AGMA-93FTM2-1993.pdf
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1、93FTM2 A -TopologicalTolerancing of Worm-GearTooth surfaces by: Vadim Kin MLitvin,1989a;Kin,sufficientfor thestudyof geartoothsurfacetolerance 1990), a different form of this Equationis preferred,andbands. we will use it later in this paper to prove a theoretical result.This form is representedas Ap
2、plication:ZA Worm-GearDrives n_- v_= 0(3a) In thisSection we consideran applicationof the where n_ is the unit normal to the worm surface and v_ istheory developed above to a particularcase of worm-gear the relative velocity of the point on the worm surface withgeometry.ZA is one of the geometriesin
3、 wide use today. respect to that of the point on the worm-gearsurface.The other such types are ZI, ZN, ZK and ZC.While the informationbelowis only pertinentto ZA geometry,the The preference that form (3a) has enjoyed overabove theoryis generalenoughto beapplied to any the years is due to the fact th
4、at its ufdizationresults inworm-gear. much less complicatedexpressions.This is not, however, a strong factor in our approach,since we make extensiveThe worm surfacein a ZA-typewormgear drive use of a symbolic algebra packageto derive the necessaryis an Archimedeshelicoid,i.e. a helicoid witha straig
5、ht expressionssymbolically,ortoapproximatethemline in the axial section.The vectorequationof the worm numerically.The disadvantageof form (3a) is that thesurface (equation (1) in this case becomes vectorof relative velocity v_ has to be derived from first principles.While we have completedthis task
6、previously, this resultsin a lesserdegreeofautomationof the solution, and is thus potentiallymore prone to errors.“ucos2,p cos0) ucosXp sinO_ r, (u,0)=(8) Gear Tooth Surface Deviationsp0-1sin_,pJ We nowturnourattentiontotheproblemof representingthedeviationsof theworm-geartooth surface resuking from
7、 the utilization of a worse-than-idealwhere _,pis the lead angle at the pitch diameter,p-rptar_p hob. The surface of such a hob is represented byis worm lead per radian, and rpis the worm pitch radius. No derivationsare performedfrom this point on. r_*(u,0)=rw(u,0)+fiw(u,0)(5)The tolerancebandscan n
8、owbeobtainedby a direct applicationof(6),whichissoNedbyasymbolic- where _(u,0)representsthe worm threadsurfaceerrornumericalmethodoutlined in (Kin, 1993). function.In line with equation(4) above, the worm-gear tootherror function _then be representedas Copyright American Gear Manufacturers Associati
9、on Provided by IHS under license with AGMA Licensee=IHS Employees/1111111001, User=Wing, Bernie Not for Resale, 04/18/2007 10:42:36 MDTNo reproduction or networking permitted without license from IHS -,-,- Examples1992). One way of overcoming the problemis to supplement3-D graphicsby axial or cross-
10、sectionsof the The parametersof the worm-geardrive usedintolerancemap.One of the cross-sectionsof the above the examplesare summarizedin Table 1.map is shown in Fig. 5. We first apply the systemof equations(4) to construct the tooth surface for one of the flanks.This flank and the gear root surface
11、are shown in Fig. 2.The same tooth surface is shown in greaterdetail in Fig. 3. CenterDistance, in8.135 Gear Ratio90:1 Worm Pitch Diameter, in2 Pitch Lead Angle, deg8.5328 NumberofStarts1 Normal Pressure Angle, deg20 Fig. 3 Table1Worm-Gear ToothSurface: Detail Worm-GearDrive Parameters 0.$ o.x -,.-.
12、_ Fig. 2,.,-,._ Worm-Gear ToothandRootSurface“ We then applythe system(6) to computetheFig.4 three-dimensionaltolerance“band“for theworm-gearThree-DimensionalWorm-Gear Tooth surface (Fig. 4).The band shows the maximum surfaceSurface Tolerance Map deviationsthat can be generatedby a wormwhose prone i
13、s within the +0.001“ tolerance band in the axial section.Such wormo. surface in the case of ZA geometryis representedby a.000s _ ,UCOS _,psin0 / +/_ COS _,psin0-/_ rw(uO)=p0-usinXp/5sinZpFig. 5 1)_,0ToleranceMap Cross-Section (9) It should be noted that the cross-sectionshown in Here the first membe
14、r of the vector sum is recognizedasFig. 5 is not constant throughoutthe map in Fig. 4.The the ideal wormsurface(8), and the second- the wormsectiondepictedis merely an example,and in order to error surface correspondingto the rectangtflar band.fully visualize the error surface, many such cross-secti
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