AGMA 07FTM02-2007 pdf download.Study of the Correlation Between Theoretical and Actual Gear Fatigue Test Data on a Polyamide by: S. Wasson, DSM Engineering Plastics.
Results
Calculations
In general contact ratios of two spur gears are in the range of 1 to 2. This means that in part of the meshing cycle, 1 tooth will carry the entire transmitted torque load. The classic theory shows this as 1/3-2/3-3/3 rule. That is, at first contact, the tooth carries 1/3 of the load and increases its share steadily to 2/3 until the preceding tooth leaves the mesh and then it carries the entire load for a short period and then symmetrically reverses this load cycle.
Our FEA shows this to be more like 2/5-3/5-5/5 for a steel gear pair, with a modulus of 206 GPa. This is reinforced in other literature also.
The deflection of the loaded tooth on the plastic driven gear is the cause of this skewed load share curve. As the loaded tooth is deflected, the rotational angle of meshing is moved out of phase, this causes both preliminary contact by the next tooth entering mesh and prolonged contact at the end of mesh by the preceding tooth. That preceding tooth is being unloaded and is straightening back to its undeflected form, see figure 5.
This increased contact, both entering and leaving mesh, will increase load sharing and thus lower the root stresses. Table 1, shows the results given by the FEA and the semi- analytic methods. You can see the effect, as the modulus decreases the FEA shows the actual stress decrease. The difference between the theoretical and actual (FEA) also becomes more significant. While most semianalytic approaches allow no dependency for root bending stresses on modulus, the FEA shows there is indeed an effect of tooth deflection which is indirectly dependent on modulus.
Fatigue tests correlation
Loads were selected by using FEA to get a reason- able number of cycles. The torques of4, 5, 6, 8 Nm were run in the Berlin test rig. The gears were run constantly at 3000 rpm and 140°C. Two materials were molded and tested; an unfilled PA46 and PEEK.
Based on the torque levels, the root stresses were calculated using the FEA and ISO 6336. They are then being compared to tensile bar fatigue data. As you can see in figure 6, the root stresses generated with FEA (labeled corrected) correlate well with the tensile specimens while the IS06336 calculations exhibit much less of a correlation. Since the uncorrected or IS06336 equations yield apparently higher allowable stress values, caution in utilizing previously generated gear data must be used, as it may portray a false safety factor.
This will depend on the loads, modulus based on temperature, and resulting tooth deflection.AGMA 07FTM02 pdf download.