anl 064 tca with shafts 1

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EES KISSsoft GmbH ++41 41 755 09 54 (Phone)

P.O. Box 121 ++41 41 755 09 48 (Fax)

Weid 10 ++41 79 372 64 89 (Mobile)

6313 Menzingen [email protected]

Switzerland www.EES-KISSsoft.ch

1 Tooth contact pattern calculation, KH

calculation

1.1 Executive summary

Below, the calculation of the contact patterns and contact stresses based on a numerical

(FEM) model inside KISSsoft is shown.

Furthermore, the calculation of KHaccording to ISO6336, Annex E is shown.

1.2 Table of content1 Tooth contact pattern calculation, KHcalculation........................................................... 1

1.1 Executive summary.................................................................................................... 1

1.2 Table of content.......................................................................................................... 11.3 Document change record............................................................................................ 2

1.4 Abbreviations .............................................................................................................2

1.5 References ..................................................................................................................2

2 Set up calculation in KISSsoft ...........................................................................................2

2.1 System data ................................................................................................................2

Tooth

contactpa

tternsandK

H


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1.3 Document change record

Revision Dated Who Comments

0 2.3.2011 HD Original document

1.4 Abbreviations

[ ] Units

1.5 References

[1]ISO6336, Annex E[2]KISSsoft 03-2011

2 Set up calculation in KISSsoft

2.1 System dataLet us look at the following gearbox, a standard industrial helical gearbox. Let us consider thetwo shafts at the output end of the gearbox, so, the tooth contact analysis is applied for the last

gear mesh. Below, the sense of rotation and the direction of the power flow is shown. Note

that a Side I and a Side II is defined as shown below.

Figure 2.1-1 Gearbox system, last stage is downwards orientated.

Side I

Side II

Gear 2, z=39Gear 1, z=12


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Figure 2.1-2 Deformed shape of the gearbox shafts

From the above, we can see that the contact will be more on Side I. Therefore, we will have to

reduce the helix angle on the pinion or put a helix angle correction such that the resultinghelix angle is smaller

2.2 Shaft data

The driving shaft is shown below

Side ISide II


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The driven shaft (output shaft) is shown below

Side I Side II

Side I Side II

Gear 2, z=39

Gear 1, z=12


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2.3.2 Gear corrections

First, let us define a tip relief. For this, use the sizing function as shown below. Press

Calculate and Accept to get the tip relief as shown below:


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Figure 2.3-2 Resulting profile modification

You can see the profile diagramm here:


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Figure 2.3-3 Adding end relief and crowning to the pinion

Now, we also add a helix angle correction to the pinion such that the helix angle is lower than

the nominal helix angle (which is 10deg). To get the information CHb=-25 ->

beta.eff=9.983deg-left, press


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Figure 2.3-5 Flank line diagramm for gear 1. Note that the green lines are the individual corrections

whereas the blue line is the resulting flank

You can see that the helix angle correction is towards the right hand side whereas the initial

hand of the helix is left hand. This means that the resulting gear still has a left handorientation but a smaller one than originally.

2.4 Set up of tooth contact analysis

In the gear calculation, add the tab for the Contact analysis as shown below:


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Figure 2.4-1 Add the tab for the tooth contact analysis

Here, do the following settings

Figure 2.4-2 Set up of tooth contact analysis

We are looking at the right flank in contact We take the tilting/bending of the gears from

the shaft deformation calculation

The torsional deformation of the gears istaken from the shaft deformation calculation Here, select the two shafts. For Gear 1 (thepinion), select the first shaft. For Gear 2 (the

pinion), select the second shaft.

We calculate the tooth contact pattern for

nominal load

The deformation is scaled with the value of

wt (in our case, it is 100%)


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Figure 2.4-1 How to display the contact stress on a flank


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In the results, we find KHas follows:

Figure 2.4-3 KHbeta of gear mesh, without optimisation

4 Improving the contact

In the above images, we can see that the contact is still a bit too much on side II. Therefore,the helix angle correction that we have chosen is too high and we need to reduce it, e.g. to -

15um only. Also, we reduce the crowning a little, to 10um only. This gives:


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Figure 2.4-2 Improved KHbeta value after optimisation of the corrections

Figure 2.4-3 Contact pattern on driving gear = gear 1 = pinion after optimisation


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Figure 2.4-4 Contact pattern on driven gear = gear 2 = wheel after optimisation


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C:\TRANSFER\EES-KISSsoft-GmbH\KISSsoft\Anleitung-zu-KISSsoft\ANL-064-TCA-with-shafts.doc 16 of 30

Explanations:

y : Width

phi.t : Static torsion

f.t : Displacement due to torsion

f.b : Displacement due to bending

f.tot : Total displacement (f.b+f.t)

f.C : Change due to flank line modification

Load distribution

Contact stiffness = 15.813 N/mm/m

y g w

1. 70.2127 mm 30.2577 m 478.4777 N/mm

2. 74.0831 mm 51.7241 m 817.9351 N/mm

3. 77.9536 mm 56.3198 m 890.6094 N/mm

4. 81.8240 mm 57.4731 m 908.8473 N/mm5. 85.6944 mm 58.4456 m 924.2260 N/mm

6. 89.5649 mm 59.2418 m 936.8160 N/mm

7. 93.4353 mm 59.8717 m 946.7771 N/mm

8. 97.3057 mm 60.3202 m 953.8696 N/mm

9. 101.1761 mm 60.6068 m 958.4021 N/mm

10. 105.0466 mm 60.7238 m 960.2513 N/mm

11. 108.9170 mm 60.6593 m 959.2318 N/mm

12. 112.7874 mm 60.4513 m 955.9430 N/mm

13. 116.6579 mm 60.0619 m 949.7855 N/mm

14. 120.5283 mm 59.5062 m 940.9978 N/mm

15. 124.3987 mm 58.7942 m 929.7387 N/mm

16. 128.2691 mm 57.9008 m 915.6109 N/mm

17. 132.1396 mm 56.8546 m 899.0667 N/mm

18. 136.0100 mm 55.6365 m 879.8045 N/mm

19. 139.8804 mm 54.2410 m 857.7363 N/mm

20. 143.7509 mm 49.4265 m 781.6034 N/mm

21. 147.6213 mm 27.7414 m 438.6875 N/mm

Explanations:

g : Flank overlap

w : Line load

wmax = 960.251 N/mm, wm = 870.687 N/mmKHb = wmax/wm = 1.103 (Calculation according to ISO 6336-1, Appendix E)

Notice: The influence of the exceeding tooth width is not taken into account in the calculation of KHbeta.


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Figure: Path of contact


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wt = 100 %, a = 200 mm, fpt = 0 m, = 0.1353268402

Figure: Transmission error


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1st Harmonic frequency [1/s] : 6.52173913

Harmonics Amplitude [m]

1. 2.124983227

2. 0.4323017983

3. 0.2125395327

4. 0.09486427952

5. 0.14131542326. 0.08580080112

7. 0.02168405216

8. 0.04891069949

9. 0.05630266734

10. 0.05762765055

Figure: FFT of transmission error


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wt = 100 %, a = 200 mm, fpt = 0 m, = 0.1353268402

Figure: Stiffness curve


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1st Harmonic frequency [1/s] : 6.52173913

Harmonics Amplitude [N/mm/m]

1. 2.676415579

2. 0.5578203278

3. 0.2268231372

4. 0.102757942

5. 0.048999324696. 0.07548357828

7. 0.09250584354

8. 0.09916733709

9. 0.05235889837

10. 0.04911862118

Figure: FFT of contact stiffness


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wt = 100 %, a = 200 mm, fpt = 0 m, = 0.1353268402

Figure: Normal force curve (Line load)


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wt = 100 %, a = 200 mm, fpt = 0 m, = 0.1353268402

Figure: Stress curve


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wt = 100 %, a = 200 mm, fpt = 0 m, = 0.1353268402

Figure: Stress curve Gear A


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wt = 100 %, a = 200 mm, fpt = 0 m, = 0.1353268402

Figure: Stress curve Gear B


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wt = 100 %, a = 200 mm, fpt = 0 m, = 0.1353268402

vg: 1.0 = 0.083 m/s

Figure: Kinematics


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wt = 100 %, a = 200 mm, fpt = 0 m, = 0.1353268402

Figure: Loss power


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wt = 100 %, a = 200 mm, fpt = 0 m, = 0.1353270606

the0il = 70.0 C, theM = 72.3 C, etaM = 21.50 mPa*s

Figure: Flash temperature (ISO TR 15144)


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wt = 100 %, a = 200 mm, fpt = 0 m, = 0.1353270606

the0il = 70.0 C, theM = 72.3 C, etaM = 21.50 mPa*s

hmin(ISO) = 0.006 m, Ra = 0.600 m

Figure: Lubricating film (ISO TR 15144)

Remark:

The report contains only the important graphics.

The other graphics can be found in menu 'Graphics' -> 'Contact analysis'.

End report lines: 156


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anl 064 tca with shafts 1

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