JP3206868B2 - Setting method of tread pattern of pneumatic tire - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a pneumatic tire in which the arrangement of pattern constituent units of a tire tread is set based on a sequence of chaotic functions. More specifically, the number of types of pitch lengths s is three or more, and the arrangement of the pattern constituent units without skipping one pitch in the order of the length is a basic principle. Tread pattern setting method for pneumatic tires that can be reduced
About the law .

[0002]

2. Description of the Related Art Various tread patterns are used for tire treads according to vehicle and road conditions. In many tread patterns, grooves in the tire axial direction are formed at intervals in the tire circumferential direction, or rib grooves are zigzag in the tire circumferential direction. By repeating in the tire circumferential direction,
A block pattern, a rib pattern, a lug pattern, or the like composed of a repetitive pattern as a pattern constituent unit row is employed.

In a tire having such a repetitive pattern, the pattern constituent units of each pattern constituent unit row are sequentially contacted with the road surface by running of the tire, and repeated noise is generated between the tire and the road surface. A sound (hereinafter referred to as a pitch sound) generated based on the pattern constituent unit is usually an unpleasant sound, and its improvement is desired.

[0004] To improve this, conventionally, by arranging a plurality of types of pattern constituent units having different lengths in the tire circumferential direction, that is, pitches, of the pattern constituent units in the tire circumferential direction, noise is dispersed in a wide frequency band. A so-called pitch variation method for producing white noise has been adopted.

[0005] There are many proposals for this white noise reduction method. For example, Japanese Patent Publication No. Sho 58-2844 (Japanese Patent Application Laid-Open No. 55-8904) and Japanese Patent Publication No. Hei 3-23366 (Japanese Patent Application Laid-Open No. 54-115801) No. 2) proposes that the pitch array is a sinusoidal periodic array. Also, Japanese Patent Publication No. Sho 62-41122 (Japanese Patent Application Laid-Open
No. 114706), the pitch arrangement of the pattern constituent units is random.

[0006] Some proposals merely specify the number of pitches, the pitch ratio, and the like, and lack specific disclosure on how to specifically arrange the pattern constituent units.

[0007]

However, in the first case, the former arrangement of the pitch is a sinusoidal periodic arrangement,
Since the pitch changes continuously and periodically, there is an advantage that the rigidity of the adjacent pattern constituent units is small and abnormal wear hardly occurs. However, the change in the rigidity of the pattern constituent unit changes periodically in accordance with the pitch change. For this reason, a force variation (RFV) in the radial direction is increased at a specific order component corresponding to the number of periods, and abnormal vibration is generated, which may increase unpleasant noise.

In the case where the pitch arrangement of the pattern constituent units is random, there is no periodic regularity, contrary to the case of the periodic arrangement. For this reason, the specific order component of the force variation does not increase, and abnormal vibration and noise rarely occur. However, there is a problem that abnormal wear is likely to occur because the pitch between adjacent pattern constituent units changes relatively largely.

The effect of pitch variation generally improves as the number s of types of pitch lengths of the pattern constituent units increases. Therefore, it is said that the number of types s is preferably 3 or more.

[0010] On the other hand, due to recent advances in die manufacturing, increasing the number of types s itself is relatively easy in manufacturing. However, as described above, even when the number s of types is three or more, the theory of noise reduction is not clear, and a new method is desired.

The present inventors have made various developments. As a result, in order to reduce the noise of the tire, the number of types having different lengths (pitch) of the pattern constituting units in the tire circumferential direction is set to three or more, and the number of adjacent types is set to be equal. Assuming that pattern constituent units are arranged without skipping one pitch having a matching length, characteristics to be provided and characteristics to be excluded from these pattern constituent unit rows have been found as follows. (1) Characteristics that the pattern constituent unit sequence should have ・ Irregularity (no periodicity) ・ Continuity of pitch change (there is relevance between neighboring pitches) ・ Similar arrangement is unlikely to occur (2) Characteristics that should be excluded from the pattern composition unit row ・ Periodicity

As a result of research and development in order to determine the arrangement of the pattern constituent units having such characteristics, attention was paid to the characteristics of the chaos function.

[0013] Chaos refers to "a seemingly disorderly and unpredictable phenomenon produced by deterministic equations that exist everywhere in the natural world, such as turbulence and rhythms in biological systems". The chaos theory is a law hidden behind such a complicated phenomenon of chaos or a theory that seeks to reveal it, and a chaos function is a function that generates a chaotic pseudo signal. .

Incidentally, regarding chaos or chaos function,
JP-A-4-86814 and JP-A-4-2219
Japanese Patent Publication No. 37 proposes a chaos generating device.
JP-A-335730 proposes a random encryption communication system using a chaotic equation, and JP-A-6-44294 proposes an apparatus for generating a disturbance signal close to an actual phenomenon using a chaotic function.

[0015] In addition, "Systems Comprehensive Research No. 169" issued by the Systems Research Institute, July 16, 1993
On page 38 of “Information Trends in Practical Use of Chaos Theory for Consumer Electronics” by Sanyo Electric Co., Ltd. One chaotic function is illustrated. FIG. 1A shows a graphic obtained by the equation (1). Note that the chaos function is hereinafter expressed in the form of X (n + 1) = fc (Xn).

[0016]

(Equation 1)

As another example of the chaos function, the following equation 2 is known.

[0018]

(Equation 2)

In this specification, even when n, i, and the like are variables, if there is no risk of confusion, the parentheses () around the variables are omitted, if necessary, for simplicity of the expression. ing.

The chaotic functions such as the above equations 1 and 2 have the following characteristics (a), (b) and (c). (A) There is a continuous change between neighboring values. (B) The relationship between distant values becomes uncorrelated. (C) Even if the initial values are very close, they are discrete as time passes. .

The characteristics that the arrangement of the pattern constituent units for the low noise of the tire should have are "irregularity",
"Continuity of pitch change". The property to be excluded is the aforementioned “periodicity”.

In the chaos function, “continuously changing between neighboring numerical values” corresponds to the “continuity of pitch length change (there is a relationship between neighboring pitches)” in the arrangement of pattern constituent units. In addition, the “correlation between distant numerical values” of the chaos function corresponds to the “irregularity (no periodicity)” in the arrangement of the pattern constituent units. Further, "discrete even if the initial values are close" corresponds to "similar arrangement is unlikely to occur" in the arrangement of the pattern constituent units. This means that the arrangement of the pattern constituent units can be prevented from being repeated in the arrangement of the pattern constituent units.

Also in this regard, it is conceivable that the arrangement of the pattern constituent units based on the chaos function disperses the above-mentioned pitch sound and makes it white noise, thereby reducing the tactile peak sound. As described above, it is expected that the arrangement of the pattern constituent units for reducing the noise of the tire can be obtained by adopting the basic concept of the chaos function.

However, it is not advisable to use the chaotic function formulas of the formulas 1 and 2 as they are to determine the arrangement of the pattern constituent units. For example, as shown in FIGS. 1 (a) and 1 (b), the chaotic function of Equation 1 is 0 to 0.5 on the horizontal axis.
And only one curve, straight line, each of which is defined separately in the two sections 0.5 and 1.0. For this reason, even if there is a possibility that the pitch can be used when the number of pitch types is two, if the number of types is three or more, 0 to 1 is replaced by three.
It must be divided into the above types. At that time, since there is only one curve and one straight line, the sequence obtained by the chaos function and the arrangement of the pattern constituent units obtained by converting the sequence are hardly preferable.

According to the present invention, in an arrangement of pattern constituent units in which the number of types of pitch s is 3 or more, a chaotic function capable of deforming by applying a chaotic function to generate a chaotic sequence for setting the arrangement of the pattern constituent units. Sequence generating function (herein,
Called a chaotic function). Furthermore, a procedure for setting the arrangement of the pattern constituent units was conceived. This makes it possible to obtain a tire that can reduce noise and is excellent in uniformity. In addition, by arranging the pattern constituent units without skipping one adjacent pitch in the order of length, it is possible to reduce noise of the tire while making sound change smooth.

According to the present invention, the noise can be reduced on the basis of arranging pattern constituent units based on a sequence generated using a chaotic function and without skipping one pitch in the order of length. Pneumatic tire tread pattern
The purpose is to provide a setting method .

[0027]

According to the present invention, there is provided a pattern forming unit sequence in which pattern forming units in which the number s of types of pitches P, which are lengths in the circumferential direction, are three or more are arranged in the tire circumferential direction.
A method for setting a tread pattern of a pneumatic tire that forms a tread pattern of a tire tread, wherein a horizontal axis and a vertical axis are each set to the number of types s in one direction from the horizontal axis, the vertical axis, and each right angle and the origin in a rectangular coordinate system. A vertical division line and a horizontal division line that form a plurality of rectangular areas on the coordinate plane by dividing are provided. The horizontal axis is Xn and the vertical axis is X (n + 1).
The definition area of each section of the horizontal axis of the chaotic function fc expressed by X (n + 1) = fc (Xn) is set as shown in the following (a), (b), and (c). (A) In the section of the shortest pitch on the horizontal axis, of all the areas arranged in the vertical direction in the shortest section of the horizontal axis, the vertical direction of the area of the same pitch and the area of the pitch vertically adjacent thereto on the larger side. (B) In the section of the longest pitch on the horizontal axis, of all the areas vertically arranged in the longest section of the horizontal axis, the area of the same pitch and the area on the smaller side thereof are vertically adjacent to each other. (C) In the section of the pitch of the length in the middle of the horizontal axis, the area of the same pitch among all the areas vertically aligned in each of these sections of the horizontal axis, and The vertical area sum of the areas of the pitch adjacent in the vertical direction on the long and short sides, this definition area The pitches adjacent to each other in the order of the pitch length are determined based on the sequence of the function values of X (n + 1) which are determined for each section of the horizontal axis and sequentially obtained by the chaotic function satisfying the following requirements. A tread for a pneumatic tire , comprising a pattern constituent unit row to be tested obtained by performing the following tests on a pattern constituent unit row in which pattern constituent units are arranged without skipping one tread. Pattern setting method
Is the law . The chaotic function fc satisfies the derivative f′c ≧ 1 in all the sections on the horizontal axis. In the section of the horizontal axis in which the shortest pitch and the longest pitch are defined, the starting point (Xc) on the small side of the section and the ending point (Xe) on the large side are f′c (Xe)> in the section with the shortest pitch. f'c (Xc) In the section having the longest pitch, f'c (Xc)>f'c (Xe) The irregularity index Vr in each order up to the eighth order is 1.5 or less.
Being below . The autocorrelation coefficient Ru is smaller than 0.5 when u> 5. Maximum dispersion coefficient PSDrm
ax satisfies the following equation. PSDrmax ≦ {100 / (Ps / P1) ¹⁰ } × (1 / Rn) + 5 × {(1 / Rn) +1} where P1 is the shortest pitch, Ps is the longest pitch, and R
n is Np / 60, Np is the total number of pattern constituent units in the pattern constituent unit row, the number SQmax of the pattern constituent units in which the pattern constituent units of the same pitch are continuous, and the total number Np of the pattern constituent units arranged in the tire circumferential direction. SQmax / Np of 0.15 or less.

According to a second aspect of the present invention, the chaotic function is:
In each section other than the section having the shortest and longest pitches on the horizontal axis, a left chaotic function Fcu passing left and right intersecting a horizontal imaginary line passing through a vertical intermediate height point of the definition area is described.
And two chaotic functions of the right chaotic function Fcd
It is characterized by consisting of .

Further, in the invention according to the second aspect, the left chaotic function Fcu is represented by a horizontal imaginary line passing through a vertical intermediate height point of the definition area, and a center point Xa in the horizontal axis direction of the section. And the right chaotic function Fcd crosses on the opposite side, and
In the same section on the horizontal axis, the function value X (n
+1) occurs in the right or left chaotic function Fcu, Fcd, the next function value X (n + 2) is also the same right or left chaotic function Fcu as the previously determined function value X (n + 1). , Fcd, and when the previously defined function value X (n + 1) occurs in the section of the horizontal axis having a smaller pitch or is an initial value, the left chaotic function Fcu
When the previously determined function value X (n + 1) occurs in the section of the horizontal axis having the larger pitch, the right chaotic function F
It is characterized in that the following function values X (n + 2) are generated in cd.

According to the third and fourth aspects of the present invention, the tire tread has two or more types of pattern constituent unit rows in which the total number of pattern constituent units in the tire circumferential direction is the same, but the arrangement of the pattern constituent units is different. Or two or more rows of pattern constituent units having different numbers of pattern constituent units in the tire circumferential direction.

As described above, the pneumatic tire of the present invention
The red pattern setting method uses a characteristic of the chaos function and uses a pattern constituent unit array arranged without skipping one pitch in the order of length, thereby improving the degree of sound dispersion and the like, and The change is smooth. In addition, the pattern constituent unit sequence is tested by various elements, thereby eliminating the unpleasant sound factor which may be included in the sequence of chaotic functions. And reduce noise. Furthermore, even when the number of types of pitches is large, the arrangement can be easily and preferably set, which can be useful for reducing the noise of the tire.

[0032]

[Aspect of the implementation of the invention] tread of a pneumatic tire according to the present invention
In the pattern setting method , a plurality of types s of pattern constituent units having three or more circumferential pitches P different from each other in the circumferential direction are converted into a sequence obtained using a chaotic function, thereby obtaining the tire circumferential direction. The tread pattern of the tire tread is formed by the pattern constituent unit rows sequentially arranged in the tire tread. This pattern constituent unit sequence is verified and adopted as a pattern constituent unit sequence to be tested.

(1) First, as shown in FIG. 2 to FIG.
The horizontal axis is Xn and the vertical axis is X (n + 1). The horizontal axis Xn and the vertical axis X (n + 1) are each perpendicular to the vertical axis X (n + 1) and in the positive direction from the origin. (Which passes through the horizontal axis and the vertical axis, respectively), the horizontal axis Xn and the vertical axis X (n + 1)
Are divided into the number s of pitch types.

By partitioning in this manner, the vertical coordinate lines K0 to Ks and the horizontal partition line K0 are placed on the positive coordinate plane of the rectangular coordinates at the intersection of the vertical and horizontal axes.
Are divided into a number of small rectangular areas surrounded by .about.Ks.

Although FIGS. 2 to 5 show the case where the number s of types of the pattern constituent units is 3 to 6, it can be similarly divided even when the number s is 7 or more. The number s of types can be set in advance when designing a tire.

(2) Next, pattern constituent units are assigned to the above-mentioned section of the horizontal axis Xn and the vertical axis X (n + 1) from the origin O with pitches P1 to Ps in order of length from small to large. As described above, the pitch refers to the circumferential length of the pattern constituent unit.

As a result, each section of the horizontal axis Xn (pitch P1
ＰPs), the areas of the sections with the pitches P1 to Ps are arranged in the direction of the vertical axis X (n + 1), that is, in the vertical direction.

When the number of types s is 3, for example,
As shown in FIG. 2, adjacent pitches P in ascending order of length
1, P2, and P3 are defined as K0 <P1 <K by section lines K0 to K3 in each section of the horizontal axis Xn and the vertical axis X (n + 1).
1, K1 ≦ P2 <K2 and K2 ≦ P3 <K3 are assigned from the origin side.

(3) In the chaotic function, in each section of the horizontal axis Xn, a definition area that is allowed to exist in the vertical direction is defined as shown in the following (a), (b), and (c). Is done. (A) In the section of the shortest pitch on the horizontal axis, of all the areas arranged in the vertical direction in the shortest section of the horizontal axis, the area of the same pitch in the vertical direction and the pitch adjacent to the area in the vertical direction on the larger side. (B) In the section of the longest pitch on the horizontal axis, of all the areas vertically aligned in the longest section of the horizontal axis, the area of the same pitch in the vertical direction and the smaller side (C) In the section of the pitch of the length between them on the horizontal axis, among all the areas vertically aligned in each section of the horizontal axis, The sum of the regions of the same pitch in the vertical direction and the regions of each one pitch vertically adjacent to each other on the long and short sides in the vertical direction. Here, all the regions arranged in the vertical direction are the same in each section of the horizontal axis Xn. One vertical direction in which s areas of pitches P1 to Ps arranged in the vertical direction are continuous It refers to the total area.

For example, in FIG. 2, in the section with the pitch P1 on the horizontal axis, the section with the pitch P1 on the vertical axis can change only in the section P1 or only in the section P2 in the vertical direction. Further, in the section P2 on the horizontal axis, from the section P2 on the vertical axis, only the inside of the section P2 and the section P1 or the section P3 can be changed in the vertical direction. Further, in the section P3 on the horizontal axis, it can change in the vertical direction only in the section P3 on the vertical axis or only in the section P2. Therefore, there is no pattern constituent unit arranged one by one in the order of pitch lengths P1 to Ps.

(4) In the pitches P1 to Ps arranged further in order of decreasing length, the adjacent long pitch P (i +
1) and the ratio P (i + 1) / Pi of the short pitch Pi is 1.
05 or more, preferably 1.10 or more and 1.50 or less.

The reason for setting it to 1.50 or less is as described above.
This is because a change in the pitch of the tread causes a change in the rigidity of the adjacent pattern constituent units, and the distribution of stress in the tread may become uneven and abnormal wear may occur.
The present inventors measured the H / T wear (heel and toe wear) for tires having two types of pitches that alternately change in the tire circumferential direction. In this test tire, the pitch ratio was changed and the measurement was performed by a drum test. The results are shown in FIG. 6 as the relationship between the ratio of the two types of pitch and the ratio of the H / T wear amount. The tire size is 205 / 65R15, the standard internal pressure and load are applied, and the pitch of the reference pattern constituting unit is 30.0 mm.
And

The variation in the amount of H / T abrasion on the periphery serves as a trigger to generate abnormal abrasion such as polygonal abrasion. From FIG. 6, it can be seen that the pitch ratio is preferably 1.5 or less.

For this reason, even when the change of the value of the sequence of chaotic functions is the maximum, the ratio of the pitches of adjacent pattern constituent units in the pattern constituent unit row is not made larger than 1.5. Thereby, the H / T wear is suppressed. When the pitch ratio is less than 1.05, the effect of dispersing the pitch sound is inferior. More preferably, the pitch ratio is 1.1 or more.

Further, the ratio Ps / P1 of the shortest pitch P1 to the longest pitch Ps is 3.0 or less, preferably 2.0.
5 or less and 1.1 or more. Even if it is larger than 3.0, the sound dispersion effect does not change, and tends to increase abnormal wear. In order to exhibit the effect of pitch variation, 1.1 or more, more preferably 1.
2 or more.

(5) Number s of types of pitches of pattern constituent units
Is described below. First, it is assumed that the pitches are set as follows. P1 = 24.0 mm P2 = 30.0 mm P3 = 36.0 mm

The definition area of the chaotic function is set for each section having the horizontal axis as shown in (a), (b) and (c). Thus, as described above, with the exclusion of the pitch sequence of inadvertent one skip, and a sequence of pitches to help reduce noise.

(6) On the other hand, the chaos function was applied and modified for setting the arrangement of the pattern constituent units. By this modification or application, a chaotic sequence generation function (which is already referred to as a chaotic function in the present specification) capable of generating a chaotic sequence for setting the arrangement of the tire pattern constituent units is converted into a pattern constituent unit. With the sequence setting procedure.

The properties to be provided by the chaotic function in the defined definition area are as follows. First, the chaotic function fc (Xn) of each section has a derivative f′c (Xn) ≧ 1 in all sections. This is because the chaotic function fc (Xn) sometimes intersects the straight line of X (n + 1) = Xn as shown in FIG. 7 (it may not intersect in the shortest and longest pitch sections). Near this intersection,
This is because, when f'c (Xn) <1, the sequence converges at this intersection and an infinite sequence cannot be generated.

Second, the properties that the chaotic function should have are:
In each section where the shortest pitch P1 and the longest pitch Ps on the horizontal axis Xn are defined, the following relationship is satisfied. That is, assuming that the starting point on the small side (ie, the origin side) in the section is Xc and the ending point on the large side (ie, the side opposite to the origin) is Xe, f′c (Xe)> f in the section with the shortest pitch 'C (Xc) In the section with the longest pitch, f'c (Xc)>f'c (Xe)

This is because, in the section having the shortest pitch P1, as shown in FIG. 8, f'c (Xe)>f'c (X
In the case of c), there is a high probability that several rows will stay in the section having the shortest pitch P1. That is, the probability that the pattern constituent units of the shortest pitch P1 are continuously arranged increases. On the other hand, when f'c (Xc)> f '(Xe) in the section of the shortest pitch, as shown in FIG. 9, the probability that the shortest pitches P1 are continuously arranged is small.

In the section of the longest pitch Ps, the relationship is opposite to that of the shortest pitch. In order to continue the longest pitch Ps to some extent, as described above, f′c (Xc)>
f'c (Xe).

As described above, the arrangement in which the pattern constituent units of the shortest pitch and the longest pitch are appropriately continued is as shown in FIG.
According to the results of the experiment shown in FIG. FIG. 10 is a graph showing the relationship between the shortest pitch P1 and the longest pitch Ps for each of the total number of pattern constituent units.
This is a result of a pitch sound test for a tire in which the ratio of the total number of pattern constituent units of the single shortest pitch (single shortest pitch) and the longest pitch (single longest pitch) that are not continuous is changed. This test was tested by sensory evaluation.
As shown in FIG. 10, it is understood that the higher the ratio of the number of individual pitches, the worse the score. However, as will be described later, the pattern constituent units of the shortest pitch or the longest pitch may not be too continuous.

(7) Next, a function that satisfies the above condition, that is, the chaotic function is obtained based on the chaotic function. The present inventors have found the following three chaotic functions. It should be noted that other chaotic functions satisfying these conditions based on the chaotic function can also be adopted in the tire of the present invention, and the use of these functions is also included in the technical scope of the present invention.

(8) Also, in this embodiment, the chaotic functions are the two left and right chaotic functions Fcu and Fcd in each of the other sections except the section of the shortest and longest pitches of the horizontal axis Xn.
Is defined. The left chaotic function Fcu intersects a horizontal virtual line Ha (shown in FIG. 14) passing through the vertical intermediate height point of the defined area on the origin side with respect to the center point Xa of the section on the horizontal axis. Pass through. The right chaotic function Fcd crosses the virtual line Ha and its opposite side (the side opposite to the origin). In the other sections except the shortest and longest pitch sections, two left and right chaotic functions Fcu and Fcd are set. The left and right chaotic functions Fcu, Fcd that do not pass through both sides of the center point Ha (pass only through one side)
Can also be adopted.

(9) -1 The chaotic function of the curve in FIG. 11 is defined by the following equation. A) The section of the shortest pitch of the horizontal axis Xn (K0 <Xn <K
1)

[0057]

(Equation 3)

B) The section (K) of the longest pitch on the horizontal axis Xn
(S-1) ≦ Xn <Ks)

[0059]

(Equation 4)

C) Sections other than A) and B) (Ki is the lower limit of the section (= Xc), K (i + 1) is the upper limit (= Xe)
And).

[0061]

(Equation 5)

Here, Xt = Xn- (Ki + K (i +
1)) / 2−εg. In addition, εg can be arbitrarily determined within a range of half of the section. In the above formula, Z1 is usually 1.0 to 2.0, Zg is 1.0 to 10.0, εg
Is set to 0 to 0.5. In this example, Z1 is 1.06 to 1.15, Zg is 2.0 to 5.0, and the absolute value of εg is 0.08 to 0.20. The sign g at the end is
In the sections P2 to P (s−1) excluding the shortest and longest sections among the sections P1 to Ps of the X axis, Z,
This is the order of the value of ε, and 2 is assigned. The sign
g has the same value in each section P2 to P (s-1).
At some point, it is represented by g.

The above εg is a left chaotic function Fcu,
In the right chaotic function Fcd, it is a value for shifting the curve from the central point Xa = (Ki + K (i + 1)) / 2 of the section on the horizontal axis. In the case of the left chaotic function Fcu passing on the origin side, εg ≧ 0, and in the case of the right chaotic function Fcd passing on the opposite side, εg ≦ 0. Further, when Xt ≧ 0, SGN (Xt) is +1 and X
When t <0, the value is -1. a and C are constants that are set so that both ends of each equation pass through the grid endpoints of the definition area of each section. Further, in the formula, i is the section on the horizontal axis Xn, that is, the order of the pitch. The origin is set to 0, and the section including the origin is set to 1.

(9) -2 The chaotic function of the curve in FIG. 12 is defined by the following equation. A) The section of the shortest pitch of the horizontal axis Xn (K0 <Xn <K
1)

[0065]

(Equation 6)

B) The section (K) of the longest pitch on the horizontal axis Xn
(S-1) ≦ Xn <Ks)

[0067]

(Equation 7)

C) Sections other than A) and B) (Ki is the lower limit of the section and K (i + 1) is the upper limit).

[0069]

(Equation 8)

Here, εg can be arbitrarily determined within a range of half of the section, and Z1 can be selected as described above.
The εg is the center point Xa = (Ki + K) of the section on the horizontal axis.
(I + 1)) / 2 is a value for shifting the curve, and in the case of the left chaotic function Fcu passing through the origin side, ε
Right chaotic function Fcd with g ≧ 0 and passing through the other side
In this case, εg ≦ 0. In addition, the code g at the end is a section P2 to P (s−P) excluding the shortest and longest sections P1 and Ps.
In 1), it is the order of z and ε that define the values, and 2 is assigned. Both ends of each of the expressions a and C are set so as to pass through the grid end points of the definition area of each section. B is A),
B) Set curves of chaotic functions in sections other than
You.

(9) -3 The chaotic function of the curve in FIG. 13 is defined by the following equation. A) The section of the shortest pitch of the horizontal axis Xn (K0 <Xn <K
1)

[0072]

(Equation 9)

B) The section of the longest pitch of the horizontal axis Xn (K
(S-1) ≦ Xn <Ks)

[0074]

(Equation 10)

C) X-axis section (Ki) other than A) and B)
ＫK (i + 1)), the origin point lower limit grid point coordinates of the defined area are (Ki, K (i−1)), and the opposite upper limit grid point coordinates are (K (i + 1), K (i + 2)). and when,
C) -1 When the right chaotic function Fcd passes on the opposite side of the origin from the center point Xa,

[0076]

[Equation 11]

C) -2 In the case of the left chaotic function Fcu passing on the origin side from the center point Xa,

[0078]

(Equation 12)

Here, Z1 and Zg can be set as described above.

(10) As described above, in this embodiment, in each section other than the section having the shortest and longest pitches of the horizontal axis Xn, the horizontal imaginary line passing through the vertical intermediate height point of the definition area is used. Two chaotic functions are set: Ha, a left chaotic function Fcu passing on the origin side of the center point Xa of the section on the horizontal axis, and a right chaotic function Fcd passing on the opposite side. .

Thus, depending on the condition, the left chaotic function Fcu and the right chaotic function Fcd passing through the opposite side
By using the different patterns, it is easy to change from the shortest pitch pattern constituent unit to the longest pitch pattern constituent unit, or from the longest pitch pattern constituent unit to the shortest pitch pattern constituent unit, and to effectively use the pitch fluctuation range. I do.

(11) In this example, one of two chaotic functions Fcu and Fcd is selected under the following conditions. First Condition When the previously determined function value X (n + 1) occurs in the same section on the horizontal axis, the same right or left chaotic function Fcu as the previously determined function value X (n + 1),
The following function value X (n + 2) is generated in Fcd. Second condition When the previously determined function value X (n + 1) occurs in the section of the horizontal axis where the pitch is smaller or is the initial value, the next function value X (n +
2). Third Condition When the previously determined function value X (n + 1) occurs in the section with the larger pitch on the horizontal axis, the next function value X (n + 2) is generated by the right chaotic function Fcd.

This is because the left chaotic function Fcu has a long pitch because its curve is shifted to the left from the straight line of X (n + 1) = Xn and the probability that X (n + 1)> Xn is high. There is a strong tendency to change to constituent units. On the other hand, the right chaotic function Fcd, on the other hand, has a high probability of X (n + 1) <Xn, and thus has a strong tendency to change to a pattern constituent unit with a short pitch.

(12) A sequence of numbers is generated by using the chaotic function of the present embodiment, and is converted into a pitch arrangement of pattern constituent units. As an example, when the number s of types in FIG. 2 is three, the case of FIG. 11A obtained by the expressions 3, 4, and 5 of (9) -1 is adopted. FIG. 14A is an enlarged view of FIG.

In the vertical and horizontal partition lines K0 to Ks (Ks = K3 in this example), the partitions are equally divided. In FIG. 14, K0 is 0, K1 is 1, K2 is 2, K3 is sequentially set to 3.

The initial value X1 is 0.56 (random number table, generated by a random number generator). Thereby, the chaotic function of the above Equation 3 in the section of the minimum pitch gives
X2 = 0.84 in the direction of the vertical axis X (n + 1) is obtained. Next, using X2 = 0.84 as the horizontal axis Xn, X3 = 1.52 is sequentially generated by the chaotic function of the above equation (3).

Since X3 enters section P2 on the horizontal axis Xn, the left chaotic function Fc defined by the section of P2
u, or the right chaotic function Fcd. However, the subsequent function value X3 occurs in the section P1 on the side of the horizontal axis where the pitch is smaller. According to the second condition, the following function value X (n + 1), that is, X4 is obtained by the left chaotic function Fcu.
= 1.66 results. In the same section P2, the following function value X5 =
1.88, X6 = 2.44 are sequentially generated.

X6 enters the section of P3 on the horizontal axis Xn, and according to the curve of Equation 4 of this section, X7 = 2.1
6, X8 = 1.48 is generated.

This X8 enters the section P2 on the horizontal axis.
Left chaotic function Fcu or right chaotic function Fcd
Is used to find X9. However, when X8 occurs in the section of the horizontal axis having the larger pitch, the third function value X9 is generated by the right chaotic function Fcd.
According to the condition, X9 = 1.34 in the right chaotic function Fcd.
Can be obtained. X10 = 1.14, X11
= 0.68 is generated.

(13) Next, it is possible to convert this sequence into a pitch arrangement by associating each section with a different pitch. In the example of FIG. 14, as described above, the section of 0 <Xn <1 corresponds to P1, the section of 1 ≦ Xn <2 corresponds to P2, and the section of 2 ≦ Xn <3 corresponds to P3.

As a result, 0.56, 0.84, 1.5
2, 1.66, 1.88, 2.44, 2.16, 1.4
The sequence of 8, 1.34, 1.14, 0.68 ...
P1, P1, P2, P2, P2, P3, P3, P2, P
2, P2, P1,... Can be converted into a pattern arrangement of pattern constituent units.

As can be seen from this arrangement, it can be seen that each pitch P changes only to the adjacent pitch in the order of the length and does not change one by one. This is naturally expected from each definition region of the chaotic function in FIGS. In FIGS. 2 to 5, two regions are included above or below the vertical direction, including a region through which a virtual bisector (X (n + 1) = Xn) extending at 45 ° from the origin passes. Only in the vertical direction. As a result, an array of pattern constituent units whose pitch changes more than one skip cannot be generated.

As described above, by not changing the pitch more than one skip , the periodicity and the like can be reduced, which is useful for dispersing the pitch sound (converting to white noise).

(14) As described above, a sequence of numbers can be selected using a chaotic function to generate a pitch arrangement of pattern constituent units. However, these may be necessary conditions for noise reduction of the tire, but may not be sufficient to satisfy the conditions. This is because the sequence generated by the chaotic function is very irregular (unpredictable), while the total number of pattern constituent units in the sequence of pattern constituent units of the tire, that is, the total number of pitches (Np) is not so large. The generated sequence may have a bias. In order to reduce the noise of the tire, it is necessary to eliminate such bias and select an optimal arrangement. As a result of various studies, it was found that the following items should be tested.

The irregularity index Vr of each order up to the eighth order
Is 1.5 or less (corresponding to claim 1). The autocorrelation coefficient Ru is smaller than 0.5 when u> 5 (corresponding to claim 1). The maximum dispersion coefficient PSDr max satisfies the following expression (corresponding to claim 1).

PSDrmax ≦ {100 / (Ps / P1) ¹⁰ } × (1 / Rn) + 5 × {(1 / Rn) +1}

Here, Rn is a dimensionless value of the total number of pitches Np, and Rn = Np / 60 as described above.
A ratio SQ max / Np of the number SQ max of the pattern constituent units in which the pattern constituent units having the same pitch are continuous to the total number Np of the pattern constituent units in the tire circumferential direction is 0.15 or less (claim). 1). By fulfilling these tests, we can confirm chaos, eliminate bias,
Various performance can be optimized. As described above, in the tire of the present invention, a pattern constituent unit sequence to be tested obtained by adding the above-described test to the pattern constituent unit sequence obtained based on the chaotic function is employed.

(15) Irregularity Index Vr The irregularity index Vr is used to confirm that the pitch train has no specific periodicity, and is performed up to the eighth order. As shown in Table 1, the periodicity check was performed up to the eighth order. As shown in Table 1, the vibration and noise generated due to each order component of the radial force change (RFV) at the time of rolling the tire are approximately the eighth order. Up to. If there is no specific periodicity up to the eighth order, it is considered that no problem occurs.

[0099]

[Table 1]

In the present specification, the irregularity index Vr refers to a value defined by the following Expressions 13 to 15,
This irregularity index Vr is set to 1.5 or less .

[0101]

(Equation 13)

Here,

[0103]

[Equation 14]

[0104]

(Equation 15)

Dj means the j-th dimensionless pitch in the pattern constituting unit sequence. dj = Pj / average pitch Pj: pitch of j-th pattern constituent unit in pattern constituent unit row Average pitch: total tire circumference CL / total pitch Np of pattern constituent unit row Np (see FIG. 15) Xj: j-th pitch Position of.

As described above, the irregularity index Vr is an index indicating the degree of periodicity of the r-th component. Irregularity index V
This indicates that the r-th periodicity increases as r increases. Further, as shown in FIG.
And the magnitude of the r-order component of the RFV has a positive correlation.
To avoid vibration and noise caused by the RFV,
The irregularity index Vr is preferably smaller than 2 according to the present invention.
Is 1.5 or less. However, in general, it does not become 0, and Vr is larger than 0.

(16) Autocorrelation Coefficient Ru The autocorrelation function Ru is a coefficient defined by Expression 16 in this specification.

[0108]

(Equation 16)

Here,

[0110]

[Equation 17]

In the above equation (16), the pitches of the pattern constituent units are P1, P2,..., Ps in ascending order, and integers 1, 2,. The pitch arrangement in the pattern constituent unit row represented by such an integer is defined as PQ (j). That is, the pitch arrangement of the pattern constituent units is P1, P1, P2, P3, P3,.
… PQ (1) = 1, PQ (2) =
1, PQ (3) = 2, PQ (4) = 3, PQ (5) = 3
…. The variable u is the amount of deviation from j of the reference pitch array PQ (j).

In equation (16), the numerator is an autocorrelation function generally called, and the denominator is a normalization constant. The reason for the division by the normalization constant is that the degree of irregularity of the period cannot be determined by a general autocorrelation function due to the magnitude of the amplitude.

Note that the autocorrelation coefficient Ru is such that when the change in the pitch sequence is sinusoidal (has complete periodicity) and the shift amount u matches the period length, Ru is 1
Becomes Periodicity decreases, irregularities increase, and shift amount u
Becomes larger, the value of Ru approaches zero. This means that there is no correlation between distant pitches and the arrangement is irregular.

The autocorrelation coefficient Ru is determined by its maximum value Ru in the range of u> 5. The present inventors have found that by setting the maximum autocorrelation coefficient Ru <0.5 in the range of u> 5, a preferable degree of irregularity of the pitch arrangement can be obtained. Still more preferably, it is better to be 1/3 or less. Note that the maximum value of the autocorrelation coefficient Ru is 0 or more.

(16) Regarding the maximum dispersion coefficient PSDr max In this specification, the maximum dispersion coefficient PSDr max is defined as the maximum value in the range where the order r is 150 or less among the PSDr values obtained by the equation (18). I have.

[0116]

(Equation 18)

Here,

[0118]

[Equation 19]

[0119]

(Equation 20)

Note that CL is the entire circumference of the tire, and Xj is the position of the j-th pitch.

The variance of the pitch sound (white noise) is obtained by PSDrmax when the order of the pitch arrangement is analyzed by Expression 18.
It is related to the value. When the PSDrmax increases, the dispersion of the sound deteriorates, and the sound approaches a pure tone sound, so that the score (sensory score) of the sensory test deteriorates as shown in FIG.
On the other hand, PSDrmax depends on the ratio (Ps / P1) between the shortest pitch P1 and the longest pitch Ps, and the total pitch number Np. Therefore, Ps / P1 is set to, for example, 1.1 for every 0.1.
Rn (= Np / 60) is set to, for example, 0.6.
The pitch arrangement was determined using a chaotic function for each combination of three values of 7, 1.17, and 1.67.

In the calculation, 50 pitch arrays were obtained for each combination by computer processing. PSDrmax was calculated from the pitch arrangement according to the equation (28). FIG. 18 shows the minimum value of PSDrmax among the PSDrmax of each of the 50 pitch arrays in each combination. FIG. 18 shows the obtained values and a curve giving a preferable margin for each value.

The test for PSDrmax for the pitch arrangement is to satisfy, for example, the following equation determined in consideration of the above curve. This test means that a relatively small pitch arrangement of PSDrmax was selected for each combination.

That is, given Ps / P1, Rn (= Np
/ 60), the PSDrmax is tested using the following equation,
This equation is satisfied. PSDrmax ≦ {100 / (Ps / P1) ¹⁰ } × (1 / Rn) + 5 × {(1 / Rn) +1} where Rn is a dimensionless value of the total pitch number Np, and Rn = Np / 60 It is.

(17) The ratio SQ of the number SQ max of pattern constituent units in which pattern constituent units of the same pitch are continuous to the total number Np of pattern constituent units in the pattern constituent unit row
max / Np is 0.15 or less.

It has been described that the shortest pitch and the longest pitch are preferably arranged appropriately and continuously. However, if the same pitch is excessively continuous, a pulsating sound such as a “wah wah wah” called a wah sound is generated, which is annoying.
FIG. 19 shows the relationship between the maximum value SQ max of the number of continuous sounds having the same pitch as the wah sound and the ratio of the number of pitches Np. When SQ max / Np increased, the wah sound deteriorated and the sensory evaluation decreased, and thus it was found that the range of SQ max / Np ≦ 0.15 was good. Note that SQ max / Np is larger than 0.

(18) As described above, in the pneumatic tire of the present invention, the arrangement of the pattern constituent units is obtained by the following procedure. Generate a sequence using chaotic functions.
The sequence is converted into a pitch arrangement of the pattern constituent units. V
Confirm the compatibility of r, Ru, PSDr max and SQ max / Np and test.

If the above test does not match, the process returns to step S, and a sequence is generated with different initial values, and the process is repeated.
Such a procedure is repeatedly and automatically calculated using a computer according to the flowchart of the program in FIG. Note that the step “PSDr max ≦ Fe
(Rn, Ps / P1) in (Rn, Ps / P1).
Means “{100 / (Ps / P1) ¹⁰ } × (1
/ Rn) + 5 × {(1 / Rn) +1} ”.

More preferably, the number of pattern constituent units at each pitch may be repeatedly calculated so as to match the expected value. For example, when the number s of types has a pitch of four, the total number Np of pattern constituent units in the pattern constituent unit row is set to six.
4, the number Np1 of the pitches P1, P2, P3, and P4.
When a condition such as setting both Np4 to 16 is added, the calculation is repeated until the condition is satisfied. At that time, the initial value may be sequentially changed. The chaotic functions and constants used can also be changed.

Further, in the above-described embodiment, when converting from a numerical sequence to a pitch arrangement, an integer value is assigned to each of the division lines K0 to Ks, and all the divisions on the horizontal axis and the vertical axis have the same length. However, it is also possible to change the length in each section, such as making the section of the shortest pitch and the section of the longest pitch smaller or larger than the others. By this work, for example, in the case where the total pitch Np of the pattern constituent unit rows is set to 64, while satisfying the requirements of the present invention,
Number N of pattern constituent units of each pitch P1, P2, P3, P4
p1 = 19, Np2 = 13, Np3 = 13, Np4 = 1
9 can be adjusted. This is shown in FIG.
9 corresponds to “necessity of parameter change” in the program chart of No. 9. As described above, the values of K0 to Ks are set such that each distribution number of each pitch is most likely to occur. For example, when the number of types s = 3, and when the number of pattern constituent units of each pitch is 21, K0 = 0, K1 = 1.13,
It is assumed that K2 = 1.87 and K3 = 3.0. On the other hand, when the numbers are 18, 27 and 18, K0 = 0, K1 = 1.
05, K2 = 1.95 and K3 = 3.0.

As shown in FIG. 21, the pneumatic tire has a plurality of types s of pattern constituent units 1A, 1B, 1C having different pitches P, which are circumferential lengths (referred to collectively as pattern constituent unit 1). Are arranged symmetrically on the tire tread and on both sides of the center rib 3 passing through the tire equator. The pattern constituent unit rows 2A, 2A, 2B, 2B (which are collectively referred to as pattern constituent unit rows 2) are arranged in the tire circumferential direction. Have been placed.

In this embodiment, the pattern constituting units 1A,
1B, 1C,... Are block patterns composed of blocks. However, it can be a rib pattern, a lug pattern, or a combination thereof. At this time, one peak portion of the zigzag rib groove, a space between the lug grooves, and the like form the pattern constituting unit 1. Further, the pneumatic tire may be configured as a radial tire or a bias tire, or as a tire for a truck or a bus, a tire for a motorcycle, or the like in addition to a tire for a passenger car.

In the block pattern shown in FIG.
In the present embodiment, the pattern constituent unit rows 2A, 2A and the pattern constituent unit rows 2B, 2B have the same total number of pattern constituent units and the same arrangement of pattern constituent units, and differ only in the phase.
However, it is also possible to make the arrangement of the pattern constituent units different assuming that the total number of the pattern constituent units in the tire circumferential direction is the same.

Further, as shown in FIG. 22, the pattern constituent unit rows 2A, 2A and the pattern constituent unit rows 2B, 2B may be different in the total number of pattern constituent units in the tire circumferential direction.
Further, the number of pattern configuration unit rows 2 can be freely changed to one or more, but is preferably about two to seven.

Further, as described above, each of the pattern constituting unit rows 2 is formed as an optimum pitch arrangement by repeating the following procedure using a computer, and as shown in the figure, for example, pitches P1, P2, P3 , P2, P
The arrangement is set as 1, P2....

As described above, the pitch is the length of the pattern constituting unit 1 in the tire circumferential direction. In the case of a block pattern, the pitch is defined as the total length of the block and one lateral groove. I have.

[0137]

EXAMPLE 1) A radial tire having a tire size of 205 / 65R15, the pattern constituent unit rows 2A and 2 shown in FIG.
A, Table 2 and 3 show tires in which the pattern constituent unit rows 2B and 2B both have the same total number of pattern constituent units and the same arrangement of pattern constituent units, and differ only in phase by about 1/3 of the average pitch. It was more prototype specification. Also, Comparative Example Product 1 shown in Table 4
For No. 2, the irregularity index Vr, the autocorrelation coefficient Ru, the maximum variance coefficient PSDrmax, and the SQmax / Np were tested, and the order analysis of the RFV was performed, and the sensory evaluation of the pitch sound was performed. The results are shown in Table 4 (the pattern constituent unit is described as pitch in each table). In each table, in the column of PSDrmax,
The value according to Equation 18 is shown in the column, and the (expression value) in the lower column is the right of the inequality.
The calculation result of the side is described.

As a reminder, the aforementioned Japanese Patent Publication No. 58-284
No. 4 (Japanese Unexamined Patent Publication No. 55-8904) shows a trial production of a tire having the tread pattern shown in FIG. 3 according to the same specifications as the tire with respect to the tire size, and a similar sensory evaluation and each test. This is shown in Comparative Example 3 in Table 4. Table 4 shows a tire based on the invention described in Japanese Patent Publication No. 3-23366 (Japanese Patent Application Laid-Open No. 54-115801) as Comparative Example 4.

[0139]

[Table 2]

[0140]

[Table 3]

[0141]

[Table 4]

In the repetitive operation by the computer program, the comparative example 3 shown in FIG. 3 of JP-B-58-2844 (JP-A-55-8904) and JP-B-3-23366 (FIG. 54-115801
No pitch row of Comparative Example 4 based on the invention described in (1). Further, in the tire of Comparative Example 3, Vr was as high as 2.46, and thus the tertiary component of RFV was 1.92 kg.
, And the degree of irregularity is small, and Ru is also large at 0.76. In Comparative Example 4, Vr was as high as 2.16, and
The fifth-order component of V is also undesirably large at 1.72 kg.

Thus, the pneumatic tire of the present invention has a
The red pattern setting method is the same
A tread pattern that can be further divided can be selected.

(2) The only difference is that the pattern constituent unit rows 2A and 2A and the pattern constituent unit rows 2B and 2B for the same tire size have the same total number of pattern constituent units in the tire circumferential direction and have different arrangements. Table 5 shows the results of prototypes of tires different from those described in the above) and the same examination.

(3) Further, pattern configuration unit row 2 in FIG.
Table 6 shows the results of a trial production of A, 2A, and pattern constituent unit rows 2B and 2B with different total numbers of pattern constituent units in the tire circumferential direction.

[0146]

[Table 5]

[0147]

[Table 6]

In each of the examples, the specific order of the RFV is not large, and the sensory evaluation of the pitch sound is good.

Each sensory evaluation was conducted by mounting a tire of the above-mentioned size on a 2.5-liter FR car and setting the air pressure to 200 kp.
Used in a. The sensory evaluation of vehicle interior sound is a good level of 3 or more using a 5-point method. In addition, the engine was coasted from 100 kph with the engine off, and evaluated. RFV measurement is JASO
Performed according to C607.

[0150]

As described above, in the pneumatic tire of the present invention, the pattern constituent units having three or more pitch lengths are skipped by one pitch in the order of the length while utilizing the characteristics of the chaotic function. The pattern constituent unit sequence arranged without performing the setting is determined. For this reason, we will first have a chaotic arrangement,
Dispersion of pitch sound while maintaining clear pitch by not changing pitch one by one (white noise)
Helps to reduce tire noise. Moreover, the irregularity index Vr, the autocorrelation coefficient Ru, and the maximum variance coefficient PSDr m
The ax and SQ max / Np are tested to eliminate an unpleasant sound factor which may be included in the sequence of chaotic functions, to reduce unpleasant pitch sound, to reduce tire noise, and to achieve excellent uniformity. Tires. Also,
By using the pattern constituent unit rows arranged without skipping one pitch in the order of length, the degree of sound dispersion is improved, the sound change is smooth, and it is easy to understand and clear, and the noise is low. It becomes a pitch arrangement that is useful for conversion.

Further, with such a configuration, even when the number of types of pitches is large, the arrangement can be easily set preferably, and this can be useful for reducing the noise of the tire. Further, depending on the condition given to the chaotic function, the pattern constituent units of the shortest pitch and the longest pitch are arranged in an appropriate sequence, and the result of the sensory evaluation of the pitch sound is enhanced.

According to the second aspect of the present invention, the left chaotic function Fcu and the right chaotic function Fcd passing through the opposite side are selectively used depending on conditions, so that the shortest pitch pattern constituent unit to the longest pitch pattern constituent unit can be used. It is easy to change the pattern configuration unit from the longest pitch to the shortest pitch in the unit or the pattern configuration unit with the shortest pitch, and the pitch variation range can be used effectively.

[Brief description of the drawings]

FIG. 1 is a diagram illustrating an example of a chaos function.

FIG. 2 is a diagram showing a definition region of a chaotic function in which the number s of types of pattern constituent units is three.

FIG. 3 is a diagram illustrating a definition region of a chaotic function in which the number s of types of pattern constituent units is four.

FIG. 4 is a diagram showing a definition region of a chaotic function in which the number s of types of pattern constituent units is 5;

FIG. 5 is a diagram showing a definition region of a chaotic function in which the number s of types of pattern constituent units is five.

FIG. 6 is a diagram showing a relationship between a pitch ratio and H / T wear.

FIG. 7 is a diagram illustrating a chaotic function.

FIG. 8 is a diagram illustrating a chaotic function of the shortest pitch section.

FIG. 9 is a diagram illustrating a chaotic function of the shortest pitch section.

FIG. 10 is a diagram showing the relationship between the ratio of the total number of pattern constituent units of the longest and short pitches to the number of single longest and short pitch pattern constituent units and noise.

FIG. 11 is a diagram illustrating a chaotic function.

FIG. 12 is a diagram illustrating another chaotic function.

FIG. 13 is a diagram illustrating another chaotic function.

FIG. 14 is a diagram illustrating a method of obtaining a sequence using a chaotic function.

FIG. 15 is a diagram illustrating Xj of the irregularity index Vr.

FIG. 16 is a diagram showing the results of sensory evaluation of irregularity index Vr and pitch sound.

FIG. 17 is a diagram showing the results of sensory evaluation of PSDr max and pitch sound.

FIG. 18 is a diagram illustrating a relationship between the minimum value of PSDrmax in a combination of Ps / P1 and Rn.

FIG. 19 is a diagram showing a result of a sensory evaluation of Sq max and a wah sound.

FIG. 20 is a flowchart of a computer program for obtaining a sequence.

FIG. 21 is a plan view showing a tread pattern according to one embodiment of the present invention.

FIG. 22 is a plan view showing a tread pattern according to another embodiment of the present invention.

[Explanation of symbols]

 1, 1A, 1B, 1C Pattern constituent unit 2, 2A, 2B Pattern constituent unit row P, P1, P2, P3, P4... Ps Pitch s Number of types of pattern constituent unit

Continuation of the front page (56) References JP-A-6-206405 (JP, A) JP-A-5-213009 (JP, A) JP-B-58-2844 (JP, B2) JP-B-3-23366 (JP) , B2) (58) Field surveyed (Int. Cl. ⁷ , DB name) B60C 11/03 B60C 19/00

Claims (4)

(57) [Claims] An air forming a tread pattern of a tire tread by a pattern constituent unit row in which pattern constituent units having three or more types of pitches P, which are lengths in the circumferential direction, are arranged in the tire circumferential direction. A method for setting a tread pattern of an inlaid tire, wherein a horizontal axis and a vertical axis in rectangular coordinates are divided into the number of types s in one direction from the horizontal axis, the vertical axis and each right angle and each origin, and a plurality of types are defined on a coordinate plane. A vertical division line forming a rectangular area, a horizontal division line are provided, and a horizontal axis, a pattern constituent unit from the origin are assigned to each division of the vertical axis in the order of small pitch, and the horizontal axis is Xn, and the vertical axis is X (n + 1), X
Of the chaotic function fc represented by (n + 1) = fc (Xn),
The definition area for each section of the horizontal axis is as follows (a),
(B) In addition to setting as shown in (c), (a) In the section of the shortest pitch on the horizontal axis, the area of the same pitch is selected from all the areas vertically arranged in the shortest section of the horizontal axis. (B) In the section of the longest pitch on the horizontal axis, among all the areas vertically aligned on the longest section of the horizontal axis, (C) In the section of the pitch of the length between the same pitch and the pitch adjacent vertically on the smaller side in the vertical direction, (c) In the section of the pitch of the length between them on the horizontal axis, the vertical direction is calculated in each of these sections of the horizontal axis. Of all the areas arranged in the vertical direction, the sum of the area of the same pitch and the area of the pitch vertically adjacent to the long side and the short side thereof in the vertical direction. In this definition area, it is determined for each section of the horizontal axis, and the following requirements X (n + 1) obtained sequentially by a chaotic function satisfying ), Based on the sequence of the function values, and without omitting one adjacent pitch in the order of the pitch length, into a pattern constituent unit sequence in which pattern constituent units are arranged.
A method for setting a tread pattern of a pneumatic tire, comprising a pattern constituent unit row to be tested obtained by performing the following tests (1) to (4). Chaotic function fc
Satisfies the derivative f′c ≧ 1 in each section of all the horizontal axes.
In the section of the horizontal axis in which the shortest pitch and the longest pitch are defined, the start point (Xc) on the small side of the section and the end point (Xe) on the large side are f'c (Xe)> in the section with the shortest pitch. f'c (Xc) In the section having the longest pitch, f'c (Xc)>f'c (Xe) The irregularity index Vr in each order up to the eighth order is 1.5 or less. The autocorrelation coefficient Ru is smaller than 0.5 when u> 5. Maximum dispersion coefficient PSDrm
ax satisfies the following equation. PSDrmax ≦ {100 / (Ps / P1) 10} × (1 / Rn) + 5 × {(1 / Rn) +1} where P1 is the shortest pitch, Ps is the longest pitch, and R
n is Np / 60, Np is the total number of pattern constituent units in the pattern constituent unit row, the number SQmax of the pattern constituent units in which the pattern constituent units of the same pitch are continuous, and the total number Np of the pattern constituent units arranged in the tire circumferential direction. SQmax / Np of 0.15 or less. 2. The left chaotic function Fcu passes through a virtual imaginary line passing through a vertical middle height point of the definition area on the origin side with respect to a center point Xa of the section in the horizontal axis direction. , And the right chaotic function Fcd crosses on the other side, and within the same section on the horizontal axis, the function value X (n
+1) occurs in the right or left chaotic function Fcu, Fcd, the next function value X (n + 2) is also the same right or left chaotic function Fcu as the previously determined function value X (n + 1). , Fcd, and when the previously defined function value X (n + 1) occurs in the section of the horizontal axis where the pitch is smaller or when it is the initial value, the left chaotic function Fcu, When the value X (n + 1) occurs in the section with the larger pitch on the horizontal axis, the right chaotic function Fcd
2. The method of setting a tread pattern for a pneumatic tire according to claim 1, wherein the following function values X (n + 2) are respectively generated. 3. The tire tread according to claim 2, wherein the total number of pattern constituent units in the tire circumferential direction is the same, but the tire tread includes two or more types of pattern constituent unit rows having different arrangements of the pattern constituent units. 2. The method for setting a tread pattern of a pneumatic tire according to 1. 4. The method for setting a tread pattern of a pneumatic tire according to claim 1, wherein the tire tread has two or more types of pattern constituent unit rows having different numbers of pattern constituent units in the tire circumferential direction. .