齒輪傳動及測量理論

1、Brner, TR-G, Folie 1Copyright ZF Friedrichshafen AG 2001 Gearing and MeasurementVerzahnung und MessungPresentation介紹Theory of Gearing and Measurement齒輪傳動及測量理論Dr. Jrg BrnerCorporate R&D Zentrale ForschungZF Friedrichshafen AGBrner, TR-G, Folie 2Copyright ZF Friedrichshafen AG 2001 Gearing and Mea

2、surementVerzahnung und Messungda齒頂圓直徑tip diameterdNa, dFa , dab有效齒頂圓直徑effective tip diameterdFa,min最小有效齒頂圓直徑min. effective tip diameterdNf,max最大有效齒頂圓直徑max. SAP diameterdNfSAP直徑SAP diameterdFf 齒根形狀直徑 root form diameter df 根圓直徑root diameterdfv 砂輪齒頂位置 （假想齒根圓直徑）SAP: start of active profile SAP:有效齒形的起點Di

3、ameters直徑da dNa, dFa prefinished contour預加工輪廓dFa,min dNf df dFf dNf,max finished contour精加工輪廓dfvBrner, TR-G, Folie 3Copyright ZF Friedrichshafen AG 2001 Gearing and MeasurementVerzahnung und MessunguThread modelStep 1: Wrap a thread around the base circle,Step 2: Unwind the thread from thebase circl

4、eStep 3: Fixed to the thread, a pen paintsthe involute.uFadenmodel第一步: 沿基圓繞線 第二步: 將線展開拉直第三步: 將筆固定于線，可畫出漸開線Developing展成Brner, TR-G, Folie 4Copyright ZF Friedrichshafen AG 2001 Gearing and MeasurementVerzahnung und MessunguStandard geometry of gear teethFlanks = involutes.Tooth thickness sb.Tip circle

5、 and root circle limit the standard tooth.u輪齒的標準幾何外形齒側(cè)面 = 漸開線齒厚 sb.齒頂圓和齒根圓限定了標準齒的形狀.Standard tooth標準齒Brner, TR-G, Folie 5Copyright ZF Friedrichshafen AG 2001 Gearing and MeasurementVerzahnung und MessunguRoll distanceEach circle segment belongsto an involute segment Length of the circle segments= le

6、ngth of the thread= roll distance u滾動距離每段圓弧都屬于一個漸開線段 圓弧長度= 線的長度 = 滾動距離 Roll distance滾動距離Brner, TR-G, Folie 6Copyright ZF Friedrichshafen AG 2001 Gearing and MeasurementVerzahnung und MessunguOne base circle generatesmany inolutes.uBase pitch = distancebetween the involutes.u一個基圓展成許多漸開線u基節(jié) = 漸開線間的距離B

7、ase pitch基節(jié)Brner, TR-G, Folie 7Copyright ZF Friedrichshafen AG 2001 Gearing and MeasurementVerzahnung und MessunguMain advantageof involute gears:Independent from the changeof the center distanceu漸開線齒輪的主要優(yōu)點:與中心局的改變無關(guān)Change of center distance中心距的改變Brner, TR-G, Folie 8Copyright ZF Friedrichshafen AG 2

8、001 Gearing and MeasurementVerzahnung und MessunguWorking pressure angle awu工作壓力角aw only defined for a gear pair 只對一對齒輪定義aw depends on the center distance aw 取決于中心距Working pressure angle 工作壓力角awawBrner, TR-G, Folie 9Copyright ZF Friedrichshafen AG 2001 Gearing and MeasurementVerzahnung und MessunguP

9、ath 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 circlesu嚙合軌跡嚙合過程中，接觸點沿嚙合軌跡移動嚙合軌跡與基圓相切嚙合長度 = 齒頂圓之間嚙合軌跡線的距離Path of contact (POC)嚙合軌跡POC嚙合軌跡Brner, TR-G, Folie 10Copyright

10、 ZF Friedrichshafen AG 2001 Gearing and MeasurementVerzahnung und MessungBase tangent length公法線長度uBase tangent length Wk u公法線長度Wk dependent on the number of 取決于測量的齒數(shù)K measuring teeth k (picture: k = 5) (圖中 k = 5)Brner, TR-G, Folie 11Copyright ZF Friedrichshafen AG 2001 Gearing and MeasurementVerzahn

11、ung und MessungPrefinished contour預加工輪廓uPrefinished gearsRoot geometry is manufacturedby hobbing or cuttingBase tangent length of prefinishedgears is different to finished gearsAttention: Change of hob or cuttercan make problemsu預加工的齒輪滾齒或銑齒加工得到齒根輪廓預加工后的基圓切線長度與最終的 基圓切線長度是不一樣的注意:更換滾刀或銑刀可能出現(xiàn)問題finished

12、contour最終輪廓（精加工后）hobbed contour滾齒后輪廓Brner, TR-G, Folie 12Copyright ZF Friedrichshafen AG 2001 Gearing and MeasurementVerzahnung und MessunguRolling a basic rackgenerates a gearuThats the principle of hobbing worm grinding u滾動齒條可以生成齒輪u這就是滾齒和蝸桿磨的原理Basic rack齒條base circle基圓Brner, TR-G, Folie 13Copyrigh

13、t ZF Friedrichshafen AG 2001 Gearing and MeasurementVerzahnung und MessunguThe root fillet is a cycloid,generated by the tool tipuTool of prefinish process:hob or cutteruUndercut is a special gear designu齒根修形是由刀頭加工得到的圓滾線u粗加工的刀具：滾刀或銑刀u根切是一種特殊的齒輪設計Root fillet齒根修形Cycloid圓滾線Tool tip刀頭rararaBrner, TR-G,

14、Folie 14Copyright ZF Friedrichshafen AG 2001 Gearing and MeasurementVerzahnung und Messungu 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 一個齒條可以生成多個齒輪有同樣的基圓 有相同的漸開線，但屬于漸開線的

15、不同部分更換變位系數(shù)（齒形改變）更換變位系數(shù)（齒形改變）Addendum modification齒頂修形Brner, TR-G, Folie 15Copyright ZF Friedrichshafen AG 2001 Gearing and MeasurementVerzahnung und MessungTable of addendum modifications變位系數(shù)表Copyright ZF Friedrichshafen AG 2001Brner, TR-G, Folie 16Copyright ZF Friedrichshafen AG 2001 Gearing and Me

16、asurementVerzahnung und MessungVariation of profile angle壓力角的變化Brner, TR-G, Folie 17Copyright ZF Friedrichshafen AG 2001 Gearing and MeasurementVerzahnung und MessunguDue to the geometric generation The probe moves linear in the transvers plane The gear rotates uDiagram of a true involuteis a vertic

17、al lineu根據(jù)幾何結(jié)構(gòu)探頭在橫截面線性移動齒輪轉(zhuǎn)動 u一條無誤差的漸開線的圖是一條垂線Measurement of involute profiles漸開線齒形的測量Brner, TR-G, Folie 18Copyright ZF Friedrichshafen AG 2001 Gearing and MeasurementVerzahnung und MessunguProfile angle deviation fHa u齒形角誤差 fHaDeviation in micrometer m 千分尺的誤差 mRelated to the measurement range 與測量范圍

18、有關(guān)uProfile form deviation ffa u齒形輪廓誤差ffaDeviation in micrometer m 千分尺誤差 mProfile deviations齒形誤差fHafHa-+ffaffa-+Brner, TR-G, Folie 19Copyright ZF Friedrichshafen AG 2001 Gearing and MeasurementVerzahnung und MessunguEvaluation range is usuallyequal to 80% of the profile lengthuEvaluation range is not

19、 equalto the required measurement range u計量范圍通常在齒形長度的80%以內(nèi)u計量范圍不等同于要求的測量范圍Evaluation range計量范圍profile measurement齒形測量100%80%Brner, TR-G, Folie 20Copyright ZF Friedrichshafen AG 2001 Gearing and MeasurementVerzahnung und MessunguTypical profile chartsu典型齒形圖Examples of profile measurement齒形測量的實例Brner,

20、 TR-G, Folie 21Copyright ZF Friedrichshafen AG 2001 Gearing and MeasurementVerzahnung und Messungu Under loadu加載時deformation of the gear teeth 輪齒變形 entry impact 嚙入沖擊 modifications are used to avoid 通過修形來避免嚙入沖擊the entry impact Profile under load加載時的齒形主動輪從動輪主動輪從動輪Brner, TR-G, Folie 22Copyright ZF Frie

21、drichshafen AG 2001 Gearing and MeasurementVerzahnung und MessunguHelical gearsScrewed transverse cut.involute in each transverse cut.same K sheet as spur gears.u斜齒輪螺旋橫切.各個橫截面中的漸開線.同直齒輪一樣的跨測齒數(shù)表（K表）Helical gears斜齒輪Brner, TR-G, Folie 23Copyright ZF Friedrichshafen AG 2001 Gearing and MeasurementVerzah

22、nung und MessunguTransverse 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 anglesu橫截面基圓 db 取決于螺旋角 b不同的 b 在橫截面上生成不同的漸開線如圖所示，橫截面上有相同的齒條，但是螺旋角不同Influence of helix angle螺旋角的影響

23、ba22costannnbzmdBrner, TR-G, Folie 24Copyright ZF Friedrichshafen AG 2001 Gearing and MeasurementVerzahnung und MessunguTwo gears in meshu嚙合的一對齒輪two base cylinders 兩個基圓柱closed thread, 繞圓柱，有閉合的曲線wrapped around the cylindersBase cylinder基圓柱Brner, TR-G, Folie 25Copyright ZF Friedrichshafen AG 2001 Gear

24、ing and MeasurementVerzahnung und MessunguHelical gearsu斜齒輪Properties of the cylinder surface 圓柱面的特征可以展開到平面上can be transformed into a planeThe cylinder can be the 這個圓柱可以是節(jié)圓，也可以是基圓 pitch cylinder or base cylinderDeveloping into the plane展開到平面Brner, TR-G, Folie 26Copyright ZF Friedrichshafen AG 2001 G

25、earing and MeasurementVerzahnung und Messungu Helical gearu斜齒輪The contact lines are straight lines. 嚙合線是直線Advantage: smooth entrance 優(yōu)點：嚙入平穩(wěn)Contact ratio is part of gear design 嚙合比是齒輪設計的重要部分Contact line嚙合線Brner, TR-G, Folie 27Copyright ZF Friedrichshafen AG 2001 Gearing and MeasurementVerzahnung und

26、 Messungu Measurement kinematicsu測量運動學probe moves linear 探頭線性運動The gear rotates 齒輪旋轉(zhuǎn)u Diagram of an ideal helixu理想的螺旋線圖是一條直線 is a line Measurement of the lead齒向的測量Brner, TR-G, Folie 28Copyright ZF Friedrichshafen AG 2001 Gearing and MeasurementVerzahnung und MessungProfile contact ratio ea齒形接觸比ea ga/petb -Face width齒寬ga - Path of contact嚙合軌跡pet - base pitch基節(jié) 2 x Modulpetga2 x Modulpetgaea 1,6ea 2bbBrner, TR-G, Folie 29Copyright ZF Friedric