GRANT
journal
ISSN 1805-062X, 1805-0638 (online), ETTN 072-11-00002-09-4
EUROPEAN GRANT PROJECTS | RESULTS | RESEARCH & DEVELOPMENT | SCIENCE
is the most critical change of amplitude. Its main cause is alterative
stiffness of teeth and shock when teeth enter the image, due to the
deformation, deviation of gaps and tooth profile from the theoretical
ones. Many other effects, i.e. vibrations transmitted into the gearing
from the driving or powered aggregate, oscillation of the shafts and
bearings, influence the vibrations in cogged wheels in a mesh. All of
these elements play a role in the enlargement of amplitude in
gearing. The total energy of the radiated noise further increases.
A specific source of noise comes from the creation of shock
influenced by the axial and side (cogged) will-power of the cogged
wheels with slanted cogging. Arises mainly in little loaded
gearwheels (eg idling internal combustion engine), or vice versa
when heavily loaded gear wheels too slowly. This contributes
irregular running the drive unit and there is a torsional vibration
(change of angular accelerations during one rotation). Consequently,
the engines of modern automobiles have a dual-mode flywheel and
clutches with an intervention absorber. Among other elements
causing noise during cogging intervention belongs so-called Air
Pocketing (related with the air pockets in lubricant) a Lubricant
Entrainment (due to the small will-power, the excess lubricant is not
squeezed from the intervention and stresses the cogging with added
dynamic forces which cause the increase in vibrations). The gearbox
includes components which can be the sources of noise and
vibrations themselves, or they create the vibrations as well as
transmit and enlarge them. Added components, such as driving
components, bearings and shafts all belong to the gearbox. The
primary components are the bearings, which are the second most
essential source of noise in cogging. Vibrations are created by
generating of rolling components in a bearing on its inner and outer
course. Their frequency is given by pitting as well as by
imperfection of the functional planes, which are created by abrasion
or by the deformation from a grip.
Fig. 1 Example of evaluation of noise gearbox of car [6]
A dominant contribution of noise in a gearbox; however, comes
from the creation of vibrations during intervention of the cogged
wheels. On Fig. 1, a total evaluation of gearbox noise in an
automobile, where the contribution of separated noise of the gearbox
intervention (defined as N and 3) is at maximum 40 % of the
gearbox noise with a contribution of 53% to the total noise, is
displayed. The remaining 47% constitute for the background noise
(defined as Bgr), inside which mainly the noise created by bearing is
incorporated.
For a detailed analysis of the causes of vibration revealed significant
impact on the gear mesh of the intensity of vibration. In [6] was
expressed that dependence on uncorrected teeth of spur gear (Fig.2).
Local minimums of noise occurring at integer values of coefficients
and gear mesh
ε
α
a
ε
β
.
Fig.2. Influence
ε
α
and
ε
β
for trefoil of noise
ε
α
ε
- coefficient profile of gear mesh, profile mesh path corresponds
to the line of contact and is the ratio of the gear mesh path in front
of the plane to pitch in front of a plane at the base circle.
β
- coefficient step in gear mesh. It is the ratio of the face width of
the teeth to the axial pitch.
Based on experiments and experience of renowned manufacturers
gears showed that reducing noise respectively vibration resistance
increases. Significant improvement in quality gears is achieved
under certain principles in coefficient
ε
α
and
ε
β
, which include:
minimum vibration is achieved at any size with
ε
α
integer value
ε
β
vibration excitation in increasing integer values of
ε
,
β
for any
ε
steadily
decreasing,
β
vibration excitation decreases with increasing value of
ε
α
for integer values of
ε
values from 1 to the value of 1.7
÷ 1.8, where there is a local
minimum,
β
is always at an absolute minimum value
ε
α
= 2.
The noise in gear transmissions particularly affects periodic change
of stiffness teeth during meshing caused by changing the number of
pairs of teeth, which are simultaneously in meshing.
3.
TEETH STIFFNESS AND THEIR IMPACT FOR
GEARBOX NOISE
Deformations of teeth are generally quantified by tooth stiffness,
which is defined as the ratio of load to deformation.
Knowledge of the deformation properties of gearing is very
important. Consider first the one tooth (Fig. 3-a). Action of the
resulting normal force F is deformed tooth. This is shown in the
figure by a thin line. The resultant deformation in the direction of
action of the normal force
δ
i
(i = 1,2 - index that distinguishes
whether it is a tooth of the pinion - drive wheel or driven wheel
tooth) consists of a deflection bending, shear, deformation in the
area of constraint and the touch deformation.
a)
b) c)
Fig. 3 a) The deformation of the tooth, b) - c) deformation of a one
pair of spur gear teeth
δ
i
F
X
1
X
2
X
ϕ
δ2
δ
δ
1
δ
2
τ
b
δ
2
=ϕ
δ2.
r
b2
ϕ
δ1
δ
1
=ϕ
δ1.
r
b1
X
1
X=X
2
X
τ
b
δ
δ
1
δ
2
δ
1
=ϕ
δ.
r
b1
1
ϕ
δ
1
Vol. 9, Issue 1
111