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1、Gearing and MeasurementVerzahnung und Messung,Presentation介绍,Theory of Gearing and Measurement齿轮传动及测量理论Dr. Jrg BrnerCorporate R&DZentrale ForschungZF Friedrichshafen AG,Gearing and MeasurementVerzahnung und Messung,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. ef
2、fective 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,Diameters直径,dfv,Gearing and MeasurementVerzahnung und Messung,Thread modelStep 1: Wrap a thread around the base circ
3、le,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 Messung,Standard geometry of gear teethFlanks = involutes.Tooth thickness sb.Tip circle and root
4、 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 MeasurementVerzahnung und Messung,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= 线的长度 =
5、滚动距离,Roll distance滚动距离,Gearing and MeasurementVerzahnung und Messung,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 pitch基节,Gearing and MeasurementVerzahnung und Messung,Main advantageof involute gears:Independent from the changeof the
6、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,Gearing and MeasurementVerzahnung und Messung,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,Gearing and MeasurementVerzahnung und Messu
7、ng,Path of contact (POC)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,Gearing and MeasurementV
8、erzahnung und Messung,Base 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 Messung,Prefinished contour预加工轮廓,Prefinished gearsRoot geometry is manufacturedby hobbing or cuttingB
9、ase 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,Gearing and MeasurementVerzahnung und Messung,Rolling a basic rackgenerates a gearThats the principle of hobbing worm
10、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,Gearing and MeasurementVerzahnung und Messung,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,T
11、ool tip刀头,ra,ra,ra,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 (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）,Addendum mo
12、dification齿顶修形,Gearing and MeasurementVerzahnung und Messung,Table of addendum modifications变位系数表,Copyright ZF Friedrichshafen AG 2001,Gearing and MeasurementVerzahnung und Messung,Variation of profile angle压力角的变化,Gearing and MeasurementVerzahnung und Messung,Due to the geometric generationThe probe
13、 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 involute profiles渐开线齿形的测量,Gearing and MeasurementVerzahnung und Messung,Profile angle deviation fHa 齿形角误差 fHaDeviation in micrometer m 千分尺的误差 mRelated
14、 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 m,Profile deviations齿形误差,Gearing and MeasurementVerzahnung und Messung,Evaluation range is usuallyequal to 80% of the profile lengthEvaluation range is not equalto the required measurement range 计量范围
15、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,rofile measurement齿形测量,Gearing and MeasurementVerzahnung und Messung,Typical profile charts典型齿形图,Examples of profile measurement齿形测量的实例,Gearing and MeasurementVerzahnung und Messung,Under load加载时deformation of the gear teeth 轮齿变形 entry impact 啮入冲击 mo
16、difications 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,Gearing and MeasurementVerzahnung und Messung,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 Measurement
17、Verzahnung und Messung,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
18、螺旋角的影响,Gearing and MeasurementVerzahnung und Messung,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 around the cylinders,Base cylinder基圆柱,Gearing and MeasurementVerzahnung und Messung,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 transforme
19、d into a planeThe cylinder can be the 这个圆柱可以是节圆，也可以是基圆 pitch cylinder or base cylinder,Developing into the plane展开到平面,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
20、设计的重要部分,Contact line啮合线,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,Gearing and MeasurementVerzahnung und Messung,Profile contact ratio ea齿形接触比,ea=
21、 ga/pet,b -Face width齿宽ga - Path of contact啮合轨迹pet - base pitch基节,ea= 1,6,ea= 2,b,Gearing and MeasurementVerzahnung und Messung,Overlap ratio eb重合比,eb= 1,b,eb= 0,8,b -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
22、 Messung,Contact lines at 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 Messung,Helical gear with 斜齿轮，参数为：,ea=2 eb=2,total 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,