In order to accurately predict the power loss generated by a meshing gear pair the gear loss factor must be properly evaluated. Several gear loss factor formulations were compared, including the author's approach.

A gear loss factor calculated considering the load distribution along the path of contact was implemented.

The importance of the gear loss factor in the power loss predictions was put in evidence comparing the predictions with experimental results. It was concluded that the gear loss factor is a decisive factor to accurately predict the power loss. Different formulations proposed in the literature were compared and it was shown that only few were able to yield satisfactory correlations with experimental results. The method suggested by the authors was the one that promoted the most accurate predictions.

According to

According to

Load dependent losses occur in the contact of the power transmitting
components. Load losses depended on the transmitted torque, coefficient of
friction and sliding velocity in the contact areas of the components. Load
dependent rolling bearing losses also depend on type and size, rolling and
sliding conditions and lubricant type

At nominal loads the power loss generated in a gearbox is mainly dependent of the gears load power losses, which puts in evidence the importance of the evaluation of the gear loss factor.

This work shows the influence of the gear loss factor formulation
(considering different gear geometries) in the prediction of the power loss.
The gear loss factor formulations will be compared with experimental results
previously published by

Originally Eq. (

Equation (

The more recent approach of

The load distribution (force per unit of length along the path of contact)
disregarding elastic effects can be calculated dividing the total normal
force

The total length of the lines of contact along the path of
contact can be calculated with the algorithm presented in Appendix

Load distribution of a helical gear with an applied torque of 320 Nm.

The gear loss factor can now be calculated according to Eq. (

Several authors

Gear loss factor comparisson with different formulas.

Assuming that

Considering the power loss generated by the gears in the gearbox (Eq.

From Ohlendof's approach (Eq.

Considering the average power loss generated between gear teeth along the
path of contact according to

The coefficient of friction extracted from the gear mesh power loss obtained
with Eq. (

Geometrical parameters of the gears.

Figure

The H501 and H951 geometries were previously tested for power loss in an FZG
test rig

Torque loss for different gear geometries lubricated with a mineral
wind turbine gear oil

Following Fig.

In order to validate the gear loss factor that was proposed, Schlenk's

Gear loss factor calculated according to different approaches.

In Fig.

Schlenk's Equation should be valid for both helical and spur gear geometries,
also

Correlation between the experimental power loss measured and the predicted with Author, Ohlendorf or KissSoft gear loss factors.

In this work several gear loss factors were compared. The gear loss factor results were indirectly compared with experimental gear power loss measurements in order to assess the validity of each one of the formulations.

An alternative formulation based on the numerical integration of the rigid
load distribution is suggested. The method presented by the authors to solve
the gear loss factor formula proposed by

The results suggest that the classical formulas are accurate only in very specific scenarios. The comparison with the experimental results indicates that the approach suggested by the authors works quite well.

This study has shown the importance of a correct evaluation of the gear loss factor in the prediction of the power loss generated in meshing gears.

Before enter the contact zone of a gear, or the path of contact which value
is given by Eq. (

When the contact starts, the length of the contacting line increases
proportionally to the coordinate of the path of contact, represented by the
first condition of Eq. (

Evolution of a single line along the path of contact.

The same equations deduced for a single line can be used, but the coordinates
should be transformed according to Eq. (

It is also possible to do a 3-D representation of the line length as function
of

The formulation presented is valid for gears with a contact ratio

For the case that one complete line is not in contact, the cycle of meshing
is slightly different and the path of contact is smaller than the transverse
pitch. In such cases usually the overlap contact ratio is

The equation is slightly different from that presented before because the
domains change in a different way as presented in Eq. (

The algorithm previously presented is based on the identification of
different domains in the meshing cycle of helical gears. However, the
different domains can be combined using stepwise functions like Heaviside
(Eq.

Using the hyperbolic tangent equation, the three domains can be expressed in
Eq. (

For the lines screened from the one considered the length is computed with
Eq. (

Using such type of function or other stepwise function is great to get a
continuous function. However, the computational time can increase due to the
expense of computing the step function. The algorithm with step function
works for all the type of gear geometries and the transverse and overlap
contact ratios (

Notation and units.

The authors gratefully acknowledge the funding supported by:

National Funds through Fundação para a Ciência e a Tecnologia (FCT), under the project EXCL/SEM-PRO/0103/2012;

COMPETE and National Funds through Fundação para a Ciência e a Tecnologia (FCT), under the project Incentivo/EME/LA0022/2014;

Quadro de Referência Estratégico Nacional (QREN), through Fundo Europeu de Desenvolvimento Regional (FEDER), under the project NORTE-07-0124-FEDER-000009 – Applied Mechanics and Product Development;