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1、Brner, TR-G, Folie 1Copyright ZF Friedrichshafen AG 2001 Gearing and MeasurementVerzahnung und MessungPresentation介绍Theory of Gearing and Measurement齿轮传动及测量理论Dr. Jrg BrnerCorporate R&D Zentrale ForschungZF Friedrichshafen AGBrner, TR-G, Folie 2Copyright ZF Friedrichshafen AG 2001 Gearing and Measure
2、mentVerzahnung und Messungda齿顶圆直径tip diameterdNa, dFa , dab有效齿顶圆直径effective tip diameterdFa,min最小有效齿顶圆直径min. effective tip diameterdNf,max最大有效齿顶圆直径max. SAP diameterdNfSAP直径SAP diameterdFf 齿根形状直径 root form diameter df 根圆直径root diameterdfv 砂轮齿顶位置 （假想齿根圆直径）SAP: start of active profile SAP:有效齿形的起点Diamet
3、ers直径da dNa, dFa prefinished contour预加工轮廓dFa,min dNf df dFf dNf,max finished contour精加工轮廓dfvBrner, TR-G, Folie 3Copyright ZF Friedrichshafen AG 2001 Gearing and MeasurementVerzahnung und MessungThread modelStep 1: Wrap a thread around the base circle,Step 2: Unwind the thread from thebase circleStep
4、 3: Fixed to the thread, a pen paintsthe involute.Fadenmodel第一步: 沿基圆绕线 第二步: 将线展开拉直第三步: 将笔固定于线，可画出渐开线Developing展成Brner, TR-G, Folie 4Copyright ZF Friedrichshafen AG 2001 Gearing and MeasurementVerzahnung und MessungStandard geometry of gear teethFlanks = involutes.Tooth thickness sb.Tip circle and ro
5、ot circle limit the standard tooth.轮齿的标准几何外形齿侧面 = 渐开线齿厚 sb.齿顶圆和齿根圆限定了标准齿的形状.Standard tooth标准齿Brner, TR-G, Folie 5Copyright ZF Friedrichshafen AG 2001 Gearing and MeasurementVerzahnung und MessungRoll distanceEach circle segment belongsto an involute segment Length of the circle segments= length of t
6、he thread= roll distance 滚动距离每段圆弧都属于一个渐开线段 圆弧长度= 线的长度 = 滚动距离 Roll distance滚动距离Brner, TR-G, Folie 6Copyright ZF Friedrichshafen AG 2001 Gearing and MeasurementVerzahnung und MessungOne base circle generatesmany inolutes.Base pitch = distancebetween the involutes.一个基圆展成许多渐开线基节 = 渐开线间的距离Base pitch基节Brn
7、er, TR-G, Folie 7Copyright ZF Friedrichshafen AG 2001 Gearing and MeasurementVerzahnung und MessungMain advantageof involute gears:Independent from the changeof the center distance渐开线齿轮的主要优点:与中心局的改变无关Change of center distance中心距的改变Brner, TR-G, Folie 8Copyright ZF Friedrichshafen AG 2001 Gearing and
8、MeasurementVerzahnung und MessungWorking pressure angle aw工作压力角aw only defined for a gear pair 只对一对齿轮定义aw depends on the center distance aw 取决于中心距Working pressure angle 工作压力角awawBrner, TR-G, Folie 9Copyright ZF Friedrichshafen AG 2001 Gearing and MeasurementVerzahnung und MessungPath of contact (POC
9、)during mesh, the point of contactmoves along the path of contact (POC)POC is tangential to the base circlesLength of action = Distance on thePOC between the tip circles啮合轨迹啮合过程中，接触点沿啮合轨迹移动啮合轨迹与基圆相切啮合长度 = 齿顶圆之间啮合轨迹线的距离Path of contact (POC)啮合轨迹POC啮合轨迹Brner, TR-G, Folie 10Copyright ZF Friedrichshafen
10、AG 2001 Gearing and MeasurementVerzahnung und MessungBase tangent length公法线长度Base tangent length Wk 公法线长度Wk dependent on the number of 取决于测量的齿数K measuring teeth k (picture: k = 5) (图中 k = 5)Brner, TR-G, Folie 11Copyright ZF Friedrichshafen AG 2001 Gearing and MeasurementVerzahnung und MessungPrefini
11、shed contour预加工轮廓Prefinished gearsRoot geometry is manufacturedby hobbing or cuttingBase tangent length of prefinishedgears is different to finished gearsAttention:Change of hob or cuttercan make problems预加工的齿轮滚齿或铣齿加工得到齿根轮廓预加工后的基圆切线长度与最终的 基圆切线长度是不一样的注意:更换滚刀或铣刀可能出现问题finished contour最终轮廓（精加工后）hobbed c
12、ontour滚齿后轮廓Brner, TR-G, Folie 12Copyright ZF Friedrichshafen AG 2001 Gearing and MeasurementVerzahnung und MessungRolling a basic rackgenerates a gearThats the principle of hobbing worm grinding 滚动齿条可以生成齿轮这就是滚齿和蜗杆磨的原理Basic rack齿条base circle基圆Brner, TR-G, Folie 13Copyright ZF Friedrichshafen AG 2001
13、Gearing and MeasurementVerzahnung und MessungThe root fillet is a cycloid,generated by the tool tipTool of prefinish process:hob or cutterUndercut is a special gear design齿根修形是由刀头加工得到的圆滚线粗加工的刀具：滚刀或铣刀根切是一种特殊的齿轮设计Root fillet齿根修形Cycloid圆滚线Tool tip刀头rararaBrner, TR-G, Folie 14Copyright ZF Friedrichshafe
14、n AG 2001 Gearing and MeasurementVerzahnung und Messung One basic rack can generate several gearswith the same base circle with the same involute, but different parts of the involutechanging addendum modification (pro) 一个齿条可以生成多个齿轮有同样的基圆 有相同的渐开线，但属于渐开线的不同部分更换变位系数（齿形改变）更换变位系数（齿形改变）Addendum modificati
15、on齿顶修形Brner, TR-G, Folie 15Copyright ZF Friedrichshafen AG 2001 Gearing and MeasurementVerzahnung und MessungTable of addendum modifications变位系数表Copyright ZF Friedrichshafen AG 2001Brner, TR-G, Folie 16Copyright ZF Friedrichshafen AG 2001 Gearing and MeasurementVerzahnung und MessungVariation of pro
16、压力角的变化Brner, TR-G, Folie 17Copyright ZF Friedrichshafen AG 2001 Gearing and MeasurementVerzahnung und MessungDue to the geometric generationThe probe moves linear in the transvers planeThe gear rotates Diagram of a true involuteis a vertical line根据几何结构探头在横截面线性移动齿轮转动 一条无误差的渐开线的图是一条垂线Measurement of in
17、volute profiles渐开线齿形的测量Brner, TR-G, Folie 18Copyright ZF Friedrichshafen AG 2001 Gearing and MeasurementVerzahnung und MessungPro deviation fHa 齿形角误差 fHaDeviation in micrometer m 千分尺的误差 mRelated to the measurement range 与测量范围有关Pro deviation ffa 齿形轮廓误差ffaDeviation in micrometer m 千分尺误差 mPro齿形误差fHafHa
18、-+ffaffa-+Brner, TR-G, Folie 19Copyright ZF Friedrichshafen AG 2001 Gearing and MeasurementVerzahnung und MessungEvaluation range is usuallyequal to 80% of the proEvaluation range is not equalto the required measurement range 计量范围通常在齿形长度的80%以内计量范围不等同于要求的测量范围Evaluation range计量范围pro齿形测量100%80%Brner, T
19、R-G, Folie 20Copyright ZF Friedrichshafen AG 2001 Gearing and MeasurementVerzahnung und MessungTypical pro典型齿形图Examples of pro齿形测量的实例Brner, TR-G, Folie 21Copyright ZF Friedrichshafen AG 2001 Gearing and MeasurementVerzahnung und Messung Under load加载时deformation of the gear teeth 轮齿变形 entry impact 啮入
20、冲击 modifications are used to avoid 通过修形来避免啮入冲击the entry impact Pro load加载时的齿形主动轮从动轮主动轮从动轮Brner, TR-G, Folie 22Copyright ZF Friedrichshafen AG 2001 Gearing and MeasurementVerzahnung und MessungHelical gearsScrewed transverse cut.involute in each transverse cut.same K sheet as spur gears. 斜齿轮螺旋横切.各个横截
21、面中的渐开线.同直齿轮一样的跨测齿数表（K表）Helical gears斜齿轮Brner, TR-G, Folie 23Copyright ZF Friedrichshafen AG 2001 Gearing and MeasurementVerzahnung und MessungTransverse cutBase circle db depends on helix angle b.Different b generates different involutesin the transvers cuts.Picture shows transverse cuts withsame ba
22、sic rack but different helix angles 横截面基圆 db 取决于螺旋角 b不同的 b 在横截面上生成不同的渐开线如图所示，横截面上有相同的齿条，但是螺旋角不同Influence of helix angle螺旋角的影响Brner, TR-G, Folie 24Copyright ZF Friedrichshafen AG 2001 Gearing and MeasurementVerzahnung und MessungTwo gears in mesh啮合的一对齿轮two base cylinders 两个基圆柱closed thread, 绕圆柱，有闭合的曲
23、线wrapped around the cylindersBase cylinder基圆柱Brner, TR-G, Folie 25Copyright ZF Friedrichshafen AG 2001 Gearing and MeasurementVerzahnung und MessungHelical gears斜齿轮Properties of the cylinder surface 圆柱面的特征可以展开到平面上can be transformed into a planeThe cylinder can be the 这个圆柱可以是节圆，也可以是基圆 pitch cylinder
24、or base cylinderDeveloping into the plane展开到平面Brner, TR-G, Folie 26Copyright ZF Friedrichshafen AG 2001 Gearing and MeasurementVerzahnung und Messung Helical gear斜齿轮The contact lines are straight lines. 啮合线是直线Advantage: smooth entrance 优点：啮入平稳Contact ratio is part of gear design 啮合比是齿轮设计的重要部分Contact
25、 line啮合线Brner, TR-G, Folie 27Copyright ZF Friedrichshafen AG 2001 Gearing and MeasurementVerzahnung und Messung Measurement kinematics测量运动学probe moves linear 探头线性运动The gear rotates 齿轮旋转 Diagram of an ideal helix理想的螺旋线图是一条直线 is a line Measurement of the lead齿向的测量Brner, TR-G, Folie 28Copyright ZF Frie
26、drichshafen AG 2001 Gearing and MeasurementVerzahnung und MessungPro ratio ea齿形接触比ea= ga/petb -Face width齿宽ga - Path of contact啮合轨迹pet - base pitch基节 petgapetgaea= 1,6ea= 2bbBrner, TR-G, Folie 29Copyright ZF Friedrichshafen AG 2001 Gearing and MeasurementVerzahnung und MessungOverlap ratio eb重合比eb=
27、1petgabbsbpetgabbsbeb= 0,8b - Face width齿宽b - helix angle螺旋角bb - base helix angle基圆螺旋角mn -Normal module法向模数pet - base pitch基节Brner, TR-G, Folie 30Copyright ZF Friedrichshafen AG 2001 Gearing and MeasurementVerzahnung und MessungContact lines at helical gear斜齿轮的啮合线Start of contact啮合起点End of contact啮合
28、终点Gear rotation (driving gear)齿轮转动（主动轮）Contact line啮合线Field of action作用面Contact starts at the root on the acute edge of driverand at the tip on the obtuse edge of the driven gear 啮合始于主动轮的齿根尖端和从动轮的齿顶钝端Brner, TR-G, Folie 31Copyright ZF Friedrichshafen AG 2001 Gearing and MeasurementVerzahnung und MessungHelical gear with 斜齿轮，参数为：ea=2 eb=2gapetbbtotal contact ratio eg is equal to the average number of teeth in contact总重合度 eg 等于啮合齿数的平均数
