U.S. patent application number 11/437306 was filed with the patent office on 2006-10-19 for tire manufacturing method for improving the uniformity of a tire.
Invention is credited to William David Mawby, George Phillips O'Brien, Eugene Marshall Persyn, James Michael Traylor.
Application Number | 20060231191 11/437306 |
Document ID | / |
Family ID | 34631099 |
Filed Date | 2006-10-19 |
United States Patent
Application |
20060231191 |
Kind Code |
A1 |
Mawby; William David ; et
al. |
October 19, 2006 |
Tire manufacturing method for improving the uniformity of a
tire
Abstract
A tire manufacturing method includes a method for optimizing the
uniformity of a tire by reducing the after cure radial force
variation. The after cure radial force variation vector is modeled
as a vector sum of each of the vectors representing contributions
arising from the tire building steps--the "tire room effect vector"
and a vector representing contributions arising from the
vulcanization and uniformity measurement steps--the "curing room
effect vector." In further detail, both the tire room and curing
room effect vectors can be further decomposed into sub-vectors
representing each radial force variation contribution for which a
measurable indicator is available. For a series of tires, the
method obtains such measurements as the before cure radial runout
(RRO) at one or more stages of the building sequence, measurements
of loading angles on the tire building equipment, and measurements
made during vulcanization process.
Inventors: |
Mawby; William David;
(Greenville, SC) ; O'Brien; George Phillips;
(Piedmont, SC) ; Persyn; Eugene Marshall;
(Comfort, TX) ; Traylor; James Michael; (Greer,
SC) |
Correspondence
Address: |
Michelin North America, Inc.;Intellectual Property Department
P.O. Box 2026
Greenville
SC
29602-2026
US
|
Family ID: |
34631099 |
Appl. No.: |
11/437306 |
Filed: |
May 19, 2006 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
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PCT/US04/39021 |
Nov 19, 2004 |
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11437306 |
May 19, 2006 |
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PCT/IB03/06462 |
Nov 21, 2003 |
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PCT/US04/39021 |
Nov 19, 2004 |
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Current U.S.
Class: |
156/110.1 ;
73/146 |
Current CPC
Class: |
B29D 2030/0665 20130101;
G01M 1/30 20130101; B29D 30/0662 20130101 |
Class at
Publication: |
156/110.1 ;
073/146 |
International
Class: |
B29C 35/00 20060101
B29C035/00 |
Claims
1. A method for improving the after cure uniformity of a tire
comprising: (a) Determining a set of vector coefficients for
estimating the after cure radial force variation of a tire; (b)
Estimating the after cure uniformity of an individual tire
comprising the sub-steps of: (i) Measuring a before cure radial
runout characteristic of said individual tire; (ii) Choosing a
harmonic of radial force variation to be optimized; (c) Optimizing
the after cure uniformity of said individual tire from said vector
coefficients, comprising the sub-steps of: (i) Estimating a loading
angle of one or more tire components according to an optimization
criterion; (ii) Loading said components on the corresponding
manufacturing tooling at said loading angle.
2. The method for improving the uniformity of a tire according to
claim 1, further comprising the steps of aligning said individual
tire at a predetermined curing room azimuth angle, loading said
individual tire in said curing mold, and curing said tire.
3. The method for improving the uniformity of a tire according to
claim 1, wherein said component comprises a tire carcass and said
tooling comprises a second stage building drum
4. The method for improving the uniformity of a tire according to
claim 1, wherein the said tire component comprises a tread and belt
assembly and said tooling comprises a building form.
5. The method for improving the uniformity of a tire according to
claim 1, wherein said optimization criterion is the magnitude of a
tire room effect vector and is substantially equal to the magnitude
of a curing room effect vector.
6. The method for improving the uniformity of a tire according to
claim 1, wherein said optimization criterion is the magnitude of a
tire room effect vector and is substantially equal to zero.
7. The method for improving the uniformity of a tire according to
claim 1, wherein a pair of said vector coefficients comprises a
first stage building drum vector.
8. The method for improving the uniformity of a tire according to
claim 1 wherein a pair of said vector coefficients comprises a
second stage building drum vector.
9. The method for improving the uniformity of a tire according to
claim 1 wherein a pair of said vector coefficients comprises a
tread and belt building form vector.
10. The method for improving the uniformity of a tire according to
claim 1 wherein a pair of said vector coefficients comprises a
transfer ring vector.
11. The method for improving the uniformity of a tire according to
claim 1 wherein said vector coefficients comprises a carcass radial
runout vector and a gain vector.
12. The method for improving the uniformity of a tire according to
claim 1, wherein said vector coefficients comprises a tread and
belt assembly radial runout vector and a tread and belt assembly
radial runout vector gain vector.
13. The method for improving the uniformity of a tire according to
claim 1, wherein said vector coefficients comprises a green tire
radial runout vector and a green tire radial runout vector gain
vector.
14. The method for improving the uniformity of a tire according to
claim 1, wherein said vector coefficients comprises a curing room
effect vector.
15. The method for improving the uniformity of a tire according to
claim 1, wherein said vector coefficients comprises an intercept
vector.
16. The method for improving the uniformity of a tire according to
claim 1, wherein a tire room effect vector comprises the vector sum
of a before cure tire effect vector, a building drum vector, and an
intercept vector.
17. The method for improving the uniformity of a tire according to
claim 16, wherein said before cure tire effect vector comprises the
vector sum of a carcass vector, a first stage building drum tooling
vector, a tread and belt assembly vector, and a tread and belt
assembly tooling vector.
18. The method for improving the uniformity of a tire according to
claim 16, wherein said vector sum of said tire room effect vector
further comprises a transfer ring tooling vector.
19. The method for improving the uniformity of a tire according to
claim 1, wherein a before cure tire effect vector comprises a
vector product of a tire gain vector and a green tire radial runout
vector of said harmonic.
20. The method for improving the uniformity of a tire according to
claim 1, wherein the step of determining said vector coefficients
is performed in a simultaneous action.
21. The method for improving the uniformity of a tire according to
claim 20, wherein said simultaneous step comprises a multivariate
least-squares regression.
22. The method for improving the uniformity of a tire according to
claim 1, wherein said radial runout characteristic is measured on a
tire carcass.
23. The method for improving the uniformity of a tire according to
claim 1, wherein said radial runout characteristic is measured on a
tire tread and belt assembly.
24. The method for improving the uniformity of a tire according to
claim 1, wherein said radial runout characteristic is measured on a
finished tire.
25. A method for improving the uniformity of a tire comprising the
steps of: (a) Determining a set of vector coefficients for
estimating the after cure radial force variation of a tire; (b)
Estimating the after cure uniformity of an individual tire
comprising the sub-steps of: (i) Measuring a before cure radial
runout characteristic of said individual tire; (ii) Choosing a
harmonic of radial force variation to be optimized; (iii)
Estimating said after cure uniformity from said vector
coefficients. (c) Aligning said individual tire at a predetermined
curing room azimuth angle, loading said individual tire in said
curing mold, and curing said tire.
26. The method for improving the uniformity of a tire according to
claim 25, wherein the step of determining a set of vector
coefficients further comprises the sub-steps of: (i) Measuring a
before cure radial runout characteristic of a plurality of tires at
least one predetermined step during the manufacture of said tires;
(i) Recording a loading angle of said finished tires in a curing
mold and curing said tires, (iii) Measuring the after cure radial
force variation for each of said tires; (iv) Extracting at least
one harmonic of the radial runout and of the radial force variation
of said tires; (v) Determining a set of vector coefficients
relating the before cure radial runout to the after cure radial
force variation of said tires cured in said mold; (vi) Storing said
vector coefficients.
27. The method for improving the uniformity of a tire according to
claim 25, wherein the step of determining a set of vector
coefficients further comprises the sub-step of recording a loading
angle of a tire carcass on a measurement fixture, and the step of
estimating the after cure uniformity of an individual tire further
comprises the sub-step of recording a loading angle of a carcass of
said individual tire on said measurement fixture.
28. The method for improving the uniformity of a tire according to
claim 27, wherein said measurement fixture is a tire building
drum.
29. The method for improving the uniformity of a tire according to
claim 27, wherein the sub-step of measuring the before cure radial
runout is carried out with a measurement fixture comprising a
tangential imaging means.
30. The method for improving the uniformity of a tire according to
claim 25, wherein the sub-step of measuring the before cure radial
runout is carried out on a tire building drum at the completion of
assembly of said tire.
31. The method for improving the uniformity of a tire according to
claim 1, wherein said steps of determining a set of vector
coefficients and estimating the after cure uniformity comprises a
multivariate least-squares regression of a set of matrix equations
corresponding to multiple building drums and multiple curing
cavities.
32. The method for improving the uniformity of a tire according to
claim 1, further comprising the steps of recording an identifier
for a specific building drum and for a specific curing
category.
33. The method for improving the uniformity of a tire according to
claim 1, wherein the step of determining a set of vector
coefficients further comprises the sub-step of recording a loading
angle of a cured tire on a uniformity measurement machine.
34. The method for improving the uniformity of a tire according to
claim 1, wherein a pair of said vector coefficients corresponds to
a uniformity machine vector.
35. The method for improving the uniformity of a tire according to
claim 1, wherein the step of determining a set of vector
coefficients is repeatedly updated using data from said individual
tire.
36. The method for improving the uniformity of a tire according to
claim 1, wherein said step of determining a set of vector
coefficients and said step of optimizing the after cure uniformity
are carried out using the first through fifth harmonics of the
radial force variation of said tire.
Description
CROSS REFERENCE
[0001] This application is a continuation of previously filed PCT
application "Tire Manufacturing Method for Improving the Uniformity
of a Tire", assigned PCT/US2004/039021, filed Nov. 19, 2004, which
is a continuation-in-part of PCT application "Tire Manufacturing
Method for Improving the Uniformity of a Tire", assigned
PCT/IB2003/006462, filed Nov. 21, 2003.
BACKGROUND OF THE INVENTION
[0002] The present invention relates to a manufacturing method for
tires, more specifically a method for improving the uniformity of a
tire by reducing the after cure radial force variation. In a tire,
and more precisely, a radial tire, the after cure radial force
variation (RFV) can be affected by many variables introduced from
the process of assembly of the green (uncured) tire and during
curing of the tire. When the radial force variation in a cured tire
exceeds acceptable limits, the result may be unwanted vibrations
affecting the ride and handling of the vehicle. For these reasons,
tire manufacturers strive to minimize the level of radial force
variation in the tires delivered to their customers.
[0003] A well-known and commonly practiced method to improve the
after cure RFV is to grind the tread surface of the tire in the
zones corresponding to excess radial force. This method is
effective, but has the drawback of creating an undesirable surface
appearance and of removing wearable tread rubber from the product.
In addition, this method requires an extra manufacturing step and
uses expensive equipment. Alternatively, the after cure RFV may be
improved by the method described in U.S. Pat. No. 5,365,781 where
the sidewalls of the cured tire are physically deformed in a
controlled manner in response to a measured uniformity
characteristic. This method eliminates the undesirable removal of
tread rubber, but still requires an extra manufacturing step and
high-cost equipment.
[0004] An alternative to after cure correction of RFV is to treat
the sources of RFV in the tire before cure. For example, it is well
known in the tire industry to stagger the starting points of the
various tire products during the assembly process, followed by
observing the effect on after cure RFV. These data are then used to
specify an optimum arrangement of product start points for each of
the tire building steps according to the configuration that best
minimizes after cure RFV. Another approach is disclosed in U.S.
Pat. No. 5,882,452 where the before cure radial runout (RRO) of the
tire is measured, followed by a process of clamping and reshaping
the uncured tire to a more circular form.
[0005] Still another approach to a manufacturing method for
improved uniformity involves a method where the factors relating to
tire building and tire curing that contribute to after cure RRO or
RFV are offset relative to a measured before cure RRO. An example
of a typical method is given in Japanese Patent Application
JP-1-145135. In these methods a sample group of tires, usually
four, are placed in a given curing mold with each tire rotated an
equal angular increment. The angular increment is measured between
a reference location on the tire, such as a product joint, relative
to a fixed location on the curing mold. Next, the tires are
vulcanized and their composite RFV waveforms recorded. The term
"composite waveform" means the raw waveform as recorded from the
measuring device. The waveforms are then averaged by superposition
of each of the recorded waveforms upon the others. Superposition is
a point by point averaging of the recorded waveforms accomplished
by overlaying the measured composite waveform from each tire. The
effects of the vulcanization are assumed to cancel, leaving only a
"formation" factor related to the building of the tire. In like
manner, another set of sample tires is vulcanized in a curing mold
and their respective RFV waveforms are obtained. The respective
waveforms are again averaged by superposition, this time with the
staring points of the waveforms offset by the respective angular
increments for each tire. In this manner, the effects of tire
building are assumed to cancel, leaving only a "vulcanization
factor." Finally, the average waveforms corresponding to the
formation factor and the vulcanization factor are superimposed. The
superimposed waveforms are offset relative to each other in an
attempt to align the respective maximum of one waveform with the
minimum of the other waveform. The angular offset thus determined
is then transposed to the curing mold. When uncured tires arrive at
the mold, each tire is placed in the mold at the predetermined
offset angle. In this manner, the formation and vulcanization
contributions to after cure RFV are said to be minimized. A major
drawback to this method is its assumption that the formation and
vulcanization contributions to after cure RFV are equivalent for
each tire. In particular, the factors contributing to the formation
factor can vary considerably during a manufacturing run. In fact,
these methods contain contradictory assumptions. The methodology
used to determine the vulcanization factor relies on an assumption
that the step of rotation of the tires in the curing mold cancels
the tire building (or formation) effects. This assumption is valid
only when the contribution of before cure RRO is consistent from
one tire to the next tire, without random contributions. If this
assumption is true, then the subsequent method for determination of
the formation factor will produce a trivial result.
[0006] Further improvements have been proposed in Japanese Patent
Application JP-6-182903 and in U.S. Pat. No. 6,514,441. In these
references, methods similar to those discussed above are used to
determine formation and vulcanization factor waveforms. However,
these methods add to these factors an approximate contribution of
the before cure RRO to the after cure RFV. The two methods treat
the measured before cure RRO somewhat differently. The method
disclosed in reference JP-6-198203 optimizes RRO effects whereas
the method disclosed in U.S. Pat. No. 6,514,441 estimates RFV
effects by application of a constant stiffness scaling factor to
the RRO waveform to estimate an effective RFV. Both these methods
continue to rely on the previously described process of overlapping
or superpositioning of the respective waveforms in an attempt to
optimize after cure RFV.
[0007] The most important shortcoming of all the above methods is
their reliance of superpositioning or overlapping of the respective
waveforms. It is well known in the tire industry that the vehicle
response to non-uniformity of RFV is more significant in the lower
order harmonics, for example harmonics one through five. Since, the
above methods use composite waveforms including all harmonics,
these methods fail to optimize the RFV harmonics to which the
vehicle is most sensitive. In addition, a method that attempts to
optimize uniformity using the composite waveforms can be shown, in
some instances, to produce after cure RFV that actually increases
the contribution of the important lower order harmonics. In this
instance, the tire can cause more vehicle vibration problems than
if the process were not optimized at all. Therefore, a
manufacturing method that can optimize specific harmonics and that
is free of the aforementioned assumptions for determining the
effects of tire formation and tire vulcanization would be capable
of producing tires of consistently improved uniformity.
SUMMARY OF THE INVENTION
[0008] In view of the above background, the present invention
provides a tire manufacturing method that can effectively reduce
the after cure radial force variation (RFV) of each tire produced.
The method of the present invention operates to optimize each
harmonic of RFV. A composite RFV signal, such as those described
above, is a scalar quantity that is the variation of the tire's
radial force at each angular position around the tire from the
average radial force corresponding to the vertical load applied to
the tire. When this composite is decomposed into its respective
harmonic components, each harmonic of RFV can be expressed in polar
coordinates as an after cure RFV vector. This vector has a
magnitude equal to the peak-to-peak magnitude of the force
variation of the respective harmonic and an azimuth equal to the
angular difference between the measuring reference point and the
point of maximum RFV.
[0009] The method of the present invention provides a significant
improvement over previous methods by employing a vectorial
representation of the several factors that contribute to the
measured after cure RFV for a tire produced by a given process. The
after cure RFV vector is modeled as a vector sum of each of the
vectors representing RFV contributions arising from the tire
building steps--the "tire room effect vector" and a vector
representing RFV contributions arising from the vulcanization and
uniformity measurement steps--the "curing room effect vector." In
further detail, both the tire room and curing room vectors can be
further decomposed into sub-vectors representing each RFV
contribution for which a measurable indicator is available. For a
series of tires, the method obtains such measurements as the before
cure radial runout (RRO) at one or more stages of the building
sequence, measurements of loading angles on the tire building
equipment, and measurements made during vulcanization process.
After vulcanization, the tires are mounted on a uniformity
measurement machine and the measured after cure RFV harmonic
components are obtained. At this point, none of the coefficients
for the magnitude and azimuth of the sub-vector components is
known.
[0010] The present invention further improves on previously
described methods since it does not rely on manipulation of the
measured, composite RFV waveforms to estimate the tire room and
curing room effects and does not rely on any of the previously
described assumptions. The present invention uses the
aforementioned measured data as input to a single analysis step.
Thus, the coefficients of all the sub-vectors are simultaneously
determined. Once these coefficients are known, the tire room effect
vector and curing room effect vector are easily calculated.
Thereafter, as the individual tires are manufactured, the before
cure RRO and other manufacturing data are measured and recorded at
one or more steps during the manufacture of the tires. These data
are input to the vector model and the magnitude and azimuth of the
tire room effect are calculated. Finally, the estimated tire room
and curing room effect vectors are used to calculate the angular
orientation of the uncured tire in the curing mold that will
minimize after cure RFV for that individual tire. In summary, A
method for improving the uniformity of a tire comprises the steps
of: [0011] (a) Determining a set of vector coefficients for
estimating the after cure radial force variation of a tire; [0012]
(b) Estimating the after cure uniformity of an individual tire
comprising the sub-steps of:
[0013] (i) Measuring a before cure radial runout characteristic of
said individual tire;
[0014] (ii) Choosing a harmonic of radial force variation to be
optimized;
[0015] (iii) Estimating said after cure uniformity from said vector
coefficients; [0016] (c) Aligning said individual tire at a
predetermined curing room azimuth angle, loading said individual
tire in said curing mold, and curing said tire.
[0017] The method of the invention just described further improves
on previous methods in its treatment of the factors relating before
cure RRO to after cure RFV. It has been found that RRO variations
on the before cure tire do not always produce an after cure RFV
contribution that is a scalar multiple of the RRO vector either in
magnitude or azimuth. Thus, a scalar representation that relies on
a simple stiffness factor can lead to erroneous result.
[0018] The contribution of green tire RRO to after cure RFV may at
least include effects owing to the radial RRO of the green tire
carcass, the RRO of the tread and belt assembly, and a certain
level of RRO owing to manufacturing tooling effects not accounted
for by any of the green tire RRO effects. In the present invention
method, the contribution of the green RRO to after cure RFV is
modeled as the vector product of a gain vector GC and a green tire
RRO vector GR1. The gain vector correctly models the transformation
from before cure RRO to after cure RFV. At least one pair of vector
coefficients corresponds to the gain vector.
[0019] A first part of the green tire vector can be estimated by
combining the first harmonic RRO vector of the green carcass, GR1C,
with a carcass gain vector, GNC. The vector product of GNC and GR1C
is known as the carcass effect vector. This effect may vary from
tire to tire.
[0020] A second part of the green tire vector may be modeled by
combining the first harmonic of the RRO vector of the green tread
and belt assembly, GR1T, with a tread and belt assembly gain
vector, GNT. The vector product of GNT and GR1T is known as the
tread and belt assembly effect vector. This effect may also vary
from tire to tire.
[0021] A third part of the green tire vector is due to "tooling"
effects not captured by GR1C or GR1T. These tooling vectors are
constant vectors and whose magnitude is not expected to vary from
tire to tire. Examples of the tooling effects are vector components
related to tire building apparatus such as the First Stage Building
drum vector, the Second Stage Building drum vector, Tread and Belt
Assembly Building drum vector, and the Transfer Ring vector. The
Intercept vector models any other constant effect not described by
any of the previous vectors.
[0022] The tooling effects allow an improvement to the accuracy of
the model. The measured RRO is the sum of the actual green tire RRO
and the RRO of the measuring device upon which the tire is
currently mounted, be it building drum or a measurement apparatus.
In this improvement of the method, the step of determining a set of
vector coefficients further compromises the sub-step of recording a
loading angle of a tire carcass on any or a combination of the
first stage tire building drum, second stage tire building drum, or
transfer ring. Likewise, the step of estimating the after cure
uniformity of an individual tire further compromises the sub-step
of recording a loading angle of a carcass of an individual tire on
the same tooling.
[0023] The tooling effects may be manipulated during the tire
building steps to minimize further the after cure RFV. This is
accomplished by altering the magnitude of the tire room effect
vector according to an optimization criterion. This method
comprises the steps of: [0024] Determining a set of vector
coefficients for estimating the after cure radial force variation
of a tire; [0025] (b) Estimating the after cure uniformity of an
individual tire comprising the sub-steps of:
[0026] (i) Measuring a before cure radial runout characteristic of
said individual tire;
[0027] (ii) Choosing a harmonic of radial force variation to be
optimized; [0028] (c) Optimizing the after cure uniformity of said
individual tire from said vector coefficients, comprising the
sub-steps of:
[0029] (i) Estimating a loading angle of one or more tire
components according to an optimization criterion;
[0030] (ii) Loading said components on the corresponding
manufacturing tooling at said loading angle.
[0031] The after cure RFV can be further improved is the
manufacturing process permits the loading of the tire in a mold at
a predetermined azimuth angle. In this instance, the optimization
criterion is that the magnitude of a tire room effect vector is
substantially equal to the magnitude of a curing room effect
vector. The green tire is then aligned at the predetermined curing
room azimuth angle, loaded in a curing mold, and cured.
[0032] In the event that the manufacturing process does not permit
the loading of the tire in a mold at a predetermined azimuth, then
the optimization criterion is to minimize the magnitude of the tire
room vector alone. In either of these methods of implementation of
the model, the RRO is measured during the building of the tire for
the RRO of the completed green carcass, the RRO of the tread and
belt assembly, and for the finished green tire. At each
intermediate step the then measured RRO may be offset by an azimuth
matching with the tooling effects.
[0033] The method of the invention has an additional advantage
owing to its simultaneous determination of the sub-vectors. Unlike
previous methods, the method of the invention does not require any
precise angular increments of the loading positions to determine
the sub-vectors. This opens the possibility to update continuously
the sub-vector coefficients using the measured data obtained during
the production runs. Thus, the method will take into account
production variables that arise during a high volume production
run.
BRIEF DESCRIPTION OF THE DRAWINGS
[0034] The invention will be better understood by means of the
drawing accompanying the description, illustrating a non-limitative
example of the execution of the tire manufacturing method for
improving the uniformity of a tire according to the invention.
[0035] FIG. 1 is a schematic representation of a tire manufacturing
process equipped to practice the method of the invention.
[0036] FIG. 2A-FIG. 2C depict schematic representations of a
uniformity measurement of the radial force variation of a tire
showing the original composite waveform as well as several harmonic
components.
[0037] FIG. 3 is a vector polar plot of the method of the invention
showing the contributions of the tire room and curing room vectors
to the after cure radial force variation of a tire.
[0038] FIG. 4 is a vector polar plot of the method of the invention
demonstrating the optimization of cured tire uniformity.
[0039] FIG. 5 is a vector polar plot of the method of the invention
showing the contribution of green tire radial runout to the tire
room effect vector.
[0040] FIG. 6 is a vector polar plot of the method of the invention
showing the effect on the green tire vector of the measurement drum
used to measure green radial runout.
[0041] FIG. 7 is a vector polar plot of the method of the invention
adding the effect of the after cure uniformity measurement
machine.
[0042] FIG. 8 is a vector polar plot of an expanded method of the
invention showing the effect on the green tire vector of additional
components effects due to green tire carcass, the tread and belt
assembly, and for the tooling effects of First Stage drum, the
Tread and Belt Assembly drum, and the Transfer Ring.
[0043] FIG. 9 is a vector polar plot of an expanded method of the
invention demonstrating the optimization of cured tire
uniformity.
DETAILED DESCRIPTION
[0044] Reference will now be made in detail to exemplary versions
of the invention, one or more versions of which are illustrated in
the drawings. Each described example is provided as an explanation
of the invention, and not meant as a limitation of the invention.
Throughout the description, features illustrated or described as
part of one version may be usable with another version. Features
that are common to all or some versions are described using similar
reference numerals as further depicted in the figures. The
following Table 1 indicates the specific terminology employed
herein. Note that the CBD_REF, FBD.sub.--REF, SBD_REF, TSR_REF, and
CAV_REF are scalar quantities for the reference angles that are
recorded during the tire manufacturing steps. TABLE-US-00001 TABLE
1 Vector Nomenclature Vector Magnitude Azimuth Radial Force (VRH1)
VRM1 VRA1 Carcass Green (RRO) FRM1C FRA1C (GR1C) Gain Carcass (GNC)
GC .theta.C Tread Green RRO FRM1T FRA1T (GR1T) Gain Tread (GNT) GT
.theta.T Green Tire RRO FRM1 FRA1 (GR1) Gain (GN) GN .theta. First
Stage Tooling TM1 TA1 (T1) Second Stage Tooling TM2 TA2 (T2) Tread
and Belt TM3 TA3 Assembly (T3) Transfer Ring Tooling TM4 TA4 (T4)
Intercept (I1) IM1 IA1 Tire Room Effect TRM1 TRA1 (TR1) Curing Room
Effect CM1 CA1 (CR1) First Stage Loading -- CBD_REF Angle Second
Stage Loading -- FBD_REF Angle Tread and Belt SBD_REF Assembly
Loading Angle Transfer Ring Loading -- TSR_REF Angle Curing Cavity
-- CAV_REF Loading Angle
[0045] Modern pneumatic tires are generally manufactured with great
care and precision. The tire designer's goal is a finished tire
that is free of non-uniformity in either the circumferential or the
lateral directions. However, the designer's good intentions
notwithstanding, the multitude of steps in the tire manufacturing
process can introduce a variety of non-uniformities. An obvious
non-uniformity is that the tire may not be perfectly circular
(radial runout or RRO). Another form of non-uniformity is radial
force variation (RFV). Consider a tire mounted on a freely rotating
hub that has been deflected a given distance and rolls on a flat
surface. A certain radial force reacting on the flat surface that
is a function of the design of the tire can be measured by a
variety of known means. This radial force is, on average, equal to
the applied load on the tire. However, as the tire rolls, that
radial force will vary slightly due to variations in the internal
tire geometry that lead to variations in the local radial stiffness
of the tire. These variations may be caused on the green tire by
localized conditions such as product joints used in the manufacture
of the green tire or inaccurate placement of certain products. The
process of curing the tire may introduce additional factors due to
the curing presses or slippage of products during curing.
[0046] FIG. 1 shows a simplified depiction of the tire
manufacturing process. A tire carcass 10 is formed on a building
drum 15. In a unistage manufacturing process, the carcass 10
remains on the drum 15. In a two-stage process, the carcass 10
would be removed from the drum 15 and moved to a second stage
finishing drum (not shown). In either case, the carcass 10 is
inflated to receive a finished tread band 20 to produce the
finished green tire 30. In one variation of the invention, the RRO
of the green tire 30 is measured by a measurement system 70 using a
barcode 35 as a reference point. The RRO waveform is stored, here
in a computer 80. The green tire 30 is moved to the curing room
where the orientation angle of the tire CAV_REF is recorded. The
tire is then loaded into a curing cavity 40 and cured. The cured
tire 30' is moved to a uniformity measurement machine 50 for
measurement and recording of the tire RFV.
[0047] FIG. 2A shows a schematic of the measured RFV for a cured
tire 30'. The abscissa represents the circumference of the tire and
the ordinate the radial force variations. FIG. 2A is the
as-measured signal and is referred to as a composite waveform. The
composite waveform may comprise an infinite series of harmonics.
The individual harmonics may be obtained by applying Fourier
decomposition to the composite signal. FIGS. 2B and 2C depict the
resulting first and second harmonics, respectively, extracted form
the composite signal. The magnitude of the first harmonic of radial
force VRM1 is defined as the difference between the maximum and
minimum force. The phase angle or azimuth of the first harmonic
VRA1 is defined as the angular offset between the reference
location for the measurement and the location of maximum radial
force. Thus, the sine wave depicted by Cartesian coordinates in
FIG. 2B can be equally shown as a vector in a polar coordinate
scheme. Such a vector polar plot is shown in FIG. 2C immediately to
the right of the sine wave plot. The RFV vector of the first
harmonic VRH1 has a length equal to VRM1 and is rotated to an angle
equal to the azimuth VRA1. In a similar manner, one can extract the
second harmonic vector VRH2 shown in FIG. 2C that has a force
magnitude VRM2 and an azimuth VRA2. The corresponding polar plot
for the H2 vector resembles the H1 vector, except that the angular
coordinate is now two times the azimuth angle.
[0048] In the description of an example of the method that follows,
the particular example is confined to the optimization of the first
harmonic H1. However, it is within the scope of the present
invention to apply the method to optimize a different harmonic such
as H2, H3, etc. Likewise, the following example describes the
optimization of radial force variation, whereas it is within the
scope of the invention to apply the method to the correction of
other uniformity characteristics such as cured tire radial runout
or lateral force variation.. In brief, the method may be used to
optimize the harmonics of any measurable uniformity characteristic
with suitable modifications to the vector equations described
below.
[0049] FIG. 3 is a vector polar plot showing the two major
contributions to first harmonic of the after cure radial force
variation, the tire room effects vector TR1, and the curing room
effects vector CR1 when no optimization has been applied. The cured
tire result VRH1 is the vector sum of these two components. A
unique attribute of the invention is the ability to optimize the
after cure uniformity by manipulation of these two component
vectors. The ability to treat these effects in vector space is
possible only when each harmonic has been extracted.
[0050] FIG. 4 now shows a schematic of the optimization step. In
this view the green tire 30 has been physically rotated by a
pre-determined angle CAV_REF so that its tire room effect vector
(TR1') now directly opposes the curing room effect vector CR1, the
latter being fixed if there are no changes to the setup or state of
the curing equipment 40. It is readily apparent that this
optimization greatly reduces the after cure result VRH1'.
[0051] The foregoing is a greatly simplified view of the factors
affecting after cure uniformity. Both the tire room and curing room
component vectors are the result of many individual factors, or
sub-vectors. Each sub-vector is a contribution to the cured tire
RFV and these vectors have units that correspond to radial force
variation, i.e. kilograms. FIG. 5 demonstrates one such sub-vector,
the effect of green tire radial runout indicated as GR1*GN. This
sub-vector represents the vector product of the green RRO (mm) and
a gain vector that models the localized radial stiffness (Kg/mm).
However, the gain vector is not a simple scalar factor as used in
previous methods, but is a true vector that accounts for
circumferential radial stiffness variation around the green tire
30. The remaining, unidentified factors are consolidated in the
Intercept vector I1. If all factors were known, then the Intercept
vector I1 would not exist. Throughout this disclosure, the
Intercept vector I1 accounts for the unidentified effects.
[0052] FIG. 6 further declinates the tire room sub-vectors showing
a first representation of the tooling effects. The measurement of
green tire RRO is preferably at the completion of tire building and
before the green tire is removed from the building drum 15. By way
of illustrated examples, the measurement drum is the tire building
drum 15, the single drum of a unistage machine, or the finishing
drum of a two-stage machine. The green tire RRO measurement may
also be performed offline in a dedicated measurement apparatus. In
either case, the radial runout of the measurement drum can
introduce a false contribution to the Green RRO vector. When the
green tire RRO is measured, the result is the sum of true tire
runout and the runout of the drum used for measurement of RRO.
However, only the green tire RRO has an affect on the after cure
RFV of the tire. As shown in FIG. 6, the method of the invention
includes a sub-vector T2 due to the measurement drum to account for
this false RRO effect.
[0053] The sub-vector advantage can also be use to improve the
curing room effects. An effect similar to the foregoing false RRO
exists for measurement of after cure RFV. That is, the measurement
machine itself introduces a contribution to the as-measured tire
RFV. FIG. 7 depicts an additional sub-vector UM1 to account for
this effect showing the difference between the measured radial
force vector VRH1 and the true radial force vector TVRH1. This
sub-vector imparts a small, but significant correction to the
rotation angle CAV_REF shown in FIG. 4 for optimizing VRH1. Studies
have shown that the inclusion of the UM1 sub-vector can improve the
magnitude VRM1 of the true radial force vector VRH1 by about 0.5 to
1.0 Kg.
[0054] The foregoing graphical representations in vector space can
now be recast as equation (1) below where each term represents the
vectors and sub-vectors shown in the example of FIG. 6. The method
can be applied to additional effects not depicted in FIG. 6 nor
described explicitly herein without departing from the scope of the
invention. VRH1=Tire Room RH1+ Curing Room RH1 (1) Substituting the
sub-vectors for the tire room yields the final modeling equation:
VRH1=(Tire Room RH1 +Building Drum+Intercept)+Curing Room RH1 (2)
or VRH1=GR1*GN+T2+I1+CR1 (3)
[0055] The first step in implementation of the method is to gather
data to build the modeling equation. The Green RRO and VRH1 vectors
are measured quantities. The challenge is to estimate the gain
vector GN, the building drum vector T2, the intercept vector I1,
and the curing room effect vector CR1. This is accomplished by
vector rotation and regression analysis.
[0056] First, a reference point on the tire, such as a barcode
applied to the carcass or a product joint that will be accessible
through the entire process is identified. In the specific example
described herein, the invention contains an improvement to account
for the radial runout of the measurement drum itself. This effect
may be significant when the tire building drum 15 is used as the
measurement drum. The loading angle FBD_REF of the tire carcass on
the measurement drum is recorded. For this specific example, the
loading angle is measured as the carcass 10 is loaded on either the
first stage of a unistage or a second stage of a two-stage machine.
It is advantageous to ensure a wide variation of the loading angle
FBD_REF within a given sample of tires to ensure accurate
estimation of the effect of the measurement drum runout on the
vector coefficients.
[0057] Next, the RRO of the finished, green tire 30 is measured by
a measurement device 70 while the tire is mounted on the finishing
stage building drum 15. Alternatively, the finished, green tire may
be moved to separate measurement apparatus and the RRO measurement
made there. This RRO measurement is repeated for multiple tires to
randomize the effects that are not modeled. There are many known
devices 70 to obtain the RRO measurement such as a non-contact
system using a vision system or a laser. It has been found that
systems for measurement of radial runout that are based on
tangential imaging are preferred to those using radial imaging. The
RRO data thus acquired are recorded in a computer 80.
[0058] Next, each green tire 30 is transferred to the curing room
and the identification of the curing cavity 40 where each green
tire is to be cured or vulcanized is recorded as well as the
orientation azimuth CAV_REF at which each green tire is loaded into
the curing cavity. It is advantageous to ensure a wide variation of
the orientation azimuth within a given sample of tires to ensure
accurate estimation of the curing cavity effect on the vector
coefficients. After each tire has been cured, the cured tire 30' is
moved to the uniformity measurement machine 50 to acquire the
radial force variation RFV for each tire. The RFV data thus
acquired are also recorded in a computer 80.
[0059] If the model is extended to include a uniformity machine
sub-vector UM1, then similar steps to those outlined above for the
building drum vector are applied at the uniformity measurement
machine. A loading angle for the cured tire on the uniformity
measurement machine U_REF, similar to the second stage carcass
loading angle FBD_REF, is recorded and stored in the computer 80
with the associated RFV data for a sample of tires. The sub-vector
UM1 can then be added to the model using the same vector analysis
procedure as described herein to obtain the building drum
sub-vector T2. The model will contain an additional pair of
coefficients to obtain a magnitude UMM1 and an azimuth UMA1 of the
sub-vector UM1 to improve the estimation of after cure RFV.
[0060] Once these data have been acquired for a suitable sample of
tires, the harmonic data are extracted from the RRO and RFV
waveforms. In the present example the first harmonic data of the
green radial runout GR1 (magnitude FRM1 and azimuth FRA1) and
radial force variation VRH1 (magnitude VRM1 and azimuth VRA1),
respectively are extracted and stored. Each vector in equation (2)
above has a magnitude and an azimuth as previously defined.
[0061] To facilitate rapid application of equation (3) in a
manufacturing environment, it is advantageous to use a digital
computer to solve the equation. This requires converting the vector
equations above to a set of arithmetic equations in Cartesian
coordinates. In Cartesian coordinates, each vector or sub-vector
has an x-component and a y-component as shown in the example below:
VRH1.sub.x=(VRM1)* COS(VRA1), and VRH1.sub.y=(VRM1)* SIN(VRA1) (4)
where the parentheses indicate the scalar values of magnitude and
azimuth of the quantity within. In like manner the independent
factors are converted from polar to Cartesian coordinates:
GR1.sub.x=FRM1 COS(FRA1) GR1.sub.y=FRM1 SIN(FRA1) (5)
CAV_REF.sub.x= COS(CAV_REF) CAV_REF.sub.y= SIN(CAV_REF) ( )
FBD.sub.--REF.sub.x= COS(FBD.sub.--REF) FBD.sub.--REF.sub.y=
SIN(FBD.sub.--REF) (7) I1.sub.x=IM1 COS(IA1) I1.sub.y=IM1SIN(IA1)
(8) The dependent vector (VRH1.sub.x, VRH1.sub.y) is sum of the
vectors in the equations below. VRH1.sub.x=GNFRM1
COS(.THETA.+FRA1)+CM1 COS(CA1 +CAV.sub.--REF)+TM1
COS(TA1+FBD.sub.--REF)+IM 1 COS(IA1) (9) VRH1.sub.y=GNFRM1
SIN(.THETA.+FRA1)+CM1 SIN(CA1+CAV.sub.--REF)+TM1
SIN(TA1+FBD.sub.--REF)+IM1 SIN(IA1) (10) Expanding these equations
with standard trigonometric identities yields: VRH .times. .times.
1 X = GN COS .function. ( .theta. ) FRM .times. .times. 1 COS
.function. ( FRA .times. .times. 1 ) - GN SIN .function. ( .theta.
) FRM .times. .times. 1 SIN .function. ( FRA .times. .times. 1 ) +
CM .times. .times. 1 COS .function. ( CA .times. .times. 1 ) COS
.function. ( CAV_REF ) - CM .times. .times. 1 SIN .function. ( CA
.times. .times. 1 ) SIN .function. ( CAV_REF ) + TM .times. .times.
1 COS .function. ( TA .times. .times. 1 ) COS .function. ( FBD_REF
) - TM .times. .times. 1 SIN .function. ( TA .times. .times. 1 )
SIN .function. ( FBD_REF ) + IM .times. .times. 1 COS .function. (
IA .times. .times. 1 ) ##EQU1## VRH .times. .times. 1 Y = GN COS
.function. ( .theta. ) FRM .times. .times. 1 SIN .function. ( FRA
.times. .times. 1 ) + GN SIN .function. ( .theta. ) FRM .times.
.times. 1 COS .function. ( FRA .times. .times. 1 ) + CM .times.
.times. 1 COS .function. ( CA .times. .times. 1 ) SIN .function. (
CAV_REF ) + CM .times. .times. 1 SIN .function. ( CA .times.
.times. 1 ) COS .function. ( CAV_REF ) + TM .times. .times. 1 COS
.function. ( TA .times. .times. 1 ) SIN .function. ( FBD_REF ) + TM
.times. .times. 1 SIN .function. ( TA .times. .times. 1 ) COS
.function. ( FBD_REF ) + IM .times. .times. 1 COS .function. ( IA
.times. .times. 1 ) ##EQU1.2## To simplify the expanded equation,
introduce the following identities: a=GNCOS(.THETA.),
b=GNSIN(.THETA.) (11) c=CM1 COS(CA1), d=CM1 SIN(CA1) (12)
Substituting these identities into the expanded form of equations
(9) and (10) yields: VRH .times. .times. 1 X = .times. a GR .times.
.times. 1 X - b GR .times. .times. 1 Y + c CAV_REF X - .times. d
CAV_REF Y + e FBD_REF X - f .times. FBD_REF Y + I .times. .times. 1
X ( 13 ) VRH .times. .times. 1 Y = .times. a GR .times. .times. 1 Y
+ b GR .times. .times. 1 X + c CAV_REF Y + .times. d CAV_REF X + e
FBD_REF Y + f .times. FBD_REF X + I .times. .times. 1 Y ( 14 )
##EQU2## The equations (13) and (14) immediately above can be
written in matrix format: VRH .times. .times. 1 X VRH .times.
.times. 1 Y = GR .times. .times. 1 X - GR .times. .times. 1 Y
CAV_REF X - CAV_REF Y FBD_REF X - FBD_REF Y 1 0 GR .times. .times.
1 Y GR .times. .times. 1 X CAV_REF Y CAV_REF X FBD_REF Y FBD_REF X
0 1 .times. a b c d e f I X I Y ( 15 ) ##EQU3## When the predictive
coefficients vectors (a,b), (c,d), (e,f), and (I1.sub.x,I1.sub.y)
are known, the equation (15) above provides a modeling equation by
which the VRH1 vector for an individual tire may be estimated. This
basic formulation can also be modified to include other process
elements and to account for different production organization
schemes. These coefficient vectors may be obtained by various known
mathematical methods to solve the matrix equation above.
[0062] In a manufacturing environment, and to facilitate real-time
use and updating of the coefficients, the method is more easily
implemented if the coefficients are determined simultaneously by a
least-squares regression estimate. All coefficients for all
building drums and cavities may be solved for in a single
regression step. Finally, the vector coefficients are stored in a
database for future use. For the example of a single mold and
single curing cavity, the coefficients have a physical significance
as follows: (a, b) is the gain vector GN in units of kgf/mm, (c, d)
is the curing room effect vector CR1 in units of kgf, (e, f) is the
building drum vector T2 in units of kgf, and (I1.sub.x, I1.sub.y)
is the Intercept vector I1 in units of kgf.
[0063] The equations listed above are for one curing cavity and one
building drum. The curing cavity and building drum are nested
factors meaning that although the actual process contains many
building drums and many cavities, each tire will see only one of
each. Thus the complete equation may include a vector for each
building drum and each curing cavity as shown below. Expanding the
model first requires the creation of the following matrices
V.sub.i,j, C.sub.i,j, and X.sub.ij, where the subscript "i" denotes
mold i and the where the subscript "j" denotes building machine
drum j, the subscript pair "ij" denotes a tire manufactured on
building drum "j" and cured in curing cavity "i": V i , j = VRM
.times. .times. 1 x VRM .times. .times. 1 y ##EQU4## C i , j = a b
c d e f I .times. .times. 1 x I .times. .times. 1 y ##EQU4.2## X i
, j = FRM .times. .times. 1 x - FRM .times. .times. 1 y CAV_REF x -
CAV_REF y FBD_REF x FBD_REF y 1 0 .times. FRM .times. .times. 1 y
FRM .times. .times. 1 x CAV_REF y CAV_REF x FBD_REF y FBD_REF x 0 1
##EQU4.3## Then the equations above can be expressed in the
succinct matrix form below for a given combination of mold and
building machine drum (indexed by i and j):
V.sub.i,j=X.sub.i,j=C.sub.i,j (16) This equation can be expanded to
accommodate multiple molds and multiple building machine drums
simultaneously in matrix formula below: V 1 , 1 V 1 , 2 V 1 , m V 2
, 1 V n , m = X 1 , 1 0 0 0 0 0 X 1 , 2 0 0 0 0 0 X 1 , m 0 0 0 0 0
X 2 , 1 0 0 0 0 0 0 0 X n , m .times. C 1 , 1 C 1 , 2 C 1 , m C 2 ,
1 C n , m ( 18 ) ##EQU5##
[0064] The final step is to apply the model to optimize the RFV of
individual tires as they are manufactured according to the
illustration shown in FIG. 4. Each tire building drum carries an
identification "j" and each curing cavity an identification "i."
Each tire carries a unique identification device, such as a
barcode. These identification tags allow the information recorded
for an individual tire to be retrieved at a later step. At the
completion of tire building, the green RRO is measured and its
harmonic magnitude FRM1 and azimuth FRA1 are recorded along with
the loading angle FBD_REF of the tire on the building or
measurement drum. When the green tire arrives in the curing room,
the curing cavity in which it will be cured will be predetermined
and the curing room effect vector information for that cavity may
be retrieved from the database. A reading device scans the unique
barcode to identify the tire, to facilitate polling the database to
find the measured and recorded tire information: FRM1 and FRA1, the
building drum identification, and the loading angle FBD_REF. Next,
a calculation is performed to estimate the tire room effect vector
by the equations below. Note that equations (17) and (18) are
identical in form to equations (9) and (10) above, but now are
being used in a predictive fashion to estimate the tire room
contribution to cured RFV. TR .times. .times. 1 x = .times. a GR
.times. .times. 1 X - b GR .times. .times. 1 Y + e FBD_REF X -
.times. f FBD_REF Y + I .times. .times. 1 X ( 19 ) TR .times.
.times. 1 Y = .times. a GR .times. .times. 1 Y + b GR .times.
.times. 1 X + e FBD_REF Y + .times. f FBD_REF X + I .times. .times.
1 Y ( 20 ) ##EQU6## The azimuth TRA1 of the tire room effect vector
TR1 is the inverse tangent of the quantity (TR1.sub.y/TR1.sub.x),
and the azimuth CA1 of the curing room effect vector CA1 is the
inverse tangent of the quantity (d/c). Again referring to FIG. 4,
the green tire 30 is rotated so that its orientation angle CAV_REF
relative to the curing cavity 40 is such that azimuth TRA1 of the
predicted tire room effect vector is opposed to the azimuth CA1 of
the curing room effect vector. This operation may be expressed in
the equation below: CAV_REF=180+TRA 1+CA1 (21) The green tire 30 is
then loaded into the curing cavity 40 at the orientation angle
CAV_REF that minimizes RFV in the cured tire 30'.
[0065] When the above method is practiced with multiple tire
building drums and multiple curing cavities, then all steps of the
method, determining the vector coefficients, estimating the after
cure RFV, and optimizing the after cure uniformity, are carried out
using the specific identifiers of the process equipment. In this
manner, a tire produced on any building machine can be cured in a
curing cavity with an optimized level of RFV.
[0066] In the case where the tire does not have a unique
identifying barcode, it is not possible to perform the entire
optimization process at the curing room. In this case, the tire
must be marked to indicate the azimuth TRA1 of the tire room effect
vector TR1 while the tire is at the tire building machine. The
azimuth of the tire room effect vector of the green tire is
calculated using the vector-regression method, and a mark is placed
on the tire corresponding to the azimuth angle TRA1. In addition,
the curing cavity 40 has been previously marked at an azimuth
(CA1-180) diametrically opposed to the curing room effect vector
CA1. When the green tire 30 is transferred to the curing room and
arrives at the curing cavity 40, the pre-applied mark on the tire
30 indicating the azimuth TRA1 is aligned with the pre-applied mark
on the curing cavity 40. In this manner, the tire room effect
vector TR1 and the curing room effect vector oppose each other and
the after cure VRH1 will be optimized.
[0067] Another advantageous and unique feature of the invention is
the ability to update the predictive coefficients vectors (a, b),
(c, d), (e, f), and (I.sub.x,I.sub.y) with the data measured from
each individual tire to account for the constant variations
associated with a complex manufacturing process. Because the green
RRO and cured RFV of individual tires are continuously measured,
the model may be updated at periodic intervals with these new
production data so as to adjust the predictive equations for
changes in the process. These updates may be appended to the
existing data or used to calculate a new, independent set of
predictive coefficient vectors that may replace the original
data.
[0068] FIG. 8 is a vector polar plot of an expanded method of the
invention showing the effect on the green tire vector GR1*GN of
additional components effects due to green tire carcass, the tread
and belt assembly, and for the tooling effects of first stage drum,
the tread and belt assembly drum, and the transfer ring. This may
be accomplished through suitable modifications of the foregoing
system of vector equations. The green tire effect vector GR1*GN is
now capable of being described by the component sub-vectors
corresponding a set of tire component sub-assemblies and a set of
tooling effects. The green tire vector GR1*GN now appears as:
GR1*GN=GR1C*GNC+GR1T*GNT+T1+T3+T1 (22) The vector equation (3)
which describes the estimated tire room effect vector TR1 becomes:
TR1=GR1C*GNCGR1T*GNT+T1T2+T3 +T4+I1 (23) and the estimated after
cure uniformity remains as in equation (1): VRH1=TR1+CR1 (24) where
TR1 is now represented by the new equation (23). One skilled in the
art may follow the same methodology as described previously in the
vector equations (4) through (15) to expand the set of predictive
equations to correspond to the expanded tire room vector equation
(23). The result below shows the x and y components of RFV: VRH
.times. .times. 1 X = .times. a GR .times. .times. 1 .times. C - b
GR .times. .times. 1 .times. C + c GR .times. .times. 1 .times. T X
- d GR .times. .times. 1 .times. T Y + .times. h CBD_REF X - j
CBD_REF Y + k .times. FBD_REF X - m FBD_REF Y + n SBD_REF X -
.times. p SBD_REF Y + q TSR_REF X - r TSR_REF Y + .times. s CAV_REF
X - t CAV_REF Y + I .times. .times. 1 X ( 25 ) VRH .times. .times.
1 Y = .times. a GR .times. .times. 1 .times. C Y + b GR .times.
.times. 1 .times. C X + c GR .times. .times. 1 .times. T Y + d GR
.times. .times. 1 .times. T X + .times. h CBD_REF Y + j CBD_REF X +
k .times. FBD_REF Y + m FBD_REF X + n SBD_REF Y + .times. p SBD_REF
X + q TSR_REF Y + r TSR_REF X + .times. s CAV_REF Y + t CAV_REF X +
I .times. .times. 1 Y ( 26 ) ##EQU7## A multiple linear regression
routine is used to estimate simultaneously coefficients vectors (a,
b), (c, d), (h, j), (k, m), (n, p), (q, r), (s, t), and (I1.sub.x,
I1.sub.y). The vector coefficients have a physical significance.
The vector (a, b) is the carcass gain vector GC and will be in
units of kgf/mm. The vector (c, d) is the tread and belt assembly
gain vector GT and will be in units of kgf/mm. The vector (h, j) is
the first stage building drum tooling vector Ti and is in units of
kgf. The vector (k, m) is the second stage building drum tooling
vector T2 and is in units of kgf. The vector (n, p) is the tread
and belt assembly building drum tooling vector T3 and is in units
of kgf. The vector (q, r) is the transfer ring tooling vector T4
and is in units of kgf. The vector (s, t) is the curing room effect
vector CR1 and is in units of kgf. The vector (I1x, I1.sub.y) is
the intercept vector and is in units of kgf.
[0069] Following the procedural steps previously described, the
expanded model may be practiced in the following illustrative
manner. In the step of determining the vector coefficients, the
method is practiced as previously described, but with additional
steps. For example, if the model is to include the first stage
building drum sub-vector T1, then it will be necessary for the data
on the sample of tires to include a recording of the carcass
loading angle on the first stage drum CDB_REF. Likewise to account
for the green tire carcass sub-vector GR1C and the carcass gain
GNC, a measurement of the RRO of the green carcass is necessary.
Here the term carcass means the components of the green tire minus
the tread and belt assembly. This is often a sub-assembly from the
first stage of a two stage building process. Likewise the tread and
belt assembly sub-vector GR1T and read gain GNT can be included
through measurements of the tread and belt assembly loading angle
SBD_REF of these tire components on a form commonly used to build
this assembly, followed by a measurement of the green RRO of the
assembly on the building form. Lastly, the transfer ring tooling
effect T4 accounts for uniformity effects introduced by the
apparatus use to transfer the tread and belt assembly 20 from the
building form to a position to be joined with the green carcass.
The tooling effect T4 is accounted for by a measurement of the
loading angle in the transfer ring TSR_REF.
[0070] These tires are then cured in a curing mold as before,
followed by measurement of the after cure RFV. The unknown
coefficients for the series of sub-vectors are determined in a
simultaneous step from a regression analysis. Finally, once the
sub-vector coefficients are known, the equations are used in a
predictive manner. FIG. 8 graphically illustrates the result of
equation (22) where the additional sub-vectors provide an
alternative means by which to estimate the tire room effect vector
TR1 for an individual tire.
[0071] The model is then applied to optimize the after cure RFV of
an individual tire. The steps described herein apply to a two-stage
building process where the carcass and tread and belt assemblies
are built as separate components, and then joined to complete the
tire. It is within the scope of the invention to apply the method
to other tire building methods. Specifically the optimization of
these tire building steps will be performed using the coefficient
derived in the model building step. Using the tooling effects and
the measured radial runout effects, the optimal relative angles of
loading of the carcass 10 and the tread and belt assembly 20 will
be generated and either marked on the elements or preferably
automatically rotated to the selected angles by machine control
systems. At the start of tire building, the first stage building
drum identification is recorded, followed by building the carcass.
Next, the carcass RRO measurements are made on the first stage drum
and the carcass effect vector GR1C*GC is computed. The tooling
contribution is known through the tooling vector T1. Alternatively,
the carcass RRO measurements may be made on the second stage
building drum, in which case the tooling vectors T1 and T2 may be
used. The tread and belt assembly steps begin with recording the
building from identification, followed applying the belts and the
tread band. Next, the tread and belt assembly RRO is measured o the
form and tread and belt assembly effect vector GR1T*GT is computed.
The tooling contribution of the building form is known through the
tooling vector T3. Finally, one records the information to identify
the second stage building drum, the transfer ring drum, and the
respective tooling vectors T2, and T4.
[0072] The optimization method may be applied in several variations
depending on the level of sophistication of the manufacturing
equipment. For the example shown in FIG. 1, the equipment allows
labeling of the tire components for identification and azimuth. The
equipment also allows for selection of curing molds and for loading
of the tire in a curing mold at an azimuth orientation determined
from the model. In this instance, the after cure RFV is reduced by
building a green tire 30 having a magnitude of the tire room effect
vector TR1 equal or nearly equal to the magnitude of the curing
room effect vector CR1. FIG. 9 represents this variation. The
optimized tire room effect vector TR1 is now shown as a dotted line
to demonstrate the matching of its magnitude to that of the curing
room effect vector CR1. In particular, FIG. 9 further demonstrates
that the manipulation of the green tire effect vector GR1C*GN, also
show by a dotted line. When the tire is thereafter match loaded in
the curing mold, the two effects are nearly equal and opposite, and
the after cure RFV is minimized. In practice, the errors in
measurement and in the accuracy of the model are such that one
would not expect to produce a tire with zero after cure RFV. If the
manufacturing equipment is less sophisticated and does not permit
the match loading in the curing mold, then the optimization may be
used simply to minimize the tire room effect vector TR1 alone.
[0073] The optimization method is applied similarly for both the
preceding examples. First, an optimization criterion is chosen
depending on the manufacturing environment. In the first of the
examples above, the intended curing mold is known and its
respective curing room effect vector CR1 is known. The optimization
criterion is the magnitude CM1 of the curing room effect vector
CR1. In the second of the examples above, the optimization
criterion is set to any desired level. For example, to minimize the
tire room effect vector TR1, the optimization criterion is set to
zero.
[0074] The optimization method is used to determine an optimum set
of loading angles on the second stage building drum FBD_REF and the
transfer ring TSR_REF to produce a tire with the predetermined
value of CM1. The curing room azimuth angle CAV_REF is
simultaneously determined for future use. The vector system just
described forms a response surface for the estimated tire room
effect vector TR1 as a function of the component sub-vectors. The
response surface may have a single maximum or several local maxima.
It has been found that the optimized solution can be efficiently
determined using a well-known non-linear, steepest descent method
based on commercially available code. As employed in the method,
the steepest descent routine is run using more than one set of
starting values to increase the likelihood that the best solution
is obtained. Other optimization methods are possible such as
quadratic optimization, linear descent, or even an exhaustive
search. The next steps are to complete the tire 30 according to the
optimized loading angles. The tread and belt package 20 is loaded
on the summit transfer ring at the predetermined angle TSR_REF, and
the carcass 10 is loaded on the second stage building drum at the
predetermined angle FBD_REF. The carcass 10 can then be inflated
and joined to the tread and belt assembly 20 to complete the green
tire 30. As an optional step for verification, the before cure RRO
of the finished tire can be measured to assess the robustness of
the model. In a final step, the green tire 30 is moved to the
curing room and then loaded into the curing cavity 40 at the
azimuth angle determined from CAV_REF that minimizes RFV in the
cured tire 30'. Experimental results obtained during the
verification of the method have shown that the present invention is
able to account for a significantly higher percentage of the cure
tire RFV than previous methods used in with the similar
manufacturing processes.
[0075] When the method is applied to minimize only the tire room
effect vector TR1, the optimization routine determines angles
FBD_REF and TSR_REF. The carcass 20 and tread and belt package 20
are loaded at these predetermined angles to finish the tire 30. In
a final step, the green tire 30 is moved to the curing room and
then loaded into any curing cavity 40 without attention to the
loading angle in the cavity 40.
[0076] It should be understood that the present invention includes
various modifications that can be made to the tire manufacturing
method described herein as come with the scope of the appended
claims and their equivalents.
* * * * *