齿轮组的情况下，实验数据显示，在典型的操作条件下运行尤其是太阳齿轮啮合表面磨损可能会遇到很大时。虽然磨损是一个大量的参数，滑动距离和接触压力的作用被证明是最重要的影响齿轮磨损参数。齿廓磨损的结果在一个独特的表面几何形状，改变了运动中的运动误差的形成齿轮啮合激励，增强的动态效果。 行星齿轮组动态建模收到近30年来极大关注。很多建议集总参数模型来预测行星齿轮组自由与强迫振动特性的研究。这些模型假定刚性齿轮，连接通过弹簧代表灵活的互相啮合齿。在这些研究中，由于齿轮间隙和时变参数，由于齿轮啮合刚度的波动非线性效应这些研究被忽视了。相应的本征线性方程组的运动造成的自然价值的解决方案模式。模型求和技术。通常用于发现因外部强迫响应位移定义为齿轮啮合传动误差激励代表议案。这些集总参数模型各不相同的自由度。包括从纯粹的扭转模型，二维或三维横扭模型。虽然这些模型曾在描述行星齿轮组的动态行为以及定性，他们缺乏某些关键功能。首先，齿轮啮合模型进行了相当关键的假设，复杂的齿轮啮合接触互动可以由一个线性弹簧和阻尼器组成一个简单的模型表示简单化。这些模型要求的齿轮啮合刚度和阻尼值，以及运动运动传递误差激励，必须在事先知道。另据估计，这些参数值确定准静态动态条件下保持不变。此外，齿轮边缘变形挠度和赫兹接触也被忽视。另一些最新的模型采用更先进的有限元素的齿轮接触力学模型。这些计算模式解决了自齿轮啮合条件的集总参数模型的缺点都作为单独的非线性接问题的蓝本。对于外部定义齿轮啮合参数需要消除这些模型。此外边缘变形和样条支撑条件是准确的参照。这些模型也是包括在故意修改，形成了专齿形变化的影响，制造错误或磨损在行星齿轮系统的动态行为的能力。 对齿轮接触磨损的研究正日益成为齿轮技术的新领域之一。最近的一些齿数磨损建模工的形式进行更加准确的，更大的系统中分析了坚实的基础。这些机型全部使用Archard的磨损模型在与齿轮接触的计算模型和相对滑动结合。这些研究集中于任直磨损预报或在一个平行轴的螺旋齿轮副配置。对齿面接触的压力均在使用上述两种模型计算，简化赫兹接触或边界元在准静态条件的公式。滑动距离的计算进行了运动学上使用了渐开线的几何形状和Archard的磨损模型进行了实证磨损系数来计算表面磨损深度分布使用。许多研究调查了磨损对齿轮动力学响应的影响。其中，光，林模拟了由Ref提出的齿形磨损过程。并预测的动态负载变化和频率变化范围的作为单个齿轮对磨损的依据。Wojnarowski和Onishchenko 做了轮齿变形对齿轮动态磨损的分析和实验研究。他们表明，当讨论齿轮传动系统的耐久性时，轮齿的配置条件对磨损的影响必须考虑进去。这些以前的模型只考虑了一对齿轮啮合时的表面磨损，没有谈及类似行星齿轮这种多个啮合面的情况。他们只关注于外啮合齿轮并且是在集中参数下的动态模型，而不考虑非线性和时变性的影响因素。 1.1 目的和内容 鉴于之前没有研究齿轮齿面磨损对于行星动态因素的影响，本研究的目的在于描述行星齿面磨损对于齿轮动态因素的影响。先前提出一个相似的可变形体动态模型将用于后续的研究中。这里主要的目的是量化这个指标。由正齿轮组成的行星齿轮组是研究对象。一个计算模型用来预测在准静态条件下齿面磨损的分布状态。磨损深度将作为动态模型的一个量化指标来比较不同动态行为与无磨损动态行为的差异。行星齿轮组的几个复杂的非线性动态特性包括齿轮不连续的跳动性和轮齿的分散性等,表面磨损对这些方面的影响也将进行讨论。 2 计算模型 这个研究基于先前开发的两个用来研究表面磨损对于动态特性和行星齿轮组的影响的模型。首