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KISSsoft Tutorial: Root optimisation __________________________________________________________________________________________

Fr Release 10/2008 Kisssoft-tut-013-E-root-optimisation.doc

Letzte nderung 30.10.2008 16:02:00 __________________________________________________________________________________________

1 Summary

1.1 Objective This tutorial will demonstrate how the root geometry affects the root strength, how the root geometry can be optimised and that the graphical method should be used when studying root strength for non-standard root geometry. Strength calculation and tooth geometry calculation will be used.

1.2 Results Three different root geometries will be examined:

1. Root geometry as resulting from a generating process with *fP=0.38 2. Root geometry as resulting from a generating process with *fP=0.45 3. Optimised root geometry (elliptical rounding)

The following resulting safety factors will be found when using ISO6336 and ISO6336 combined with graphical method:

SF based on rating along ISO6336

SF based on rating along ISO6336 using graphical method

Geometry 1 (*fP=0.38) 2.5957 2.4722 Geometry 2 (*fP=0.45) 2.7601 2.6477 Geometry 3 (elliptical) 2.7601* 2.8466 Improvement from Geometry 1 to Geometry 3

6%* 15%

Table 1.2-1: Comparison between bending strength safety factors calculated.

It is clearly visible that by optimising the root geometry, the safety factor against bending failure can be increased by 15%. However, this optimised root rounding requires a special tool (modified hob). It is therefore recommended for mass production (e.g. by form grinding) or if the gears are formed by e.g. wire eroding or sintering.

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*Note that using the unmodified ISO6336 method (or other methods like DIN3990 or AGMA2001) does not allow for assessment of a modified root geometry. This can be seen from the results not changing from Geometry 2 to Geometry 3.

1.3 Theory The value fP is the radius of the root of the reference profile of the gear as shown below:

Figure 1.3-1: Reference profile of the gear, fP.

The strength rating according to ISO6336 uses only one single point in the root where the factors YF and YS are calculated. This point is defined by the contact between a tangent to the root intersecting the symmetry line at a 30 angle and the root itself. YF and YS are then calculated as shown in formulas (2) and (3) respectively. The resulting root stress is then calculated according to formula (1).

(1)

(2) (3)

Figure 1.3-2: Calculation of root stress according to ISO6336.

However, this point defined above may not be the point with the highest stress if the root geometry is modified. KISSsoft therefore includes a modification in the calculation methods, allowing for calculation of YF and YS factors along the whole of the root. In this case, the point where YF*YS reaches is maximum, is taken as the point where the strength rating is performed. Only this methods allows for a study of the effect of an optimised root rounding.

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1.4 Course of this tutorial In section 2, the root safety factor is calculated according to the un-modified ISO6336 method (Method B). However, the effect of a root optimisation can not be considered using this method. The root safety factor is therefore only calculated for geometry 1 and 2.

In section 3, the root safety is then calculated using the graphical method (an optional modification to ISO6336 by KISSsoft). Here, the effect of the optimised root rounding can be shown clearly.

The comparison between the results generated is shown in Table 1.2-1.

In section 4, some explanations and comments are given.

All calculations/modifications are done for gear 1 only.

2 Strength rating according to ISO6336

2.1 For geometry 1 (*fP=0.38) The example used in this tutorial can be opened using File / Open and selecting CylGearPair 1 (spur gear), sees figure below or using the Module tree window Tab Projects and select CylGearPair 1 (spur gear).

Figure 2.1-1: Open file dialog, choose CylGearPair 1 (spur gear). Select calculation method to be ISO6336, Method B. To check the reference profile used, use the tab Reference profile. Here, a standard reference profile (1.25/0.38/1.00) according ISO 53.2 Profil A is used.

Figure 2.1-2: Set calculation method.

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Figure 2.1-3: Standard reference profile as used for first calculation.

Quit the N window by pressing Ok, get back to the main window. In the main window, execute the strength calculation by pressing (Calculate). In the lower section of the main window, the resulting safety factors are shown. Note SF (for bending) of gear 1.

Figure 2.1-4: Resulting safety factor against bending for gear 1 after calculation.

The resulting gear geometry is shown in a graphic window. It may be made a floating window by dragging it from using the right mouse button (bottom right marking in Figure 2.1-4. For a later comparison, press both buttons Save Gear 1, Save Gear 2 (in order marking in Figure 2.1-5).

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Figure 2.1-5: Resulting tooth geometry with *fP=0.38.

2.2 For geometry 2 (*fP =0.45) In a first step, the maximum possible value for *fP has to be determined. For this, choose the tab Reference profile and select Own Input from the reference profile list. Then type in a value of e.g. 0.55 for *fP.

Figure 2.2-1: Modifying *fP.

Press (Calculate) and the following warning will occur, indicating that the value for *fP=0.55 is too large. The maximum possible value is *fP=0.4719.

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Figure 2.2-2: Warning that *fP as defined is too large.

The value for *fP has to be corrected. Adjusting the value for *fP to a sensible value. So modify the value to *fP=0.45. Then, press now. No warning will occur now.

Figure 2.2-3: Resulting safety factor against bending for gear 1 with *fP=0.45.

Now, the safety factor (root strength of gear 1) has increased:

Look in the 2D graphics to see the old and new tooth form superimposed (use zoom +- buttons). In blue, the root with *fP=0.45is shown. In black, the old tooth form with *fP=0.38 (the one that was saved previously) is shown.

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Figure 2.2-4: Now, both tooth forms (old/black with *fP=0.38 and new/blue with *fP=0.45) are shown.

2.3 For geometry 3 (elliptical root rounding) As the strength rating according to ISO6336 is based on the reference profile only, this calculation can not be performed. Therefore, assessing the effect of a modified root rounding if not based on a basic rack is impossible with ISO6336. For this, the graphical method should be used as shown in the next section.

3 Strength rating using graphical method

3.1 For geometry 1 (*fP =0.38) Go back to the Reference profile and set back the value for *fP to *fP=0.38 again and get back to the tab Basic Data.

Figure 3.1-1: Reset value of *fP to *fP=0.38 again.

Now, the option to calculate along graphical method has to be activated. Go in the tab Basic Data to the group Strength and press details. A new window is shown Define details of strength. There, choose using graphical method from the Drop-down list beside form factor YF and YS. Quit the window by pressing [Ok].

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Figure 3.1-2: Activation of "graphical method" in Define datails of strength.

The strength calculation can now be repeated in the main window by pressing . Note that the safety factor is a bit lower due to the change in the calculation method:

Figure 3.1-3: Resulting safety factor gear 1 with *fP =0.38 using "graphical method".

3.2 For geometry 2 (*fP =0.45) Go to the tab Reference profile and set value for *fP to *fP =0.45 and press :

Figure 3.2-1: Resulting safety factor SF1 with *fP=0.45 using "graphical method".

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3.3 For geometry 3 (elliptical root rounding) To add the elliptical root modification, start the tooth form calculation by choosing the tab Tooth form.

Figure 3.3-1: Start tooth form calculation.

In the following window, add the tooling operation Elliptic foot modification by pressing right mouse click on automatic.

Figure 3.3-2: Adding tool option in tooth form calculation.

Then, press the sizing button next to the field Modification from diameter to define where the elliptical rounding modification should start. Also, right mouse click on the icon Elliptic foot modification and selection of choose as result will make sure that tooth is modified.

Figure 3.3-3: Define start of modification, activate step.

Back in the tab basic Data strength can (now that the tooth geometry has been calculated) now be calculated by pressing . Note the change in safety factor gear 1:

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Figure 3.3-4: Resulting safety factor gear1 with optimised root rounding.

4 Comments and explanations

4.1 Step: Automatically When opening the tooth form calculation, a first manufacturing step, the default step, is already visible Automatically (automatic).

Figure 4.1-1: Default step in tooth form calculation.

This step will calculate the gear based on the reference profile as defined in the Tab Reference Profile. Therefore, when adding the elliptical root modification, it does make a (small) difference whether *fP =0.38 or *fP =0.45 has been defined in the Tab Reference Profile. This because the elliptical modification is only the second manufacturing step (the first one being a generating operation with the automatic rack which is based on the reference profile defined). Hence, the resulting tooth form is slightly different.

By modifying the value for Factor for root rounding, the shape of the elliptical curve can be modified slightly. The value Curve length at root diameter defines the length of a circular arc between two elliptical sections.

Figure 4.1-2: Factor for definition of curvature radius.

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Figure 4.1-3: Definition of arc length / curve length at root diameter.

4.2 Calculation of internal gears For internal gears, the calculation according to DIN3990, ISO6336 and AGMA2001 is quite inaccurate (however, in the proposed new version of the ISO6336, the situation will be improved). We therefore recommend to use the graphical method whenever you calculate an internal gear. To use the graphical method, module ZA15 is required.

4.3 Calculation of tool to generate elliptical root If now a tool geometry should be generated that in turn will generate the above define elliptical modification, proceed as follows: Press right mouse click on Elliptic foot modification, choose Add operation/Calculate Ref. profile.

Figure 4.3-1: Reverse calculation to define a tool from a given gear geometry.

Then, press F5 Calculate and choose Manufacture Gear 1 from Drop-down list in the Graphics window Geometry:

Figure 4.3-2: Calculate tooth form, define display

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Figure 4.3-3: Gear geometry (blue) and geometry of resulting tool (green). In a final step, the tool can be displays. Select in graphics window Tool Gear 1 from list and the tool geometry will be displays. The tool geometry can now be exported for manufacturing of the tool.

Figure 4.3-4: Choose tool to be displayed.

Figure 4.3-5: Display of tool geometry.

The Tool can now be exported to dxf or iges.