Tooth contact patterns and KHβ 1 Tooth contact pattern...

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Revision: 0 Autor: HD Date: 2.3.2011 Approved: HD Date: 2.3.2011

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1 Tooth contact pattern calculation, KHβ

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 KHβ according to ISO6336, Annex E is shown.

1.2 Table of content 1 Tooth contact pattern calculation, KHβ calculation........................................................... 1

1.1 Executive summary.................................................................................................... 1 1.2 Table of content.......................................................................................................... 1 1.3 Document change record............................................................................................ 2 1.4 Abbreviations ............................................................................................................. 2 1.5 References .................................................................................................................. 2

2 Set up calculation in KISSsoft ........................................................................................... 2 2.1 System data ................................................................................................................ 2 2.2 Shaft data.................................................................................................................... 3 2.3 Gear data .................................................................................................................... 4

2.3.1 Basic data ........................................................................................................... 4 2.3.2 Gear corrections ................................................................................................. 5

2.4 Set up of tooth contact analysis.................................................................................. 8 3 Calculation of contact......................................................................................................... 9 4 Improving the contact....................................................................................................... 11 5 Example report of tooth contact analysis ......................................................................... 14

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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 data Let us look at the following gearbox, a standard industrial helical gearbox. Let us consider the two 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. Note that the right flank is in contact! If we look at the deformation of the gearbox, we can see the following:

Side I

Side II

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


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 resulting helix angle is smaller

2.2 Shaft data The driving shaft is shown below

Side I Side II


The driven shaft (output shaft) is shown below

2.3 Gear data

2.3.1 Basic data The basic gear data as used is shown below. Note Gear 1 and Gear 2 as indicated above.

Side I Side II

Side I Side II

Gear 2, z=39

Gear 1, z=12


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:

Figure 2.3-1 Sizing of profile modification (tip relief) Then you get:


Figure 2.3-2 Resulting profile modification You can see the profile diagramm here:

In the face width direction, the following corrections should be applied: all corrections are applied on the pinion (which is Gear 1) only and no corrections are on the gear. We want to put 40um end relief on the pinion, on both sides (side I and side II). The length should be 1/10 of the total face width. Also, we put a crowning of 25um. This is done by using the “+” button to add lines to the table and then enter/select the corrections:


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

Figure 2.3-4 Adding the helix angle correction on the pinion You can see the flank line diagram here:


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 hand orientation 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:


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 is taken from the shaft deformation calculation

Here, select the two shafts. For Gear 1 (the pinion), 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%)

Now, run the calculation by pressing

3 Calculation of contact

Once the calculation is completed, we can display the contact stress on the flank as shown below:


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

Figure 2.4-2 Contact stress on Gear 2 / Gear B (the gear on the output shaft)


In the results, we find KHβ as 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:

Figure 2.4-1 Modified corrections on gear 1 (crowning and helix angle modification is changed) Once we repeat the calculation, we now find the stress patterns are more balanced in the centre of the face and KHβ is also reduced:


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


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

Public EES KISSsoft GmbH Weid 10 / P.O. Box 6313 Menzingen Switzerland www.EES-KISSsoft.ch

Title: No.: Date: Manager: HD Email: [email protected]

Revision: 0 Autor: HD Date: 2.3.2011 Approved: HD Date: 2.3.2011


5 Example report of tooth contact analysis KISSsoft - Release 03-2011 KISSsoft evaluation File Name : Unnamed Changed by : Dinner on: 02.03.2011 at: 10:32:10 Calculation of path of contact under load Mesh gear 1 - gear 2 (Right Tooth Flank) Shaft file A: C:_292_A.w10, selected gear: Gear5(c5 6) Shaft file B: C:_292_B.w10, selected gear: Gear6(c5 6) Partial load for calculation 100.0 0 % Center distance [a] 200.0 0 mm Single pitch deviation [fpt] 0.0 0 µm Coefficient of friction [µ] 0.1 4 Torque [T1] 2945.2 3 Nm min max Delta µ sigma Transmission error (µm) -226.1970 -221.0994 5.0976 -223.1440 1.5633 Stiffness curve (N/mm/µm) 16.1341 22.0002 5.8661 19.6264 1.9517 Line load (N/mm) 0.0000 1126.9901 1126.9901 679.2393 274.1363 Torque Gear 1 (Nm) 2943.2773 2948.0056 4.7283 2945.3369 0.9054 Torque Gear 2 (Nm) 9199.5020 9440.9912 241.4893 9314.3494 82.6795 Loss power (W) 0.0000 30.7474 30.7474 11.1572 7.5764 Flash temperature (°) 72.3034 127.6216 55.3182 94.3402 12.8000 Lubricating film (µm) 0.0056 0.0818 0.0762 0.0192 0.0055 Hertzian stress (N/mm²) 2221.1083 1285.8008 Transverse contact ratio under load[Epsa'] 1 .28 Overlap ratio under load [Epsb'] 0.5 2 Total contact ratio under load[Epsg'] 1.8 0 KHbeta Calculation Gear 1 Point in polar co-ordinates: R = 47.059 mm , phi = 310.693 ° Displacement calculated in direction 335.078 ° y phi1.t f1.t f1.b f1.tot f1.C


1 70.2127 mm 0.0000° 0.0000 mm 0.0185 mm 0.0185 mm 0.0319 mm 2 74.0831 mm 0.0001° 0.0001 mm 0.0191 mm 0.0191 mm 0.0095 mm 3 77.9536 mm 0.0001° 0.0001 mm 0.0196 mm 0.0197 mm 0.0040 mm 4 81.8240 mm 0.0003° 0.0003 mm 0.0201 mm 0.0203 mm 0.0019 mm 5 85.6944 mm 0.0005° 0.0004 mm 0.0205 mm 0.0209 mm 0.0001 mm 6 89.5649 mm 0.0008° 0.0006 mm 0.0210 mm 0.0215 mm -0.0017 mm 7 93.4353 mm 0.0011° 0.0008 mm 0.0213 mm 0.0221 mm -0.0032 mm 8 97.3057 mm 0.0014° 0.0011 mm 0.0216 mm 0.0227 mm -0.0045 mm 9 101.1761 mm 0.0018° 0.0014 mm 0.0219 mm 0.0233 mm -0.0057 mm 10 105.0466 mm 0.0023° 0.0018 mm 0.0221 mm 0.0239 mm -0.0067 mm 11 108.9170 mm 0.0028° 0.0021 mm 0.0223 mm 0.0244 mm -0.0075 mm 12 112.7874 mm 0.0034° 0.0026 mm 0.0224 mm 0.0250 mm -0.0081 mm 13 116.6579 mm 0.0040° 0.0030 mm 0.0225 mm 0.0255 mm -0.0086 mm 14 120.5283 mm 0.0046° 0.0035 mm 0.0226 mm 0.0261 mm -0.0088 mm 15 124.3987 mm 0.0054° 0.0040 mm 0.0225 mm 0.0266 mm -0.0089 mm 16 128.2691 mm 0.0061° 0.0046 mm 0.0225 mm 0.0271 mm -0.0088 mm 17 132.1396 mm 0.0069° 0.0052 mm 0.0224 mm 0.0276 mm -0.0085 mm 18 136.0100 mm 0.0078° 0.0059 mm 0.0222 mm 0.0281 mm -0.0081 mm 19 139.8804 mm 0.0087° 0.0065 mm 0.0220 mm 0.0285 mm -0.0074 mm 20 143.7509 mm 0.0097° 0.0073 mm 0.0217 mm 0.0290 mm -0.0033 mm 21 147.6213 mm 0.0107° 0.0080 mm 0.0214 mm 0.0295 mm 0.0176 mm Gear 2 Point in polar co-ordinates: R = 152.941 mm , phi = 310.754 ° Displacement calculated in direction 335.139 ° y phi2.t f2.t f2.b f2.tot f2.C 1 140.2127 mm 0.0000° -0.0000 mm -0.0140 mm -0.0140 mm 0.0000 mm 2 144.0831 mm -0.0000° -0.0001 mm -0.0142 mm -0.0143 mm 0.0000 mm 3 147.9536 mm -0.0001° -0.0002 mm -0.0145 mm -0.0146 mm 0.0000 mm 4 151.8240 mm -0.0001° -0.0002 mm -0.0147 mm -0.0150 mm 0.0000 mm 5 155.6944 mm -0.0001° -0.0003 mm -0.0150 mm -0.0153 mm 0.0000 mm 6 159.5649 mm -0.0001° -0.0004 mm -0.0153 mm -0.0156 mm 0.0000 mm 7 163.4353 mm -0.0002° -0.0004 mm -0.0155 mm -0.0159 mm 0.0000 mm 8 167.3057 mm -0.0002° -0.0005 mm -0.0158 mm -0.0162 mm 0.0000 mm 9 171.1761 mm -0.0002° -0.0005 mm -0.0160 mm -0.0165 mm 0.0000 mm 10 175.0466 mm -0.0002° -0.0005 mm -0.0163 mm -0.0168 mm 0.0000 mm 11 178.9170 mm -0.0002° -0.0006 mm -0.0165 mm -0.0171 mm 0.0000 mm 12 182.7874 mm -0.0002° -0.0006 mm -0.0168 mm -0.0174 mm 0.0000 mm 13 186.6579 mm -0.0003° -0.0006 mm -0.0171 mm -0.0177 mm 0.0000 mm 14 190.5283 mm -0.0003° -0.0007 mm -0.0173 mm -0.0180 mm 0.0000 mm 15 194.3987 mm -0.0003° -0.0007 mm -0.0176 mm -0.0183 mm 0.0000 mm 16 198.2691 mm -0.0003° -0.0007 mm -0.0178 mm -0.0185 mm 0.0000 mm 17 202.1396 mm -0.0003° -0.0007 mm -0.0181 mm -0.0188 mm 0.0000 mm 18 206.0100 mm -0.0003° -0.0008 mm -0.0183 mm -0.0191 mm 0.0000 mm 19 209.8804 mm -0.0003° -0.0008 mm -0.0186 mm -0.0194 mm 0.0000 mm 20 213.7509 mm -0.0003° -0.0008 mm -0.0188 mm -0.0196 mm 0.0000 mm 21 217.6213 mm -0.0003° -0.0008 mm -0.0191 mm -0.0199 mm 0.0000 mm


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/µm y g w 1. 70.2127 mm 30.2577 µm 478.4777 N/ mm 2. 74.0831 mm 51.7241 µm 817.9351 N/ mm 3. 77.9536 mm 56.3198 µm 890.6094 N/ mm 4. 81.8240 mm 57.4731 µm 908.8473 N/ mm 5. 85.6944 mm 58.4456 µm 924.2260 N/ mm 6. 89.5649 mm 59.2418 µm 936.8160 N/ mm 7. 93.4353 mm 59.8717 µm 946.7771 N/ mm 8. 97.3057 mm 60.3202 µm 953.8696 N/ mm 9. 101.1761 mm 60.6068 µm 958.4021 N/ mm 10. 105.0466 mm 60.7238 µm 960.2513 N/ mm 11. 108.9170 mm 60.6593 µm 959.2318 N/ mm 12. 112.7874 mm 60.4513 µm 955.9430 N/ mm 13. 116.6579 mm 60.0619 µm 949.7855 N/ mm 14. 120.5283 mm 59.5062 µm 940.9978 N/ mm 15. 124.3987 mm 58.7942 µm 929.7387 N/ mm 16. 128.2691 mm 57.9008 µm 915.6109 N/ mm 17. 132.1396 mm 56.8546 µm 899.0667 N/ mm 18. 136.0100 mm 55.6365 µm 879.8045 N/ mm 19. 139.8804 mm 54.2410 µm 857.7363 N/ mm 20. 143.7509 mm 49.4265 µm 781.6034 N/ mm 21. 147.6213 mm 27.7414 µm 438.6875 N/ mm Explanations: g : Flank overlap w : Line load wmax = 960.251 N/mm, wm = 870.687 N/mm KHb = wmax/wm = 1.103 (Calculation according to I SO 6336-1, Appendix E) Notice: The influence of the exceeding tooth width is not taken into account in the calculation of KHb eta.


Figure: Path of contact


wt = 100 %, a = 200 mm, fpt = 0 µm, µ = 0.135326840 2 Figure: Transmission error


1st Harmonic frequency [1/s] : 6.52173913 Harmonics Amplitude [µm] 1. 2.124983227 2. 0.4323017983 3. 0.2125395327 4. 0.09486427952 5. 0.1413154232 6. 0.08580080112 7. 0.02168405216 8. 0.04891069949 9. 0.05630266734 10. 0.05762765055 Figure: FFT of transmission error


wt = 100 %, a = 200 mm, fpt = 0 µm, µ = 0.135326840 2 Figure: Stiffness curve


1st Harmonic frequency [1/s] : 6.52173913 Harmonics Amplitude [N/mm/µm] 1. 2.676415579 2. 0.5578203278 3. 0.2268231372 4. 0.102757942 5. 0.04899932469 6. 0.07548357828 7. 0.09250584354 8. 0.09916733709 9. 0.05235889837 10. 0.04911862118 Figure: FFT of contact stiffness


wt = 100 %, a = 200 mm, fpt = 0 µm, µ = 0.135326840 2 Figure: Normal force curve (Line load)


wt = 100 %, a = 200 mm, fpt = 0 µm, µ = 0.135326840 2 Figure: Stress curve


wt = 100 %, a = 200 mm, fpt = 0 µm, µ = 0.135326840 2 Figure: Stress curve Gear A


wt = 100 %, a = 200 mm, fpt = 0 µm, µ = 0.135326840 2 Figure: Stress curve Gear B


wt = 100 %, a = 200 mm, fpt = 0 µm, µ = 0.135326840 2 vg: 1.0 = 0.083 m/s Figure: Kinematics


wt = 100 %, a = 200 mm, fpt = 0 µm, µ = 0.135326840 2 Figure: Loss power


wt = 100 %, a = 200 mm, fpt = 0 µm, µ = 0.135327060 6 the0il = 70.0 °C, theM = 72.3 °C, etaM = 21.50 mPa* s Figure: Flash temperature (ISO TR 15144)


wt = 100 %, a = 200 mm, fpt = 0 µm, µ = 0.135327060 6 the0il = 70.0 °C, theM = 72.3 °C, etaM = 21.50 mPa* s hmin(ISO) = 0.006 µm, Ra = 0.600 µm 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

Tooth contact patterns and KHβ 1 Tooth contact pattern...

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