1、. . STD-AGMA 75FTML-ENGL 1775 Ub7575 000Lib44 T42 95FTM1 “Hidden Runout” by: Robert Smith, R.E. Smith “hidden runout“ and “variable velocity“ gears when discussing the occurrence of this phenomenon relative to some shaved gears. If a gear has runout, it will have a large accumulated pitch variation.
2、 If it does not have runout, it may still have a large accumulated pitch variation that is the result of mout somewhere in , k the manufxturing process. If a certain amount of runout in a gear is undesirable, the same amount of accumulated pitch variation will be just as undesirable, even if it has
3、little or no runout. 1.2. Radial vs. Tangential effects. Runout is a radial phenomenon and accumulated pitch variation is a tangential phenomenon. Gears work in a tangential direction, rather than radial. Therefore accumulated pitch variation is more directly related to transmission error. It isnt r
4、unout, per se, that is the culprit, but it is the resulting accumulated pitch variation. The main purpose of gearing is to transmit uniform rotary motion from one shaft to another, under their operating conditions. If this motion is not uniform, the gears are said to have transmission error. 13. Dan
5、gers of “Hidden Runout“. The problem with hidden runout is that it is not detected by the inspection methods that are in most prevalent use. A “ball check“ of runout (V,), Figure 1, will not find it and neither will “double flank composite“ testing of total composite error (TCE, V ,), Figure 2. Both
6、 of these methods measure gear quality in a radial direction, rather than tangential. They, therefore, will miss the most important characteristic which is transmission error (a 1 COPYRIGHT American Gear Manufacturers Association, Inc.Licensed by Information Handling ServicesSTD-AGHA 95FTML-ENGL I99
7、5 tangential measure). These inspection methods can pass a gear as a very high quality level, but they will have poor performance such as positional inaccuracy or variable velocity. Note: Figures 1,2, and 4 are fiom AGMA 2000-A88, Gear Classification and Inspection Handbook w I Fig 1 Runout Check, O
8、ver Pin, Ball Probe Fig 2 Gear Rolling FMre Oouble Flank Testing) 2.0. DESCRIPTION OF HIDDEN RUNOUT. A gear of the type described above, with “hidden runout“, will have the following characteristics: 2.1. Near Uniform Tooth Thickness and Tooth Space Widths. Any tooth thickness or space width measure
9、d around such a gear will have very little difference in size. It may be only .Ol“ to .O2“. However, there will be a difference in the tooth flank positions. This is a sinusoidal variation that has oniy a smail difference between any two adjacent flanks, but accumulates in an ; Y:; 2: 7 27 1.2 37.8
10、1 2) 1.3 41.2. 7 30 -2.9 31.3 7 31 -1.7 36.7 7 32 2.b 39 O 33 -0.7 3813 4 21 2.1 39.9 , ?! -!.! 2i.a 1 that measurements of runout by a “bail check“, or double flank composite (TCE) test are very misleading for these types of gears. 5.1.1. Shaved Gear. Figures 5 and 6 show data for a gear finished b
11、y shaving. Figure 5a. and 5b. are of the gear, as hobbed, with runout. Figures 6a. and 6b. show the results of the same gear after shaving. In adition, the shaved gear was tested by double flank composite method and showed a TCE of only .0007“. 5.1.2. Ground Gear. Figures 7a. and 7b. show data for a
12、 gear finished by threaded wheel grinding with an electro-mechanical (non-CNC) type machine. In order to simplie the data presentation, only every third tooth is plotted. For the purposes of this paper, this is valid for the display and determination of accumulated pitch variation, but not for indiv
13、idual pitch errors. In addition, a double flank composite test showed only .0007“ for TCE. 2.00 riathSI D 0.0020 0-0040 ladu ?ice a IXII vu vu WdiV -it 716.5 -17.4 -21.2 I 21.5 27.b 7 29.9 I 31.7 7 33.5 I 32.5 7 36.7 I- 37.2 I 39.6 7 36.8 I- 37.5 f. 39.7- r 38.3 7 3e.1 7 35.9 7 32.6 32.0 721.1 28-b
14、722.1 -19.7 -18.0 - 14.b 14.1 9.9 I 7-2 0.9 3.9 0.2 5-90 2.6 1.7 1.8 -0.9 b.2 0.5 2.1 -2.8 0.7 2.2 -l.b -0.1 -2.7 -2.8 -0.6 -3.2 -0.4 -5.6. -3.1 -1.7 -3.6 0.4 -4.9 -2-7 a 36 37 31 39 .O 41 42 1 Fig. Se Inda Piot (Hobbed Shpved) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 1) 20 21 n 23 2b 2s 26 27 2
15、1 29 30 31 32 33 3b 35 36 37 31 39 40 41 42 1 slot 1 2 3 b 5 6 7 8 9 10 11 12 13 1b 15 16 17 18 19 20 21 22 23 24 25 26 27 21 29 30 31 32 .33 3b 35 36 37 31 39 40 bl 42 - “E7 18.7. 18.5 17.4 11.5 11.7 7.b 6.1 6.5 3.9 1.4 -5.7 -3.Y -7.3 -11.5 -12.5 -16.3 -16.2 -1b.O -16.6 -15.) -17.1* -15.b -14.8 -12
16、.0 -10.6 42.1 9.9 -7.2 -2.2 1.0 -1.5 0.2 3.7 7.6 Y.D 9.0 10.0 11.8 17.7 16.6 16.6 .LIooII+ a* O.OOD20 inldiv tcft 4.0040 -0.0020 0.0 0.0020 0.0010 111.1I111x :* : t :* :* :* :* :* :* 0: 0: *: *a *: t t *: a a -i *a *: *t *i *i *: *: 1. a* :* z* 89 I. 1 I I* I.!IIX.I!.X 6 COPYRIGHT American Gear Manu
17、facturers Association, Inc.Licensed by Information Handling ServicesSTD-AGMA 75FTML-ENGL 1975 Ub87575 000Lib52 O19 irr(0n %dir tcft - lX. . lI VLe 0.0020 0.0040 Indu - u*+ 0.00020 wdv flLlI.-lII -0.0040 -0.0020 0.0 0.0020 *: -: 0: .: *: 0: *: a: *: 0: -: -: 0: .I i* :. I. :- :- :- :. I. :. -. Ian 0.
18、0040 .11 Sioc iicb &dex vu v.= 1 16.2 2 -2.8. 13.4 3 -1.9 11.5 4 -2.1 9.4 5 -1.6 7.8 6 -1.2 6.5 7 -2.0 4.6 8 -0.5 4.0 9 -1.0 3.0 10 -0.5 2.5 11 -0.3 2.2 12 -0.2 2.0. 13 0.5 2.5 I4 0.6 3.2 15 0.9 4.1 16 1.6 5.7 17 1-7 7.4 I8 2.0 9.4 19 2.0 11.5 20 2.3 13.1 21 2.2 15.9 22 2.1 18.0 24 2.2 22.5 25 1.8 2
19、4.3 26 1.6 25.8 27 1.6 27.5 28 1.5 29.0 29 1.4 30.4 30 0.6 31.0 31 0.9 31.9 32 0.6 31.4. 33 -0.6 31.m 34 -0.5 31.4 35 -0.5 30.9 36 -1.5 29.3 37 -1.3 21.0 31 -1.5 26.5 39 -1.4 25.2 40 -2.1 23.1 41 -2.2 20.9 42 -2.3 18.6 1 -2.5 16.1 23 2.3. 20.3 -1 0.000: X-.l*.Il I :%o 0.0020 1 - Slot 1 2 3 4 5 6 7 8
20、 9 10 11 I2 13 19 IS 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 ?ire Slor VrC haont -p. -0.3 -0.3 -0.7 -0.5 -1.0 -1.4 -1.2 -2.5. -1.9 -2.0 -1.9 -2.1 -2.2 -1.8 -1.3 -1.4 4.1 -1.4 -1.1 -0.1 -0.3 721.3 I-. 24.1 I 26.3 28.1 30.2 2.1 5 7 31.6 1.4 6 P 33.3 1.7 7 v 34.
21、9 1.6 8 ? 35.2 0.3 9 7 35.7 0.5 10 7 35.7 0.0 I1 ? 35.9. 0.2 12 r 35.2 -0.6 I3 7 34.1 -1.1 14 7 32.5 -1.6 I5 -30.9 -1.6 16 I 28.4 -2.5 17 26.9 -1.6 18 -24.5 -2.4 19 721.9 -2.6 20 19.2 -2.7. 21 16.7 -2.5 22 714.1 -2.6 23 12.3 -1.8 24 -10.1 -2.2 25 7.9 -2.1 26 r 6.1 -1.a 27 I 4.u -1.3 28 I 3.7 -1.1 29
22、 2.5 2.1 2.0. 2.2 3.0 I 3.8 - 5.5 6.9 1- 1.8 1- 10.1 -13.5 715.8 I i0.b l- 21.1 .*I.LX - 1 2-1* 2 2.2 3 1.8 4 1 7 0.2 0.5 0-2 0.7 1.3 1-6 1.6 1.4 2.1 1.9 1.6 2.2. 2.1 1.9 -1.2 30 -0.5 31 -0.1 32 0.2 33 0.8 34 0.s 3s 1.7 36 1.4 37 1.8 38 2.1 39 2-6 40 2.4 41 2.5 1 1.7 42 1.9 :* 1.9 1. 1.7 I. 1.1 I- 0
23、.6 0.5 0.0 11x111.1.1.1 I1. . 11 Fig. 6a index Plot ( Shad gear - with hobbed runoat) Fig. 6b. Runorit Plot (Shaved gear - wib hobbed moat) mnmr 0.00050 war Ugh+ - -0.0100 -0.mo 0.0 0.0050 O.OIO0 11111-11.-.11 Ilft -0.5 Li*+ 0.00050 Wdiv tcft var vu IIX IIl.-Il-.-I vu v.= Clot tsh Indu 0.0100 0.0050
24、 0.0 0.0050 0.0100 Indu Pits blot Slot 1 4 7 10 I3 16 19 22 25 28 31 34 37 40 43 46 49 32 55 50 61 64 67 70 73 76 79 82 15 18 91 1-53J - 1 1- 52.0 -1.5 4 I- 48.5 -3.5 7 1- 46.0 -2.5 10 1- 42.5 -3.5 13 1- 37.0 -5.5 16 I- 28.5 -8.5 i9 I- 20.0 -8.5. 22 1- 13.0 -7.0 25 t- 9.0 -4.0 28 ,- 7.5 -1.5 31 I 7.
25、0 -0.5 34 r 6.0 -1.0 37 I 5.0- -1.0 40 I 5.0 0.0 43 I 6.5 1.5 46 I- 9.0 2.5 49 I- 13.0 4.0 52 I- 15-5 2.5 55 I- 19.5 4.0 sa I- 55.0 5.5 61 I- 32.5 7.5. 64 I- 38.5 b.0 b7 143.5 5.0 70 47.0 3.5 73 I- 51.0 4.0 76 I- 51.0 0.0 79 1- 53.5 2.5 12 1-.54.0 0.5 15 I- 54.09 0.0 88 1- 53.5 -0.5 91 -1.1 0.3 0.6
26、-0.3 -0.2 .: 1*.1II11-1.1.-.1 0.9 1.2 2.0. 1.7 1.8 0.8 1.3 1.1 1.3 1-3 0.1 -1-2 -1.0 -0.2 -0-9 -1.4 -1.9 -2.7. -1.4 -0.5 0.5 -1.0 -l.b -0-5 0.0 Fig. fb. RunoutPlot (GroundGear) Fig. 7a Index Plot (Ground Gear) 7 COPYRIGHT American Gear Manufacturers Association, Inc.Licensed by Information Handling
27、ServicesSTD-AGHA 95FTML-ENGL 1795 = Ob87575 0004b53 T55 risht 0.00: vu va 1 I I 1 sla i- sada 0.0200 0.0100 1 70.1 6 -11-5 5a.6 11 4-5 50.2 16 -3-4 46.7 21 -2.7 44.0 26 -5.0 39.0 31 -7.6 31.4 36 -10.4 21.0 41 -4.5 16.5 46 -6.5 10.0. 51 56 61 Lb 71 7b a1 a6 1 6 101 106 Ill 116 121 126 131 136 141 146
28、 151 156 1 5.6 15.6 0.2 15.9 8.3 24.2 12.5 36.7 11.7. 55.4 12.2 67.7 10.4 a6.9 12.2 9.2 -9 109.1 a.2 117.3 5.1 231.3 7.S 139.1 2.7 141.1 4.5 146.1 1.5 147.1- -3.8 144.0 4.7 139.3 g.3 131.D -25. 60105.4 -17.9 a7.5 -17.3 70.3 *.a 76.5 8.0 126.1 , wdiv Ml . lIlI vu 7, D9.7 o.0100 o.ww I- . -106 -114.4
29、-119.5 ,-132 - 5 -150.5 7152.9 -157.0 7157.1. -154.3 7148.2 ,-.114.a -140.3 l-133.1 ,-lU.O ,- 7.5 I- aa.3 ,- 44.5 I- 76.6 I- 64.7 ,-. 56.3 14.0 10.0. 12.2 I- 16.5 1- 52.3 I- 71.6 I- 2i.a sa.9 . l.!Ilt ?ice slot VU 17.0 6 7.6 11 0.5 16 4.7 21 11.0 26 7.a 11 10.2 36 2.4 41 4.0 46 0.1 51 -1.0 56 -6.1 6
30、1 -15.1 66 -19.19 71 -16.5 76 -9.2 a1 -11.6 I6 -ll. I -0.5 6 -11.a 101 -.i 106 -1.1 111 -0.) 116 -3.1 121 -5.1 126 -4.0 111 2.2 136 4.3 141 lD.3 146 25.5. 151 l.d 156 13.3 3 Fig. 8a. Index Plot (Hobbedgear) 5.13. Hobbed Gear. Figures 8a. and 8b. show &ta of a “hobbed only“ gear made on a machine tha
31、t had a badly worn final drive gear (worn wheel) on the workspindle. Again, only every fifth tooth is plotted for the reasons expressed in 5.1.2. above. 5.1.4. Phasing of Right and Lefi Flank Index Measurements. Figures 5a., 6a., 7a, and 8a. are plotted with the metal (teeth) shown on the right and
32、left side of the chart. The tooth space is represented as the gap shown between the plots of individual right and left tooth flanks. As noted in 2.2.7., Laskin, et al, 21 discusses the phase relationship between right and left flank index data for a gear produced with ordinary sinusoidal mout. The p
33、hase shift between the two sinusoidai index curves will be approximately twice the pressure angle at the standard pitch diameter. This is evident in Figure 5a Figure 5b. lists the calculated phase shift at the bottom of the chart. This has been underlined. The gear used for Figures 5 and 6 (before a
34、nd after shaving) had a standard pressure angle of 20 degrees. Hidden mout, however, yields an entirely different situation, as shown in 2.2.7. The right and left flank index mes have little or no phase shift (see Figures 6,7, and 8). It can also be seen that there is a nearly constant space width (
35、gap between the two index curves) for Figures 6a., 7a, and 8a. U*+ o.ooiw wdlr wt x1I11lx1 slot - -0.0200 -0.01 0.0 0.0100 0.0200 1- -1.4 . 6 G.2 11 -7.0 16 -3.4 *I 0: 0: *I 21 -4.7 26 -12.F 31 -11.3 36 -9.7 41 -6.2 *I 46 -2.1 51 4.9 56 -2.1 61 -4.1 66 4.4 71 0.8 76 53 a1 6.6 B6 1 6 101 106 111 116
36、121 126 131 136 141 146 151 156 7.) 7-2 5-1 8.1- LO 4.7 4.5 3.6 1-5 4.9 5.3 4.5 1.4 0.8 -1.3 Fig. 8b. Rumut Plot (Hobbed gear) Space width variation is evident in the charts with phase shift, while it remains constant in charts without phase shift. 5.1.5. Transmission Error Tests. Transmission error
37、 measurements (single flank composite test) of the shaved gear example are shown in Figure 9. The single flank total composite error (V J is .0042“. The accumulated pitch (VJ portion of the single flank composite error is .0037“. It can be seen that there is a direct relationship between index readi
38、ngs (accumulated pitch variation) and the single flank transmission error &ta (see Table 1). There is no relation between the transmission error tests and ordinary runout measurements (bail check) or double Bank TCE for this type of gear. Yet it is transmission mr that is functionally important. 6.0
39、. “FALSE“ CORRECTION of ONE FLANK by OFFSETTING ECCENTRICITY. Gears that have ordinary runout from eccentricity can be salvaged by a rework operation. This is done by determining the high point and amount of eccentricity and then producing a new bore or 8 COPYRIGHT American Gear Manufacturers Associ
40、ation, Inc.Licensed by Information Handling Services1 STD-AGMA 75FTML-ENGL L975 9 Ob87575 0004b54 771 D FIGURE 10. SINGLE FLANK TRANSMISSION ERROR TEST OF SHAVED GEAR SUMMARY OF INSPECTION RESULTS Gear Type Runout Ball Check v, shaved As Hobbed .0036“ After Shaving .00047“ Ground .00047“ Bobbed .002
41、“ 7.0. CONCLUSIONS. Double Sile ACC. Pitch Flank TCE Flank TCE Variation “Hidden runout“ unknowingly exists in many gears produced today. Think of how many shaved gears are produced for use in automobiles. It even happens in gears produced on some types of grinding machines where users expect the gr
42、eatest .0007“ .0042“ .o03 to .0034“ precision. One way to prevent it from happening, in these processes, is to control the runout before the finishing operation. v, v, v, .o037 to .0039“ .0007“ -0047 to .0049“ .O138 to .0147“ TABLE i journal that is concentric with the pitch circle of the teeth. Thi
43、s gear will now have very little runout or accumulated pitch variation. It will also have very little tooth thickness variation around the gear, as checked from the new bore location. However, this is not the case with a gear that has “hidden runout“. It would be possible to machine a new bore or jo
44、urnal that would reduce or eliminate the accumulated pitch variation on one side of the gear teeth, but there would now be runout (from eccentricity), tooth thickness variation, and accumulated pitch variation on the other sides of the gear teeth. The gear would have limited applications. It would b
45、e useful if it were to run in one direction only, and tooth thickness or backlash variation was not a concern. The most prevalent methods of runout control are the use of a ball check, over one pin test, or double flank composite TCE measurement. Yet these methods do not find “hidden runout“. The us
46、e of typical runout measurements are helpful during some stages of the manufacturing process, but they are not sufficient for the control of final gear quality. Index and transmission error measurements should become the prevalent methods of control for runout, “hidden runout“, and accumulated pitch
47、 variation. This provides the best control of the functional characteristics of a gear. The Standards of gear quality should not use runout as a measured parameter of quality level. They should speciQ the use of accumulated pitch variation. 9 COPYRIGHT American Gear Manufacturers Association, Inc.Li
48、censed by Information Handling ServicesSTD-AGHA 75FTML-ENGL 1995 D Ob87575 0004b55 828 A , - -. ACKNOWLEDGMENT. The author wishes to recognize the contribution of Lee Andrew (deceased), of the Garrett Corporation, who many years ago directed my attention to this subject which led to my undertaking t
49、his study and report. REFERENCES. i Bohle, F., “Toward More Economical Gear Inspection“, AGMA paper 239.05, 1957. 2 Laskin, I., Smith, RE., and Lawson, E., “Effect of Radial Runout on Element Measurements“, AGMA Technical Paper, 93FTM6 10 COPYRIGHT American Gear Manufacturers Association, Inc.Licensed by Information Handling Services
