其它资料analysing the geometry of cylindrical worm gears

1、KISSsoft 03/2017 Tutorial 16Analysing the Geometry of Cylindrical Worm Gears with Enveloping Worm WheelKISSsoft AGRosengartenstrasse 48608 Bubikon SwitzerlandTel: +41 55 254 20 50Fax: +41 55 254 20 51infoKISSsoft.AG www.KISSsoft.AGContents1TaskTask3Starting the drive element of wo

2、rm gear with enveloping (globoid) worm wheel3Input data in the main screen4Special features of worm gear teeth flank surfaces6Input data for the gear pair6Inputting tolerances82Strength calculation92.1Results of the rating and geometry calculation1010.03.20172 / 171Task1.1 TaskTo calculate a worm ge

3、ar with center distance 100 mm. The worm has 2 teeth and the worm wheel has 41 teeth. The axial/transverse module is 4. The pressure angle at the normal section is 20. The worms facewidth is 60 mm. You should select a sensible facewidth for the worm wheel. The axis tolerance is js7.The worms tooth t

4、hickness deviation in the normal section is between 0 and -0.04 mm. The tooth thickness deviation for the worm wheel is between -0.128 and -0.168. The external diameter of the worm is 44 -0.01 mm. The root diameter is 26.4 -0.110 mm. The effective tip clearance is 0.8 mm. The root radius coefficient

5、 is 0.2. The inside radius diameter is 134.4 mm.The tolerance for the external diameter of the worm wheel is between 0 and -0.01 and for the active root diameter it is between -0.360 and -0.473. The worm is to be manufactured with accuracy grade 6 as specified in DIN 3974. The worm wheel is to be ma

6、nufactured with quality 7. The lead direction is to the left. The worms flank form is ZI.1.2 Starting the drive element of worm gear with enveloping (globoid) worm wheelYou can call KISSsoft as soon as the software has been installed and activated. Usually you start theprogram by clicking StartProgr

7、am following KISSsoft user interface:FilesKISSsoft03-2017KISSsoft03-2017.ThisopenstheFigure 1. Starting KISSsoft, initial windowIn the Modules tree window, click the Modules tab to call the Worms with enveloping worm wheels calculation:10.03.20173 / 17Figure 2. Call to the worm gear calculation1.3 I

8、nput data in the main screenAfter you call the Worms with enveloping worm wheels, the input screen appears. To only perform a geometry calculation, disable the Calculation - Rating option in the menu.Figure 3. Input screen for wormsInput values for the axial/transverse module, number of teeth, quali

9、ty, and worm face width in the Basic data tab. You must also input the center distance (1). The subsequent interim value is calculated becauseonly the lead angle needs to be calculated. To do this, click the Convert button(2) and then clickCalculate (3) to determine the lead angle. Finally, click Ac

10、cept (4) to transfer this data to the main screen (see Figure 4).10.03.20174 / 1712Figure 4. Interim state with the Sizing lead angle input screenClick the Details button to call the Define details of geometry sub-screen and then select appropriate flank form ZI. You must also input the inside diame

11、ter of the worm gear as 134.4 mm.theFigure 5. Interim status with Define details of geometry input screen10.03.20175 / 17341.4 Special features of worm gear teeth flank surfacesThe flank surfaces of a worm gear are defined in a different way from those in cylindrical gears.Figure 6. Calling the info

12、rmation graphic to describe wheel rim width b2R and wheel width b2HThen click the Sizingbutton to calculate the facewidth.Figure 7. Calculated wheel rim width b2R1.5 Input data for the gear pairIn the Reference profile tab, select Own Input as the predefined tool profile. Thenclick theappropriate Co

13、nvertbutton to calculate the tip and the addendum and dedendum coefficients for theworm. When you click Accept, these values are transferred to the main screen.10.03.20176 / 17Figure 8. Calculating the worm root or tip diameterInput 0.2 as the root radius factor. The effective tip clearance is then

14、used to determine the root or tip diameter for the worm wheel. The root diameter is calculated from:(center distance - tip diameter of worm/2 - tip clearance)2 = (100 - 44/2 - 0.8) 2 = 154.4 mm. The tip diameter is calculated from:(center distance - root diameter of worm/2 - tip clearance) 2 = (100

15、- 26.4/2 - 0.8) 2 = 172 mm.Once again, click the relevant Convertbutton to convert the dedendum and addendum coefficient atthe worm wheel. Then click Accept to transfer the values to the main screen.Explanation: when you call the worm gear calculation, the system already provides predefined base set

16、tings. However, the default profile 1.25 / 0.38 / 1 ISO 53 A does not match what we want. The software already shows that it has calculated the tip diameter detailed above.The particular geometry of globoid worm gears also means that you need to calculate the throat radius and the external diameter

17、de2.Figure 9. Geometry of globoid worm gears10.03.20177 / 17In the Basic data tab, click the Details button to open the Define details of geometry sub-screen. Then click the Sizing button to run the required calculations for the throat radius rk and the external diameter de2. For more information se

18、e Figure 10.Figure 10. Calculating throat radius rk, the external diameter de, throat center distance ark and chamfering center distance ae1.6 Inputting tolerancesIn the Tolerances tab, select Own Input instead of using the predefined dimensions. Then input the tooth thickness allowance in accordanc

19、e with the default values and then enter the tip diameter allowance.Figure 11. Inputting tooth thickness tolerance and tip diameter allowancesThen check the root diameter allowance and modify it if necessary. Now select the center distance tolerance.Figure 12. Center distance tolerance input10.03.20

20、178 / 17The following changes must now be made so you can perform the strength calculation later on: facewidth of worm is 60 mm, increase the required facewidth of the worm wheel b2R to 31 mm and the external diameter de2 to 181.41 mm.Figure 13. Final inputsThese are the results of the calculation.2

21、Strength calculationThe various different calculation methods are documented in the manual (Chapter 16). Please refer to the notes if you have any questions. To open the prepared example used in this tutorial, click FileOpen and select WormGear 1 (DIN3996 Example 1).Figure 14. Opening the example ca

22、lculation10.03.20179 / 172.1 Results of the rating and geometry calculationKISSsoft Release03/2017 KISSsoft Calculation programs for machine designFileNameDescription:WormGear 1 (DIN3996, Example 1)KISSsoft exampleChanged by:jreison: 23.02.2017at: 10:19:55WORM GEAR ANALYSISDrawing or article number:

23、 Worm:Gear:0.000.00.000.0Calculation method(Geometry:DIN 3996:2012DIN 3975:2002)Geometry calculation from axial module WORM WHEEL Worm drivingWorking flank gear 1: Right flank Power (kW)Speed (1/min) Torque (Nm) Application factor Required service lifeNumber of starts (1/h)PnTKAHNs5.3021500.033.7544

24、.50073.2587.2821.0025000.000.001. TOOTH GEOMETRY AND MATERIALShape of flank:ZI (ISO/DTR 10828.2:2011) WORM WHEEL 100.000ISO 286:2010Center distance (mm) Centre distance tolerance Measure js7Shaft angle () Transverse module (mm) Normal module (mm) Axial module (mm)Pressure angle at normal section ()

25、Mean lead angle ()Hand of gear Number of teeth Facewidth (mm)Wheel rim width b2R (mm) Wheel width b2H (mm) Facewidth for calculation (mm) Accuracy grade (manufacturing)Internal diameter gearbody (mm)aSigma mtmnmxalfn gamma90.00004.00003.90474.000020.000012.5288left260.00leftzb1b2Rb2H b1, b2Vqualdi41

26、31.0031.0030.8360.00670.00134.40MaterialWorm:16 MnCr 5 (1), Case-carburized steel, case-hardenedISO 6336-5 Figure 9/10 (MQ), Core hardness =25HRC Jominy J=12mmHRC28 CuSn12Ni2-C-GZ, Bronze, untreatedDIN 3996:2005Gear 2:10.03.201710 / 17 WORM WHEEL HRC 59Surface hardness 95Pulsating shear strength (N/

27、mm)Fatigue strength for Hertzian pressure (N/mm) Material Coefficient YWMaterial lubrication coefficient Tensile strength (N/mm) Yield point (N/mm)Youngs modulus (N/mm) Poissons ratioRoughness average value DS, flank (m) Roughness average value DS, root (m) Mean roughness height, Rz, flank (m)Mean r

28、oughness height, Rz, root (m)HBWFlim Hlim YWWML_PolyG430.0090.00520.000.951.75300.00180.001500.00BSERAHRAFRZHRZF1000.00695.002060000.3000.500.503.003.00981000.3502.002.008.008.00Gear reference profile Reference profile Dedendum coefficient Root radius factor Addendum coefficientTip radius factor1 :1

29、.20 / 0.20 / 1.0 DIN 867:1986hfP* rhofP* haP* rhoaP* hprP* alfprP hFaP* alfKP1.2000.200 (rhofPmax*= 0.498) 1.0000.0000.0000.0000.0000.000Protuberance height coefficient Protuberance angleTip form height coefficientRamp anglenot toppingGear reference profile Reference profile Dedendum coefficient Roo

30、t radius factor Addendum coefficientTip radius factor2 :1.20 / 0.20 / 1.0 DIN 867:1986hfP* rhofP* haP* rhoaP* hprP* alfprP hFaP* alfKP1.2000.200 (rhofPmax*= 0.498) 1.0000.0000.0000.0000.0000.000Protuberance height coefficient Protuberance angleTip form height coefficientRamp anglenot toppingSummary

31、of reference profile gears: Dedendum reference profileTooth root radius Refer. profile Addendum Reference profile Protuberance height coefficient Protuberance angle ()Tip form height coefficientRamp angle ()hfP* rofP* haP* hprP* alfprP hFaP*alfKP1.2000.2001.0000.0000.0000.0000.0001.2000.2001.0000.00

32、00.0000.0000.000Type of profile modification:Tip relief (m)none (only running-in)Ca0.00.0Lubrication typeType of oil (Own input) Lubricant baseOil bath lubrication l: ISO-VG 220Synthetic oil based on Polyglycol10.03.201711 / 17Kinem. viscosityKinem. viscosityoil at40 C (mm/s)nu40 nu100roOil TSTU220.

33、0037.001.02073.22620.000oil at 100 C (mm/s)Specific density at 15 C (kg/dm) Oil temperature (C)Ambient temperature (C) WORM WHEEL 20.00020.000Generating angle ()Pressure angle at normal section ()alfa0alfnIndications for the manufacture of the worm wheel according to ISO 14521:(Only valid for worm w

34、heels which are manufactured with a hob similar to the worm.)Mean lead angle of the worm () Transverse module (mm) Reference diameter (mm) Reference operating diameter Throat radius (mm)Throat center distance (mm) Facewidth chamfer angle () Chamfering center distance (mm) External diameter (mm)Tip d

35、iameter (mm) Profile shift coefficientPitch on reference circle (mm)gamma mtddmrka_rk theta a_theta dedax-worm p212.52884.0000164.000164.00014.000100.0000.0000100.000181.410172.0000.000012.566(mm)Indications for the manufacture of the worm wheel as a cylindrical gear(This specification is only a sug

36、gestion. It is necessary to do a calculation of the exact geometry using the crossed- helical calculation!)Pressure angle at Transverse section () Pressure angle at axial section ()Helix angle at reference circle () Lead angle at reference diameter () Transverse module (mm)Axial module (mm)Helix ang

37、le at operating pitch circle () Operating pitch diameter (mm)Profile shift coefficientalftalfxbeta gamma mtmx betas dwx-DIN3960(59.205)(20.448)(77.471)(12.529)(18.000)( 4.000)(77.471)(36.000)( 0.0000)20.44859.20512.52977.4714.00018.00012.529164.0000.0000Overall transmission ratio Gear ratioBase heli

38、x angle ()Reference centre distance (mm) Diametral factor qSum of profile shift coefficients Profile shift coefficientProfile shift (x*m) (mm)itotu betab adq Summexi x-wormx*mx-20.50020.50011.762100.0009.0000.00000.00000.00000.00000.0000(The profile shift is related to the axial module of the worm s

39、ubject to ISO TR 14521:2010/DIN 3975:2002. )Tip alteration (mm) Theoretical tip clearance (mm) Effective tip clearance (mm) Reference operating diameter Reference diameter (mm) Base diameter (mm)Tip diameter (mm)Tip form diameter (mm)(mm)k*mnc c.e/i dmddbdadFa dFa.e/i0.0000.8001.059/ 0.96336.0000.00

40、00.8000.877/ 0.782164.000164.000153.666172.000172.000172.000/ 171.990(mm)44.00044.00044.000/ 43.99010.03.201712 / 17Tip diameter allowances (mm) Root diameter (mm)Generating Profile shift coefficientManufactured root diameter with xE (mm)Ada.e/i df xE.e/idf.e/i0.000/ -0.01026.4000.000/ -0.010154.400

41、-0.0450/ -0.0591154.040/ 153.92726.400/ 26.290Lead height (mm)Axial pitch (mm)pzpx25.13312.566eps_aTransverse contact ratio (approximate value following Thomas-Charchut)1.911For ZI-worms:Base diameter (mm) Base lead angle () Base pitch (mm)dbgambpb18.43123.46311.5272. FACTORS OF GENERAL INFLUENCE WO

42、RM WHEEL Nominal circum. force at pitch circle (N) Axial force (N)Radial force (N) Normal force (N)Circumferential speed reference circle (m/s)Sliding velocity an mean circle (m/s) Number of load cycles (in mio.)FtFaFrFnvvgmNL1875.2-7162.02847.38343.72.8272.8962249.9997162.0-1875.2-2847.30.628109.75

43、6Data of reference gearbox: Equivalent Youngs modulus (N/mm) Surface roughness of worm (m) Center distance (mm)Transmission ratioEredT RaTaTuTdm1TpmT*hT*sT*150622.000.500100.00020.50036.0000.9620.07030.800Reference operating diameter(mm)164.000Characteristic value for mean Hertzian pressureCharacter

44、istic value for mean lubricant gap thickness Characteristic value for mean sliding pathPhysical characteristic values:Characteristic value for mean lubrication Space width Characteristic value for mean Hertzian pressure Characteristic value for mean sliding pathh*pm*s*0.06920.947030.2850Efficiency a

45、ccording method C: Rolling bearing with set support Bearing loss-power (kW) Number of sealings (worm-shaft) Sealing loss power (kW)Idle loss power (kW) Base friction number Size factor Geometry factor Roughness factorMaterial Coefficient YW Mean tooth friction number Tooth friction angle () Meshing

46、efficiency (%) Mesh loss power (kW) Total loss power (kW)Total efficiency (%)PVLPnVDPVDPV0muOTYSYGYRYWmuzmrozetazPVZPVetaGes0.12620.0460.1530.02451.0001.0061.0000.9500.02341.34190.0020.4770.80284.87210.03.201713 / 17Gear mass temperature: Lubrication typeWorm submerges into lubricant Cooling area of

47、 wheel-pair (cm)Heat-transfer coefficient wheels (W/m/K) Gear mass temperature (C)Oil sump temperature (C)Oil bath lubricationARalfLtheMtheS50.84024439.99077.173.23. WEAR STRENGTH ACCORDING METHOD B,CMean lubricant gap thickness (m) (hminm calculated with etaOM= Pressure factorFactor for lubricant s

48、tructure Factor for start Characteristic valueWear intensity Wear intensity Wear path (m)Wear removal (mm)hminm 0.0642 Ns/m2 theM=77.1)WHWSWNSKwJOTJwsWm delWn0.24801.00002.61401.00000.64845.10181e-0108.92817e-0108158290.728Permissible tooth thickness reduction (coefficient in module) Permissible mas

49、s decrease (kg)Normal tooth thickness at tip circle (mm)DeltaS0.300san2.907(mm)san.e/i2.778/2.731Permissible wear on flank (mm)Limited by: Permissible tooth thickness decrease Safety against wearRequired safetyAs information:delWlimn1.171SWSWmin1.6081.100Achievable service life (with SW =1.100) (h)L

50、h36551.074. PITTING RESISTANCE ACCORDING METHOD B,C WORM WHEEL 149673.38367.361.0000.8511.0001.0001.000442.7661.2051.000Equivalent Youngs modulus (N/mm) Mean contact stress (N/mm)Life coefficient Speed factor Size factor Lubrication factor Ratio factorBoundary value of average contact stress (N/mm)

51、Safety factor for contact stressRequired safety As information:Achievable service life (with SHmin =Ered sigHm ZhZVZSZoilZusigHG SHSHmin1.000) (h)Lh76640.675. DEFLECTION SAFETYBearing distance l1 (mm) Distance l11 (mm) Deflection (mm)Boundary value bending (mm)Safety for deflectionl1l11delm dellim S

52、del150.00075.0000.0300.0802.63210.03.201714 / 17Required safetySdelmin1.0006. TOOTH ROOT STRENGTH ACCORDING METHOD C WORM WHEEL Calculation taking into account the decrease of the tooth thickness due to wear (with minimum (delWn, delWlimn)Tooth thickness at root (mm) Tooth form factorContact ratio factor Lead coefficient Rim thickness (mm)Rim thickness coefficientNominal shear stress at tooth root (N/mm)No Quality reduction by small plastic deformation is accepted. Life coefficientBoundary value of shear stress at tooth