Gear: CuSn12-C-GZ, Bronze, untreated
------- WORM---------------- WHEEL ----
Surface hardness HRC 61 HBW 95
Yield point (N/mm?) [sigs] 850.00 150.00
Youngs modulus (N/mm?) [E] 206000 88300
Poisson's ratio [ny] 0.300 0.350
Fatigue str. tooth root tension (N/mm?) [tauFlim] 430.00 92.00
Fatigue str. Hertzian stress (N/mm?) [sigHlim] 1500.00 425.00
Average roughness, Ra, tooth flank (?m) [RAH] 0.60 1.30
Mean roughness height, Rz, flank (?m) [RZH] 4.80 0.00
Mean roughness height, Rz, root (?m) [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:& L1 G' Q2 q) l7 k# I
(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 L1 p3 q5 O) u(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 (?m) [fpx, fp2] 8.50 13.00
Difference between adjacent pitches (?m) [fux, fu2] 11.00 16.00
Total deviation of the slope (?m) [Fpz] 11.00
Total cumulative pitch deviation (?m) [Fp2] 51.00
Profile angular deviation (?m) [fHa] 7.50 11.00
Profile deviation (?m) [ffa] 11.00 15.00
Profile total deviation (?m) [Fa] 13.00 19.00
Runout tolerance (?m) [Fr] 18.00 35.00
Total tangential composite deviation (?m) [Fi'] 29.00 56.00
Tooth-to-tooth tangential composite deviation (?m)
[fi'] 15.00 22.00
' h/ I' P% t F3 c- F/ q* h+ [
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