Designing low-noise gears

Vibrations in the audible frequency range between 20 Hz and 20 kHz can be detected as noise, and may also lead to component fatigue and cost-intensive damage. These undesirable effects can already be avoided in the design phase by analyzing and optimizing the excitation behavior of the gearbox. With its user-friendly implementation of scientifically proven methods, the FVA-Workbench simulation platform can be used for exactly this purpose.
What causes vibrations in the tooth mesh?

Multiple gear teeth engage simultaneously. The contact ratio indicates the average number of tooth pairs. Changing of the tooth pairs in mesh and differing amounts of bending of the teeth across the tooth depth results in varying gear stiffness across the path of contact. Cyclical stiffness changes cause vibrations and noise in systems due to excitation. This also applies to tooth contact. The variable gear stiffness is shown in figures 1a and 2a. The excitation behavior in tooth contact can be determined from the transmission error, which is the change of rotation at the gear output with uniform rotational movement at the gear input.

Influencing the excitation behavior

In practice, the excitation behavior can be significantly influenced by the following parameters:

  • The macro-geometry of the gear
  • The micro-geometry of the gear


When designing cylindrical gears, careful selection of the macro-geometry can have a positive influence on the excitation behavior. For example, Müller demonstrates in his dissertation that a contact ratio of an average of 1.75 teeth in engagement and whole-integer overlap ratios can be used to minimize the excitation [Müller, R.: Schwingungs- und Geräuschanregung bei Stirnradgetrieben. Diss. TU München, 1990].

It is also important to consider the load. The contact ratio is increased by the load and the resulting elastic bending, so it may not be practical to optimize the gear precisely to the specified minima (contact ratio of 1.75 and whole-integer overlap ratio).


Forces in the gear mesh caused by transmitted torque can cause considerable deformation in the gear system. This often leads to an uneven contact pattern, increased pressure, and poor excitation behavior. Variable local deformations mean increased excitation. These local deformations can be compensated for with modifications. A suitable microgeometry can be used to optimize the excitation of the gears.

The influence of the micro-geometry on the excitation behavior is shown in video 1. It is clear that adjustments to the modification also decrease the excitation. Thus, it is essential that both face and profile modifications are optimally designed so that the contact pattern under nominal load is as homogenous and complete as possible.

For loads that deviate from the nominal load, the modifications are usually no longer suitable for the existing deformations, and the noise excitation is increased. In many cases, it is necessary for the gear to have a low excitation over a wide load range.

In contrast to unmodified gears, tip relief in particular has a positive effect. This type of tooth flank modification limits the excitation only moderately, even with significant overcorrection. The last two modifications in video 1 clearly show how little overcorrection of the tip relief negatively affects the excitation.

Video 2 shows the influence of torque on the excitation of a modified stage. Different torque stages from 30 % to 270 % of the nominal load are simulated. All cross-influences, such as non-linearity from the bearing stiffness and deformation in the tooth contact, are completely considered in each calculation. From a load of 130 %, it is clearly shown that the applied modification is no longer sufficient. The excitation increases on an almost linear basis with increasing load, which corresponds to the behavior of an unmodified gear.

In the FVA-Workbench, a load spectrum can be used to calculate the excitation under different loads. The changes to the amplitudes of the rotational travel or the force excitation over the load are available as a result. This makes it possible to easily compare different operating points.

Proposed modifications according to Sigg (AGMA, Paper 109.16 AGMA, 1965) are a suitable starting point for the optimization.

Video 1: Influence of the gear modification on the excitation behavior


Video 2: Transmission error over the load


Designing low-noise gears in the FVA-Workbench

The FVA-Workbench includes all of the tools necessary for designing low-noise gears. In addition to consideration of the excitation using the transmission error, the force excitation and the associated natural frequencies can also be taken into consideration. As the transmission error is often not suitable for comparing two gear variants, the tooth force level can also be shown in the FVA-Workbench. The tooth force level analyzes the excitation amplitudes in the audible range, and is perfectly suited for comparing gear variants.

What have we learned?
  • Noises are created as a result of forced excitation in tooth contact
  • Noise excitation can be reduced by selecting an appropriate contact ratio when designing the gear
  • Modifications that compensate for deformations can significantly reduce the excitation
  • Multiple operating points can be calculated and compared with the FVA-Workbench
  • 50 years of cutting-edge research is made accessible and easy to use

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