1、09FTM03AGMA Technical PaperProducing Profile andLead Modifications inThreaded Wheel andProfile GrindingBy Dr. A. Trich, GleasonCorporationProducing Profile and Lead Modifications in Threaded Wheeland Profile GrindingDr. Antoine Trich, Gleason CorporationThe statements and opinions contained herein a
2、re those of the author and should not be construed as anofficial action or opinion of the American Gear Manufacturers Association.AbstractModerngearboxesarecharacterizedbyhightorqueloaddemands,lowrunningnoise,andcompactdesign.In order to fulfill these demands, profile and lead modifications are bein
3、g applied more and more. The mainreasonfortheapplicationofprofileand orleadmodificationistocompensateforthedeformationoftheteethdue to load, thus ensuring proper meshing of the teeth which will result in optimized tooth contact pattern.Thispaperwillfocusonhowtoproduceprofileandleadmodificationsbyusi
4、ngthetwomostcommongrindingprocesses,threadedwheelandprofilegrinding. Inaddition,moredifficultmodifications,suchasdefinedflanktwist or topological flank corrections, will also be described in this paper.Copyright 2009American Gear Manufacturers Association500 Montgomery Street, Suite 350Alexandria, V
5、irginia, 22314September 2009ISBN: 978-1-55589-956-13Producing Profile and Lead Modifications inThreaded Wheel and Profile GrindingDr. Antoine Trich, Gleason CorporationIntroductionModern gear boxes are characterized by hightorque load demands, low running noise behaviorand compact design. In order t
6、o fulfil these de-mands gears are more and more modified in termsofprofileandleadmodifications. The mainreasonsare to compensate for the deformation of the teethdue to load, and to ensure a proper meshing toachieve an optimized tooth contact pattern(Figure 1).Figure 2 shows typical flank modificatio
7、ns whichmay be subdivided into profile and flank modifica-tions 1. Both modification types are definedseparately but can be superimposed. The mostcommon modifications are profile and lead crown-ing in order to get a good contact pattern withouthavingcontactonbothendsoftheflankateitherthetiporrootare
8、a. Otherdesignsaretipandrootrelief,and end relief. Profile or lead angle modificationsareusedtocompensatefordeformationoftheteeththemselves but also shaft deformation within thegear box resulting in non parallel axes. All thesemodifications can be combined and thus result incomplex flank modificatio
9、ns 2, 3.Besides these “standard” modifications it is alsopossible to define so called topologicalmodifications where each point on the tooth flankhasitsownamountofmodification4. Thesekindsof modifications are much more difficult to producethan the standardmodifications. Scores ofpublica-tions deal w
10、ith methods and ways of determiningthe optimized modification for gear sets under loadconsideringgearbox andshaft deflectionas wellasdynamiceffects5,6. Thispaperdoes notconcen-trate on such an approach, but describes how toproduce these kinds of modifications in the twomost common fine finishing tec
11、hnologies, threadedwheel and profile grinding.Threaded wheel grindingThreaded wheel grinding is characterized by a highproductivity due to the continuous processkinematic and is used mainly for small to mid sizegears up to module 7 to8 witha minimumdiametralpitchof3.175. Hencethistechnologyisusedmai
12、nlyin automotive and light truck applications but alsofor larger gears with high numbers of teeth andsmall modules for instance used in printingmachines or industrial gear boxes. Figure 3 showsthe required kinematic for threaded wheel grinding1.Figure 1. Reasons to modify gears4Figure 2. Typical fla
13、nk modificationsFigure 3. Kinematic in threaded wheel grindingA machine for threaded wheel grinding needsseveral axes to perform the required kinematic.First of all the gear to be ground and the threadedgrinding wheel have to be swivelled into a certainangle which is the sum of the gear helix angle
14、andthe wheel lead angle 0. Both, gear and wheel aremating together like a gear set. Hence the rotationof the wheel nswhich results in the cutting speed vc(red arrows in Figure 3) and the rotation of the gearnwhave to be synchronized. In order to removematerial from the teeth the gear or the wheel ne
15、edsa radial infeed motion (blue arrow) perpendicular to5thegearaxis. Besidesthatthewheelhastoperforman axial feed motion (green arrow) along the gearaxis. Incasethatthegearishelical asshown inthisfigure, it must fulfil an additional rotational move-ment in order to follow the lead. Since the contact
16、areabetweenthewheelandthegearissmallerthanthe wheel width, a fourth motion is required (yellowarrow) to shift the wheel along its face width, thususingthefullfacewidth. Thisisthesocalledshiftingand can be done continuously during the axialmovementordiscontinuouslyafteragrindcycle. Allof the above de
17、scribed movements must be syn-chronized precisely in order to achieve good gearquality 1. This synchronization is done by the ma-chine axis following the mathematical equationspresented in the bottom section of Figure 3.When cutting the wheel and the gear along theworkingsectionwegetthenormalsection
18、shownonthe right hand side of Figure 3. Here one can seethe rack profile of the wheel characterised by thewheel pressure angle 0and the lead which ismodule mn0times times number of threads z0.Due to the mating movement this rack profile isfinally generating the involute shape of the gear.The shown k
19、inematic will result in a perfect gearwithout any kind of modifications.The above mentioned flank modifications can beachieved by using threaded wheel grinding. Thusall profile modifications haveto begenerated bythedressing tool since this is defining the exact shapeof the rack profile. All flank mo
20、difications areproduced by the machine kinematic (Figure 4). Incase the gear needs a certain profile modificationsuch as crowning, acorresponding shapehas tobedressedintotherack profilein orderto generatetherequired amount of profile crowing during the grindcycle 7.Figure 5 shows two different dress
21、ing principlesused in threaded wheel grinding 7. The left handside shows the most common method using dress-ingdiscswhicharecopyingtheirshapeintotherackprofile. Hence the shape of the profile modificationmustbeknownwhendesigningandproducingsuchadressingdisc. Atypicalresultusingsuchdressingdiscs is s
22、hown in Figure 6. The profile on left andright flank includes a tip relief as well as a slightprofile crowning. The flexibility of such a dressingtool is very limited and in principle can only be usedfor one type of gear but due to the line contact be-tween the dressing tool and the grinding wheel t
23、hedressing operation is relatively short (3.9 min forexample shown in Figure 6).Figure 4. Modifications in threaded wheel grinding.6Figure 5. Dressing principles in threaded wheel grinding.Figure 6. Profile generation by conventional dressingConsidering longlead timesfor conventionaldress-ing tools
24、it might be necessary in some cases to bemoreflexible. Thuscontourdressing,shown ontheright hand side of Figure 5, can be used to achievethe highest possible flexibility. In this case a dress-ing tool is used which is generating the requiredwheel shape by NC motions. The shape of thedressing disc it
25、self is independent from the wheelrack profile. This opens a wide area for profilemodifications but on the other hand the dressingoperation needs much longer dressing time 7.A typical result using contour dressing is shown inFigure 7. The required profile was defined by socalled K-charts and was pro
26、grammed using themachine interface presented in Figure 8. Such acontour dressingcycle needs about 30-40 minutescompared to 4-5 minutesfor conventionaldressingconsidering normal dressing conditions. So theadvantage of is offset by longer dressing times.7Figure 7. Profile generation by contour dressin
27、gFigure 8 shows a typical dialog of modern machinesoftware for programming profile modifications iscase of contour dressing. Left and right flanks canbe programmed separately. The user defines thetarget profile of the gear and the machineautomatically calculates the corresponding rackgeometry and al
28、l required movements for thecontour dressing cycle.Figure 8. Contour dressing programming interface8As mentioned above lead modifications aregeneratedbythemachinekinematic. Thereforethekinematic for threaded wheel grinding described inFigure 3 has to be superimposed by additionalmovementstoachieveth
29、emodifications. SoFigure9 explains the two main principles which are usedforthesemovements. Aspresentedonthelefthandside a change in the radial infeed (x-axis) results inmore or less stock removal on left and right flank.Hence if a symmetricallead crowningis requiredasshown in Figure 10 a curved sha
30、pe x-movement independence of the z-position (face width of thegear) is necessary, defined by a function x(z).Changing the tangential feed (Y-movement) asshown on the right hand side of Figure 9 withoutchangingtherotationalpositionofthegearresultsinmore stock removal on one flank and less stockremov
31、al on the opposite flank.Figure 9. Generation of lead modificationsgenerated by a parabolic function: X(Z)Figure 10. Example for symmetrical lead crowning9By superimposing the two functions x(z) and y(z)any kind of lead modifications can be achieved. Anexample how to achieve an unsymmetrical leadcro
32、wning is shown in figure 11.In this case a parabolic function has been chosenfor both additional movements y(z) and x(z). Theparabolic y(z) function leads in a hollow shapecrowning on the left flank and a barrel shapecrowningontherightflankwhilethe sameparabolicfunction for the additional x(z) movem
33、ent results ina barrel shape crowning on both flanks. Since bothfunctions are superimposed the result is a straightlead flank on the left flank and a crowned flank onthe right flank. Figure 12 shows a grinding resultusing this method and proves how beautifully thismethod works. This principle can al
34、so be used toachieve much more complex modifications.Y(Z)=aZ2+bZ+cX(Z)=aZ2+bZ+cFigure 11. Principle to achieve unsymmetrical lead crowninggenerated by combining function X(Z) and Y(Z)Figure 12. Example for an unsymmetrical lead crowning10Up to now profile and flank modifications werehandledseparatel
35、y. Butwhengrindinghelicalgearslead modifications always influence the profilemodification. The reason for that is the contact linebetween the grinding wheel and the gear toothwhich runs diagonal over the tooth as shown inFigure13. Henceallpointsalongthislinearegener-ated at the same time. So in case
36、 of grinding asymmetric lead crowning, a parabolic function x(z)as mentioned above will result in a change of radialinfeed over the face width “b” of the gear. Usuallythehighpointofacrowningissettothemiddleoftheteeth in terms of face width andprofile heightrepre-sented by the blue point in Figure 13
37、. Since allpoints along the line of contact are generated at thesame time, this results that the root area, repre-sented by the red point, achieves its crowninghighpoint displaced to the top of the gear. The tiparea which is represented by the green point,achieves its highpoint more displacedto theb
38、ottomof the gear. Hence the lead crowning is onlysymmetrical in the middle of the gear. If we wouldmeasure the lead crowning in the root(red line)andtip area (green line) of the tooth the crowning wouldbe displaced looking like a lead angle error. At thesame time this also effects the profile modifi
39、cation.The middle section has no profile error but a slightcrowning just being effected by the lead crowning.Thetop andbottom profilelines areshowing aclearprofile angle error. The above described effect isthe so called twist phenomena and appears whengrinding helical gears with a lead crowning. Fig
40、ure14 shows a grinding result where this effect can beseen. The amount of twist error which is defined astheabsolutechangeinprofileangleerrorfromtoptothe bottom is for this example about 25 mm andmuch more than the allowed tolerance. Hence thisphenomena is not desired.So the question now is, how can
41、 this effect becompensated for and/or controlled? When lookingtoFigure13or14itbecomesobviousthatamethodis required which allows to grind different profilemodifications at different sections along the gearface width which is nothing else than topologicalmodifications. So inorder tocompensate orcontro
42、lthe twist phenomena it is necessary to at leastpartially compensate the profile angle error whichchanges from top to the bottom on the gear, and inaddition to that is different in terms of its sign on leftand right flank. Gleason has a patented method todo such a compensation which can also be used
43、 togrind topological modifications as mentionedabove.Figure 13. Contact line and twist generation in threaded wheel grinding11Figure 14. Twisted tooth flankThis method works with a modified wheel shapealong the wheel face width. As shown in Figure 15on the right hand side the grinding wheel is notdr
44、essed in a cylindrical shape but rather in a hollowshape. This can easily be done during the dressingcycle by just infeeding the dressing toolperpendicular to the wheel axis using again a para-bolic function across the wheel face width. Henceno additional machine axis is necessary. Whenlookingtothed
45、etailonthelefthandsideofFigure15one can see how such a dressed hollow shapegrinding wheel effects the grinding result. Assum-ing the gear being ground in this area wouldgenerate teeth with different pressure angles onright and left flank. The right flank would be groundwith a pressure angle which is
46、 the pressure angle of the rack profile plus an angle while the leftflank would begenerated witha pressureangle ofminus . The angle is the angle deviation be-tween the perpendicular and the shortest distancebetween the gear center and the curved datum line(dotted line) of the rack profile.Figure 15.
47、 Principle of twist compensation12So it become obvious that by choosing differentpositions along the wheel face width one caninfluence the profile pressure angle generated onthe gear teeth. Since the above described profileangleerrorisnothingmorethanadifferentpressureangle it becomes obvious how to
48、compensate or tocontrol this effect. Therefore the gear iscontinuously shifted along the wheel face widthwhileperformingtheaxialstrokeasshowninFigure16. The result is that the right side of the wheelgrinds the top part of the gear while the wheelmiddle portion grinds the middle section of the gearan
49、d the left wheel side grinds the bottom section ofthe gear 8.Thinking about the effect described with Figure 15,this method will result in gear teeth having differentpressure angles from the top to the bottom anddifferent signs on left and right flanks. Since thiseffect is superimposed with the natural amount oftwist it is obvious that by using this method one cancompensate for or control the amount of twist. Butthis method can also be used to create differentkinds ofprofile modificationsalong theface widthofthe gear which may be other than
