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WORMGEAR ANALYSIS Drawing or article number: worm: 0.000.0 Gear: 0.000.0 Calculation-method Only geometrycalculation (Geometry: ISO 14521) Geometry calculation from axial module 1. TOOTHGEOMETRY AND MATERIAL Shape of flank: ZK ------- WORM---------------- WHEEL ---- Centre distance (mm) [a] 100.000 Centre distance tolerance ISO 286Measure js7 Axis angle (°) [Sigma] 90.0000 Transverse module (mm) [mt] 5.0000 Normal module (mm) [mn] 4.9029 Axial module (mm) [mx] 5.0000 Pressure angle at normal section (°) [alfn] 20.0000 Mean lead angle (°) [gamma] 11.3099 Helix left left Number of teeth [z] 2 31 Facewidth (mm) [b1] 30.00 Wheel rim width b2R (mm) [b2R] 30.00 Wheel width b2H (mm) [b2H] 30.00 Facewidth for calcul. (mm) [b1, b2] 30.00 30.00 Accuracy grade (manufacturing) [Vqual] 6 7 Internal diameter gearbody (mm) [di] 0.00 0.00 Material worm: 18CrNiMo7-6, Case-carburized steel, case-hardened ISO6336-5 Figure 9/10 (MQ), core strength >=25HRC Jominy J=12mm<HRC28 Gear: CuSn12-C-GZ, Bronze, untreated ------- WORM---------------- WHEEL ---- Surface hardness HRC 61 HBW 95 Yield point (N/mm²) [sigs] 850.00 150.00 Youngs modulus (N/mm²) [E] 206000 88300 Poisson's ratio [ny] 0.300 0.350 Fatigue str. tooth root tension (N/mm²) [tauFlim] 430.00 92.00 Fatigue str. Hertzian stress (N/mm²) [sigHlim] 1500.00 425.00 Average roughness, Ra, tooth flank (µm) [RAH] 0.60 1.30 Mean roughness height, Rz, flank (µm) [RZH] 4.80 0.00 Mean roughness height, Rz, root (µm) [RZF] 20.00 0.00 Material Coefficient YW [YW] 1.00 Material lubrication coefficient [WML_Min] 1.60 Tool or reference profile of gear 1 : Reference Profile 1.25 / 0.38 / 1.0ISO 53.2 Profil A Addendum factor [haP*] 1.000 Dedendum coefficient [hfP*] 1.250 Tip radius factor [rhoaP*] 0.000 Root radius factor [rhofP*] 0.380 Tip form height coefficient [hFaP*] 0.000 Protuberance height factor [hprP*] 0.000 Protuberance angle [alfprP] 0.000 Ramp angle [alfKP] 0.000 not topping Tool or reference profile of gear 2 : Reference Profile 1.25 / 0.38 / 1.0ISO 53.2 Profil A Addendum factor [haP*] 1.000 Dedendum coefficient [hfP*] 1.250 Tip radius factor [rhoaP*] 0.000 Root radius factor [rhofP*] 0.380 Tip form height coefficient [hFaP*] 0.000 Protuberance height factor [hprP*] 0.000 Protuberance angle [alfprP] 0.000 Ramp angle [alfKP] 0.000 not topping Sum of reference profile gears: Dedendum reference profile (module) [hfP*] 1.250 1.250 Tooth root radius Refer. profile (module) [rofP*] 0.380 0.380 Addendum Reference profile (module) [haP*] 1.000 1.000 Protuberance height (module) [hprP*] 0.000 0.000 Protuberance angle (°) [alfprP] 0.000 0.000 Buckling root flank height (module) [hFaP*] 0.000 0.000 Buckling root flank angle (°) [alfKP] 0.000 0.000 Generating angle (°) [alfa0] 20.000 Pressure angle at normal section (°) [alfn] 20.000 Indications forthe manufacture of the worm gear according to DIN3975:. j; n/ a! m- E: B% y
(Only valid for worm gears which are manufactured with a hob similar to theworm) Mean lead angle of the worm (°) [gamma] 11.3099 Transverse module (mm) [mt] 5.0000 Reference diameter (mm) [d] 155.000 Meancircle diameter (mm) [dm] 150.000 Outside diameter (mm) Tipgroove mean radius (mm) Profile shift coefficient [x-DIN3975] -0.5000 Pitch (mm) [p2] 15.708 Indications forthe manufacture of the worm gear as a cylindrical gear
4 e9 f+ a9 o, Z, ] (This specification is only asuggestion. It is necessary to do a calculation of the exact geometry using thecrossed-helical calculation!) Pressure angle at Transverse section (°) [alft] (61.683) 20.452 Pressure angle at axial section (°) [alfx] (20.364) 59.091 Helix angle at reference diameter (°) [beta] (78.690) 12.586 Lead angle at pitch diameter (°) [gamma] (11.310) 77.414 Transverse module (mm) [mt] (25.000) 5.024 Axial module (mm) [mx] ( 5.000) 25.000 Helix angle at operating pitch diameter (°) [betas] (77.471) 12.529 Operating pitch diameter (mm) [dw] (45.000) 155.000 Profile shift coefficient [x-DIN3960] (0.0000) -0.5099 Gear ratio 15.500 Base helix angle (°) [betab] 10.620 Reference centre distance (mm) [ad] 102.500 Shape number q [q] 10.000 Sum of the Addendum modification [Summexi] -0.5000 Profile shift coefficient [x-DIN3975] 0.0000 -0.5000 Profile shift coefficient (x*m) (mm) [x*mx] 0.0000 -2.5000 (The addendum modification is related to the axial module of the wormsubject to DIN3975) Modification of tip diam. (mm) [k] 0.000 0.000 Theoretical tip clearence (mm) [c] 1.250 1.250 Effective tip clearence (mm) [c.e/i] 1.512/ 1.405 1.340/ 1.233 Meancircle diameter (mm) [dm] 50.000 150.000 Reference diameter (mm) [d] 155.000 Base diameter (mm) [dB] 145.313 Tip diameter (mm) [da] 60.000 160.000 Tip chamfer/ tip rounding (mm) [hK] 0.000 0.000 Tip form circle (mm) [dFa] 60.000 160.000 (mm) [dFa.e/i] 60.000/59.990 160.000/159.990 Tip diameter allowances (mm) [Ada.e/i] 0.000/-0.010 0.000/-0.010 Root diameter (mm) [df] 37.500 137.500 Generating Profile shift coefficient [xE.e/i] -0.5450/-0.5588 Manufactured root diameter with xE (mm) [df.e/i] 37.500/37.364 137.155/137.021 Lead height (mm) [pz] 31.416 Axial pitch (mm) [px] 15.708 8. MEASURES FORTOOTH THICKNES Tooth thickness tolerance worm: Worm according Niemann Gear: Wormwheel according Niemann ------- WORM---------------- WHEEL ---- Tooth thickness allowance (normal section) (mm) [As.e/i] 0.000/-0.049 -0.161/-0.210 Axial Distance Without Backlash (mm) [aControl] 99.775/ 99.637 Backlash free centre-distance, Tolerances (mm) [jta] -0.225/-0.363 No of teeth over which to measure [k] 3.000 Base tangent length ('span') (no backlash) (mm) [Wk] 36.759 Actual base tangent length ('span') (mm) [Wk.e/i] 36.608/36.562 Diameter of contact point (mm) [dMWk.m] 149.696 Base tangent length ('span'): Can only be measured, if the worm-wheel ismanufactured like a cylindrical gear Theor. ball/roller diameter (mm) [dm] 8.211 8.045 Actual ball/roller diameter (mm) [DMeff] 9.000 8.000 Theor. dim. centre to ball (mm) [MrK] 80.060 Actual dimension centre to ball (mm) [MrK.e/i] 79.795/79.713 Diameter of contact point (mm) [dMMr.m] 51.899 149.473 Theor. dimension over two balls (mm) [MdK] 159.925 Actual dimension over balls (mm) [MdK.e/i] 159.396/159.231 Outer diameter of grinding wheel(mm) [daS] 500.000 Set angle of grinding wheel (°) [beta] 11.3099 Theoretical dim. over 3 wires (mm) [Md3R] 64.089 Actual dim. over 3 rolls (mm) [Md3R.e/i] 64.089/63.957 Tooth thickness (chordal) in pitch diameter (mm) ['sn] 7.701 5.880 Actual chordal tooth thickness (mm) ['sn.e/i] 7.701/7.652 5.720/5.671 Tooth thickness on axial cut (mm) [smx] 7.854 Actual tooth thickness (mm) [smx.e/i] 7.854/7.804 Tooth gap in axial cut (mm) [emx] 7.854 Actual tooth gap (mm) [emx.e/i] 7.854/7.904 Chordal height from da.m (mm) [ham1, ha2] 4.997 2.551 Centre distance deviation (mm) [Aa.e/i] 0.018/-0.018 Circumferential backlash (transverse section) (mm) [jt] 0.277/0.151 Normal backlash (mm) [jn] 0.255/0.139 9. TOLERANCES ------- WORM----------------WHEEL ---- According DIN 3974: Accuracy grade [Vqual] 6 7 Single normal pitch deviation (µm) [fpx, fp2] 8.50 13.00 Difference between adjacent pitches (µm) [fux, fu2] 11.00 16.00 Total deviation of the slope (µm) [Fpz] 11.00 Total cumulative pitch deviation (µm) [Fp2] 51.00 Profile angular deviation (µm) [fHa] 7.50 11.00 Profile deviation (µm) [ffa] 11.00 15.00 Profile total deviation (µm) [Fa] 13.00 19.00 Runout tolerance (µm) [Fr] 18.00 35.00 Total tangential composite deviation (µm) [Fi'] 29.00 56.00 Tooth-to-tooth tangential composite deviation (µm) [fi'] 15.00 22.00
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發(fā)表于 2012-5-31 11:59:49