Note: Descriptions are shown in the official language in which they were submitted.
CA 02582737 2007-04-04
Title of the invention
Out-of-round rotation disk for a timing drive
S
Description
Field of the invention
The invention relates to an out-of-round or noncircular rotation disk for a
timing
drive and to a method for constructing and designing a rotation disk of this
type.
The present invention relates, furthermore, to a computer system for designing
a rotation disk of this type.
Background of the invention
Synchronous drive systems, such as, for example, systems based on control
belts, are in widespread use in motor vehicles and in industrial applications.
In
motor vehicles, for example, control belts or control chains are used for
driving
camshafts which open and close engine inlet and outlet valves. Other devices,
too, such as, for example, water and fuel pumps, may likewise be driven by
means of a belt of this type or a chain of this type.
Strand oscillations, as they may be referred to, constitute system-specific ef-
fects on wrap-around gears of this type. In principle, a tension means, such
as,
for example, a chain or a belt, used in wrap-around gears may be excited into
transverse, longitudinal and torsional oscillations. Such oscillations of the
ten-
sion means may appreciably disturb the operation of an overall drive system.
Their occurrence leads to noises and increased structural loads on components
of the drive system due to dynamic force peaks which shorten the useful life
of
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the overall system. Furthermore, for example, in the event of an impact of the
belt strand against adjacent parts which is brought about by transverse
oscilla-
tions, both these parts and the belt itself, too, may be damaged. Even after a
short time, a failure of the overall drive system may therefore occur. Such
strand oscillations are excited by a drive torque of the internal combustion
en-
gine which takes place nonuniformly. In this case, moreover, fluctuations in
the
belt or chain stresses may arise, which may likewise cause higher wear and a
shorter useful life of the belt or chain.
It is known, in drive systems of this type, to provide noncircular or out-of-
round
belt disks, in order to attempt to avoid or rule out such oscillations.
DE-A 195 20 508 discloses a rotating belt drive system for an internal combus-
tion engine, in which a control belt runs around two driven belt disks coupled
to
a camshaft of an engine and around a drive belt disk which is coupled to a
crankshaft of the engine. In this case, it is proposed to reduce torsional
oscilla-
tions by means of an out-of-round belt disk which is illustrated as a camshaft
belt disk.
Utility model publication DE 203 19 172 discloses a noncircular rotation compo-
nent which consists of a rotor having a plurality of teeth arranged on the
circum-
circle of the rotor, each tooth possessing a crown and a depression being lo-
cated between each pair of teeth lying next to one another, and the crowns of
the teeth lying on a curved circumference which forms the circumcircle of the
rotor. In this case, the circumcircle of the rotor has a noncircular profile
with at
least two projecting regions which alternate with drawn-back regions. The spac-
ing between the centerpoints of the crowns of each pair of teeth lying next to
one another and, furthermore, the profile of the depressions between each pair
of teeth lying next to one another are essentially identical. The spacing
between
the centerpoint of each crown and the axis of the rotor on the circumcircle
var-
ies, in order to achieve said noncircular profile.
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In this case, although the design of out-of-round disks of positive tension
gears
is described, the approach described nevertheless contains weaknesses in
terms of methodology. Thus, the utility model publication mentioned assumes a
basic contour in the form of a polygon. This means that an out-of-round disk
provided with teeth has an enveloping line which is approximated by a polygon.
On account of this approach, in the further design of the disk, a chord length
is
used for chain drives and an arc length for toothed belt drives. Furthermore,
a
highly deformed tooth contour arises due to the oblique position of the teeth
arranged on the disk.
Object of the invention
An object of the present invention, then, was to provide, against the
background
of the prior art mentioned, a rotation disk and a corresponding method for de-
signing a rotation disk of this type, in order to eliminate the abovementioned
disadvantages.
Summary of the invention
Proceeding from the prior art mentioned and from the considerations to be de-
rived from this, the present invention provides an out-of-round rotation disk
hav-
ing the features of patent claim 1, a method for designing a rotation disk of
this
type, having the features of patent claim 6, a computer program having the fea-
tures of patent claim 10 and a computer system having the features of patent
claim 13.
According to patent claim 1, a rotation disk rotatable over an angle of
rotation
about an axis of rotation is provided, the rotation disk having a rotation
disk con-
tour possessing at least one elevation, a predetermined number of teeth ar-
ranged on the rotation disk contour and having a respective centerpoint, the
centerpoints of teeth in each case adjacent being at a predetermined spacing,
a
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rotation disk radius which depends functionally on the angle of rotation and
on a
mean radius and a rotation disk looping curve resulting from this, the mean ra-
dius being selected such that a continuous arc length of the rotation disk
loop-
ing curve is equal to the product of the predetermined spacing of the center-
points of adjacent teeth and the nuniber of teeth.
Out-of-round means, within the scope of the present invention, that the radius
of
the disk is not constant, and this may be accompanied by a nonuniform trans-
mission ratio. By means of an out-of-round rotation disk, a timing drive may
experience an excitation, that is to say an excitation to oscillation, which
results
from the disk shape, that is to say the not ideally round shape. As already
men-
tioned initially, rotation disks which are out-of-round in this way may be
used for
the absorption of torsional oscillations in timing drive systems. Causes of
tor-
sional oscillations of this type may be, inter alia, in a combustion process
of an
engine or in nonuniform drive torques of other assemblies, such as, for exam-
ple, pumps. In systems of this type, a correct positioning and profiling of
teeth of
a corresponding rotation disk assume major importance, so as to avoid unnec-
essary loads on a tension means used, such as, for example, a belt or a chain,
in contact with the rotation disk or with the wheel. On the other hand, the
con-
sequence would be a shortened useful life of the tension means.
By a rotation disk according to the invention being used, the oscillation
behavior
of wrap-around gears designed as nonuniformly transmitting gears can be
calmed. Examples of this are found, for example, in the timing and assembly
drives used in automobile construction. However, the rotation disks according
to
the invention can be employed independently of any particular application, for
example also in sectors of textile or office machines.
In the rotation disk according to the invention, the length, covered during a
360
rotation, of the rotation disk looping curve arising from the rotation disk
contour
is equal to the circumference of a round disk which is obtained as a product
of
the predetermined number of teeth and of the predetermined respective spacing
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of adjacent teeth, the rotation disk radius dependent on the angle of rotation
and on the mean radius being used to calculate the length of the rotation disk
looping curve. In this case, a specific mean radius is obtained, which,
however,
may vary, depending on the functional formulation for the rotation disk
radius.
5 What is achieved thereby is that ttie circumference of ttie out-of-round
rotation
disk exactly corresponds, in the effective plane, to that of a round disk. The
ex-
act determination of the circumference or of the length, covered during a 360
rotation, of the rotation disk looping curve is important, since a
transmission
ratio is thereby determined directly, and, to that extent, this is
functionally rele-
vant. Thus, for example, in a timing drive of a passenger car, the
transmission
ratio between a crankshaft used and a camshaft correspondingly used must be
exactly 2:1.
In a further possible embodiment of the rotation disk according to the
invention,
the rotation disk radius can be expressed by a harmonic development of the
following form:
r(r) = rõKaõ + 8n cos(ntt + yx)
in this case rmeaõ being the mean radius, Sr; being an out-of-roundness ampli-
tude, n; being the number of elevations of the rotation disk contour, 4z being
a
phase position and t being a running parameter composed of an interval from 0
to 2rr. As already mentioned, the mean radius is in this case not constant,
but
variable. The mean radius may vary, for example, as a function of the selected
number of elevations n,, also designated below as order, of ttie phase
positions
ep or else of the out-of-roundness amplitudes Sri. The rotation looping curve
as
a three-dimensional curve can be given in coordinate form by means of the an-
gle-dependent radius as follows:
(x(t), y(t))=(r(t)cos(t), r(t)sin(t))
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The mean radius can then be determined in that an arc length, covered during a
360 rotation, of the rotation looping curve given in parameter form (x(t),
y(t)) is
calculated, to be precise by carrying out an integration of the arc lerigth
differen-
tial over an interval of 0 to 2r, and the resulting arc length is equated to
the
product of the predetermined number Z of teeth and the predetermined spacing
D of teeth in each case adjacent:
,T
ZDz~ f x'2(t)+ y'(r)dt
0
In this case, therefore, an arc length between two teeth in the form of the
rota-
tion disk looping curve segment is used instead of the chord length or the
spac-
ing of two centerpoints of adjacent teeth. This approach is more complicated
in
terms of methodology, but leads to correct results in the case of increasing
out-
of-roundnesses. It may be noted, in this context, that, in chain drives, a
chord
length must be used instead of the arc length, since a polygon effect, as it
is
known, comes into effect here on account of the rigidity of the individual
chain
links.
In a further conceivable embodiment of the rotation disk according to the
inven-
tion, the teeth of the rotation disk are oriented such that their respective
center
line is perpendicular to the tangent, contiguous to the respective centerpoint
of
the teeth, of the rotation disk looping curve. Such an orientation of the
teeth
may considerably reduce a load, wherever it may occur, on a tension means
used. In an orientation of tooth spaces occurring between the teeth over a
poly-
gon, the profile of the teeth is distorted. Such distortion, in turn,
.stresses a ten-
sion means used. A residual deformation which nevertheless remains may be
remedied, if appropriate, by a position-dependent and therefore radius-
deperiderit variation in the tooth profile.
In another embodiment of the rotation disk according to the invention, a
looping
arc formed by a tension means at least partially looping around the rotation
disk
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always follows the rotation disk looping curve. This means that the looping
arc
formed by the tension rneans has the greatest possible bearing contact with
the
rotation disk. This means, furthermore, that the rotation disk looping curve
al-
ways possesses a nonnegative curvature.
The present invention relates, furthermore, to a method for designing at least
one rotation disk rotatable over an angle of rotation about an axis of
rotation for
a timing drive, the at least one rotation disk having a rotation disk contour
pos-
sessing at least one elevation, a predetermined number of teeth arranged on
the rotation disk contour and having centerpoints, the centerpoints of teeth
in
each case adjacent being at a predetermined spacing, a rotation disk radius
dependent functionally on the angle of rotation and on a mean radius and a
rotation disk looping curve resulting from this. In the method, in this case,
the
mean radius is determined such that a continuous arc length of the rotation
disk
looping curve is equal to the product of the predetermined spacing of ttie cen-
terpoints of adjacent teeth and the predetermined number of teeth.
In a possible embodiment of the method according to the invention, the
rotation
disk radius is determined by a harmonic development of the following form:
r(t)=rõK,,,,+~gr;cos(rtrt+p)
in this case r,,,ean corresponding to the mean radius, Sr, to an out-of-
roundness
amplitude, n; to the number of elevations, ~% a phase position and t a running
parameter composed of an interval from 0 to 2n. The mean radius rn,o~n is in
this
case variable and is determined separately in each case for a specific formula-
tion, that is to say for a specific selection of the number of elevations,
that is to
say the order, the phase positions or the out-of-roundness amplitudes.
Furthermore, it is conceivable to orient the teeth such that their respective
cen-
ter line is perpendicular to the tangent, contiguous to the respective
centerpoint
of the teeth, of the rotation disk looping curve.
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Moreover, it is conceivable to select the rotation disk contour in such a way
that
the rotation disk looping curve resulting from this always possesses a nonnega-
tive curvature. What is achieved thereby is that a tension means looping
around
the rotation disk has the greatest possible bearing contact with the rotation
disk.
The present invention relates, furthermore, to a product for carrying out a
method according to the invention, the product being a computer program with
a program code which, when the computer program is run on a computer, is
suitable for carrying out a method according to the invention. The computer
program may in this case be stored on a computer-readable medium.
Furthermore, a computer-readable data carrier with a computer program stored
on it is provided, comprising a program code which, when the computer pro-
gram is run on a computer, is suitable for carrying out a method according to
the invention.
Moreover, a computer system with a storage means is proposed, in which a
computer program with a program code is stored, which, when the computer
program is run on a computer, is suitable for carrying out a method according
to
the invention.
It will be appreciated that the features mentioned above and those yet to be
explained below may be used not only in the combination specified in each
case, but also in other combinations or alone, without departing from the
scope
of the present invention.
Brief description of the drawings
The invention is described in detail by means of an exemplary embodiment,
with reference to the drawing in which:
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figure 1 shows a diagrammatic illustration of an embodiment of a
rotation disk according to the invention.
Detailed description of the drawings
Figure 1 shows an out-of-round rotation disk 1. The rotation disk 1 has four
ele-
vations 2. Furthermore, a predetermined number Z of teeth 4 are arranged on
the rotation disk contour 3. In the case illustrated here, 21 teeth are
provided on
the rotation disk contour 3. In this case, a minimum diameter dmin and a maxi-
mum diameter dmax can be determined, and, from these, a diameter difference
Ad. In the present case, the diameter difference Ad is predetermined at 5 mm.
The number n of elevations 2 corresponds to the order which therefore amounts
to 4 here. By means of these particuiars, then, a rotation disk looping curve
can
be specified, in a first approximation, as a three-dimensional curve in the
form
of (x(t), y(t)), as follows:
x(r) = r(t) cos(t) _(r,.~õ +A~/
4 cos(nt)) cos(t)
y(t) = r(t) sin(t) _ (n,w.õ + 6 ~/4 cos(nr)) sin(t)
a phase position rpr of 0 being assumed. The out-of-roundness amplitude sr is
obtained as od/4. Furthermore, a spacing D in each case between two center-
points of adjacent teeth, what is known as a division, was predetermined at
9.525 mm.
By integrating the differential of the arc length of the rotation disk looping
curve
over ari interval of 0 to 271:
2&
x'(t)+y'(t)dr
0
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and by equating with the product of the predetermined number Z of teeth and
the predetermined division D:
,1
5 ZD= f x7(t) + y'(r)dt ,
0
a mean radius is obtained as:
rn, - = 31.6383
this then resulting in the disk contour of:
x(t) = (31.6383 + 1.25cos(4r)) cos(t )
for t E [0.2n[
y(r) _ (31.6383 + 1?5 cos(4t)) sin(t)
It can be seen in this case that, depending on the selected or suitable
functionaf
formulation of the angle-dependent radius, a different mean radius is
obtained.
Thus, the mean radius and, coupled to this, the angle-dependent radius are
always adapted to the basic system. The rotation disk looping curve occurring
in
each case is therefore adapted highly flexibly to existing stipulations. The
exact
determination of the mean radius or the length of the rotation disk looping
curve
as an image of the out-of-round contour of the rotation disk is highly
relevant in
functional terms and is in direct relation to a transmission ratio of the
rotation
disk. Thus, for example, a transmission ratio between a camshaft and a crank-
shaft in the timing drive of a passenger car must be exactly 2:1. Only by an
ex-
act determination of the mean radius or of the rotation disk looping curve can
such stipulations be fulfilled.
Furthermore, an orientation of teeth takes place such that the center line of
a
tooth is perpendicular to the tangent to the rotation disk looping curve. A
slight
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residual deformation nevertheless possibly remains and could be remedied by a
position-dependent and therefore radius-dependent variation in the tooth
profile.
Moreover, a tension means, in the overall run of its looping arc, is as far as
pos-
sible always to lie on the disk. This means that a looping arc formed by a ten-
sion means at least partially looping around the rotatiori disk always follows
the
rotation disk looping curve. This is equivalent to the requirement that the
rota-
tion disk looping curve is always to possess a nonnegative curvature.
This requirement must always be taken into account in selecting the parameters
in the harmonic formulation made.
The present invention, in all aspects, has many applications in devices which
require a noncircular rotation disk, and it is used especially in synchronous
drive
devices. These may be, for example, an internal combustion engine. The inven-
tion, however, may also be used in devices other than synchronous drive de-
vices. The out-of-round or noncircular shape of the rotation disk may be pro-
vided at many different locations in a drive device. The selection of the
rotation
disk contour depends on other components of a drive device, In this case, a
uniform noncircular profile or a nonuniform profile or contour for the
rotation disk
may arise. In these circumstances, for reasons of performance and useful life,
a
tension means and the rotation disk must fit with one another as well as possi-
ble.
