1 Overview
1.1 Task
This tutorial shows how tooth root geometry influences tooth strength and how it can be optimized. It recommends you use the "Graphical method" if you want to study the root strength of non-standard root geometry.
To do this, you use the strength calculation and tooth geometry calculation.
1.2 Results
Three different root geometries are to be examined:
1. resulting root geometry, with a tool root radius factor 
P=0.38
2. resulting root geometry, with a tool root radius factor =0.45
3. optimized root geometry (elliptical rounding)
The following results for safety factors are found when you use a combination of ISO 6336 and
ISO 6336 and the "Graphical method":
Table 1.1 Comparison of calculated safety factors for tooth root bending strength safety factors
depending on method As you can clearly see, by optimizing the root geometry, the safety factor against bending failure has been increased by 16%. However, this optimized root rounding requires a special tool (modified cutter). For this reason, we recommend you use this method for mass production (e.g. by form grinding) or if the gears are manufactured by wire erosion or sintering.
*Note: if you use the unmodified ISO 6336 method (or other methods like DIN 3990 or AGMA
2001) you cannot estimate a modified root geometry. You can see this because the results from Geometry 2 to Geometry 3 do not change.
1.3 Theory
The value fP is the radius of the root of the reference profile of the gear as shown below:
Figure 1.1 Reference profile of the gear,
The strength rating specified in ISO 6336 uses only a single point in the root where 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). The resulting root stress is then calculated in accordance with formula.
Figure 1.2 Calculating the tooth root stress as specified in ISO 6336
The actual construction of the root rounding therefore implies a larger or smaller degree of error.
KISSsoft therefore includes a modification in the calculation methods, allowing for the calculation of YF and YS factors along the whole of the root. In this case, the point at which the
product of YF*YS reaches the maximum is taken as the point where the strength rating is performed.
This is the only method that allows you to evaluate the effect of optimized root roundings.
1.4 Other contents of this tutorial
In section 2, the root safety factor is calculated according to the unmodified ISO 6336 method
(Method B). However, you cannot use this method to take into account the effect of root optimization. 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 ISO 6336 by KISSsoft). Here you can clearly see the effect of optimized root rounding.
The comparison between the calculated results is shown in Table 1.1
Further explanations and comments are given in section 4.
All calculations/changes are performed only for Gear 1.
2 Strength calculation as specified in ISO6336
2.1 For Geometry 1 (=0.38)
To open the example used in this tutorial, click "File/Open" and select "CylGearPair 1 (spur gear)" or click the "Example" tab.
Figure 2.1 Open example calculation "CylGearPair 2 (spur gear)"
The selected calculation method is ISO 6336, Method B. To check which reference profile was
used, click the "Reference profile" tab. In this example a standard reference profile (1.25/0.38/1.00) as specified in ISO 53.2 profile A has been used.
Figure 2.2 Selected calculation method
Figure 2.3 Standard reference profile as used for first calculation
Figure 2.4 Result of calculating the safety factor of the tooth root stress in Gear 1
The resulting tooth form is displayed in a graphics window. Click the button (upper right marking) to make it into a floating window and enlarge it. You can save the tooth forms so they can be compared later on. To do this, follow the steps marked in Figure 2.5
Figure 2.5 Resulting tooth form with =0.38
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