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防爆型有轨运输牵引机车变速箱的设计
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OPTIMUM DESIGN OF MULTISPEED GEARBOXES AND MODELING OF TRANSMISSION COMPONENTS Prof. dr Boidar Rosi, dr Aleksandar Marinkovic, Mr Aleksandar VenclAbstract: By applying the optimum design in the field of gear transmission design it is possible to define the optimal relations between the parameters of the complete gear transmission, and of each transmission stage separately. This paper presents a one criterion procedure for gear transmission optimization and multicriterion optimization procedure for each transmission stage. Second part of the paper is focused on modeling of cylindrical gears that are common used machine elements and main parts of gear transmissions. These models are made using part and assembly design module in CATIA V5R11 software. On the end of paper some applications of models in finite elements analysis and optimization are also described 。Keywords: optimum design, multistage gearbox, computer added design, gears modeling, CATIA1. Introduction：Concept from optimization and decision theory can play an important role in all stages the design process. The optimizing design theory applying and methodology will be illustrated on a multispeed gearbox example. Gearboxes present a very important group of machine members, which are utilized in a great number of engineering fields and which must satisfy very rigorous technical requirements regarding reliability, efficiency, precise manufacturing of gears, bearing, etc. In addition, the latest achievements in the fields of technology and testing of the preciseness of manufacturing gears, bearings, etc., have been applied to the manufacturing process. The development of the computer technology，together with the corresponding computer programs (Auto CAD, Solid Works, CATIA, etc.), have very quickly found their place in the development of the expert system for gearbox design at a high technical level. Thus, it can freely be said nowadays that the gearbox design is no longer a “routine job”, which in most cases based upon the designers experience and knowledge. This paper demonstrates the application of a nonlinear multicriteria optimization method, with the purpose to build such a powerful method as a module into the gearbox design expert system. The introduction of some criteria considering the desirable performances, combined with high quality gearbox component modeling represents a significant step towards the reality of a gear train model. 2. Gearbox decomposition Gearboxes represent complex mechanical systems that can be decomposed into the corresponding number of gears with corresponding interaction. This means that the procedure for multistage gearbox optimization can also be carried out through the corresponding number of stages. During the first optimization stage, characterized by comparatively small number variables, the distribution of transmission ratio per gearbox stages is defined from the conditions of the minimal volume of the gear sets. During the second stage, the multicriteria optimization problem is solved by introducing a greater number of criteria which represent the essential gearbox performances. Thereby, it is necessary to satisfy the restrictions from the following aspects: load distribution, stresses, kinematics and correct conjugate gear action. The target function for multistage gearbox representing the volume of the gear sets can be written in the form the following relation 1:f(x) = 0.25d13jI(1+uI2)+jIId32/d12jI(1+uII2)+.) (1)where:uI, uII the transmission ration for particular transmission stages of multistage gearbox; d1, d3 diameters of kinematics circles of the driver gears; j=b/d1 ratio of width of the gear and diameter of the driver gear kinematics circle. For the target function stated, it is also necessary to define the functional restrictions from the standpoint of the surface strength for the first stage of gearing, which can be written in the following form: G（x）=Z(2KT1)/d13 (U1+1)/U1SH1/SH (2)and, from the standpoint of the volume strength:g(x)=KY(2T1)/(1d12m1) f1/SF(3)In the exactly analogous way, the functional restrictions from the standpoint of the surface and volume strength for other transmission stages of gearboxes are determined. Commencing from the technical requirement concerning the transmission ratio of a gearbox, it is also necessary to determine the functional restriction in the form of the equation: h1(x)=u-u1u2u3u(n)=0 (4)Basing upon the determined target function and the restrictions, it can be noticed that this problem belongs to the field of nonlinear optimization with the restrictions in the form of inequalities. For the solution of this problem, the computer program SUMT, based on the mixed penalty functions, has been applied. Fig. 1 shows a graphic representation of the results of the computer program SUMT. Basing upon the section of the corresponding functions, the domains of the optimum transmission ratios for the multistage gearboxes are defined in the following way: Figure.1: The relation between the volume of gear trainand overall gear ratio.To complete this analysis of decomposed gearbox, here are added a pair of restrictions in the form of inequalities, based on stress restrictions:- tooth gear stress for I stage gear - tooth-root gear stress for II stage gearBased on gear stress relations the value of gear module is determinated:- for contact stress - for contact stress Fig. 2 shows graphical interpretation of relations (7) and (8) in function of tooth number Z1. Upper of two lines on the Fig. 2 presents values of gear module determinated on contact stress and lower one for values determinated on tooth-root stress. The lines and admissible space on Fig. 2. indicate that contact stress relation for gear module (7) is prior and is to be used for gear dimensions dermination. Figure. 2: Diagram of module values up to tooth number3. Gears modelingGears are very important machine elements today and they are common used in different kinds of gearboxes and transmissions.Especially cylindrical gears are most applicable because of their very high efficiency and not complicated production. Modeling of cylindrical gears is very important process in machine design, as for making real model of gearbox, such for gear and transmission structure analysis and optimization. Last years this process can be done very fast and qualitative using new software tools such as CATIA. This software is very complex, but some main modules like Part design and Assembly design are in use for cylindrical gear modeling. The main problem in any gears modeling is to define a real gear tooth and after that to import it into gear body making. Cylindrical gears modeling consists of several phases, depends from gear body and kind of its production: The first phase of gear modeling is definition and making real involute gear teeth profile. The second phase, in case of cutting or pressed gear body, is to use Part design CATIA module to make gear body. The third phase, only in case of welding way made gear body, is to use Assembly design module to connect all its parts. All this phases consists of several operations and it will be described separately in followed chapters. Every chapter gives principal facts of general modeling, some special operations with advantages of using CATIA software in gears modeling and examples of different cylindrical gears that are modeled. In analysis of internal and external gear profiles there are four different lines in one pitch, which defines complete profile of gear. So there are the involute profile arc, profile foot circle arc, addendum circle arc and trochoid arc as a connection 4. In analytic-kinematics way for profile definition is to define a lot of restrictions and constrains for setting parameter equations each of this profile arcs and angles. After some matrix transformations matrix parameter equation for contact line of engaged gear tooth profiles can be de-terminated. Based on this analytic-kinematics model computer program is developed to define points of gear profiles 5. Gears modeling is very useful and important, as to make real gear transmission simulation, so for lot of other analysis. Different software tools are in use today for machine design and machine elements modeling, as ACAD, Mechanical Desktop, Pro Engineer and last years Solid Works, CATIA etc.But it can be seen that gear modeling (especially internal gears) with real profiles is more complicated compared with modeling of all other machine elements. Here will be presented the possibilities of cylindrical gears modeling using CATIA V5R11 software. Depends of production way and form of gear body it is possible to use Part design module or Assembly design module of CATIA software. For designing simplest cylindrical gear (flat) first step is to define correct sketch, where involute profile tooth coordinates (from first phase) should be imported. After that designer can apply Sketch based features (Create pad), to get cuted gear model as is shown at Fig. 3. Figure 3: Simplest model of cylindrical gearOne step forward is designing a press made gear body, that could be modeled by rotating scatch made figure, or like simulation of production process. On Fig. 4 it is given a gear model made also by using scatch and few Sketch-Based, Dress-Up and Transformation Features. Presented gears are common in use and they have an external involute profile. But in some cases, like planetary gear train designing, it is necessary to make a model of internal profiled gear. For this purpose designer has to calculate a new table with involute profile coordinates, by using external gear as a tool for making internal profile. After that properly sketch and other features as for other cylindrical gears modeling has to be used.Figure 4: Press made model of cylindrical gearAssembly design is another module in CATIA which is in use in aim to complete all parts and standard elements that are already modeled in Part or Shape design modules. Besides that it is possible to insert new bodies in existing assembly and also to do Boolean Operations between bodies if it is necessary. These Boolean operations between bodies are Assemble Bodies, Intersect Bodies, Add Bodies, Remove Bodies, Trim Bodies, Remove Lumps, etc. The best sample of using Assembly design is cylindrical gear made by welding number of separated elements. It means that this type of gear consists of many elements that are modeled in Part design. The main part is outer plate with involute profiles that are welded with central cylinder with two circle plates and six stiffeners at both sides (Fig. 5). Figure 5: Cylindrical gear made by weldingA gear modeling is very significant because of many applications that could be done: After completing assembly it is possible to do kinematics simulations, using another CATIA module DMU. Internal and external gears models can be used for solving a lot of problems in mechanical engineering, such as structural analysis, contact pressure between corresponding gears and also thermal and many other analyses 8. A typical example for this could be following structural analysis made using finite element method, where Fig. 6 shows gear model made of 77633 tetrahedrons which makes 18965 nodes. Figure 7: Gear model in form of finite element netStress values (Fig. 7) represent critical constructive points where gear is high loaded which could be also very useful in design and optimization process and procedure.Figure 7: Stress values of loaded gear model calculated in structural analysis4. ConclusionThe paper represents a brief illustration of a wider study undertaken with the aim of building the powerful multicriteria optimization methods into the expert system for gearbox design. It points out the necessity of decomposition multistage gearboxes as complex mechanical systems. In the way, the gearboxes optimization procedure is also carried out through the corresponding number of stages. In this first optimization stage, the domains of the practical application of gearboxes are defined, whereas, during the second stage, the multicriteria optimization problem is solved.To resume the point of this modeling part of paper, here could be said that it presents only a brief of cylindrical gears modeling possibilities in CATIA software. Besides presentation of modeling in Part and Assembly design modules, at the end of this paper it is to add that CATIA is powerful and today may by completest design software in engineering with wide range of applications.References：1 RosiB, 1993.: Parameter Investigation and Optimization of Planetary Gear Train Transmission, Ph.D Thesis, Mechanical Engineering Faculty, University of Belgrade 2 Arora J.S, 1989.: Introduction to optimum design, McGrawHill Book Company, New York 3 RosiB., MarinkoviA.: Planetary gear transmission as a tribosystem: Efficiency calculation and simulation, TG Jahres Symposium, Wien, November 2003. 4 Colbourne, J. R., 1987: The geometry of Involute gears, Springer-Verlag, New York 5 RosiB., Rinkovec B., MarinkoviA., PavloviN.: The analytical-kinematics method for definition of internal cylindric gears,Yugoslav Conference “IRMES 2002”, Faculty of Mechanical Engineering Srpsko Sarajevo, Jahorina BIH, September 2002, Proceedings, pp. 625-630. 6 RosiB.: Planetary gear trains, Monography, Faculty of Mechanical Engineering, University of Belgrade, edited in year 2003. 7 RosiB., MarinkoviA., Vencl , 2004.: Cylindrical Gears modeling using CATIA software,4th International Conference “RADMI 04“, Zlatibor, Serbia and Montenegro, August- September 2004., Proceedings on CD, pp. 73-77. 8 RosiB., MarinkoviA., Vencl , 2004.: Modeling and Structural Optimization of Cylindrical Gears construction profiles,Yugoslav Conference “IRMES 04”, Faculty of Mechanical Engineering Kragujevac, Kragujevac, September 2004, Proceedings, pp. 173-178. 英文文献中文翻译多速变速箱的优化设计传动部件的建模博日达尔洛赛克教授，亚历山大马林科维奇博士，亚历山大温瑟主席摘要: 通过应用优化设计中的齿轮传动装置设计领域，可以分别定义每个传输级的完整齿轮传动装置的参数之间的最佳关系，并且。本文提出了一个标准程序，齿轮传动优化和多标准优化程序为每个传输阶段。纸张的第二部分被集中在圆柱齿轮是常用的机械元件和齿轮传动装置的主要部分的建模。这些模型使用的部分，并在CATIA V5R11软件的装配设计模块进行。对底纸的有限元分析和优化模型的一些应用程序也有所说明。关键字：多级变速箱的优化设计，计算机辅助设计，齿轮，建模，CATIA1、简介优化与决策理论的概念是所有阶段的设计中的一个重要的过程。将用一个多速变速箱来举例说明优化设计的理论和应用方法。变速箱是重要组机器部件，它涉及了大量工程研究领域，同时它必须满足非常严格的技术要求以达到其可靠性，效率，精密制造的齿轮，轴承等，此外，在该领域的最新研究技术和严谨的测试制造已应用于齿轮，轴承等的制造过程。计算机技术的发展，与相应的计算机程序（Auto CAD，Solid Works，CATIA，等），很快被发并用于研发高级的减速器设计系统。因此，变速箱的设计不再被看做是一个“日常工作”，而是设计者经验和知识的结晶。本文演示的应用非线性多目标优化方法，以目的建立这样一个强大的方法，当一个模块在变速箱设计专家系统。简介一些标准考虑到理想的性能，结合高质量齿轮箱部件模型是对现实的一个重要步骤一个齿轮火车模型。1 变速箱分解变速箱表示复杂的机械系统可以分解成相应的与相应的交互齿轮数。这意味着对于多级变速箱的程序优化也可以通过进行相应数量的阶段。在第一个优化阶段，特点是比较小的变量数，传动比的分配每箱的阶段是在定义的条件该齿轮体积最小集。在第二阶段，多目标优化问题的求解通过引入更多的标准表示的基本的变速箱性能。从而，必须满足的限制以下几个方面：负荷分布，应力，运动学正确的共轭齿轮的行动。多级变速箱的目标函数表示该齿轮组的体积可以写在表格下面的关系 1 ：f(x) = 0.25d13jI(1+uI2)+jIId32/d12jI(1+uII2)+.) (1)注释：Ul，UII特定的传动比多级齿轮传动的阶段；D1，D3直径的司机，运动学界齿轮；J=B/D1的齿轮直径宽度比驱动齿轮的运动学圈。 对目标函数的声明，它也是必要的从的角度定义的功能限制第一阶段为齿轮的表面强度，这可以写在下面的表格： G（x）=Z(2KT1)/d13 (U1+1)/U1SH1/SH (2)而且，从强度角度量：g(x)=KY(2T1)/(1d12m1) f1/SF(3) 在完全类似的方式，功能限制从表面的立场其他的传输阶段的体积力确定了变速箱。从开始的技术要求对变速器传动比，它也要确定在功能上的限制该方程形式：h1(x)=u-u1u2u3u(n)=0 (4)根据确定的目标函数和的限制，可以注意到这个问题属于非线性优化领域的不等式的形式的限制。为解决方案这个问题，计算机程序SUMT法，基于混合罚函数，已经被应用。图1显示的结果的图形表示计算机程序SUMT。基于截面相应的功能，的域对于多级最佳传动比变速箱是通过以下方式定义：图。1：轮系总传动比和体积之间的关系完成此分析分解变速箱，这是增加了一个对的形式的限制不等式，基于应力的限制：-I级齿轮齿应力-II级齿轮齿应力基于齿轮应力关系价值的齿轮模块法：-对接触应力-齿罗斯应力图2显示的图形解释的关系（7）和（8）的齿数Z1功能。上两个在图2线路提出了齿轮模数值并对接触应力和较低的值对齿根应力的测定。线和在图2中可容空间。表明，接触应力齿轮模块的关系（7）优先，是用于齿轮的尺寸测定。齿数Z1图。2：模块值达齿数图3。齿轮建模在今天它是非常重要的机械零件，齿轮他们是普遍使用的不同类型的变速箱和传动装置。特别是圆柱形的齿轮是最适用的具有很高的效率和不复杂的生产。建模圆柱齿轮在机非常重要的过程设计，为使齿轮箱实际模型，如齿轮和传动结构的分析优化。去年的这个过程可以很快速定性使用新的软件工具，如CATIA。这个软件是很复杂的，但一些主要模块部分的设计和装配设计中采用圆柱齿轮建模。主要问题任何齿轮建模是定义一个真正的齿和之后，将其导入到齿轮体的制备。圆柱形的齿轮建模包括几个阶段，取决于齿轮体及其生产方式：齿轮建模过程的第一阶段是定义和真正的渐开线齿轮齿廓。第二阶段，在切割或挤压齿轮箱体，部分是利用CATIA模块进行设计齿轮机构。第三阶段，只有在焊接方法齿轮本体，是使用组件设计模块将所有部件。所有这些阶段包括多种经营它将分别描述在后续的章节。每一章的主要事实的一般建模，具有使用一些特殊的操作CATIA软件在齿轮建模与实例不同的圆柱齿轮，建模。内齿轮齿廓曲线有一节四个不同的线和外部环境分析，明确了齿轮的完整轮廓。所以有渐开线齿廓圆弧，圆弧形脚，齿顶圆弧摆线弧作为连接 4 。在分析运动学方法对轮廓定义是定义一个很大的限制设置和约束方程的参数轮廓圆弧角。经过矩阵变换接触线啮合矩
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