齿轮传动及测量理论一类教资

1、brner, tr-g, folie 1copyright zf friedrichshafen ag 2001presentation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苍松课资brner, tr-g, folie 2copyright zf friedrichshafen ag 2001da齿顶圆直径tip diameterdna, dfa , dab有效齿顶圆直径effective tip diam

2、eterdfa,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diameters直径da dna, dfa prefinished contour预加工轮廓dfa,min dnf df dff dnf,max finished contour

3、精加工轮廓dfv苍松课资brner, tr-g, folie 3copyright zf friedrichshafen ag 2001uthread 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.ufadenmodel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展成苍松课资brner, t

4、r-g, folie 4copyright zf friedrichshafen ag 2001ustandard geometry of gear teethflanks = involutes.tooth thickness sb.tip circle and root circle limit the standard tooth.u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标准齿苍松课资brner, tr-g, folie 5copyright zf friedrichshafen ag 2001uroll dista

5、nceeach circle segment belongsto an involute segment length of the circle segments= length of the thread= roll distance u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滚动距离苍松课资brner, tr-g, folie 6copyright zf friedrichshafen ag 2001uone base circle generatesmany inolutes.ubase pitch = distancebetw

6、een the involutes.u一个基圆展成许多渐开线u基节 = 渐开线间的距离base pitch基节苍松课资brner, tr-g, folie 7copyright zf friedrichshafen ag 2001umain advantageof involute gears:independent from the changeof the center distanceu渐开线齿轮的主要优点:与中心局的改变无关change of center distance中心距的改变苍松课资brner, tr-g, folie 8copyright zf friedrichshafe

7、n ag 2001uworking pressure angle awu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awaw苍松课资brner, tr-g, folie 9copyright zf friedrichshafen ag 2001upath of contact (poc)during mesh, the point of contactmoves along the path of conta

8、ct (poc)poc is tangential to the base circleslength of action = distance on thepoc between the tip circlesu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啮合轨迹苍松课资brner, tr-g, folie 10copyright zf friedrichshafen ag 2001base tangent length公法线长度ubase tangent length wk u公法

9、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)苍松课资brner, tr-g, folie 11copyright zf friedrichshafen ag 2001prefinished contour预加工轮廓uprefinished gearsroot geometry is manufacturedby hobbing or cuttingbase tangent length of prefinishedgears is different to fin

10、ished gearsattention: change of hob or cuttercan make problemsu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 contour滚齿后轮廓苍松课资brner, tr-g, folie 12copyright zf friedrichshafen ag 2001urolling a basic rackgenerates a gearuthats the principle of hobbing

11、worm grinding u滚动齿条可以生成齿轮u这就是滚齿和蜗杆磨的原理basic rack齿条base circle基圆苍松课资brner, tr-g, folie 13copyright zf friedrichshafen ag 2001uthe root fillet is a cycloid,generated by the tool tiputool of prefinish process:hob or cutteruundercut is a special gear designu齿根修形是由刀头加工得到的圆滚线u粗加工的刀具：滚刀或铣刀u根切是一种特殊的齿轮设计root

12、 fillet齿根修形cycloid圆滚线tool tip刀头rarara苍松课资brner, tr-g, folie 14copyright zf friedrichshafen ag 2001u 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)u 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

13、，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齿顶修形苍松课资brner, tr-g, folie 15copyright zf friedrichshafen ag 2001table of addendum modifications变位系数表copyright zf friedrichshafen ag 2001苍松课资brner, tr-g, folie 16copyright zf friedrichshafen ag 2001variation of profile angle压力角的变化苍松课资brner, tr

14、-g, folie 17copyright zf friedrichshafen ag 2001udue to the geometric generation the probe moves linear in the transvers plane the gear rotates udiagram of a true involuteis a vertical lineu根据几何结构探头在横截面线性移动齿轮转动 u一条无误差的渐开线的图是一条垂线measurement of involute profiles渐开线齿形的测量苍松课资brner, tr-g, folie 18copyrig

15、ht zf friedrichshafen ag 2001uprofile angle deviation fha u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uprofile form deviation ffa u齿形轮廓误差ffadeviation in micrometer m 千分尺误差 mprofile deviations齿形误差fhafha-+ffaffa-+苍松课资brner, tr-g, folie 19copyright zf friedrichsh

16、afen ag 2001uevaluation range is usuallyequal to 80% of the profile lengthuevaluation range is not equalto the required measurement range u计量范围通常在齿形长度的80%以内u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%苍松课资brner, tr-g, folie 20copyright zf friedrichshafen ag 2001utypical profile

17、chartsu典型齿形图examples of profile measurement齿形测量的实例苍松课资brner, tr-g, folie 21copyright zf friedrichshafen ag 2001u under loadu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苍松课资brner, tr-g, folie 2

18、2copyright zf friedrichshafen ag 2001uhelical gearsscrewed transverse cut.involute in each transverse cut.same k sheet as spur gears.u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斜齿轮苍松课资brner, tr-g, folie 23copyright zf friedrichshafen ag 2001utransverse cutbase circle db depends on helix angle b

19、.different b generates different involutesin the transvers cuts.picture shows transverse cuts withsame basic rack but different helix anglesu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ba22costannnbzmd苍松课资brner, tr-g, folie 24copyright zf friedrichshafen

20、ag 2001utwo gears in meshu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 cylindersbase cylinder基圆柱苍松课资brner, tr-g, folie 25copyright zf friedrichshafen ag 2001uhelical gearsu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 ca

21、n 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展开到平面苍松课资brner, tr-g, folie 26copyright zf friedrichshafen ag 2001u helical gearu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contac

22、t line啮合线苍松课资brner, tr-g, folie 27copyright zf friedrichshafen ag 2001u measurement kinematicsu测量运动学probe moves linear 探头线性运动the gear rotates 齿轮旋转u diagram of an ideal helixu理想的螺旋线图是一条直线 is a line measurement of the lead齿向的测量苍松课资brner, tr-g, folie 28copyright zf friedrichshafen ag 2001profile contact 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 2 x modulpetga2 x modulpetgaea 1,6ea 2bb苍松课资brner, tr-g, folie 29copyright zf friedrichsha