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1、Brner, TR-G, Folie 1Copyright ZF Friedrichshafen AG 2001认识到了贫困户贫困的根本原因，才能开始对症下药，然后药到病除。近年来国家对扶贫工作高度重视，已经展开了“精准扶贫”项目Presentation介绍Theory of Gearing and Measurement齿轮传动及测量理论Dr. Jrg BrnerCorporate R&D Zentrale ForschungZF Friedrichshafen AG Gearing and MeasurementVerzahnung und MessungBrner, TR-G, Foli
2、e 2Copyright ZF Friedrichshafen AG 2001认识到了贫困户贫困的根本原因，才能开始对症下药，然后药到病除。近年来国家对扶贫工作高度重视，已经展开了“精准扶贫”项目da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 di
3、ameterdfv 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Diameters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dfv Gearing and MeasurementVerzahnung und MessungBrner, TR-G, Folie 3Copyright ZF Friedrichshafen AG 2001认识到了贫困户贫困的根本原因，才能开始对症下药，然后药到病除。近年来
4、国家对扶贫工作高度重视，已经展开了“精准扶贫”项目Thread modelStep 1: Wrap a thread around the base circle,Step 2: Unwind the thread from thebase circleStep 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 Gearing and MeasurementVerzahnung und MessungBrner, TR-G
5、, Folie 4Copyright ZF Friedrichshafen AG 2001认识到了贫困户贫困的根本原因，才能开始对症下药，然后药到病除。近年来国家对扶贫工作高度重视，已经展开了“精准扶贫”项目Standard geometry of gear teethFlanks = involutes.Tooth thickness sb.Tip circle and root 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 Gearing and Meas
6、urementVerzahnung und MessungBrner, TR-G, Folie 5Copyright ZF Friedrichshafen AG 2001认识到了贫困户贫困的根本原因，才能开始对症下药，然后药到病除。近年来国家对扶贫工作高度重视，已经展开了“精准扶贫”项目Roll distanceEach circle segment belongsto an involute segment Length of the circle segments= length of the 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
7、长度 = 滚动距离 Roll distance滚动距离 Gearing and MeasurementVerzahnung und MessungBrner, TR-G, Folie 6Copyright ZF Friedrichshafen AG 2001认识到了贫困户贫困的根本原因，才能开始对症下药，然后药到病除。近年来国家对扶贫工作高度重视，已经展开了“精准扶贫”项目One 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 pi
8、tch基节 Gearing and MeasurementVerzahnung und MessungBrner, TR-G, Folie 7Copyright ZF Friedrichshafen AG 2001认识到了贫困户贫困的根本原因，才能开始对症下药，然后药到病除。近年来国家对扶贫工作高度重视，已经展开了“精准扶贫”项目Main 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 G
9、earing and MeasurementVerzahnung und MessungBrner, TR-G, Folie 8Copyright ZF Friedrichshafen AG 2001认识到了贫困户贫困的根本原因，才能开始对症下药，然后药到病除。近年来国家对扶贫工作高度重视，已经展开了“精准扶贫”项目Working 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
10、awaw Gearing and MeasurementVerzahnung und MessungBrner, TR-G, Folie 9Copyright ZF Friedrichshafen AG 2001认识到了贫困户贫困的根本原因，才能开始对症下药，然后药到病除。近年来国家对扶贫工作高度重视，已经展开了“精准扶贫”项目Path of contact (POC)during mesh, the point of contactmoves along the path of contact (POC)POC is tangential to the base circlesLength
11、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 Gearing and MeasurementVerzahnung und MessungBrner, TR-G, Folie 10Copyright ZF Friedrichshafen AG 2001认识到了贫困户贫困的根本原因，才能开始对症下药，然后药到病除。近年来国家对扶贫工作高度重视，已经展开了“精准扶贫”项目Bas
12、e 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) Gearing and MeasurementVerzahnung und MessungBrner, TR-G, Folie 11Copyright ZF Friedrichshafen AG 2001认识到了贫困户贫困的根本原因，才能开始对症下药，然后药到病除。近年来国家对扶贫工作高度重视，已经展开了“精准扶贫”项目Pref
13、inished 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）hobb
14、ed contour滚齿后轮廓 Gearing and MeasurementVerzahnung und MessungBrner, TR-G, Folie 12Copyright ZF Friedrichshafen AG 2001认识到了贫困户贫困的根本原因，才能开始对症下药，然后药到病除。近年来国家对扶贫工作高度重视，已经展开了“精准扶贫”项目Rolling 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 cir
15、cle基圆 Gearing and MeasurementVerzahnung und MessungBrner, TR-G, Folie 13Copyright ZF Friedrichshafen AG 2001认识到了贫困户贫困的根本原因，才能开始对症下药，然后药到病除。近年来国家对扶贫工作高度重视，已经展开了“精准扶贫”项目The 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
16、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rarara Gearing and MeasurementVerzahnung und MessungBrner, TR-G, Folie 14Copyright ZF Friedrichshafen AG 2001认识到了贫困户贫困的根本原因，才能开始对症下药，然后药到病除。近年来国家对扶贫工作高度重视，已经展开了“精准扶贫”项目 One basic rack can generate several gearswith the same base cir
17、cle with the same involute, but different parts of the involutechanging addendum modification (profile shift) 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 modification齿顶修形 Gearing and MeasurementVerzahnung und MessungBrner, TR-G, Folie 15Copyright ZF Friedrichshafen AG 2001
18、认识到了贫困户贫困的根本原因，才能开始对症下药，然后药到病除。近年来国家对扶贫工作高度重视，已经展开了“精准扶贫”项目Table of addendum modifications变位系数表Copyright ZF Friedrichshafen AG 2001 Gearing and MeasurementVerzahnung und MessungBrner, TR-G, Folie 16Copyright ZF Friedrichshafen AG 2001认识到了贫困户贫困的根本原因，才能开始对症下药，然后药到病除。近年来国家对扶贫工作高度重视，已经展开了“精准扶贫”项目Variati
19、on of profile angle压力角的变化 Gearing and MeasurementVerzahnung und MessungBrner, TR-G, Folie 17Copyright ZF Friedrichshafen AG 2001认识到了贫困户贫困的根本原因，才能开始对症下药，然后药到病除。近年来国家对扶贫工作高度重视，已经展开了“精准扶贫”项目Due to the geometric generationThe probe moves linear in the transvers planeThe gear rotates Diagram of a true in
20、voluteis 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 involute profiles渐开线齿形的测量 Gearing and MeasurementVerzahnung und MessungBrner, TR-G, Folie 18Copyright ZF Friedrichshafen AG 2001认识到了贫困户贫困的根本原因，才能开始对症下药，然后药到病除。近年来国家对扶贫工作高度重视，已经展开了“精准扶贫”项目Profile angle deviation fHa 齿形角误差 fHa
21、Deviation in micrometer m 千分尺的误差 mRelated to the measurement range 与测量范围有关Profile form deviation ffa 齿形轮廓误差ffaDeviation in micrometer m 千分尺误差 mProfile deviations齿形误差fHafHa-+ffaffa-+ Gearing and MeasurementVerzahnung und MessungBrner, TR-G, Folie 19Copyright ZF Friedrichshafen AG 2001认识到了贫困户贫困的根本原因，才
22、能开始对症下药，然后药到病除。近年来国家对扶贫工作高度重视，已经展开了“精准扶贫”项目Evaluation range is usuallyequal to 80% of the profile lengthEvaluation 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profile measurement齿形测量100%80% Gearing and MeasurementVerzahnung und MessungBrner
23、, TR-G, Folie 20Copyright ZF Friedrichshafen AG 2001认识到了贫困户贫困的根本原因，才能开始对症下药，然后药到病除。近年来国家对扶贫工作高度重视，已经展开了“精准扶贫”项目Typical profile charts典型齿形图Examples of profile measurement齿形测量的实例 Gearing and MeasurementVerzahnung und MessungBrner, TR-G, Folie 21Copyright ZF Friedrichshafen AG 2001认识到了贫困户贫困的根本原因，才能开始对症
24、下药，然后药到病除。近年来国家对扶贫工作高度重视，已经展开了“精准扶贫”项目 Under load加载时deformation of the gear teeth 轮齿变形 entry impact 啮入冲击 modifications are used to avoid 通过修形来避免啮入冲击the entry impact Profile under load加载时的齿形主动轮从动轮主动轮从动轮 Gearing and MeasurementVerzahnung und MessungBrner, TR-G, Folie 22Copyright ZF Friedrichshafen AG
25、2001认识到了贫困户贫困的根本原因，才能开始对症下药，然后药到病除。近年来国家对扶贫工作高度重视，已经展开了“精准扶贫”项目Helical 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 Gearing and MeasurementVerzahnung und MessungBrner, TR-G, Folie 23Copyright ZF Friedrichs
26、hafen AG 2001认识到了贫困户贫困的根本原因，才能开始对症下药，然后药到病除。近年来国家对扶贫工作高度重视，已经展开了“精准扶贫”项目Transverse cutBase circle db depends on helix angle b.Different b generates different involutesin the transvers cuts.Picture shows transverse cuts withsame basic 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
27、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 Gearing and MeasurementVerzahnung und MessungBrner, TR-G, Folie 24Copyright ZF Friedrichshafen AG 2001认识到了贫困户贫困的根本原因，才能开始对症下药，然后药到病除。近年来国家对扶贫工作高度重视，已经展开了“精准扶贫”项目Two gears in mesh啮合的一对齿轮two base cylinders 两个基圆柱closed thread, 绕圆柱，有闭合的曲线wrapped ar
28、ound the cylindersBase cylinder基圆柱 Gearing and MeasurementVerzahnung und MessungBrner, TR-G, Folie 25Copyright ZF Friedrichshafen AG 2001认识到了贫困户贫困的根本原因，才能开始对症下药，然后药到病除。近年来国家对扶贫工作高度重视，已经展开了“精准扶贫”项目Helical 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 cyli
29、nder can be the 这个圆柱可以是节圆，也可以是基圆 pitch cylinder or base cylinderDeveloping into the plane展开到平面 Gearing and MeasurementVerzahnung und MessungBrner, TR-G, Folie 26Copyright ZF Friedrichshafen AG 2001认识到了贫困户贫困的根本原因，才能开始对症下药，然后药到病除。近年来国家对扶贫工作高度重视，已经展开了“精准扶贫”项目 Helical gear斜齿轮The contact lines are straig
30、ht 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 line啮合线 Gearing and MeasurementVerzahnung und MessungBrner, TR-G, Folie 27Copyright ZF Friedrichshafen AG 2001认识到了贫困户贫困的根本原因，才能开始对症下药，然后药到病除。近年来国家对扶贫工作高度重视，已经展开了“精准扶贫”项目 Measurement kinematics
31、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 Gearing and MeasurementVerzahnung und MessungBrner, TR-G, Folie 28Copyright ZF Friedrichshafen AG 2001认识到了贫困户贫困的根本原因，才能开始对症下药，然后药到病除。近年来国家对扶贫工作高度重视，已经展开了“精准扶贫”项目Profile co
32、ntact 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= 2bb Gearing and MeasurementVerzahnung und MessungBrner, TR-G, Folie 29Copyright ZF Friedrichshafen AG 2001认识到了贫困户贫困的根本原因，才能开始对症下药，然后药到病除。近年来国家对扶贫工作高度重视，已经展开了“精准扶贫”项目Overlap ratio eb重合比eb= 1pet
33、gabbsbpetgabbsbeb= 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 Gearing and MeasurementVerzahnung und MessungBrner, TR-G, Folie 30Copyright ZF Friedrichshafen AG 2001认识到了贫困户贫困的根本原因，才能开始对症下药，然后药到病除。近年来国家对扶贫工作高度重视，已经展开了“精准扶贫”项目Contact lines at
34、helical gear斜齿轮的啮合线Start of contact啮合起点End of contact啮合终点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 Gearing and MeasurementVerzahnung und MessungBrner, TR-G, Folie 31Copyright ZF Friedrichshafen AG 2001认识到了贫困户贫困的根本原因，才能开始对症下药，然后药到病除。近年来国家对扶贫工作高度重视，已经展开了“精准扶贫”项目Helical 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 Gearing and MeasurementVerzahnung und Messung
