1、April 2011 Translation by DIN-Sprachendienst.English price group 11No part of this translation may be reproduced without prior permission ofDIN Deutsches Institut fr Normung e. V., Berlin. Beuth Verlag GmbH, 10772 Berlin, Germany,has the exclusive right of sale for German Standards (DIN-Normen).ICS
2、25.060.99!$nOT“1754449www.din.deDDIN ISO 3408-5Ball screws Part 5: Static and dynamic axial load ratings and operational life(ISO 3408-5:2006)English translation of DIN ISO 3408-5:2011-04Kugelgewindetriebe Teil 5: Statische und dynamische axiale Tragzahl und Lebensdauer (ISO 3408-5:2006)Englische be
3、rsetzung von DIN ISO 3408-5:2011-04Vis billes Partie 5: Charges axiales statiques et dynamiques de base et dure de vie(ISO 3408-5:2006)Traduction anglaise de DIN ISO 3408-5:2011-04www.beuth.deDocument comprises pagesIn case of doubt, the German-language original shall be considered authoritative.170
4、3.11 A comma is used as the decimal marker. Contents Page National foreword .3 National Annex NA (informative) Bibliography.3 1 Scope 4 2 Normative references 4 3 Terms and definitions4 4 Symbols and subscripts .5 4.1 Symbols 5 4.2 Subscripts 6 5 Basic axial load ratings .7 5.1 Basic static axial lo
5、ad rating, C0a.7 5.2 Basic dynamic axial load rating, Ca.7 6 Modified axial load ratings8 6.1 Modified static axial load rating, C0am.8 6.1.1 General equation8 6.1.2 Correction for surface hardness, fh08 6.1.3 Correction for accuracy, fac9 6.2 Modified dynamic axial load rating, Cam9 6.2.1 General e
6、quation9 6.2.2 Correction for surface hardness, fh9 6.2.3 Correction for accuracy, fac9 6.2.4 Influence of material melting process, fm9 7 Life.10 7.1 Equivalent rotational speed and equivalent axial load 10 7.1.1 General10 7.1.2 Ball screw with backlash between ball nut and screw shaft.10 7.1.3 Bal
7、l screw with preloaded ball nuts on screw shaft 13 7.2 Nominal life, L or Lh.15 7.2.1 Ball screw with backlash between ball nut and screw shaft.15 7.2.2 Ball screw with preloaded ball nuts on screw shaft 16 7.2.3 Resulting life, Lr.16 7.2.4 Nominal life, Laror Lhar, with reliability factor, far(see
8、Table 3) .16 7.3 Modified life, Lmor Lhm17 7.3.1 Ball screw with backlash between ball nut and screw shaft.17 7.3.2 Ball screw with preloaded ball nuts on screw shaft 17 7.3.3 Modified resulting life, Lmr17 7.3.4 Modified life, Lmaror Lhmar, with reliability factor, far(see Table 3)17 2 DIN ISO 3408
9、-5:2011-04 National foreword This standard has been prepared by Technical Committee ISO/TC 39 “Machine Tools”, Working Group WG 7 “Ball screws”. The responsible German body involved in its preparation was the Normenausschuss Werkzeugmaschinen (Machine Tools Standards Committee). ISO 3408 consists of
10、 the following parts, under the general title Ball screws: Part 1: Vocabulary and designation Part 2: Nominal diameters and nominal leads Metric series Part 3: Acceptance conditions and acceptance tests Part 4: Static axial rigidity Part 5: Static and dynamic axial load ratings and operational life
11、The DIN Standard corresponding to the International Standard referred to in this document is as follows: ISO 3408-1 DIN ISO 3408-1 National Annex NA (informative) Bibliography DIN ISO 3408-1, Ball screws Part 1: Vocabulary and designation 3 DIN ISO 3408-5:2011-04 1 Scope This part of ISO 3408 specif
12、ies the calculation schemes for static and dynamic load ratings, and operational life, in order to obtain comparable values for the design and use of ball screws. NOTE The calculations have been based primarily on publications by Prof. G. Lundberg and A. Palmgren Acta Politechnica, mech. Eng. series
13、 Vol. I, No. 3, Stockholm, Sweden. Part 7, 1947. This part of ISO 3408 is applicable under the following preconditions: elastic deformation of ball and balltrack; hardness of balltrack basically exceeds a minimum of HRC 58; conformity frsand fr n 0,5; the quality of steel of which the ball screw is
14、made is equivalent to that of ball bearing steel or similar steel alloys; optimum lubrification is always provided. 2 Normative references The following referenced documents are indispensable for the application of this document. For dated references, only the edition cited applies. For undated refe
15、rences, the latest edition of the referenced document (including any amendments) ISO 3408-1, Ball screws Part 1: Vocabulary and designation 3 Terms and definitions For the purposes of this document, the terms and definitions given in ISO 3408-1 apply. Ball screws Part 5: Static and dynamic axial loa
16、d ratings and operational life 4 DIN ISO 3408-5:2011-04 4 Symbols and subscripts 4.1 Symbols Symbol Description Unit Contact angle degrees, Geometry factor Lead angle degrees, 11, 12, 21, 22Reciprocal curvature radii mm1l Axial ball / ball track deflection m CaBasic dynamic axial load rating N CamMo
17、dified dynamic axial load rating N CiDynamic axial load rating for the ball screw per single loaded turn N CnDynamic axial load rating for the ball nut per single loaded turn N CsDynamic axial load rating for the ball screw shaft per single loaded turn N C0aBasic static axial load rating N C0amModif
18、ied static axial load rating N DpwBall pitch circle diameter mm DwBall diameter mm facAccuracy factor farReliability factor fcGeometry factor fhHardness factor for dynamic axial load rating fh0Hardness factor for static axial load rating fmMaterial processing factor fopOperational preload factor fr
19、nConformity factor of ball nut frsConformity factor of ball screw shaft f1, f2, f3Geometry factor F Axial load, force NFaActual axial load N FlimLimit load at which contact between balls and ball tracks will be lost by operating load N FmEquivalent axial load N FmaEquivalent actual axial load N 5 DI
20、N ISO 3408-5:2011-04 Symbol Description Unit FprPreload N i Number of loaded turns k0Characteristic of basic static axial load rating L Life revolutionsLarLife with reliability factor revolutions LhLife h LharLife with reliability factor h LhmModified life h LhmarModified life with reliability facto
21、r h LmModified life revolutions LmarModified life with reliability factor revolutions LmrModified resulting life revolutions LrResulting life revolutions n Rotational speed min1nmEquivalent rotational speed min1PhLead mmq Time %rnBall track radius of ball nut mm rsBall track radius of ball screw sha
22、ft mm zlNumber of effectively loaded balls per turn zuNumber of unloaded balls in the recirculation system where balls are recirculated after one turn 4.2 Subscripts Symbol Description j Number of loadings 1 Refers to load direction 1 2 Refers to load direction 2 (1) Refers to ball nut 1 (2) Refers
23、to ball nut 2 6 DIN ISO 3408-5:2011-04 5 Basic axial load ratings 5.1 Basic static axial load rating, C0aThe basic axial load rating is calculated from the following equations: 20a 0 l wsin cosCkzi D = (1) pwluwintegercosDzzD=(2) hpwarctanPD=(3) ()()0w111221227,74kD =+(411 21w2D= (5) 12rs w1f D=(6)
24、22pwwcoscos22DD=(7) NOTE The calculation of the basic static axial load rating C0ais based on a maximum deformation of 0,000 1Dw. 5.2 Basic dynamic axial load rating, CaIn the case of optimal load distribution (parallel load directions in ball screw shaft and in ball nut), the basic dynamic axial lo
25、ad rating is derived from the following basic interrelations: 0,86a iCCi= (8) where 0,310 / 3ssn1iCCCC=+(9) with () ()0,86 1,32/3 1,8sc l wcos tan cosCf z D= (10) 0,41c12rs19,32112ffff=(11)7 DIN ISO 3408-5:2011-04 1sin10 13f=(12) ()()1, 3 90,321/ 311f=+(13) wpwcosDD = (14) 0,41rns3nrs1212fCfCf=(15)
26、nrnwrfD= (16) srswrfD= (17) 1, 7 2 3311f=+(18) zl, see Equation (2) 6 Modified axial load ratings 6.1 Modified static axial load rating, C0am6.1.1 General equation 0am 0a h0 acCCff= (19) 6.1.2 Correction for surface hardness, fh0A deviation in hardness has to be corrected by 3h0actual hardness HV101
27、654 HV10f=u (20)The hardness factors shall only apply to ball bearing steel or similar steel alloys. 8 DIN ISO 3408-5:2011-04 6.1.3 Correction for accuracy, facSee Table 1. Table 1 Accuracy factor, fac(reference data) Class 0, 1, 3 and 5 7 10 fac1 0,9 0,7 6.2 Modified dynamic axial load rating, Cam6
28、.2.1 General equation am ahacmCCfff= (21) 6.2.2 Correction for surface hardness, fh2hactual hardness HV101654 HV10f=u See paragraph immediately following Equation (20) (22) 6.2.3 Correction for accuracy, facThe correction for accuracy, fac, for dynamic axial load is the same as for static axial load
29、, see Table 1. 6.2.4 Influence of material melting process, fmSee Table 2. Table 2 Material factor, fm(reference data) Ball bearing steel fmAir melted 1,0 Vacuum degassed 1,25 Electro slag remelted 1,44 Vacuum remelted 1,71 If other than air melted steel is used, the ball screw supplier shall specif
30、y the selected melting process in the data sheets. 9 DIN ISO 3408-5:2011-04 7 Life 7.1 Equivalent rotational speed and equivalent axial load 7.1.1 General In the case of variable rotational speed and variable axial load, the equivalent values Fmand nmare used for the life calculation: At variable ro
31、tational speed the following applies for the equivalent rotational speed nm(see Figure 1): m1100njjjqnn=(23) At variable axial load and variable rotational speed, the following applies for the equivalent axial load Fm(see Figure 2): 33mm1100njjjjnqFFn=(24) At variable axial load and constant rotatio
32、nal speed, the following applies for the equivalent axial load Fm(see Figure 2): 33m1100njjjqFF=(25) Figure 1 Equivalent rotational speed nmFigure 2 Equivalent axial load Fm7.1.2 Ball screw with backlash between ball nut and screw shaft 7.1.2.1 Unidirectional external axial load applied See Figure 3
33、. 10 DIN ISO 3408-5:2011-04 Key 1 ball nut 2 screw shaft aForward travel. sBackward travel. Figure 3 Ball screw with backlash and unidirectional axial loading For calculation of equivalent axial load use Equation (23) and (24) or variable rotational speed, Equation (25) for constant rotational speed
34、. 7.1.2.2 Bidirectional external axial load applied See Figure 4. Key Key 1 ball nut 2 screw shaft aForward travel. sBackward travel. Figure 4 Ball screw with backlash and bidirectional axial loading 11 DIN ISO 3408-5:2011-04 For calculation of equivalent axial load, use Equation (23) for variable r
35、otational speed see Figure 5 a) 33m1,2 1,2m1100njjjjnqFFn=(26) for constant rotational speed see Figure 5 b) 33m1,2 1,21100njjjqFF=(27) a) Variable speed b) Bidirectional axial loading Figure 5 Calculation of equivalent axial load 12 DIN ISO 3408-5:2011-04 7.1.3 Ball screw with preloaded ball nuts o
36、n screw shaft See Figure 6. Key 1 ball nut (1) 2 ball nut (2) 3 screw shaft aFa(1) jbFa(2) jFigure 6 Preloaded ball screw Due to the application of an external axial load to a preloaded ball screw (backlash elimination between nuts and screw shaft), one ball nut will be additionally loaded and the o
37、ther relieved (see Figure 7). Key 1 ball nut (1) 2 ball nut (2) Figure 7 Preload diagram 13 DIN ISO 3408-5:2011-04 3/2lim pr2F F= (28) The preloaded ball nut (1) or (2) will be additionally loaded by an external axial load see Figure 8 b). The actual axial load to this ball nut is for the external l
38、oad 12limorjjF FFu , the following equation: 3/21, 2a(1),(2) op pr3/2op pr12jjFFfFfF=+op0,6f = (reference data) (29) NOTE Due to the fact that the preload decreases over the operational life of ball screws, the average operational preload is set to 60 % of the original preload. a(2),(1) a(1),(2) 1,2
39、jjjFFF= (30) for the external load 12limorjjF FF , then: a(1) 1 a(2) 2orjj j jF FF F= (31) and a(2) a(1)or 0jjFF= (32) For the calculation, use: a) at variable rotational speed see Figure 8 a) Equation (23) for equivalent rotational speed, for the equivalent actual axial load see Figure 8 c) and d)
40、33ma(1),(2) a(1),(2)m1100njjjjnqFFn=(33) b) at constant rotational speed 33ma(1),(2) a(1),(2)1100njjjqFF=(34)14 DIN ISO 3408-5:2011-04 a) Variable rotational speed b) to d) Variable axial loads Key 1 load direction 1 is loading ball nut (1) 2 load direction 2 is loading ball nut (2) a Resulting load
41、 for ball nut (1), caused by preload. b Resulting load for ball nut (2), caused by preload. Figure 8 Actual and equivalent actual axial loads 7.2 Nominal life, L or Lh7.2.1 Ball screw with backlash between ball nut and screw shaft 7.2.1.1 Unidirectional external axial load applied Life in revolution
42、s: 36am10CLF=(35.1) 15 DIN ISO 3408-5:2011-04 Life in hours: hm60LLn=(36.1) 7.2.1.2 Bidirectional external axial load applied Life in revolutions: 36a1,2m1,210CLF=(37.1) 7.2.2 Ball screw with preloaded ball nuts on screw shaft Life in revolutions: 36a1,2ma(1),(2)10CLF=(38.1) 7.2.3 Resulting life, Lr
43、The resulting life of the bidirectionally axial loaded ball screw with backlash or of the preloaded ball screw shall be calculated in revolutions: ()9/1010/9 10/9r1 2LL L=+ (39.1) In hours: see Equation (36.1). 7.2.4 Nominal life, Laror Lhar, with reliability factor, far(see Table 3) Life in revolut
44、ions: ar arL Lf= (40.1) respectively ar r arL Lf= (41.1) Life in hours: har h arL Lf= (42.1) Table 3 Reliability factor, farReliability % far90 1 95 0,62 96 0,53 97 0,44 98 0,33 99 0,21 16 DIN ISO 3408-5:2011-04 NOTE There are other factors reducing life, shock loads, vibrations, temperature, lubric
45、ation, misalignment etc., the consideration of which might be required. 7.3 Modified life, Lmor Lhm7.3.1 Ball screw with backlash between ball nut and screw shaft 7.3.1.1 Unidirectional external axial load applied Life in revolutions: 36ammm10CLF=(35.2) Life in hours: hmm60LLn=(36.2) 7.3.1.2 Bidirec
46、tional external axial load applied Life in revolutions: 36amm1,2m1,210CLF=(37.2) 7.3.2 Ball screw with preloaded ball nuts on screw shaft Life in revolutions: 36amm1,2ma(1),(2)10CLF=(38.2) 7.3.3 Modified resulting life, LmrThe resulting life of the bidirectionally axial loaded ball screw with backla
47、sh or of the preloaded ball screw shall be calculated in revolutions: ()9/1010/9 10/9mr m1 m2LL L=+ (39.2) Life in hours: see Equation (36.2). 7.3.4 Modified life, Lmaror Lhmar, with reliability factor, far(see Table 3) Life in revolutions: mar m arL Lf= (40.2) respectively mar mr arL Lf= (41.2) Life in hours: hmar hm arL Lf= (42.2) 17 DIN ISO 3408-5:2011-04
