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摘要齿轮机构是现代机械中最重要的传动机构，应用十分广泛。它是依靠轮齿齿廓直接接触来传递运动和动力的，具有传动比恒定，传动效率高，使用寿命长，适用范围广及承载能力高等特点，但也存在对制造和安装精度要求较高以及成本较高等缺点。使用MATLAB编程软件可以简化齿轮设计中的计算过程，只需将参数输入就可以计算出正确的结果。此设计编写了三个程序，分别为绘制标准直齿圆柱齿轮渐开线曲面，直齿轮几何尺寸设计，以及两齿轮相对滑动系数相等时的变位系数的选择。在编写程序的过程中需用到一些特殊曲线公式，例如绘制渐开线曲面轮廓时就用到了此曲线在直角坐标系中的表达式。另外，程序在运行中可能需要在程序代码中设置初始值，以便计算出正确的结果，所选初始值的大小应尽量接近正确的结果，在计算中有可能会出现输入值相同而计算结果不同，这可能是软件本身的问题，还需要弥补。本次设计一对齿轮，根据给定的参数，使用Matlab计算出齿轮的其他参数及几何尺寸。关键词：齿轮机构，Matlab计算，初始值，几何尺寸ABTRACTGearsofmodernmachineryarethemostimportanttransmissionmechanism,awiderangeofapplications.Itistorelyondirectcontactwithgeartoothprofileandthepowertotransfertheexercise.MATLABprogrammingsoftwareusedtosimplifythecalculationofgeardesignprocess,simplyentertheparametersyoucancalculatethecorrectresults.Thepreparationofthisdesign,threeprocedures,respectively,renderingthestandardspurgearinvolutesurfaces,thedesignofspurgeargeometry,aswellasthecoefficientofrelativeslidingbetweengearchangeswhenthesameselectioncoefficient.Inthepreparationoftheproceduresrequiredtoprocesssomespecialcurveformula,suchasdrawinginvolutesurfacecontoursontheuseofthiscurveintheCartesiancoordinatesystemofexpression.Inaddition,theproceduresintheoperationcodemayneedtosettheinitialvalueforthepurposeofcalculatingthecorrectresult,thesizeoftheinitialvalueselectedshouldbeascloseaspossibletocorrecttheresultsofthecalculationintheinputvaluemaybecalculatedthesametheresultisdifferent,thismaybethesoftwareitself,butalsoneedtobefilled.Thedesignofapairofgears,accordingtothegivenparameters,theuseofMatlabtocalculatetheotherparametersandgeargeometry.Thisisthedesignofapairofgear.Inaccordancewiththegivenparameters,theuseofMatlabtocalculatetheotherparametersandgeargeometry.KEYWORDS:gears，Matlabprogramming，Initialvalue，geargeometrydimension目录目录·····················································································································3第一章前言··········································································································51.1MATLAB简介············································································51.2变量、函数与表达式·································································61.2.1MATLAB变量名的定义规则·················································61.2.2数学运算符号以及标点符号···············································71.2.3数学函数·······································································71.2.4数组与矩阵····································································71.2.5MATLAB有两种常用的工作方式···········································7第二章渐开线齿轮机构···························································································82.1渐开线齿轮的简介····································································82.1.1渐开线齿廓曲线······························································82.1.2渐开线的极坐标方程式·····················································92.1.3渐开线齿廓曲线的计算····················································102.2渐开线直齿轮变位系数的选择····················································102.2.1关于渐开线直齿轮变位系数··············································102.2.2最小变位系数的求法·······················································112.2.3齿轮干涉对变位系数的限制··············································112.2.4变位齿轮的啮合传动及几何尺寸········································112.3按两齿轮相对滑动系数相等时的变位系数选择·······························13第三章使用MATLAB编写简单程序············································································153.1Matlab编程绘制标准直齿圆柱齿轮渐开线曲面······························153.1.1制作MATLAB界面····························································153.2Matlab编程计算直齿轮的几何尺寸·············································183.2.1设计MATLAB界面的过程··················································183.3按等滑动系数原则选择变位系数·················································20结论···················································································································21致谢···················································································································22参考文献··········································································································23附录一··············································································································24附录二··············································································································27附录三··············································································································37第一章前言本次设计的目的是使用Matlab编一个程序，实现齿轮参数及几何尺寸的计算。齿轮机构用于传递原动机与工作机之间的运动和动力。它可以实现不同的匀速运动或按预定规律变化的运动，也可以改变运动的形式，如将转动转化为移动或相反。齿轮传动是机械中应用最为广泛的一种传动装置。这是因为它具备一系列显著的优点：（1）可以实现精确的匀速和变速运动，某些精密的减速装置，其运动误差可控制在1角分以内。（2）既可用于高速和重载的传动，又可用于精密和微小的机械与仪表中，目前已有圆周速度200m/s和传动功率500OOKW的齿轮装置，而在微机械中，近年已制造出直径为数十微米的齿轮。本次设计需要使用Matlab语言。1.1MATLAB简介MATLAB是“矩阵实验室”(MatrixLaboratory)的缩写，它是一种以矩阵运算为基础的交互式程序语言。它把科学计算、结果的可视化和编程都集中在一个使用非常方便的环境中。典型的MATLAB应用包括:数值和符号计算，数据分析、检测和可视化，建模、仿真和科学与工程绘图，应用程序接口。MATLAB工作空间，双击Windows桌面上的快捷图标或者从开始菜单的程序子菜单中单击MATLAB6.5，在屏幕上创建一个MATLAB窗口。如图1-1所示：图1-1Matlab主界面它主要包括以下几个窗口:CommandWindow(指令窗口):MAI，LA