1、 g49g50g3g38g50g51g60g44g49g42g3g58g44g55g43g50g56g55g3g37g54g44g3g51g40g53g48g44g54g54g44g50g49g3g40g59g38g40g51g55g3g36g54g3g51g40g53g48g44g55g55g40g39g3g37g60g3g38g50g51g60g53g44g42g43g55g3g47g36g58ICS 25.060.99 Ball screws Part 5: Static and dynamic axial load ratings and operational lifeBRITISH
2、 STANDARDBS ISO 3408-5:2006BS ISO 3408-5:2006This British Standard was published under the authority of the Standards Policy and Strategy Committee on 29 September 2006 BSI 2006ISBN 0 580 49280 XAmendments issued since publicationAmd. No. Date Commentscontract. Users are responsible for its correct
3、application.Compliance with a British Standard cannot confer immunity from legal obligations. National forewordThis British Standard was published by BSI. It is the UK implementation of ISO 3408-5:2006.The UK participation in its preparation was entrusted to Technical Committee MTE/1, Machine tools.
4、A list of organizations represented on MTE/1 can be obtained on request to its secretary.This publication does not purport to include all the necessary provisions of a Reference numberISO 3408-5:2006(E)INTERNATIONAL STANDARD ISO3408-5First edition2006-06-15Ball screws Part 5: Static and dynamic axia
5、l load ratings and operational life Vis billes Partie 5: Charges axiales statiques et dynamiques de base et dure de vie BS ISO 3408-5:2006ii iiiContents Page Foreword iv 1 Scope . 1 2 Normative references . 1 3 Terms and definitions. 1 4 Symbols and subscripts 2 4.1 Symbols . 2 4.2 Subscripts . 3 5
6、Basic axial load ratings 4 5.1 Basic static axial load rating, C0a4 5.2 Basic dynamic axial load rating, Ca4 6 Modified axial load ratings. 5 6.1 Modified static axial load rating, C0am5 6.1.1 General equation. 5 6.1.2 Correction for surface hardness, fh0. 5 6.1.3 Correction for accuracy, fac. 6 6.2
7、 Modified dynamic axial load rating, Cam. 6 6.2.1 General equation. 6 6.2.2 Correction for surface hardness, fh6 6.2.3 Correction for accuracy, fac. 6 6.2.4 Influence of material melting process, fm. 6 7 Life 7 7.1 Equivalent rotational speed and equivalent axial load. 7 7.1.1 General. 7 7.1.2 Ball
8、screw with backlash between ball nut and screw shaft 7 7.1.3 Ball screw with preloaded ball nuts on screw shaft . 10 7.2 Nominal life, L or Lh12 7.2.1 Ball screw with backlash between ball nut and screw shaft 12 7.2.2 Ball screw with preloaded ball nuts on screw shaft . 13 7.2.3 Resulting life, Lr13
9、 7.2.4 Nominal life, Laror Lhar, with reliability factor, far(see Table 3) 13 7.3 Modified life, Lmor Lhm. 14 7.3.1 Ball screw with backlash between ball nut and screw shaft 14 7.3.2 Ball screw with preloaded ball nuts on screw shaft . 14 7.3.3 Modified resulting life, Lmr. 14 7.3.4 Modified life, L
10、maror Lhmar, with reliability factor, far(see Table 3). 14 BS ISO 3408-5:2006iv Foreword ISO (the International Organization for Standardization) is a worldwide federation of national standards bodies (ISO member bodies). The work of preparing International Standards is normally carried out through
11、ISO technical committees. Each member body interested in a subject for which a technical committee has been established has the right to be represented on that committee. International organizations, governmental and non-governmental, in liaison with ISO, also take part in the work. ISO collaborates
12、 closely with the International Electrotechnical Commission (IEC) on all matters of electrotechnical standardization. International Standards are drafted in accordance with the rules given in the ISO/IEC Directives, Part 2. The main task of technical committees is to prepare International Standards.
13、 Draft International Standards adopted by the technical committees are circulated to the member bodies for voting. Publication as an International Standard requires approval by at least 75 % of the member bodies casting a vote. Attention is drawn to the possibility that some of the elements of this
14、document may be the subject of patent rights. ISO shall not be held responsible for identifying any or all such patent rights. ISO 3408-5 was prepared by Technical Committee ISO/TC 39, Machine tools. ISO 3408 consists of the following parts, under the general title Ball screws: Part 1: Vocabulary an
15、d 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 BS ISO 3408-5:20061Ball screws Part 5: Static and dynamic axial load ratings and
16、 operational life 1 Scope This part of ISO 3408 specifies 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. Lundber
17、g and A. Palmgren Acta Politechnica, mech. Eng. series 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
18、 0,5; the quality of steel of which the ball screw is 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 refere
19、nces, only the edition cited applies. For undated references, 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 a
20、pply. BS ISO 3408-5:20062 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 CamModified dynamic axial load rati
21、ng 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 C0amModified static axial load rating N
22、 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 nConformity factor of ball nut
23、 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 BS ISO 3408-5:20063Symbol Descript
24、ion 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 factor h LmModified life revolutions Lmar
25、Modified 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 shaft mm zlNumber of effectively loaded
26、 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 to ball nut 2 BS ISO 3408-5:20064 5
27、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) 22pwwcoscos22DD=(7) NOTE The calculation
28、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 load rating is derived from the following b
29、asic 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)BS ISO 3408-5:200651sin10 13f=(12) ()()1, 3 90,321/ 311f=+(13) wpwcosDD = (14) 0,41rns3nrs1212fCfCf=(15) nrnwrfD= (16) srswrfD= (17) 1, 7 2 3311f=+(18)
30、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 HV101654 HV10f=u (20)The hardness factors shall only
31、 apply to ball bearing steel or similar steel alloys. BS ISO 3408-5:20066 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, Cam6.2.1 General equation am ahacmCCfff= (21) 6.2.2 Corr
32、ection 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, see Table 1. 6.2.4 Influence of material melting p
33、rocess, 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 specify the selected melting process in the data sheets. B
34、S ISO 3408-5:200677 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 rotational speed the following applies for the equivalent ro
35、tational 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 rotational speed, the following applies for the equivalent axial
36、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. BS ISO 3408-5:20068 Key 1 ball nut 2 screw shaft aForwar
37、d 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. 7.1.2.2 Bidirectional external axial load applied See Figure 4
38、. Key Key 1 ball nut 2 screw shaft aForward travel. sBackward travel. Figure 4 Ball screw with backlash and bidirectional axial loading BS ISO 3408-5:20069For calculation of equivalent axial load, use Equation (23) for variable rotational speed see Figure 5 a) 33m1,2 1,2m1100njjjjnqFFn=(26) for cons
39、tant 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 BS ISO 3408-5:200610 7.1.3 Ball screw with preloaded ball nuts on screw shaft See Figure 6. Key 1 ball nut (1) 2 ball nut (2) 3 screw shaft
40、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 other relieved (see Figure 7). Key 1 ball nut (1) 2 ball nut (2) Figure 7 Pre
41、load diagram BS ISO 3408-5:2006113/2lim 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 load 12limorjjF FFu , the following equation: 3/21, 2a(1),(2) op pr3/2op pr12jjFFfF
42、fF=+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) 1,2jjjFFF= (30) for the external load 12limorjjF FF , then: a(1) 1 a(2) 2orjj j jF FF
43、 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) 33ma(1),(2) a(1),(2)m1100njjjjnqFFn=(33) b) at constant rotational speed 33ma(1),(
44、2) a(1),(2)1100njjjqFF=(34)BS ISO 3408-5:200612 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 for ball nut (1), caused by preload. b Resulting load for ball nut (2), caused by prel
45、oad. 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 revolutions: 36am10CLF=(35.1) BS ISO 3408-5:200613Life in hours: hm60LLn=(36.1) 7.2.1.2 Bidirecti
46、onal 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, LrThe resulting life of the bidirectionally axial loaded ball screw with backlash or of the pre
47、loaded 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 revolutions: ar arL Lf= (40.1) respectively ar r arL Lf= (41.1) Life in hours: har h arL Lf= (42.1)
48、Table 3 Reliability factor, farReliability % far90 1 95 0,62 96 0,53 97 0,44 98 0,33 99 0,21 BS ISO 3408-5:200614 NOTE There are other factors reducing life, shock loads, vibrations, temperature, lubrication, 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 Bidirectiona
