Advantages of Local Load Carrying Capacity Approaches Compared to Standardized Methods

The FVA-Workbench features the world's most comprehensive library of standard methods for calculating the load carrying capacity of cylindrical gears. In addition to the latest national and international standards such as ISO 6336, DIN 3990, and AGMA 2101, the library also includes calculation guidelines for all major classification societies, the calculation of plastic gears according to VDI 2736, as well as all older versions of these standards.

The load capacity calculation is always preceded by a rolling simulation with one or two tools to determine the cylindrical gear geometry. This ensures that the gear can realistically be manufactured and will run as intended.

In addition to the geometry and the material used, the load distribution during mesh has a significant influence on the load capacity of a cylindrical gear. In the calculation, the influence of uneven load distribution across the face width is taken into consideration via the face load factor K (DIN 3990 and ISO 6336) or KH (AGMA 2101). However, the formulas included in the standards only provide a very rough estimation. A detailed deformation analysis of the complete gear system is necessary to be able to quantitatively evaluate the effective influences on the load distribution across the face width.

In the FVA-Workbench, the total gear deformation is calculated based on a method developed for FVA and validated using deformation measurements at the Technical University of Munich Institute of Machine Elements, or FZG. The following elastic deformations and static displacements can be taken into account, among others:

  • Gear stiffness
  • Flank modifications
  • Shaft deflection and torsion
  • Deflections and clearances of rolling and plain bearings
  • Casing deformations
  • Manufacturing deviations

The deformation analysis in the FVA-Workbench can be performed in a few seconds, even with complex gear structures. The face load factor is automatically determined for each cylindrical gear stage and can be taken into account in the selected load carrying capacity calculation. 

The calculation of the load distribution across the face width of a planetary stage can be used as an example (Figure 1). If the load distribution across the face width in this stage is calculated based on the torsion of the sun pinion, as in a simplified calculation according to the standard, the result for this example is a face load factor of K = 1.83 with a maximum load on the output side of the sun pinion (Figure 2a). However, if the tilting of the planet gears due to deformation, the play of the planet bearings, and the elastic deformation of the planet carrier including the deformation of the pin are also considered, the result is a face load factor of K = 1.65, and with the maximum load located on the opposite end of the gear (Figure 2b).


This example demonstrates that a simplified consideration of gear deformations leads to incorrect modification design in practice, and as a result can lead to one-sided flank damage (Figure 3).

The detailed system-wide deformation calculation in the FVA-Workbench enables a more precise calculation of the load carrying capacity and a practice-oriented optimization of face modifications. This can be used not only to avoid damage, but also to identify hidden load carrying capacity reserves. Cost savings can then be achieved by reducing component sizes and the associated reduced resource usage. While the influence of uneven load distribution across the face width can be evaluated in standard load carrying capacity calculations using the face load factor K, as described above, uneven load distribution across the tooth depth cannot be represented in detail.


The following factors can lead to increased flank pressure in the tooth root area of the flank:

  • Edge stress in the contact area of the tooth tip edge for helical gears
  • Load peaks due to short lines of contact at the start and end of contact for helical gears
  • Small radii of curvature at the pinion base with large tooth ratios
  • Small radii of curvature near the base circle of a gear mesh

The standard methods assume a suitable profile modification. Only in ISO 6336 (2019) does the newly introduced fZCa factor lead to a somewhat qualitative consideration of a non-existent or non-optimized profile modification.

With the FVA-Workbench, on the other hand, the influence of uneven load and pressure distribution over the tooth depth can be more closely examined during the design of a gear. The local load of each point on the flank is calculated for this purpose. Here, too, proven calculation methods from /1/ are applied, in which the local gear tooth stiffnesses are calculated on an analytical basis using a plate model. This analytical approach allows a very high resolution with a short calculation time. In addition, the FVA-Workbench also offers an FE-based approach, which was developed in FVA Research Project 128 at the Laboratory for Machine Tools and Production Engineering (WZL) of RWTH Aachen University. The local load distribution determined in this way forms the basis for additional local load parameters:

  • Local flank pressure
  • Local tooth root stress
  • Local sliding speed and lubricant film thickness
  • Local contact temperature
  • Local safety against micropitting

Figure 4 shows an example of the pressure distribution of a helical gear with a tooth ratio of 4, with and without profile modification, calculated with the FVA-Workbench. 

It can be seen that the local pressure increases as the equivalent radius of curvature decreases toward the tooth root of the pinion. Together with the edge stresses simultaneously occurring in the contact area of the tip edge of the mating gear, this leads to very high local pressure peaks which make a profile modification necessary. The required profile modifications can be easily designed with the FVA-Workbench, which then lead to uniform pressure distribution and thus uniform material utilization across the tooth flank (Figure 4b). In this way, damage resulting from these locally overloaded areas in the contact area of the tip edge of the mating gear, such as the triangular flank chipping shown in Figure 5, can be reliably prevented.