1、91 FTM 1vCNC Bevel Gear Generators and FlaredCup Formate Gear Grindingby: Theodore Krenzer, The Gleason WorkscAmerican Gear Manufacturers AssociationI I I II- TECHNICAL PAPERCNC Bevel Gear Generators and Flared Cup Formate Gear GrindingTheodore J. KrenzerThe Gleason WorksThe Statementsandopinionscon
2、tained hereinarethoseof theauthor andshould notbe construed as an official action oropinion of the AmericanGearManufacturersAssociation.ABSTRACT:Full CNC bevel generators achieve the relative position between the tool and work with simple mechanisms andelectronic controls. As a result, the gearengin
3、eer has new freedoms for the control of gear tooth shapes and contactcharacteristics. This paper defmesthe flared cup Formate gear grindingprocess and the motions that can be applied tothe process. Surface comparisoncharts and toothcontact analysisare usedto demonstratethe effects of the freedoms.Co
4、mparisons of jobs designed with and without the motionsare included, vCopyright 1991American Gear ManufacturersAssociation1500 King Street, Suite 201Alexandria, Virginia, 22314October, 1991ISBN: 1-55589-574-3CNC BEVEL GEAR GENERATORS ANDFLARED CUP FORMATE GEAR GRINDINGTheodore J. Krenzer, Director o
5、f Research and DevelopmentThe Gleason Works, Rochester, New YorkNew freedoms of motion available with CNC generators make wheel surface has a normal radius of curvature less than thepossible improved tooth contact on bevel and hypoid gears, conventional tool, and the inside wheel surface has a norma
6、l_ Mechanical machines by their nature are inflexible, and require radius of curvature greater than the conventional tool. Linea special mechanism for every desired motion. These mechanisms contact exists between the work and the wheel. The wheel isv are generally exotic and expensive. As a result,
7、it was not until positioned relative to the gear blank so that at the calculatedthe introduction of CNC generators that engineers started mean position on the gear tooth surface the correct spiral andexploring motion possibilities and their effect on tooth contact, pressure angles are produced. The
8、tilted axis of the wheel is ina plane normal to the tooth surface. In achieving this setup theThis paper covers the exploitation of new motion freedoms to tilted axis is offset from the conventional tool axis. The tooth isimprove tooth contact patterns on gear sets manufactured by the swept out by r
9、otating the flared wheel about the axis of theFormate face milling duplex process. (The duplex process is a conventional tool axis. See Figure 2.manufacturing method where both flanks are completed in asingle operation.) As the wheel is dressed its radii change, which requirescompensating machine ch
10、anges to maintain the proper toothStarting with a brief background of the flared cup process, the geometry. Making these setting changes manually on mechanicalpaper proceeds to describe the possible linear and angular motion machines was a problem. Tooth geometry often varied from partvariations, an
11、d their effect on the gear tooth surface. The paper to part. Full CNC machines, where wheel radius can beconcludes with the use of Tooth Contact Analysis (TCA) to accurately determined, are programmed to automaticallyevaluate the enhancement of the Formate duplex process made compensate for wheel si
12、ze changes resulting from dressing.possible by applying these motions.Wheel life is a function of the radius change which occurs as aFlared Cup Process result of dressing. Over the useful life of a wheel, the relativeWhen cutting face milled gears using the Formate process, the curvature decreases b
13、etween the convex tooth surface and thecutter is positioned relative to the gear blank, so that the correct inside wheel surface, and increases between the concave toothspiral and pressure angles will be produced. The gear blank is surface and the outside wheel surface. Although the final toothheld
14、stationary and a tooth slot is form cut by infeeding the surface is produced by line contact, at any instant surface contactcutter. The part is indexed one pitch and the process is repeated, exists between the wheel and work in proportion to the depth ofSee Figure 1. When the cutter is replaced by a
15、 grinding wheel, grind. The contact area is dependent on the relative curvaturecontact exists over the entire length and depth of the tooth between the wheel and work, the variation in the contact areasurface. Heat buildup results, causing a tendency for surface between the two tooth sides is used t
16、o determine wheel life. Asdamage due to burning. The Formate flared cup grinding process a rule of thumb, good results are obtained when the differencewas developed to overcome this problem, in contact area between the two sides of the tool does not exceed- the ratio of 2 to 1. Figure 3 shows sectio
17、ns of a tooth andThe flared cup process uses a wheel which is tilted out of the grinding wheel at three stages of wheel life; ideal, new wheel and- work. (Thirty degrees of tilt is commonly used.) The outside spent wheel.J l or. / _jrkthslotf JJ“ _/ _2;_a_/flaredtool- _FIGURE 1 “ axis/_ _FIGURE 2CON
18、VENTIONAL FORMATE SETUPFORMATE FLARED CUP SETUPNew FreedomsThree angular and three linear motions define the relativemotions that can exist between any two bodies, in this casebetween the flared cup tool and the work gear. One of theangular freedoms is used to sweep out the tooth surfaces.Therefore,
19、 effectively only two angular freedoms are available forcontact pattern control.At any instant in sweeping out the tooth surfaces the CNCgenerator has the capability to change the relative orientationbetween the contact line and the gear tooth. Motions to achieve ._._a change could be defined in any
20、 number of reference systems. !For this case all of the motions are defined based on the L_. :-_x- Iinstantaneous radial plane; that is the plane containing the / “_-_,_conventional tool axis and the radial line to the mid-height point iaealwheelonthecontactline. _-.jThe freedoms are defined as foll
21、ows: ;1. rotational motion in the instantaneous radial plane. _ ;_.L_ II2. rotational motion about the instantaneous radial line.new wheel3. linear motion along the conventional tool axis.4. linear motion along the instantaneous radial line.5. linear motion perpendicular to the instantaneous radiall
22、ine.Figure 4 is a sketch of a flared cup setup showing these motions, spentwheelThe angular motions pivot about a point at mid-tooth depth andmid-slot width. A timed relationship exists between the motionsand the angular position of the wheel as it is swept through thetooth slot. Although a number o
23、f functions could be used to FIOURE3define the relationships, polynomial expressions were selected. CONTACTAREAVARL_TIO_1. Radial Tilt /- This angular motion is a tilting of the tool in the /instantaneous radial plane as the tooth is swept out. The ,_x- effect is to change the pressure aangle on bot
24、h flanks of / “_the tooth as the grind line moves from the tooth center / worksection. The change increases the pressure angle on one i/gearflank, and decreases the pressure angle on the other flank 1as compared with the conventional Formate tooth. At / Iany tool phase angle position designated by A
25、 a, the radial /tilt of the tool is given by:Aa = AIAg+AzA_t2+A3Aet3+A4Aa 4 where A1, A2, As, A4 are the coefficients that control the - - *motion.Figure 5 schematically illustrates the change in surface ot pointtopology on the convex and concave flanks of a geartooth. The solid ilnes represent the
26、baseline surface andthe dashed lines represent the surface resulting from asecond order change in Aa. It can be seen that metal isremoved on each side of the center section at the bottomof the convex flank and at the top of the concave flankof the gear teeth. The opposite effect occurs at the topof
27、the convex side and at the bottom of the concave side.The A1 coefficient produces a velocity in the normaldirection at A a = 0, the setup must be altered to FIGURE4accommodate the velocity when this coefficient is used. FLAREDCUPMOTIONS2. Tangential Tilt where L1, 1.,2,1.3,L4 are the coefficients th
28、at control the- This angular motion is a tilting of the tool around the motion.instantaneous radial line as the tooth is swept out. Thev effect again, is to change the pressure angle on both Since the L1 coefficient produces a velocity in the normalflanks of the tooth as the grind line moves from th
29、e tooth direction at Aa =0, the setup must be altered to holdcenter section. In this case the pressure angle is spiral and pressure angle at the mean point when thisincreased or decreased on both flanks, as compared with coefficient is used.the conventional tooth. At any tool phase angle positiondes
30、ignated by Aa, the tangential tilt of the tool is given Figure 7 schematically illustrates the change in surfaceby: topologydue to a secondordercharigein A1.It canbeseen that metal is left on at the inside and outside ofAI_= BtAtt+BzAt2+B3A_t3+B4Att4 both tooth flanks.where B1, B2, B3, B4 are the co
31、efficients that control the 4. Radial Motionmotion. This motion is a movement of the tool along theinstantaneous grind radius between the tool and the workFigure 6 schematically illustrates the change in surfacegear. The effect is to modify the surface topology in thetopology due to a second order c
32、hange in A IL It can be opposite manner on the tooth flanks. Metal is removedseen that metal is removed on each side of the center on one flank and metal is left on the other flank, assection at the top of both tooth flanks. The opposite compared with the conventional Formate tooth. At anyeffect occ
33、urs at the bottom of both tooth flanks, tool phase angle position designated by Art, the change inposition of the tool relative to the work in the3. Axial Motion instantaneous radial direction is given by:This linear motion is one that has been describedpreviously L2. It is an advance or withdraw of
34、 the work Ar = R1A_t+R2AetZ+R3Act3+R4Aa 4along the conventional tool axis. The effect is to modifythe surface topology in the same manner on both tooth where R_, R_ R3, R4 are the coefficients that control theflanks. More metal is either removed or left on the tooth motion.flanks in the lengthwise d
35、irection as compared with theconventional Formate tooth. At any tool phase angle Since the R_ coefficient produces a velocity in the normal_ position designated by Aa, the change in position of the direction at An=0, the setup must be altered totool relative to the work in the direction of the cutte
36、r axis accommodate the velocity when this coefficient is used.is given by:Al = I.qAcx+IqA_xZ+L3Aa3+L4 An4GILE_._IIUIG_S PRO_r_hHIE_T DRTr- ?,:PS,S1 IZIIE-IO:_g21.0e)RIEF(_O(.ID3 _URF_C- GTMRI_TJOI,FN_P- (DASHED)SURFGiCJ-I_TMIRK._T;IIO1,PRRADELTIrl *_-.O Z:LIERTICRLDI:STRtiCPr AT goal| TP 4._01615 _t
37、l.H TTP *.*0“31 Ztl.Ir R_OT-.ikOi01 Ztl.H ROOT-uO,U04Ztl._CRLIrLrGICTOR:_VlI_G 1.COIItET G4.IkO_F SO01.10T_SIJRFrN_:rIGF7 ., RI_OM_CRI.: I_EThLGK .ti41 _ZH.TEP C_IIUI_ GF_RGL,T._I_ItLV,I_.: PROGI_I!l_;t ORT- ?.,_5,+1 ItllE-lO:2_-_;- _* 1- _ .f _ i -_“ t I II / Lf-_ _,“,_URFRCleDZRF _, RRE0_CRL“ flET
38、FL 011.gO1 ZN.TP C.OltCFIUG_EP_FIGURE 5TOPOLOGY GRAPH OF SECOND ORDER Aa CHANGECI.LPRS_N IIOl_ PIRO_RRtlIE_T I_RTE- ?/25/91 IXPIE-IO:S+JP_! .011)It_P“ (_0LZO) SLIQIP_CI_- GTlIR_rSOIt_I?.lOII_ I;LEI_(_I M(_I_ PROP_RI+ TE_;!_1_ (DIrer;IllD) _;LIQF_C_- _TtmlG.I_OI.dPAQB1DELII_ BIm-.01I_RT;CRL DI:STIPlP
39、ICIPlIT RCIOIT TIP -.IIOILI41 tH.H TXP -.I012 211.I _O(IT i.I01I _PII.I! RO()T 1.101_ TII._CRI.IP PRCTORSm411_ 1.10YH_ 1.10IIIET GI.IO ,+ _1D:Ir _4101,I0 +.-“ / I/+/ / * i _ _ _, P-“_“ I f,“ i j,+ !,z / JI +_“ _,r. I .“ V%.Ii #SIJffrN:E lYrPF fil;SOM_(:NE: HETItL 011 .1101 rN.TTp C:O;II.IEXGE_A(;ILE
40、_SOtl MOAI_; Plil_l_N IV_T O_?E- ?,_5/91 IIHE-11 : lt,21 .OR1_tEF (SIX.X03 _LI_FIA_E- OTIIII_ISOX/:8;P.XOII_LE_;O(I Ul_l_ PROI_ItRI_TIrSTOELII_ I_lm-.OtUERTICRL 9I,_TRNCE RT I;OClI+ TZP -,lO13+J ZN.I ROOT 1,10114 ZH,H ROOT I.I0111 tH._IRG 1.+0I_ET l;ll,lO.; t ,/S _“:_ r+21 /I-.If.Ty-,_. , _ .-+I“.,“
41、 _ .-f ./_ t- I /l/ ,q /.,I/-. _ , -“ _ v“I / I / .+, /.“I I1+,.,+“,/,.SlJItFN:E DZIrF .e N_OU:_;_L: llLrrll. OH .IDX |H.TIP (_ItV:RLIE Glrl_AFIGURE 6- TOPOLOGY GRAPH OF SECOND ORDER Al$ CHANGECLP-IqSMNIICRKSPRO_RII_HIES_T rlnTE- ?,25.,_1. |ZNE-11.“ 2 -_i .0ilREP (_:OLII) _URIrAC4-(_TmK.,I$01,M_TOdl
42、lI_I.P.I_M,IUORK_PRO_IMIIM_- (DIM_HI_D)_URIr_CE- GTI,MI_I_BOX/P_IflLIDELII_LL41-._IIERTICALOI:GTI_IM:E_T ROOfI ITP 41.I011_ ZN.H ITP i.iOi_ IN,1 ROOTi.il01_5 IH.H _O_T t.lk00,l.:3 ZII.Xlll_ 1.40VH/_ 1.110IIIET ,4.Q0Dill“ _iI011.410,. .-CJ,“ I “ .- , _ I I.“ +“ I _, _1 ., ._“_ I.,-.+ , _ ._.+- ,._* ,
43、.-+/ _._ +.+_.c_ “+,_1t_,i .(._-“ -“- “_“ “ ii “+/“ ! I i_. +,“ it i. , i.- i,y,SURFRO_IrF/ RRflOi4S_RL_“ I_ETRL011 ,tO_ 1_0TiP COIIUEXGE_RR_I.LP_I_OIIII_I_S PRI_GI111IE_T 0_o “/,P.S,M. IX_E-11:3 -I_?.1.0dl!I_1r (_OLID) SLmP_CE-GTI,MI_I:8OI,_2:).Otl_C (I)I_I_HIED):GLiflFIqCE-P.TMI_I_|_tOI,P_I_L6_Llf
44、l L.2m-.02tI(RTICRL IDISIdlEE M flOKIfI lIP l.eOl_+4J Ill.H lip l.OOO_l ZH.! I_OOTdi.I0134 IH.H ROOTI.IOI_P Ill.1_ItLtr P“IhC:?OIlS101P_G 1.10Vm_ 1.101HIT I,I,il 0D_Ir _M_OI .dlOI I L ,“ I “-,.-. .+,4_r_ I/“,“ “ I a .,.+“_I I _,+“+“_ _“, _ _+_+ l II “+_, I I ./“ I I I%-.,.I , “TI I +.“ -“_ “ I c_CI:
45、II.E:BETPI_ON .1105 ZII.TIP _OP_I_J_I_IEhRFIGURE 7TOPOLOGY GRAPH OF SECOND ORDER A1 CHANGEthe new motion freedoms should make grinding more attractiveFigure 8 schematically illustrates the change in surface as a final finishing process because of the ability to develop- topology, due to a second ord
46、er change in Ar. It can be contact patterns with a wide range of characteristics.seen that metal is removed on the convex side and metalis left on the concave side on each side of the tooth Typically, gear sets used in automotive and truck applicationscenter section, cover the range from two to seve
47、n diametral pitch. Three setswithin this range were designed using the standard duplex method5. Tangential Motion plus the new motions. Blank data for the sets is given inThe tool can also be moved in a direction perpendicular TABLE I.to the instantaneous grind radius. The effect is to modifythe sur
48、face topology in the opposite manner on the tooth Small Automotive - When the diametral pitch is six or higher, theflanks. It has an effect similar to the effect described need for added flared cup motions can be questioned. Figure 16above for a change in radial motion. At any cutter phase is a TCA
49、comparison of the duplex job designed without addedangle position designated by An, the change in position motions on the left and with added motions on the right. Theof the tool relative to the work, in a direction jobs were designed with very little transmission motion variation.perpendicular to the instantaneous radial is given by: Both designs are similar. Substantial pattern length was obtainedwithout the introductio
