1、 STD-AGHA SbFTMLL-ENGL L9Sb m b87575 000449 277 E 96FTM11 DIN 3996: ANew Standard for Calculating the Load Capacity of Worm Gears by: Prof. Dr.-Ing. Bernd-Robert Hhn and Dr.-Ing. Karl Steingrver, Gear Research Centre, FZG I I TECHNICAL PAPER STD-ALMA SbFTMLL-ENGL L99b Ob87575 U004950 T99 = DIN 3996:
2、 A New Standard or Calculating the Load Capacity of Worm Gears Prof. Dr.-Ing. Bernd-Robert Hhn and Dr.-Ing. Karl Steingrver, Gear Research Centre, FZG nie statements and opinions contained herein are those of the author and should not be comed as an official action.or opinion of the American Gear ma
3、nufacture Association. Abstract During the last years the load capacity of worm gears was raised about 30%. The reasons for this are the introduction of synthetic oiis, optimization of the worm gear geometry and manufacturing improvements. The forthcoming new standard DIN 3996 “Caldation of load cap
4、acity of cylindrical worm gear pairs takes into account these developments. This standard contains the following load capacily limits: wear, pitting, tooth breakage, temperature and worm deflection. Also, efficiency was taken into consideration. In most cases the calculation methods are based on res
5、uits of tecent investigations, which wen performed on worm gear test rigs at the FZG. In the case of wear, pitting and tooth breakage test results and their influence on DIN 3996 are shown. The caldation method for wear resistance is based on the fact that the wear intensity of a materiaulubricant c
6、ombination is a function of the lubricant fiim hicknes and the lubricant structure. The main influence parameter on pitting resistance is the Hertzian stress. For tooth root strength the caldation method is based on a nominal shear stress theory, in case of worm deflection on the deflection curve of
7、 a cylindrical shaft. The appiicaticm of this new standard for gears in practice is discussed by recaicuiating some examples. Copyright 0 1996 American Gear vanufacturers Association Alexandria, Virginia, 22314 1500 King street, suite 201 October, 1996 ISBN: 1-55589-678-2 STD-AGHA SbFTMLL-ENGL 177b
8、m b87575 0004951 925 DIN 3996: A new Standard for Calculating the Load Capacity of Worm Gears Bernd-Robert Hhn and Karl Steingrver Gear Research Centre, FZG, Germany 1 Introduction Modern worm gear drives are used more and more in heavy duty service, thus the knowledge of the load capacity limit is
9、important. The main load capacity limits of gear drives with worms made of case carburized steel and worm wheels made of bronze are wear, pittings, tooth breakage, and temperature (see Figure II. rotational speed n, _t Fig. 1 : Load Capacity Limits (acc. to II 1 /) as a Function of the Rotational Sp
10、eed Up to now in the case of worm gears, there was no German standard for calculating their load capacity. Other standards like B.S. 721 I91 and AGMA 6034-892 1101 have not been widespread in Germany. Many companies apply the calculation method published in 111. Now, a DIN standard, whereby in indus
11、try and university have cooperated together, for gear drives has been developed, which takes into consideration the improve- ments of worm gears during the last decades. The forthcoming new standard DIN 3996 “Calculation of load capaciy of cylindrical worm gear pairs“ takes into account the failure
12、limits mentioned above and also temperature. In the case of scuffing, research work has been not yet sufficiently carried out so as to introduce a reliable calculation method. I. 1 General Working Principle of DIN 3996 Although the calculation methods for the above mentio- ned kinds of damage have d
13、ifferent origins, the basic principle of the calculation procedures is the same for each type of damage: For a recalculation procedure the operating conditions must be given or specified. With the geometrical data and the operating conditions of the gear drive actual values of the respective criteri
14、on for the dif- -1- ferent types of damage can be calculated. These actual values are compared to limiting values. The result is a sa- fety factor S which can be determined acc. equation (1 l: limiting value actuai value S= If this safety factor shows low values a comparably high damage risk has to
15、be expected, a high safety factor means low risk of damage. This is similar to the proce- dure for spur and helical gears in DIN 3990 and IS0 6336 or bevel and hypoid gears in DIN 3991. 1.2 Field of Application In most cases the limiting values of the endurable loads have been determined in experime
16、nts with worm gears of different centre distances and different gear ratios. in these experiments the influence of various worm and wheel materials as well as different lubricants were investigated. The experiments were performed at the FZG (Forschungsstelle fr Zahnrder und Getriebebau, Tech- nical
17、University Munich). The results are documented in Ill, 121, 131, and 141. Further data on the load capacity is . based on the operating experience of industrial com- panies. The calculation methods presented in DIN 3996 can be used for gear drives with worm and wheel materiais and lubricants as list
18、ed below: Worm materiais: Case carburizing steel (e.g. 1 6MnCr51, case hardened Through hardening steel (e.g. 42CrMo4), flame or induction hardened * Nitriding steel (e.g. 31CrMoV91 Centrifugally cast bronze: (e.g. GZ-CuSnl2, Worm wheel materials: GZ-CuSn12Ni, GZ-CuAI1 ON). These bronzes should have
19、, as far as it is possible, a homogenous structure, the mean grain size should be below 150 pm. * Grey cast iron (e.g. GG-25) Spheroidal graphite iron (e.g. GGG-40) * Mineral oils containing mild additives Polyglycols with basic oil E0:PO =0:1 and 1 :1 lubricants: (EO alphaolefins Etylenoxyde, PO P
20、Propylenoxyde) and Poly- 2 Physical Parameters Although the physical reasons of the worm gear failures are not researched in every detail, their main influence parameters are known. Important influence parameters are the mean Hertzian stress uHm, the lubricant film thickness hminm and the sliding pa
21、th s,. Different worm gear drives cannot directly be compared by these parame- ters because these are influenced by working conditions, the materials of worm and wheel and the lubricant. In order to be able to compare the surface durability of worm gears, generalizing non-dimensional parameters are
22、defined, pi for the mean Hertzian stress, h* for the mean lubricant film thickness and s* for the mean sliding path. These relative parameters are independent of size, load, material and lubricant and thus only a function of the worm and wheel geometry. The derivations of these parameters are descri
23、bed in /7/ and 181. These physical parameters can be determined using numerical methods. Because these methods (computer programs) are rather complicated, relatively simple approximating equations can be used instead. The following approximations are described from 151. For cylindrical worm gears wi
24、th involute flank form they can be calculated from the equations (21 to (41: pm = 1.03 (0.4 + - X + 0.01 4 - 0.083.- b2H U mx 1 +- + q+5o*(u+l)/u 6.9 15.947.5 -4 h = 0.018+ 9 +-+- 1x U 7.864q + z2) z2 110 36300 (3) bJK7 370.4 em, 21 3.9 S = 0.78 + 0.21 *U + S.S/tan Y, (4) It is obvious, that these n
25、on-dimensional parameters only cover geometrical data. With these non-dimensional parameters and the working conditions the actual values of the Hertzian stress uHm, the lubricant film thickness hminm, and the sliding path s, can be calculated with equations (51 to (7). Tooth strength and shaft defl
26、ection are calculated directly, as usual. -2- STD-AGHA SbFTMLL-ENGL LS7b b87575 0004753 7TB red 4 the calculation of efficiency is based on results performed on a three disk machine (coefficient of friction) and on worm gear test rigs. In the theoretical investigations, non-dimensional physical para
27、meters were defined. With these parameters worm gear drives of different size and gear ratio can be com- pared directly. These parameters are implemented in the calculation methods for wear and surface durability. The calculation of the wear load capacity is based on the hypothesis, that the wear in
28、tensity of a materiaMubricant combination is a function of the lubricant film thickness and the lubricant structure. The main influence parameter on pitting is obviously the Hertzian stress. In the case of tooth root breakage, the calculation method is based on a nominal shear stress theory. Worm de
29、flection can be calculated approximately from the curve of a cylindrical shaft. The calculation procedures described in DIN 3996 were verified by recalculating worm gear drives of different sizes and different gear ratios. The results correspondend well with the experience and observations of the ma
30、nu- facturers. 1 O Nomenclature a centre distance mm b2, facewidth of wheel mm c, constant, used instead of the viscosity exponent m2/N df root diameter mm d, mean diameter mm h non-dimensional parameter - mean lubricant film thickness - hminm mean lubricant film thickness mm distance between bearin
31、gs of the worm mm abrasive wear mg/h axiale module mm rPm rotational speed non-dimensional parameter - mean Hertzian stress - Hertzian stress N/mm2 non-dimensional parameter - mean sliding path - mm tooth root chord sliding path mm gear ratio - nominal gear ratio sliding velocity m/s rack shift coef
32、ficient of wheel number of theeth - equivalent modulus of elasticity N/mm2 N tangential force wear intensity .I wear intensity of a material/lubricant combination - parameter - lubricant structure / film thickness - life h load cyle - kW actual input power kW rated input power Pm arithmetic surface
33、roughness diameter quotient, q = d,/m, - - safety factor - safety factor - tooth breakage safety factor - pitting -. safety factor - wear _- safety factor - worm deflection output torque Nm materialllubricant factor - wear - lubricant/structure factor - wear - geometry factor - coefficient of fricti
34、on tooth form factor - tooth breakage life factor - tooth breakage surface factor - coefficient of friction size factor - coefficient of friction material factor - coefficient of friction lead factor - tooth breakage gear ratio factor - tooth breakage life factor - pitting _- lubricant factor - pitt
35、ing - size factor - pitting -_ -. - _- . - - - -_ - - - - 11 - STD-AGHA SbFTHLL-ENGL 179b = Ob87575 OD049b2 700 speed factor - pitting pressure angle pitch angle mean Hertzian stress limiting value of the contact stress endurance limit of the contact stress angular velocity oil temperature efficienc
36、y dynamic viscosity at bulk temperature coefficient of friction (local) basic coefficient of friction mean coefficient of friction kinematic viscosity at 4OoC actual deflection limiting value of the deflection abrasive wear in the normal section mm K.: Friction and Efficiency of Worm Gears. 3eme Con
37、gres Mondial des Engrenages et des Transmis- sions, P. 235 - 245 (1992) /7/ Wilkesmann, H.: Berechnungvon Schneckengetrie- ben mit unterschiedlichen Zahnprofilformen. Diss. TU Mnchen (1 974) Predki, W.: Herttsche Drucke, Schmierspalthhen und Wirkungsgrade bei Schneckengetrieben. Diss. Ruhr-Universit
38、t Bochum (1 982) /9/ British Standards Institution: Specification for Worm Gearing. BS 721 (1984) i1 O/ Manufacturers Associaton: AMERICAN NATIONAL STANDARD - Practice for Enclosed Cylindrical Wormgear Speed Reducers and Gear- motors. AGMA 6034892 (1 992) /I 1 1 Predki, W.: Stand der Schneckengetrie
39、beentwick- lung. Konstruktion 43 (1991) S. 233-238 /8/ 6,imnpermissible wear mm 12 Appendix 7F nominal shear stress N/mm2 7Flim shear endurance limit N/mm2 7FG N/mm2 Subscripts should be known. In the following a calculation acc. DIN 3996 is shown by a step-by-step process for example II. Besides th
40、e data listed in Table 5 and in Chapter 8.1 the following data limiting value of the shear stress 1 2 m 11 /1/ 121 /3/ /4/ /5/ /6/ worm limiting value worm wheel normal section mean value transverse section References Niemann, G.; Winter, H.: Maschinenelemente 111,2. Auflage. Springer Verlag, Berlin
41、, Heidelberg, New York, Tokyo (1983) Huber, G.: Untersuchungen ber Flankentragfhig- keit und Wirkungsgrad von Zylinderschnecken- getrieben. Diss. TU Mnchen (1 978) Mathiak, D.: Untersuchungen ber Flankentrag- fhigkeit, Zahnfutragfhigkeit und Wirkungsgrad von Zylinderschneckengetrieben (Evolventen- S
42、chnecken). Diss. TU Mnchen (1 984) Neupert, K.: Verschleitragfhigkeit und Wirkungs- grad von Zylinder-Schneckengetrieben. Diss. TU Mnchen (1 990) Steingrver, K.: Untersuchungen zu Verschlei, Verlustgrad und Fressen bei Zylinder-Schneckenge- trieben. Diss. TU Mnchen (1 993) Winter, H.; Hhn, B.-R.; Mi
43、chaelis, K.; Steingrver, pressure angle: a! (dmj = m, * q) mean diameter of the worm: d, mean diameter of the wheel: dm2 (dm2 = 2 -a-dml) root diameter of the wheel: df2 rack shift coefficient of wheel: x . arithmetic surface roughness distance between bearings equivalent modulus of elasticity: dyna
44、mic viscosity at constant for the viscosity exponent facewidth of the wheel: b2H of the worm: Ra of the worm: Il bulk temperature: VOM - polyglycol: Ca (- mineral oil: Ca = 20 O = 60 mm = 300 rnm = 285.6 mm = 45 mm =o = 0.5 pm = 290.5 mm = 150622 N/IIUII = 0.045 Ns/m2 = 1.3 = 1.7 loe8) Basic calcula
45、tions: mean sliding velocity: vgm = (dml i 2 * nl) / (9550 6 cos y) vgm = (60 / 2 - 500) i (9550 cos 7 1.3) = 1.6 m/s - 12- STD-AGMA SbFTMLL-ENGL L7Sb I Ob87575 00047b3 b47 M tangential force at the wheel: Ftm2 = 2000 FtmP = 2000 T2 I dm2 2850 I 300 = 19000 N number of load cycles at the wheel: NL =
46、 i, e60 en, /u NL = 25000.60 * 500 I25 = 30 lo6 Nondimensional parameters: parameter pm* for the mean Hertzian stress acc. equation (21: pm* = 1 .O3 (0.4 + x/u + 0.01 z2 - 0.08342H/m, + (2q-1 )0-5/6.9 + (q +50.(u + 1 )/u) / (15.9+37.5q) + (2.70-1 )OS5/6.9 + (lo+ 50G5 + 1)/25) I (15.9+37.5*10) = 1.1
47、pm* = 1 .O3 (0.4 + 0125 + 0.01 -50 - 0.08345/6 parameter h* for the mean lubricant film thickness acc. equation (3): h* = 0.018 -k q/(7.86-(q+z2) + 1/z2 + 1110 h* = 0.018 + 10/(7.86-(10+2) + 1/50 + O1110 - 25136300 + 45/(370.4.6) - (2-10-l)0.5/21 3.9 - u136300 + b2/(370.4m,) - (2q-1)o-5/213.9 = 0.05
48、8 parameter so for the mean sliding path acc. equation (4): s* = 0.78 + 0.21 il + 5.6jtan -ym P* = 0.78 + 0.21-25 + 5.61tan 17.3 = 34.06 Hertzian stress, lubricant film thickness and sliding path: mean Hertzian stress acc. eauation (5): ,Hm = 4iT - (pm* - ,-i o3 - i a3)0.5 = 4/a (I. 1 2850.103 * 150
49、622 1 1803)0.5 uHm = 362.3 N/mm2 mean lubricant film thickness acc. equation (6): hminm = 21 * h* caoe6 - lOMO” hminm = 21 * 0.058 .( I.3-ItT8)06 * 0.045*7 . a1.39 . E 0.03 0.13 red 7801.39 750622.03 I 2850O. = O. 139 pm Efficiency: basic coefficient of friction acc. Fig. 3: po = 0.027 (vgm = 1.6 m/s, lubrication with poly- glycol E0:PO =0:1) size factor acc. equation (9): Y, = 100 1 aloa5 Y, = 100 I 180)0.5 = 0.75 geometry factor acc. equation (1 O): Y, = (0.07 I 0.
