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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