DIN 32711-2-2009 Shaft to collar connection - Polygon profile P3G - Part 2 Calculation and dimensioning《轴环连接 多边形轮廓P3G 第2部分 计算和定尺寸》.pdf

1、March 2009 Translation by DIN-Sprachendienst.English price group 6No 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

2、1.120.10!$Z)d“1550665www.din.deDDIN 32711-2Shaft-to-hub connection P3G polygon profile Part 2: Calculation and dimensioningEnglish translation of DIN 32711-2:2009-03Welle-Nabe-Verbindung Polygonprofil P3G Teil 2: Berechnung und DimensionierungEnglische bersetzung von DIN 32711-2:2009-03Liaison arbre

3、 moyeu Polygon profil P3G Partie 2: Calcul et dispositionTraduction anglaise de DIN 32711-2:2009-03Together with DIN32711-1:2009-03,supersedesDIN 32711:1979-03www.beuth.deDocument comprises pagesIn case of doubt, the German-language original shall be considered authoritative.807.11 DIN 32711-2:2009-

4、03 A comma is used as the decimal marker. Contents Page Foreword3 1 Scope 4 2 Normative references 4 3 Calculation principles .4 3.1 Symbols 4 3.2 Calculating mechanical properties and dimensions4 3.2.1 General4 3.2.2 Shaft stresses 5 3.2.3 Surface pressure in the connection.5 3.2.4 Tensile stress i

5、n the hub.6 3.3 Recommended parameters for calculating dimensions6 Annex A (informative) Examples of calculations .7 Figures Figure 1 Minimum hub wall thickness of s P3G polygon hub . 6 Figure A.1 Diagram showing loads. 7 2 DIN 32711-2:2009-03 Foreword This standard has been prepared by Working Comm

6、ittee NA 060-34-32 AA of Section Antriebstechnik of the Normenausschuss Maschinenbau (Mechanical Engineering Standards Committee). The polygon shaft-hub connections are used for transmitting torques between machine components. They are suitable for permanent and/or repeatedly detachable connections,

7、 as well as for interference fits. The original version of this standard, DIN 32711, was published in March 1979. As this was before the rapid spread of NC machining technology, the standard was based on the kinematics of a mechanically-controlled polygon grinding machine made by a German manufactur

8、er. This meant that it was not absolutely necessary to include the equation in the standard. Now that it is possible to produce polygon-profile shafts and hubs on a variety of CNC machine tools, this omission has become apparent and therefore the standard has been revised. The present standard is a

9、revised version of the 1979 edition of DIN 32711. It takes into account technological progress made since then, particularly developments in the field of NC machining. For this reason, the fundamental mathematical principles of polygon profiles required for writing NC programs have now been added to

10、 the standard. In the process of revising the standard for P3G polygon profiles, it was subdivided into two parts. Part 1 contains information on the profile geometry, in particular the equations required for NC-supported production processes. Part 2 contains data which designers require to calculat

11、e the dimensions of polygon joints. The classical calculation model described here should be replaced in due course by other formulae corresponding to the respective state of engineering practice. Great importance has been placed on ensuring the interchangeability of the parts manufactured in accord

12、ance with the standard. This standard comprises the following parts: Part 1: General information and geometry Part 2: Calculation of mechanical properties and dimensions Amendments This standard differs from DIN 32711:1979-03 as follows: a) Figures 1 and A.1 have been added; b) the standard has been

13、 divided into two parts; c) editorial revisions have been made. Previous editions DIN 32711: 1979-03 3 DIN 32711-2:2009-03 1 Scope This standard applies to the calculation of the dimensions and load-bearing capacity of P3G polygon profiles, as well as to the production of parts with such profiles. T

14、he scope of this standard extends to industrial products, e.g. those used in general engineering, and in machine tool, motor vehicle and aircraft construction, as well as in the electronics industry. 2 Normative references The following referenced documents are indispensable for the application of t

15、his document. For dated references, only the edition cited applies. For undated references, the latest edition of the document (including any amendments) applies. DIN 32711-1, Shaft-to-hub connection P3G polygon profile Part 1: General information and geometry 3 Calculation principles 3.1 Symbols d1

16、(d4) diameter of equal-thickness section, in mm ztensile stress, in N/mm2d2(d5) external circular diameter, in mm p specific surface pressure, in N/mm2d3(d6) diameter of inner circle, in mm Pzulpermissible specific surface pressure, in N/mm2e1(e2) eccentric size, in mm z,zulpermissible tensile stres

17、s, in N/mm2l hub length, in mm Rp0,20,2 % proof strength, in N/mm2s minimum hub wall thickness, in mm Wppolar moment of resistance, in mm3Mttorsional moment, in Nmm Wxequatorial moment of resistance, in mm3Mbbending moment, in Nmm Ippolar moment of inertia, in mm4 torsional stress, in N/mm2A cross-s

18、ectional area, in mm2bbending stress, in N/mm23.2 Calculating mechanical properties and dimensions 3.2.1 General The calculation formulae recommended here apply to the calculation of both torsion and bending stresses, as well as to the calculation of the polygon shaft-to-hub connection under static

19、loads, whereby an interference of zero between the shaft and the hub is assumed. When calculating safety margins, the stress values calculated using the formulae (torsion stress, bending stress, surface pressure and tensile stress) shall be compared to the permitted material characteristics. 4 DIN 3

20、2711-2:2009-03 3.2.2 Shaft stresses The stresses calculated here are stresses acting at the boundary of the contact zone. 3.2.2.1 General 3.2.2.2 Stresses due to torsion The torsional stress arising from an applied torsional moment Mtis calculated using the following equation: ptWM= where Wpis the p

21、olar moment of resistance, which can be calculated as follows: 1p41111p2084dIAededW+= where 212144edA = applies to the cross-sectional area of the polygon profile, and 41212141p64332eeddI = applies to the polar moment of inertia. . 3.2.2.3 Stresses due to bending The torsion stress arising from an a

22、pplied bending moment Mbis calculated using the following equation: xbbWM= where Wxis the equatorial moment of resistance, which can be calculated as follows: =412121412x643321eedddW 3.2.3 Surface pressure in the connection The surface pressure arising from an applied torsional load is calculated us

23、ing the following equation: ()20/75,02111tdedlMp+This surface pressure is to be matched to the permissible surface pressure pzulof the shaft or hub to be connected when calculating the required connection dimensions. 0,2pzul9,0 Rpp Note: The effects of bending loads are neglected here. 5 DIN 32711-2

24、:2009-03 3.2.4 Tensile stress in the hub The tensile stresses caused by torsional loads on the hub lead to an expansion of the hub, which, in the worst-case scenario, can lead to hub failure if the wall thickness of the hub is inadequate. The minimum wall thickness s (see Figure 1) can be estimated

25、fairly accurately as a function of the permissible tensile stress in the hub: lMsdzulz,t444,1:mm35lMsdzulz,t42,1:mm35For most common applications, it is recommended that of the material from which the hub is manufactured should be applied. 0,2pzulz,R=Figure 1 Minimum hub wall thickness of s at P3G p

26、olygon hub 3.3 Recommended parameters for calculating dimensions For general applications, it is recommended that the following decisive action parameters be taken into account when calculating the dimensions of a polygon shaft-to-hub connection: stresses and bin the shaft; the surface pressure p on

27、 the connections contact surfaces, and the minimum wall thickness s. Annex A contains an example illustrating the procedure. 6 DIN 32711-2:2009-03 Annex A (informative) Examples of calculations Designing a P3G polygon connection to withstand a given torsion load. Given parameters: mm251=d mm20=l Nm1

28、50t=M 2Nabezul,z,N/mm300= Figure A.1 Diagram showing loads To be calculated: shaft torsion stress; surface pressure in the connection; minimum wall thickness. Dimensions: Taken from Table 1 of DIN 32711-1:2009-03 mm80mm251, = edCross-section: 2222121mm83,48280442544= ,edA 7 DIN 32711-2:2009-03 8 Pol

29、ar moment of inertia: 4422441212141pmm400378,0648,0253322564332= eeddI Polar moment of resistance: 341p41111pmm610225400372083,4828,08258,04252084=+=+=dIAededW Torsional stress: 2ptN/mm47,5761020001150=WM Surface pressure: ()()222111tN/mm7,9520/258,02575,020000115020/75,0=+=+ dedlMp Minimum hub wall thickness: mm2,720300000115044,144,1:mm35zulz,t4=lMsd