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Author: M. Hoffmann; Last update: 07.09.2018
KISSsoft 03/2018 – Instruction 053
Crossed helical gear pair, combination of a steel worm with a plastic gear and deep tooth form
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Contents
1 Calculation example ................................................................................................................ 3
1.1 Task ........................................................................................................................................................ 3
1.1.1 Calculation procedure ......................................................................................................................... 3 1.1.2 Results of calculation with normal tooth thickness .............................................................................. 6
1.2 Required modification of tooth thickness, given sn (e.g. 0.5 x mn) ....................................................... 6
1.2.1 Alteration of calculation data ............................................................................................................... 7
1.3 Additional possibilities as profile correction ............................................................................................. 9 1.4 Consider the mutated tolerances under extreme working temperatures ................................................ 9 1.5 Calculation test ...................................................................................................................................... 10
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1 Calculation example
1.1 Task
Presetting: Because of the different E-modules concerning the material (steel 210000 MPa, and 3000 MPa for
plastics) there is an uneven distribution of the tooth thickness. Thus the tooth thickness has to be reduced for the
worm and enlarged the gear.
A common breakdown of the tooth thickness proportions for the worm is 20-40 % and for the crossed helical gear
60-80%. For toothing without profile modification normal tooth thickness constitutes x mn/2, that means 50% for
each – worm and gear.
The normal tooth thickness sc has to be reduced by sc 0.5x mn what relates to a tooth thickness distribution of
ca 34% for the worm compared to 66% for the gear.
The root strength of the plastic gear may be significantly enlarged by reducing the steel worm – so the gear teeth
get larger. In the meanwhile, the root and tip circle are kept approximately equal.
Therefore, the used formula of the standard DIN 3960 are:
- Tooth thickness at the reference circle of a gear with profile shift: sc = mn(/2+2 x tan n)
- Root diameter: df = d + 2 x mn – 2 hfp
1.1.1 Calculation procedure
Open the calculation module for the crossed helical gear calculation. Enter the following values for a crossed
helical gear pair.
Figure 1. Input tab “Basic date”
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Figure 2. Input tab “Reference profile”
Figure 3. Input tab “Tolerances”
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Figure 4. Input tab “Rating”
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1.1.2 Results of calculation with normal tooth thickness
------- WORM---------------- WHEEL ----
Center distance (mm) [a] 24.500
Centre distance tolerance DIN 58405:1977 j10
Shaft angle (°) 90.0000
Normal module (mm) [mn] 0.8000
Normal module at pitch circle (mm) [msn] 0.8000
Helix angle at reference circle (°) [beta] 80.0000 10.0207
Pressure angle at normal section (°) [alfn] 14.500
Lead angle at reference diameter (°) [gamma] 10.0000 79.9793
Helix angle at pitch circle (°) [betas] 79.9799 10.0200
Number of teeth [z] 2 49
Shape of flank: ZI
Facewidth (mm) [b] 15.00 6.00
Facewidth for calculation (mm) [beH] 2.72 2.72
Hand of gear right right
Accuracy grade [Q-DIN3961:1978] 8 10
Sum of profile shift coefficients [Summexi] -0.0133
Profile shift coefficient [x] 0.0000 -0.0133
Generating Profile shift coefficient [x.e/i] -0.0250/ -0.0774 -0.2105/ -0.3428
Chordal tooth thickness (no backlash) (mm) [sc] 1.257 1.251
Actual chordal tooth thickness (mm) [sc.e/i] 1.246 / 1.225 1.169 / 1.115
Figure 5. Results and tooth form1
1.2 Required modification of tooth thickness, given sn (e.g. 0.5 x mn)
First calculate the profile shift factor: x = sn/(2 mn tan n); the result in the example: x =-0.9667 x has to be
set as follows: x=-1.0
1 File: z2_z49_m08_Step1.Z17
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1.2.1 Alteration of calculation data
Figure 6. Activate flaged checkboxes
Correct the previous calculation (section 1.1.2) x1= -1.0, i.e.
reduce the worm x1(new) = x1(previous) - x x1= 0.0 - 1.0 = -1.000 and
enlarge the gear x2(new) = x2(previous) + x x2= -0.0133+1.0 = 0.9867:
Figure 7. Enter the “Profile shift coefficient” x1
Run the calculation and confirm the warning message.
Figure 8. Displayed warning
Enter the “Root radius factor” as follows: *fP2 = 0.179
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Reference profile changes, so that the root and tip circle stay the same.
Figure 9. New „Reference profile“
According to the chosen settings derived from the previous calculation there apply following results:
hfP1(new) = h*fP1(previous) - x (dedendum) h*fP1 = 1.5 - 1.0 = 0.50
haP1(new) = h*aP1(previous) + x (addendum) h*aP1 = 1.3 + 1.0 = 2.30
hfP2(new) = h*fP2(previous) + x (dedendum) h*fP2 = 1.5 + 1.0 = 2.50
haP2(new) = h*aP2(previous) - x (addendum) h*aP2 = 1.30 - 1.0 = 0.30
Tooth thickness (chordal) in pitch diameter (mm)
['sn] 0.843 1.664
(mm) ['sn.e/i] 0.833 / 0.811 1.583 / 1.528
The results show that the tooth thickness factor changed: sn=0.5 mn = 0,414 mm.
That relates to a distribution of ca 34% (for the worm) compared to ca 66% (for the gear).
Figure 10. New results and tooth form2
So the root strength of the crossed helical gear improved from 0.48 to 0.69 – what relates to an amelioration of
ca 45%.
2 File: z2_z49_m08_Step2.Z17
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1.3 Additional possibilities as profile correction
Profile corrections may improve the run properties (acoustic) even more. The future manufacturing process has
to be considered, so the properties can be consequently enhanced by driving into a block-situation. The chosen
values are just an example to show the various possibilities. For an exact value definition experience and a
certain strategy are demanded. Furthermore, all conditions must be known which have to be fulfilled by the
gearbox.
Figure 11. A sharp-edged tooth tip of the worm inserts into the root of the crossed helical gear
Figure 12. Stress optimized elliptic root modification reduces stress peaks in the root region.
Figure 13. Elimination of manufacturing errors leads to better acoustic.
Figure 14. Necessary addition for the manufacturing of injection molding3
1.4 Consider the mutated tolerances under extreme working temperatures
The large length expansion of plastics may lead to jamming under differing and extreme working temperatures
(-40°C /+80°C).
3 File: z2_z49_m08_Step3.Z17
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Figure 15. Operating backlash
1.5 Calculation test
Finally, check the automatic entries for the diameters of pins or balls for the measurement.
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Figure 16. Worm in normal section and actual measurement ball
Figure 17. Gear in normal section and actual measurement ball
Figure 18. Current inputs
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Figure 19. Tooth form 2D 3D skin model4
4 File: z2_z49_m08_Step4.Z17
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