AGMA 918-A93-1993 Summary of Numerical Examples Demonstrating the Procedures for Calculating Geometry Factors for Spur and Helical Gears《直齿轮和螺旋齿轮用计算几何系数的数字示例演示程序摘要》.pdf

1、. AGMA 918-A93 , a/ c= Reproduced By GLOBAL AGMA 1012-F90, Gear Nomenclature, Definitions of Terms with, Symbols. 2.2 Symbols The symbols used in the geometry factor formulas are shown in table 1. NOTE - The symbols, definitions and terminology used in this information sheet may differ from other AG

2、MA documents. The user should not assume that familiar symbols can be used without a careful study of these definitions. Units of measure are not shown in table 1 because the equations are in terms of unity normal module or unity normal diimetral pitch. AGMA 919-A93 Symbols C %L - blpo %r 4hs hlW +r

3、 w vb yr co 0 tool 1 pinion 2 gear Terms angular displacement of gear angular displacement of tool distance from pitch point to points “F and “S angle to center “S” of tool tip radius auxiliary angle locating point “s” abscissa of criiical point “F radii of curvature of profiles at point of contact

4、stress calculation radii of curvature of profile at mean radius tool tip radius minimum radius of curvature of fillet curve standard transverse pressure angle standard normal pressure angle generating pressure angle iteration value for generating pressure angle load angle pressure angle at radius wh

5、ere tool tooth is pointed operating normal pressure angle pressure angle at point “s” on tool pressure angle at load application point operating transverse pressure angle standard helix angle base helix angle operating helix angle angle of inclination of helical contact line Subscripts n normal or v

6、irtual spur gear r 0 El erating or running sence of a subscript indicates transverse 3 Numerical examples Eleven numerical examples, based on actual gear- sets, are presented to demonstrate the calculation of both geometry factors, I and J, using the proce- dures outlined in AGMA 908-B89. 3.1 .l Acc

7、urate spur gears This example demonstrates a spur gearset which meets the criteria of table 5-l in AGMA 908-B89 for load sharing and is therefore considered loaded at the highest point of single tooth contact. 3.12 Inaccurate spur gears 3.1 Examples The following examples were selected to illustrate

8、 the various types of gearing and geometry features found in most of todays gearing. This example, which uses the same geometry as 3.1 .l, does not meet the criteria in table 5-l of AGMA go 0.014910 0.014910 0.014910 - cp“- 0.349386 - nz 0.358675 0.349112 fb“ n(i +l) 0.349386 0.349112 0.349111 - Var

9、iable 1 a Pn no K S P If c.F P UT Y IYl ant 0.785398 0.000187 -1.325365 -1.761865 0.099917 0.685481 1.179814 24.257896 1.142721 4.452621 0.689143 0.689143 0.630626 Pinion: iteration for critical point 2 3 4 0.630626 0.605889 0.605442 0.000257 0.000270 0.000271 -1.589244 -1.645464 -1.646525 -2.025744

10、 -2.081964 -2.083025 0.113499 0.116204 0.116255 0.517127 0.489685 0.489187 1.127191 1.119292 1.119150 24.334854 24.349198 24.349464 1.065763 1.051418 1.051153 3.441053 3.322607 3.320554 0.085121 0.001485 0.000000 0.085121 0.001485 0.000000 0.605889 0.605442 0.605442 Gear: iteration for generating pr

11、essure angle 6 Variable 1 2 3 4 5 6 inv $; 0.014894 0.014894 0.014894 v- 0.358546 0.349263 0.348989 nl v - n(i +l) 0.349263 0.348989 0.348988 Gear: iteration for critical point Variable 1 2 3 4 5 6 an ho CS 9 (32 Bn GlF %F k Y Y IYl %i 0.785398 0.586171 0.541381 0.539939 0.539938 0.000232 0.000349 0

12、.000386 0.000387 0.000387 -1.641409 -2.097854 -2.251830 -2.257242 -2.257248 -2.077909 -2.534354 -2.688330 -2.693742 -2.693748 0.053295 0.064581 0.068083 0.068205 0.068205 0.732103 0.521590 0.473298 0.471734 0.471733 1.224450 1.158420 1.144696 1.144259 1.144259 50.535758 50.627373 50.652661 50.653515

13、 50.653516 1.239255 1.147640 1.122352 1.121498 1.121497 5.034538 3.586125 3.374076 3.367760 3.367754 1.003017 0.160620 0.004867 0.000005 0.000000 1.003017 0.160620 0.004667 0.000005 0.000000 0.586171 0.541381 0.539939 0.539938 0.539938 AGMA 916-A93 Table 2B - Accurate spur gears , example 3.1.1 Gear

14、set Pinion mn = 0.2WOW q = 51 on = 20.0000 n,1 = lWO0 Input data g +“ni m” r,“0 = 5Wo.W0000 ni = 4698.463104 mG = 5W1.02OWO To1 = 0.349626 R,l = o.ol4wg R,:! = 1.570796 T1 = 0.015061 R1 an kzo KS KF ;: h?.F %F hF Y Y “nl pF co ch SF H L M 9 3f = -0.WOW8 = 0.014910 = 0.349111 = 25.500422 = 5000.08273

15、7 = 0.605442 = 0.00027 1 = -1.646525 = -2.083025 = 0.116255 = 0.489187 R2 Rbl cfl x Asn nC h a0 X0 Pa0 6 a0 = 104.000000 = 0.490385 = 26.612500 = 52.887000 = 26.612500 = 25.5WWO = 52.OWWO = 25.5WWO = 48.864016 = 17.881130 = -0.112700 = 0.0215oo = 10000.000000 = 1.456500 = o.owwo = 0.436500 = 0.00990

16、0 1.119150 24.349464 1.051153 3.320554 o.wowo 0.605442 0.469891 0.000000 1 .ooowo 2.238300 0.18OWO 0.150ooo 0.45owo 1.955632 1 .wowo J factor aear n = 104.000000 rn = 52.OWWO nb = 48.864016 cn4 = - n2 = nb2 = - na2 = c,6 = - C nl = - na = fN)nW= 0.365937 5 = -0.142235 sn = 1.467257 +: LF qnF hF Y Y

17、anl pF 0 ch SF H L M 9 KY Y J = -Q.OOWO8 = 0.014894 = 0.348988 = 51.998536 = 4999.859214 = 0.539938 = 0.000387 = -2.257248 = -2.693743 = 0.068205 = 0.471733 = 1.144259 = 50.653516 = 1.121497 = 3.367754 = 0.000000 = 0.539938 = 0.462105 = o.ooww = 1 .ooww = 2.288518 = 0.18WW = 0.15ww = 0.45ww = 1.9323

18、15 = 1 .ooww = 0.879759 = 0.46 7 AGMA 919-A93 Table 3A - inaccurate spur gears , example 3.1.2 Pinion: iteration for generating pressure angle Variable 1 2 3 4 5 6 inv 41; 0.014910 0.014910 0.014910 0“. 0.358675 0.349386 0.349112 - nr v n(i +l) 0.349386 0.349112 0.349111 - Pinion: iteration for crit

19、ical point Variable 1 2 3 4 5 6 a 0.785398 0.493311 0.415646 0.413704 0.413704 - cl 0.000187 0.000348 0.000424 0.000427 0.000427 - K -1.325365 -1.978607 -2.320097 -2.330343 -2.330347 - S 3 -1.761865 0.099917 -2.415107 0.131500 -2.756597 0.146393 -2.766843 0.146832 -2.766847 0.146833 - s“ 0.685481 0.

20、361811 0.269253 0.266872 0.266871 - CF 1.179814 1.084906 1.062498 1.061951 1.061951 liti 24.257896 2.180642 24.425387 2.013150 24.494373 1.944165 24.496365 1.942173 24.496365 1.942172 - Y“; 8.171188 5.651664 5.408071 5.404076 5.404074 - Y 2.386698 0.438935 0.010502 O.OOQOQ4 0.000000 - IYl 2.386698 0

21、.438935 0.010502 0.000004 0.000000 - an1 0.493311 0.415646 0.413704 0.413704 0.413704 - Gear: iteration for generating pressure angle Variable 1 2 3 4 5 6 inv ; 0.014894 0.014894 0.014894 c#Y. 0.358546 0.349263 0.348989 ?u v n(i +l) 0.349263 0.348989 0 348988 Gear: iteration for critical point Varia

22、ble 1 2 3 4 5 6 an 0.785398 0.471085 0.368409 0.364454 0.364451 bw 0.000232 0.000456 0.000601 0.000608 0.000608 - % -1.641409 -2.556479 -3.220720 -3.254026 -3.254052 - KF -2.077909 -2.992979 -3.657220 -3.690526 -3.690552 - en 0.053295 0.074778 0.088748 0.089434 0.089435 - Vni 4 Go = 5000.000000 n1 =

23、 4698.463104 mG = 5001.020000 T,l = 0.349626 Rol = 0.01 4979 4, = 1.570796 T1 ,= o.015061 R1 an ko KS KF en pn %lF %.F hF Y Y anl pF w ch SF H L M Kf KY = -o.oooou8 = 0.014910 = 0.349111 = 25.500422 = 5000.082737 = 0.413704 = 0.000427 = -2.330347 = -2.766847 = 0.146833 = 0.266871 R2 Rbl c4 n Asn nC

24、h a0 X0 Pa0 6 a0 = 104.000000 = 0.490385 = 26.612500 = 52.887000 = 26.612500 = 255OOOOO = 52.OOOOOO = 25.500000 = 48.864016 = 17.881130 = -0.112700 = 0.0215oo =1oooo.oooooo = 1.456500 = 0.000000 = 0.436500 = 0.009900 1.061951 24.496365 1.942172 5.404074 0.000000 0.413704 0.469891 0.000000 1.000000 2

25、.123901 0.180000 0.150000 0.450000 1.485424 1.000000 J factor aear n = 104.000000 rn = 52.OOOOOO nb = 48.864016 C n4 = - rn2 = - nb2 = - na2 = c,fj = - C,l = - ma = 52.887000 mn4nW= 0.414051 xg = y-:5; sn = . $d = 0.385039 rnL nO no nbo rs no + ns hv+ns sno inV$npo hns I2 in;, +Li ri Go an f-G20 KS

26、KF en Pn LZF ln.F hF Y Y “nl PF w ch SF H L M Kf KY Y J = 52.724286 =1oooo.oooooo = 5ooo.ooamo = 4698.463104 = 5001.020000 = 0.349626 = 0.014979 = 1.570796 = 0.015061 = -0.000008 = 0.014894 = 0.348988 = 51.998536 = 4999.859214 = 0.364451 = 0.000608 = -3.254052 = -3.690552 = 0.089435 = 0.275016 = 1.0

27、92424 = 50.788502 = 1.935784 = 5.208114 = o.oooooo = 0.364451 = 0.462105 = 0.000000 = 1.000000 = 2.184848 = 0.18OOOO = 0.150000 = 0.45oooo = 1.513080 = 1.oooooo = 0.451108 = 0.30 9 AGMA 919-A93 Table 4A - Conventional helical gears, example 3.1.3 Pinion: iteration for generating pressure angle Varia

28、ble 1 2 3 4 5 6 inv ; 0.014937 0.014937 0.014937 $“- 0.358888 0.349589 0.349314 - Ill $” n(i +l) 0.349589 0.349314 0.349313 Pinion: iteration for critical point Variable 1 2 3 4 5 6 a 0.785398 0.530778 0.484332 0.483773 co 0.000102 0.000174 0.000194 0.000194 K -0.801380 -1.119323 -1.216848 -1.218144

29、 s P -1.210580 0.186208 -1.528523 0.220419 -1.626048 0.229993 -1.627344 0.230119 $I;zi r; GO an kzo KS KF ;I LF qn.F hF Y Y “nl pF 0 ch sF H L M 9 KY Y J = -0.000006 = 0.014902 = 0.349050 = 47.712763 = 5547.995640 = 0.366645 = 0.000516 = -3.064981 = -3.474181 = 0.093552 = 0.273093 = 1.111685 = 46.56

30、7098 = 1.984505 = 5.325507 = 0.000000 = 0.366645 = 0.434174 = 5.236189 = 1.286597 = 2.223369 = 0.180000 = 0.15OoOO = 0.450000 = 1.524664 = 0.932426 = 0.558144 = 0.54 11 Table 5A - Low axial contact ratio (LACR) helical gears, example 3.1.4 Pinion: iteration for generating pressure angle Variable 1 2

31、 3 4 5 6 inv ; 0.014937 0.014937 0.014937 - $“* 0.358888 0.349589 0.349314 - nl 9” - - n(i +l) 0.349589 0.349314 0.349313 Pinion: iteration for critical point Variable 1 2 3 4 5 6 a 0.785398 0.664320 0.651858 0.651758 Pn 0.000102 0.000130 0.000134 0.000134 no K -0.801380 -0.919094 -0.934027 -0.93414

32、9 s 3 -1.210580 0.186208 -1.328294 0.199679 -1.343227 0.201299 -1.343349 0.201312 P“ 0.599190 0.464641 0.460559 0.450446 CF 1.157476 1.123738 1.120528 1.120502 TlF 10.767751 10.825179 10.831698 10.831751 - hF 1.222488 1.165060 1.158541 1.158488 Y 4.231279 3.548075 3.492580 3.492145 Y 0.512316 0.0442

33、17 0.000348 0.000000 - IYl 0.512316 0.044217 0.000348 0.000000 an1 0.664320 0.651858 0.651758 0.651758 Gear: iteration for generating pressure angle Variable 1 2 3 4 5 6 inv Q; 0.014902 0.014902 0.014902 t$“- 0.358611 0.349324 0.349050 - m 0” n(i +l) 0.349324 0.349050 0.349050 Gear: iteration for cr

34、itical point Variable 1 2 3 4 5 6 an 0.785398 0.541421 0.476957 0.474521 0.474518 - lllzo 0.000198 0.000329 0.000383 0.000386 0.000386 - Ks -1.554759 -2.132880 -2.394107 -2.405443 -2.405456 - KF -1.963959 -2.542080 -2.803307 -2.814643 -2.814656 - en 0.056632 0.071897 0.078164 0.078431 0.078432 - Pn

35、0.728766 0.469524 0.398793 0.396090 0.396087 - LF 1.235535 1.160451 1.142289 1.141610 1.141609 - %.F 46.328373 46.439304 46.478542 46.480158 46.480160 - hF 1.516735 1.405803 1.366566 1.364950 1.364948 - Y 6.035126 4.127370 3.848488 3.839332 3.839321 - Y 1.472435 0.266065 0.009375 0.000011 0.000000 -

36、 IYl 1.472435 0.266065 0.009375 0.000011 0.000000 - ani 0.541421 0.476957 0.474521 0.474518 0.474518 - 12 AGMA 916-A93 Table 5B - Low axial contact ratio (LACR) helical gears, example 3.1.4 Input data Gearset Pinion m mn = 0.166667 q = 21 ; Vni ri 60 = 0.014937 Rbl = 0.349313 C4 = 11.651910 X = 5S8.

37、528439 A Sn O1n Clno KS KF en bz LF %F hF Y Y “nl pF Co ch SF H L M Kf % 0.651758 nc 0.000134 ha0 -0.934149 x0 -1.343349 Pa0 0.201312 ijao 0.450446 = 86.OOOOOO = 0.244186 = 12.400175 = 45.518909 = 12.400175 = 10.870400 = 44.516876 = 10.8704oO = 41.657612 = 16.904890 = 0.000000 = 0.024000 =1oooo.oooo

38、oo = 1.476000 = 0.000000 = 0.409200 = 0.006100 1.120502 10.831751 1.158463 3.492145 0.000000 0.651758 0.435535 5.236189 1.000000 2.241005 0.180000 0.15oooo 0.45oooo 1.900525 1.000000 J factor aear n = 95.426087 rn = 47.713044 nb = 44.835595 Cn4 = 17.382131 n2 nb2 na2 cn6 cnl = 11.650859 = 10.948227

39、= 13.180635 = 21.769309 = 14.430000 na = QNnW= 0.387686 4$li ri GO an hlo KS KF ;: hlF q?lF hF Y Y anl pF co ch sF H L M Kf KY Y J = 47.845108 = 11096.056659 = 5548.028330 = 5213.441281 = 5549.095130 = 0.349594 = 0.014974 = 1.570796 = 0.015046 = -0.000006 = 0.014902 = 0.349050 = 47.712763 = 5547.995

40、640 = 0.474518 = omo386 = -2.405456 = -2.814656 = 0.078432 = 0.396087 = 1.141609 = 46.480160 = 1.364948 = 3.839321 = 0.000000 = 0.474518 = 0.434174 = 5.236189 = 1.000000 = 2.283219 = 0.18OOOO = 0.15oooo = 0.45oooo = 1.796876 = 1.000000 = 0.706122 = 0.52 13 Table 6A - Conventional helical gears, diff

41、erent tools, example 3.1.5 Pinion: iteration for generating pressure angle Variable 1 2 3 4 5 6 inv I$; 0.014923 0.014923 0.014923 cp“- 0.358773 0.349479 0.349204 nz v n(i +l) 0.349479 0.349204 0.349204 Pinion: iteration for critical point Variable 1 2 3 4 5 6 a 0.785398 0.489843 0.423246 0.422544 c

42、 0.000161 0.000301 0.000356 0.000357 K -1.428714 -2.146816 -2 A58926 -2.462757 S 3 -1.548714 0.108435 -2.266816 0.148603 -2 0.164394 578926 -2.582757 0.164585 k 0.676963 0.341240 0.258852 0.257959 CF 1.174504 1.122203 1.108587 1.108439 IIg Y %i G GO an %zo KS KF en fin %lF qnF hF Y Y anl pF w ch SF

43、H L M Kf % Y J 19 AGMA 918-A93 Table 9A - Helical sun and planet gear, example 3.1.8 Pinion: iteration for generating pressure angle Variable 1 2 3 4 5 6 inv $; 0.030017 0.030017 0.030017 $“. 0.451838 0.437112 0.436527 tll v n(i +l) 0.437112 0.436527 0.436526 Pinion: iteration for critical point Var

44、iable 1 2 3 4 5 6 a 0.785398 0.550858 0.516528 0.516292 Pn 0.000092 0.000150 0.000163 0.000163 n0 K -0.755647 -1.020756 -1.081818 -1.082267 S P -0.845647 0.183552 -1.110756 0.215756 -1.171818 0.222565 -1.172267 0.222614 - s“ 0.601846 0.335102 0.293964 0.293678 - CF 1.203951 1.180769 1.177409 1.17738

45、6 P YT 2.003974 9.761434 9.808402 1.957006 9.818742 1.946666 9.818818 1.946590 6.604027 5.308212 5.241281 5.240928 Y 1.548908 0.182230 0.001237 0.000000 IYl 1.548908 0.182230 0.001237 0.000000 ani 0.550858 0.516528 0.516292 0.516292 - Gear: iteration for generating pressure angle Variable 1 2 3 4 5

46、6 inv $; 0.026131 0.026131 0.026131 - $“* 0.431629 0.418269 0.417773 - Cli +I) 0.418269 0.417773 0.417772 Gear: iteration for critical point Variable 1 2 3 4 5 6 Cr, 0.785398 0.532078 0.480780 0.479829 0.479829 - blo 0.019982 0.033342 0.037361 0.037442 0.037442 - KS -0.595631 -0.815390 -0.887999 -0.

47、889483 -0.889484 - 9 -0.775631 -0.995390 -1.067999 -1.069483 -1.069484 - != - cy = 1.000000 I = 0.146 G6 pinion nl = 18.000000 ROI = 10.938611 RI = 9.448671 Rbl = 8.486309 Cd = 6.471560 x = 0.542000 Asn = 0.018000 nC =10000.000000 h, = 1.146000 x0 = 0.000000 Pm = 0.090000 sao = 0.000000 J factor pin

48、ion n = 20.828460 rn = 10.414230 rnb = 9.488498 C n4 = - rn2 = nb2 = na2 = +j = - C nl = - ma = 11.904170 mOnW= 0.768580 xg = 0.522699 n %.L r2.L nO no nbo GO ns inV4%s sno inv%zpo hns I2 iIN; “ni r?i riY0 Orn ho KS KF en pn Gl.F Q2.F hF Y Y anl pF 0 ch SF H L M Kf KY = 2.058274 = 0.639785 = 11.7654

49、08 =11571X6413 = 5785.683206 = 5243.609743 = 5786.739206 = 0.436723 = 0.030060 = 1.570796 ,= 0.030111 = 0.000033 = 0.030017 = 0.436526 = 10.415169 = 5786.204859 0.516292 0.000163 -1.082267 -1.172267 0.222614 0.293678 1.177386 9.818818 1.946590 5.240928 0.000000 0.516292 0.116121 7.694021 1.363320 2.354772 0.14oOOo 0.110000 0.500000 1.671480 0.903789 Y = 0.801215 J = 0.55 aear G6 n1 mG %l Rol Ro2 T1 Rl R2 Rbl c, x Asn nc ha0 X0 Pa0 6 a0 = 24.000000 = 0.750000 = 10.938611 = 13.911314 = 10.938611 = 9.448671 = 12.598228 = 9.448671 = 11.315079 = 7.66