JPH08108711A - Pneumatic tire - Google Patents

Abstract

PURPOSE: To reduce a noise by forming a pattern out of pattern constitution unit rows containing a pattern constitution unit in each cell along horizontal and vertical axes, with the units arrayed at the prescribed pitch in the order of length skipping one or more adjacent pitches. CONSTITUTION: A tread pattern is made of pattern constitution units having a different number of types S with a pitch P equal to or above three, and the definition zone of a chaos function fc expressed as X(n+1)=fc(Xn) is determined as the summation of all vertically arranged zones for each cell along a horizontal axis, provided that the horizontal axis is expressed as Xn and a vertical axis as X(n+1). In other words, zones having a pitch ratio equal to or less than 1.5 is selected, provided that a small pitch assigned to each cell in vertical and horizontal directions is used as a denominator and a large pitch as a numerator, and the summation of the zones is used as a definition zone. Also, the pitch P has a calibrated pattern constitution unit row obtained from the calibration of a pattern constitution unit rows including pattern constitution units so laid as to skip one or more adjacent pitches arranged in the order of pitch length along peripheral direction via the conversion of a sequence obtainable from the function fc. According to this construction, a noise can be lowered and uniformity can be improved.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a pneumatic tire capable of reducing unpleasantness due to noise during traveling, on the basis that the arrangement of pattern constituent units of a tire tread is set on the basis of a sequence of chaotic functions. .

[0002]

2. Description of the Related Art Various tread patterns are used for tire treads in order to maintain the frictional force with the road surface depending on the conditions of the vehicle and the road surface. In many tread patterns, grooves in the tire axial direction are formed at intervals in the tire circumferential direction, or rib grooves are formed in a zigzag pattern in the tire circumferential direction. By repeating in the tire circumferential direction, a block pattern, a rib pattern, a lug pattern, etc., which are repetitive patterns that form a pattern constituent unit row, are adopted.

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

In order to improve this, conventionally, by arranging a plurality of types of pattern constituent units having different lengths in the tire circumferential direction of the pattern constituent units, that is, pitches, in the tire circumferential direction, noise is dispersed in a wide frequency band. The so-called pitch variation method that produces white noise has been adopted.

There are many proposals for this white noise conversion method, for example, Japanese Patent Publication No. 58-2844 (Japanese Patent Laid-Open No. 55-8904) and Japanese Patent Publication No. 3-23366 (Japanese Patent Laid-Open No. 54-115801). No.), there is one in which the pitch array is a sinusoidal periodic array. In addition, Japanese Examined Patent Publication No. 62-41122 (Japanese Patent Application Laid-Open No. 57-41122)
No. 114706), the pitch arrangement of the pattern constituent units is random.

Some proposals merely define the number of pitches, pitch ratio, etc., but lack a specific disclosure of how to specifically arrange the pattern constituent units.

[0007]

However, first of all, the former pitch array is a sinusoidal periodic array:
Since the pitch changes continuously and periodically, there is an advantage that the change in rigidity of adjacent pattern constituent units is small and abnormal wear does not easily occur. However, the change in the rigidity of the pattern constituent unit changes periodically corresponding to the change in the pitch. For this reason, the force variation (RFV) in the radial direction becomes large with a specific order component that matches the number of cycles, and abnormal vibration may occur, which may rather increase unpleasant noise.

[0008] Further, the one in which the pitch arrangement of the pattern constituent units is random has no periodic regularity, which is completely opposite to the case of the periodic arrangement. Therefore, the specific order component of the force variation does not increase, and abnormal vibration and noise are rarely generated. However, there is a problem that abnormal wear is likely to occur because the pitch between adjacent pattern constituent units changes relatively greatly.

As the number of types s of pitch lengths of the pattern constituent units increases, the effect of pitch variation generally improves. Therefore, it is preferable that the number of types s is 3 or more. On the other hand, the number of types s is relatively large in terms of production due to the recent progress in mold manufacturing.
However, in the conventional proposals for noise reduction, the theory of noise reduction cannot be said to be clear, and a new method is desired.

The present inventors have made various developments,
For low noise of the tire, it is assumed that the number of types in which the length (pitch) of the pattern constituent units in the tire circumferential direction is different is 3 or more. (1) Characteristics that the pattern constituent unit row should have Regularity (no periodicity) -Continuity of pitch change (relationships between neighboring pitches) -Similar arrangements are unlikely to occur (2) Characteristics of pattern constituent unit sequences to be excluded-Periodicity I found that.

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 chaotic function.

Chaos refers to "a seemingly chaotic and unpredictable phenomenon produced by deterministic equations existing everywhere in nature such as turbulence and rhythms in biological systems." Further, this chaos theory is a law hidden behind such a complicated phenomenon of chaos or a theory for trying to reveal it, and a chaos function is a function for generating a chaotic pseudo signal. .

Regarding chaos and chaos function,
JP-A-4-86814 and JP-A-4-2219
Japanese Laid-Open Patent Publication No. 37-37 proposes a chaos generating device, and also Japanese Patent Laid-Open No. 4-
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.

Also, "System Research No. 169" issued by System Research Institute, Inc., July 16, 1993
The following formulas are given on page 38 of “Materials for Chaos Theory Practical Application to Consumer Equipment” by Sanyo Electric Co., Ltd. A chaotic function of 1 is illustrated. The figure obtained by this equation 1 is shown in FIG. The chaotic function will be expressed in the form of X (n + 1) = fc (Xn) hereinafter.

[0015]

[Equation 1]

As another example of the chaotic function, the following expression 2 is known [shown in FIG. 1 (b)].

[0017]

[Equation 2]

In the present specification, if n, i, etc. are variables, if there is no possibility of confusion, in order to simplify the equations, if necessary, omit () around variables. ing.

The chaotic function as expressed by the equations 1 and 2 has the following characteristics (a), (b) and (c). (A) There is a continuous change between neighboring numbers. (B) The relationship between distant numbers becomes uncorrelated. (C) Even if the initial values are very close to each other, they are discrete with each other over time. .

The characteristic that the arrangement of the pattern building units for low noise of the tire should have is "irregularity" as described above.
"Continuity of pitch change" and "It is difficult for similar sequences to occur." The property to be excluded is the "periodicity".

In the chaos function, "continuously changing between neighboring numerical values" corresponds to "continuity of pitch length change (relationship between neighboring pitches)" of the arrangement of pattern constituent units. . Further, the fact that the separated numerical values are uncorrelated with the chaotic function corresponds to the above-mentioned "irregularity (there is no periodicity)" in the arrangement of the pattern constituent units. Furthermore, "the initial values are discrete even if they are close to each other" corresponds to "the similar arrangement is unlikely to occur" in the arrangement of the pattern constituent units. This means that in the arrangement of the pattern constituent units, it is possible to prevent repetition of the arrangement of the pattern constituent units. Also in this respect, it is conceivable that the audible peak sound can be reduced by determining the arrangement of the pattern constituent units based on the chaos function to disperse the pitch sound and generate white noise. Tend. 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 idea of the chaotic function.

However, it is not advisable to use the chaos function equations of the above equations 1 and 2 as they are to determine the arrangement of the pattern constituent units. For example, the chaotic functions of Equations 1 and 2 are 0 to 0 on the horizontal axis as shown in FIGS.
There is only one curve, each straight line, defined separately in the two sections 0.5 and 0.5-1.0.
Therefore, even if there is a possibility of being used when the number of types of pitch is 2, it is 0 when the number of types of pitch is 3 or more.
~ 1 must be divided into 3 or more types. At that time, since there is only one curve and one straight line, the sequence obtained by this chaos function or the sequence of the pattern constituent units obtained by converting the sequence cannot be a very suitable sequence for reducing the noise of the tire. .

The present invention adopts the characteristics of a chaotic function in an array of pattern constituent units having different pitches s of 3 or more and is applied and modified to set the array of pattern constituent units, and a chaotic sequence. We have devised a chaotic sequence generation function (called chaotic function in this specification) that can generate Furthermore, I came up with a procedure for setting the arrangement of pattern constituent units. As a result, the tire can be reduced in noise and has excellent uniformity.

Further, by arranging a pattern constitutional unit having three or more kinds of pattern constitutional units and skipping one or more pitches adjacent to each other in the order of the pitch length, a pitch arrangement is obtained. The idea is to give flexibility to the pitch arrangement and to enable pitch arrangement with a high degree of freedom.

According to the present invention, noise is reduced by providing a pattern constituent unit row in which pattern constituent units are arranged with a pitch arrangement in which one or more adjacent pitches are skipped in the order of pitch length. The purpose of the invention is to provide a pneumatic tire.

[0026]

SUMMARY OF THE INVENTION According to the present invention, a pattern constitutional unit row in which three or more kinds of pattern constitutional units s having different pitches P in the circumferential direction are arranged in the tire circumferential direction, A pneumatic tire forming a tread pattern of a tire tread, wherein the coordinates are obtained by dividing the horizontal axis and the vertical axis in the right-angled coordinate with the horizontal axis and the vertical axis at each right angle and in one direction from the origin to the number of types s. A vertical dividing line and a horizontal dividing line that form a plurality of rectangular areas on the surface are provided.
Further, the pattern constituent units from the origin are assigned to the sections on the horizontal axis and the vertical axis in ascending order of pitch, and the horizontal axis is Xn and the vertical axis is X (n + 1), and X (n +
1) = Definition area of the chaotic function fc represented by fc (Xn) for each section on the horizontal axis is assigned in the vertical axis direction among all areas arranged in the vertical direction in each section on the horizontal axis And the pitch assigned to the horizontal axis is the denominator of the smaller pitch, and the larger pitch is the numerator, the ratio of the pitches is the sum of the areas that are 1.5 or less. In each section of the horizontal axis in, and the following,
Based on the sequence of the function values of X (n + 1) sequentially obtained by the chaotic function satisfying the requirement of 1), and further including the pattern constituent units arranged at intervals of one or more pitches adjacent in the order of length. The pneumatic tire is characterized in that it is composed of the above-mentioned pattern constituent unit sequence, and that the pattern constituent unit sequence is provided with a pattern constituent unit sequence to be tested obtained by performing the following tests. The chaotic function fc is the derivative f′c ≧ 1 in each section on the horizontal axis. In the section in which the shortest pitch and the longest pitch are defined, at the start point (Xc) on the small side of the section and at the end point (Xe) on the large side, f'c (Xe)>f'c in the section of the shortest pitch (X
c) In the section with the longest pitch, f'c (Xc)>f'c (X
e) The irregularity index Vr is smaller than 2. The autocorrelation coefficient Ru is smaller than 0.5 when u> 5. The maximum dispersion coefficient PSDrmax satisfies the following formula. PSDrmax ≦ {100 / (Ps / P1) 10} ×
(1 / Ra) + 5 × {(1 / Rn) +1} where P1 is the shortest pitch, Ps is the longest pitch, and R is
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 arrangement of the pattern constituent units in the tire circumferential direction. Ratio SQmax / Np of 0.15 or less.

Further, in the invention of claim 2, the chaotic function has a horizontal direction passing through a vertical intermediate height point of the defined region in each of the sections other than the section having the shortest pitch and the longest pitch on the horizontal axis. The pneumatic tire is characterized in that two chaotic functions, a left chaotic function Fcu passing right and left and a right chaotic function Fcd, are set on a virtual line.

Further, in the invention of claim 3, the left chaotic function Fcu is located on a horizontal imaginary line passing through a vertical intermediate height point of the definition region, and is located at a position more than the center point Xa of the section in the horizontal axis direction. The chaotic function Fc on the right side that intersects with the origin
d passes through on the opposite side, and within the same section on the horizontal axis, the previously determined function value X (n + 1) is
When generated by the right or left chaotic functions Fcu and Fcd, the next function value X (n + 2) is also the same as the previously defined function value X (n + 1).
u, Fcd, and the previously defined function value X (n +
When 1) occurs in the section on the side with a smaller pitch on the horizontal axis or is the initial value, the chaotic function Fcu on the left is used, and the previously defined function value X (n + 1) is the section on the side with a larger pitch on the horizontal axis. When it occurs in the right chaotic function Fcd,
Pneumatic tires characterized by producing the following function values X (n + 2), respectively.

Further, in the invention of claim 4, the tire tread has two or more kinds 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. A pneumatic tire, and claim 5.
The present invention is a pneumatic tire in which a tire tread is provided with two or more types of pattern constituent unit rows having different total numbers of pattern constituent units in the tire circumferential direction.

[0030]

BEST MODE FOR CARRYING OUT THE INVENTION In the pneumatic tire of the present invention, pattern constituent units of different types s having three or more pitches P, which are circumferential lengths, are obtained by using a chaotic function. The tread pattern of the tire tread is formed by the sequence of pattern constituent units sequentially arranged in the tire circumferential direction. Also, this pattern composition unit sequence is
It is tested and adopted as the pattern constituent unit string of the test object.

(1) First, as shown in FIGS. 2 to 5, in a Cartesian coordinate of the origin 0, to suit a chaotic function,
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 perpendicular to each other, and are divided in the positive direction from the origin by the number of types s in the vertical direction, dividing lines K0 to Ks, and dividing lines K0 to Ks in the horizontal direction (each K0 is By passing the horizontal axis and the vertical axis respectively, the horizontal axis Xn and the vertical axis X (n + 1)
Are divided into the number of pitch types s.

By partitioning in this way, the rectangular coordinate plane is partitioned into a large number of rectangular areas surrounded by the vertical partition lines K0 to Ks and the horizontal partition lines K0 to Ks. .

Although FIG. 2 to FIG. 5 show the case where the number of types s of the pattern constitutional units is 3 to 6, they can be similarly divided even if they are 7 or more. Although the number of types s can be set in advance when designing a tire, it is usually set to about 9 types or less from the viewpoint of manufacturing. .

(2) Next, the pattern constituent units of the pitches P1 to Ps in order of increasing length from the origin O are assigned to the section of the horizontal axis Xn and the vertical axis X (n + 1). As described above, the pitch refers to the circumferential length of the pattern constituent unit (when it is meant that the pitch is particularly long, it may be referred to as "pitch length".
When there is no misunderstanding, for simplicity, the pattern unit may be simply referred to as pitch).

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

Taking the case where the number of types s is 5 as an example,
As shown in FIGS. 4 and 5, the pitches P1, P2, P3, P4, and P5 that are adjacent to each other in the ascending order of length are defined by partition lines K0 to K5 in each partition of the horizontal axis Xn and the vertical axis X (n + 1). , K0 <P1 <K1, K1 ≦ P2 <K2, K2 ≦ P3
<K3, K3 ≦ P4 <K4, K4 ≦ P5 <K5 are assigned from the origin side.

(3) Each chaotic function has a horizontal axis Xn,
A defined area that is allowed to exist in the vertical direction is defined.

The horizontal axis is Xn and the vertical axis is X (n + 1).
Is defined as the definition area for each section on the horizontal axis of the chaotic function fc represented by X (n + 1) = fc (Xn). As described above, this defined area is defined as the sum of the areas selected from all the areas arranged in the vertical direction for each section on the horizontal axis.

In the present invention, in each of the regions arranged in the vertical direction, the smaller pitch of the pitches assigned in the vertical axis direction and the pitch assigned in the horizontal axis direction is used as the denominator for each of the regions, and the larger one is used. A region having a pitch ratio of 1.5 or less when the pitch is taken as a numerator is selected, and the sum of these selected regions becomes the defined region. Here, all the regions lined up in the vertical direction mean one vertical total region in which s regions of pitches P1 to Ps lined up in the vertical direction in each section of the horizontal axis Xn are continuous.

As described above, the change in pitch in the tread causes a change in the rigidity of the adjacent pattern constituent units so that the stress distribution in the ground contact surface is not uniform and abnormal wear is caused. This is because it may occur. From the viewpoint of pitch variation, 1.05 or more,
Preferably it is 1.10 or more. H / T wear (heel and toe wear) was measured for tires having two types of pitches and alternating in the tire circumferential direction. In this test tire, the pitch ratio was changed and the drum test was conducted. The result is shown in FIG. 6 as a 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 were applied, and the pitch of the reference pattern constituent units was set to 30.0 mm.

The variation of the H / T wear amount on the circumference triggers abnormal wear such as polygonal wear. It can be seen from FIG. 6 that the pitch ratio is preferably 1.5 or less.

Therefore, as described above, the pitch ratio is 1.
The vertical region sum of 5 or less is calculated by the chaotic function fc
The definition area for this section on the horizontal axis. Thereby, the change range of the chaotic function in each section on the horizontal axis is set. As a result, even when the change of the value of the sequence of chaotic functions is maximum, the pitch ratio of the adjacent pattern constituent units in the pattern constituent unit string is prevented from becoming larger than 1.5, and the H / T Controls wear.

(4) Number of pitch types s of pattern constituent units
Will be described below. First, assume that the pitches are set as follows, respectively. P1 = 19.4 mm P2 = 25.0 mm P3 = 30.0 mm P4 = 36.9 mm P5 = 46.6 mm This corresponds to the case 1 of FIG. 4 (a).

First, considering a region lined up in the vertical direction with respect to the section P1 on the horizontal axis Xn, P2 / P1 = 1.29 <1.
5 and P3 / P1 = 1.55> 1.5. Therefore, when the definition area in the vertical direction is included up to the dividing line K3 parallel (horizontal direction) to the horizontal axis Xn, the pitch ratio is 1.
It may be more than 5. Therefore, P1 on the horizontal axis Xn
In this section, an area between the section lines K0 to K2 in the horizontal direction in the direction of the vertical axis X (n + 1) (sections P1 and P2 on the vertical axis) is determined as the definition area of the chaotic function.

Secondly, consider the definition area for the section P2 on the horizontal axis Xn. P2 / P1 = 1.29 ≦ 1.5, P3
/P2=1.20≦1.5, P4 / P2 = 1.48 ≦
1.5 and P5 / P2 = 1.86> 1.5. Therefore, the vertical region in which the change in pitch length does not exceed 1.5 is the region between the section lines K0 to K4 in the horizontal direction in the vertical axis X (n + 1) direction. This area sum is determined as the definition area of the chaotic function. This is the section P1, P on the vertical axis X (n + 1)
2, P3, P4.

Thirdly, considering the definition area of the section P3 on the horizontal axis Xn, similarly, the vertical area that does not exceed the pitch length change of 1.5 is the horizontal direction in the vertical axis X (n + 1) direction. It is an area between the demarcation lines K1 to K4. This area sum is determined as the definition area of the chaotic function. This is the vertical axis X
(N + 1) sections P2, P3, and P4 are obtained.

Similarly, as shown in FIG. 4 (a),
In the section of P4 on the horizontal axis Xn, P2, P3, P4 in the vertical direction,
The area P5 is the definition area. In the section P5 on the horizontal axis Xn, the areas P4 and P5 in the vertical direction are the definition areas.

(5) As described above, when setting the definition region of the chaotic function, the small length within the pitches P1 to Ps of the partition in the direction of the horizontal axis Xn or the vertical axis X (n + 1) in each region. The denominator is the pitch of and the numerator of the other is the ratio of the pitches is 1.5 or less, and the vertical region sum is defined as the definition region. It is not necessary to set the ratio Ps / P1 between the shortest pitch P1 and the longest pitch Ps within 1.5.

The ratio Ps / P1 between the shortest pitch P1 and the longest pitch Ps is 3.0 or less, preferably 2.5 or less. Moreover, it shall be 1.1 or more. Even if it is larger than 3.0, the sound dispersion effect does not change, and the abnormal wear tends to increase. Further, in order to exert the effect of pitch variation, it is 1.1 or more, preferably 1.20 or more.

(6) Further, in the pitches adjacent to each other in the order of length, the ratio P (i + 1) / Pi of the adjacent long pitch P (i + 1) and short pitch Pi is 1.05 or more, preferably 1.10 or more. , And less than 1.5. When the value is equal to or more than the above value, the pitch sound dispersion effect is small and the noise is large.

Table 1 summarizes the necessary conditions that the pitch must satisfy and the possibility of pitch change for each "case" shown in FIGS. When the definition area in any of the cases of FIGS. 2 to 5 is used, it is necessary to satisfy the “pitch condition” in Table 1.

[0052]

[Table 1]

(7) The characteristics that the chaotic sequence generation function modified by applying the chaotic function (which is already called the chaotic function in this specification) should have in the defined region are:
It is as follows.

First, the chaotic function fc (X
n) is a derivative f′c (Xn) ≧ 1 in all sections.

This is because the chaotic function fc (Xn) is as shown in FIG.
, There is a case where it intersects with a straight line of X (n + 1) = Xn (in some cases, it does not intersect in the section with the shortest pitch and the longest pitch). This is because when f′c (Xn) <1 in the vicinity of this intersection, the number sequence converges at this intersection and an infinite number sequence cannot be generated.

The characteristic that the second chaotic function should have is
In each section in which the shortest pitch P1 and the longest pitch Ps of the horizontal axis Xn are defined, the following relationships must be satisfied.
That is, the start point on the small side (that is, the origin side) in the section is X.
c, X is the end point on the large side (that is, the side opposite to the origin)
In the shortest pitch section, f'c (Xe)>f'c (X
c) In the section with the longest pitch, f'c (Xc)>f'c (X
e)

This means that in the section with the shortest pitch P1, as shown in FIG. 8, f'c (Xe)>f'c (X
The probability of several sequences staying in the section having the shortest pitch P1 is high. That is, the probability that the pattern constituent units with the shortest pitch P1 are arranged consecutively becomes high. On the other hand, when f′c (Xc)> f ′ (Xe) is set in the shortest pitch section, the probability that the shortest pitch P1 is continuously arranged becomes small as shown in FIG.

In the section of the longest pitch Ps, the relationship is opposite to that in the case of the shortest pitch, and f'c (Xc)>
The relation of f'c (Xe) is preferable.

Thus, the arrangement in which the shortest pitch and longest pitch pattern constituent units are appropriately continuous is shown in FIG.
According to the result of the experiment shown in. FIG. 10 shows that for each of the total number of pattern constituent units of the shortest pitch P1 and the longest pitch Ps,
It is the result of testing the pitch sound of tires in which the ratio of the total number of individual shortest pitches (single shortest pitches) and longest pitches (single longest pitches) that are not continuous in individual pieces is changed. This test was tested by sensory evaluation.
As shown in FIG. 10, it can be seen that the larger the ratio of the number of individual pitches, the worse the score. However, as will be described later, the pattern constituent units having the shortest pitch or the longest pitch may not be too continuous.

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

Further, in this embodiment, the chaotic function defines two chaotic functions Fcu and Fcd on the left and right in each of the other sections except the section of the shortest and the longest pitch on the horizontal axis Xn. The left chaotic function Fcu intersects a horizontal imaginary line Ha (shown in FIG. 23) passing through the vertical intermediate height point of the definition 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 is the imaginary line H
Pass a and the opposite side (the side opposite to the origin). As described above, two chaotic functions Fcu and Fcd on the left and right are set in the other sections except the section with the shortest pitch and the longest pitch. It should be noted that the left and right chaotic functions Fcu that do not pass both sides of the center point Ha (pass only one side of the center point Ha),
Fcd can also be adopted.

(9) -1 FIGS. 11 to 14 (FIGS. 13 and 14)
In each case, the chaotic function of the curve of the number of types of pattern constituent units s = 5) is defined by the following equation. A) Section of the shortest pitch on the horizontal axis Xn (K0 <Xn <K
1)

[0063]

(Equation 3)

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

[0065]

[Equation 4]

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

[0067]

(Equation 5)

Here, Xt = Xn- (Ki + K (i +
1)) / 2-εg. Also, in the above formula,
Is 1.0 to 2.0, Zg is 1.0 to 10.0, and the absolute value of 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 code g at the end is a section P excluding the shortest and longest sections among the sections P1 to Ps on the X axis.
2 to P (s-1) is the order of the values of Z and ε whose values are determined, and 2 to are assigned.

The above εg is the chaotic function Fcu on the left,
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 the origin side, εg ≧ 0, and in the case of the right chaotic function Fcd passing the opposite side, εg ≦ 0. Further, SGN (Xt) is +1, X when Xt ≧ 0.
When t <0, it takes -1. a and C are constants set so that both ends of each equation pass through the lattice end points of the definition area of each section.

(9) -2 In each of FIGS. 15 to 18, the chaotic function of the curve of the number of kinds of pattern constituent units s = 5) is defined by the following equation. A) Section of the shortest pitch on the horizontal axis Xn (K0 <Xn <K
1)

[0071]

(Equation 6)

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

[0073]

(Equation 7)

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

[0075]

(Equation 8)

Here, εg can be arbitrarily set within the range of half of the interval as described above, and b and Z1 can be selected as described above. The εg is a value for shifting the curve from the center point Xa = (Ki + K (i + 1)) / 2 of the section on the horizontal axis, and the left chaotic function Fc passing the origin side.
In the case of u, εg ≧ 0, and in the case of the right chaotic function Fcd passing on the opposite side, εg ≦ 0. The symbol g at the end indicates the section P excluding the shortest and longest sections P1 and Ps.
2 to P (s-1), the order is Z and ε whose values are determined, and 2 to are assigned. Both ends of the expressions a and C are set so as to pass through the grid end points of the definition area of each section.

(9) -3 A chaotic function of a curve of FIGS. 19 to 22 (the number of types of pattern constituent units is S = 5 in FIGS. 21 and 22) is defined by the following equation. A) Section of the shortest pitch on the horizontal axis Xn (K0 <Xn <K
1)

[0078]

[Equation 9]

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

[0080]

[Equation 10]

C) X-axis section (Ki) other than A) and B)
~ K (i + 1)), where the origin-side lower limit grid point coordinates of the definition area are (Ki, Ko) and the opposite-side upper limit grid point coordinates are (K (i + 1), Kp), C) -1 When the chaotic function Fd on the right passes through the side opposite to the origin from the central point Xa,

[0082]

[Equation 11]

C) -2 In the case of the left chaotic function Fcu passing the origin side with respect to the central point Xa,

[0084]

(Equation 12)

Here, Z1 and Zg can be selected within the above range.

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

As a result, by changing the left and right chaotic functions depending on the conditions, the pattern constituent unit with the shortest pitch is changed to the pattern constituent unit with the longest pitch, or the pattern constituent unit with the longest pitch is changed to the pattern constituent unit with the shortest pitch. This facilitates the use of the pitch fluctuation range.

(11) In this example, one of the two chaotic functions Fcu and Fcd is selected under the following conditions. First Condition When the previously defined 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 defined function value X (n + 1),
Fcd yields the next function value X (n + 2). Second Condition When the previously defined function value X (n + 1) occurs in the section on the side of the horizontal axis where the pitch is small or is the initial value, the next function value X (n +
2) occurs. Third Condition When the previously determined function value X (n + 1) occurs in the section on the side of the horizontal axis where the pitch is large, the right chaotic function Fcd produces the next function value X (n + 2).

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

(12) Now, a sequence of numbers is generated by using the chaotic function of this embodiment as described above, and the sequence is converted into a pitch arrangement of pattern constituent units. As an example, regarding “Case 1” of FIG. 4A, “Case 1” of FIG. 13A obtained by Equations 3, 4, and 5 of (6) -1 above.
The case of is adopted. Note that FIG. 23A is enlarged and shown in FIG.

In the vertical and horizontal division lines K0 to Ks (Ks = K5 in this example), assuming that the divisions are equal, in FIG. 23, K1 is 1, K2 is 2, and K5 is 5 sequentially.
And

When 0.49 is taken as the initial value X1 (in this example, it is generated by a random number generator or a random number table in the range of 0 to 5), the vertical axis is calculated by the chaotic function of the above-mentioned equation 3 in the minimum pitch section. X2 in the X (n + 1) direction = 0.73
Is obtained. Next, with this X2 = 0.73 as the horizontal axis Xn, X3 = 1.27 is obtained by the chaotic function of the above expression 3.
Are sequentially generated.

Since this X3 enters the section P2 on the horizontal axis Xn, the left chaotic function Fc defined in the section P2 is defined.
u1 or the right chaotic function Fcd1 will be used. However, the function value X3 ahead of this occurs in the section P1 on the side where the horizontal axis has a smaller pitch. Therefore, according to the second condition, the following function value X (n
+1), ie X4 = 1.75. In the same section P2, the next function value X5 = 3.13 is generated by the same left chaotic function Fcu1 according to the first condition.

Since X5 enters the P4 section on the horizontal axis Xn, the left chaotic function Fcu defined in the P4 section.
3 or the chaotic function Fcd3 on the right will be used.
However, when viewed from the section P4, X5 is generated in the section P2 on the side where the horizontal axis has a smaller pitch, and therefore the next chaotic function Fcu3 is the next function value X (n + 1), that is, X6 = 2.
30 results.

This X6 enters the section of the section P3 on the horizontal axis,
Left chaotic function Fcu2 or right chaotic function Fc
You will use d2. However, X7 occurs in the section where X6 has a larger pitch on the horizontal axis. Therefore, on the basis of the third condition, the right chaotic function Fcd has the following function value X
Yields 7. That is, in the right chaotic function Fcd2, X7 =
1.97 can be obtained. In this way, a sequence of numbers is sequentially generated.

(13) Next, this sequence of numbers can be converted into a pitch array by associating each section with a different pitch. In the example of FIG. 23, as described above, a section of 0 <Xn <1 is P1, a section of 1 ≦ Xn <2 is P2, a section of 2 ≦ Xn <3 is P3, and 3 ≦ Xn.
The section of <4 corresponds to P4, and the section of 4 ≦ Xn <5 corresponds to P5.

As a result, 0.49, 0.73, 1.2
The sequence of 7, 1.75, 3.13, 2.30, 1.97 ... P1, P1, P2, P2, P4, P3, P2
... can be converted into a pitch array of pattern constituent units.

As can be seen from this arrangement, the pitches change from P1 and P3 to the adjacent pitches in the order of length (the same applies to P5), but between P2 and P4, there is one distance, that is, 1 The pitch is changing without skipping. This is what is expected from each domain of the chaotic function of FIGS. In this section, each definition region is represented by a virtual bisector (X) at an angle of 45 ° extending from the origin in FIGS. 3 to 5.
Including a region through which (n + 1) = Xn passes (as a starting point), a maximum of three small rectangular regions in total in the vertical direction have a total of three regions that are continuous in the vertical direction. Therefore, there is a possibility that an arrangement of pattern constituent units whose pitch changes by one skip occurs.

The domain of definition of the chaotic function in the case 1 of FIG. 4A (FIG. 23) is the virtual bisector (Xn + 1 = Xn).
Including the region through which is passed, a maximum of a total of three small rectangular regions are vertically continuous in the vertical direction in the sections P2 and P4 on the horizontal axis Xn. In such a case,
When the chaotic function of Case 1 is used, the pitch is set so as to satisfy P4 / P2 ≦ 1.5 in the pitch.

As described above, the present invention is required to include an arrangement of pattern constituent units whose pitch is changed by one or more when the pitch ratio is 1.5 or less. The reason for this is that the pitch array includes such an array that changes to a distant pitch, but the flexibility of the array increases, the array can be more irregular, and the pitch sound can be dispersed (white noise conversion). ) Is improved.

Table 1 shows the pitch ratio to be satisfied as the "pitch condition" to be set in each case of FIGS. 2 to 5.

Since the problem of abnormal wear occurs when uncontrolled pitch change is allowed, pitch change is controlled within a predetermined range while adopting the chaotic function as described above.

(14) As described above, the number array can be selected by using the chaotic function to generate the pitch array of the pattern constituent units. However, although these are necessary conditions for reducing the noise of tires, there are cases in which they are not sufficient conditions in some cases. This is because the sequence generated by the chaotic function is very irregular (unpredictable), while the total number of pattern building units in the pattern building unit sequence of the tire, that is, the total number of pitches (Np), is not so large. Bias may be mixed in the generated sequence. In order to reduce the noise of tires, 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 is smaller than 2 (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 / Ra) + 5 × {(1 / Rn) +1} Here, Rn is a dimensionless value of the total number Np of pitches, and Rn = Np / 60 as described above. The ratio SQ max / Np of the number SQ max of the pattern constituent units in which the pattern constituent units of the same pitch are continuous and the total number Np of the pitches in the tire circumferential direction of the pattern constituent units is 0.15 or less (claim) Equivalent to 1).

By satisfying these tests, chaoticity can be confirmed, bias can be eliminated, and various performances can be optimized.
As described above, in the tire of the present invention, the pattern constituent unit sequence of the tested object obtained by adding the above-mentioned test to the pattern constituent unit string obtained based on the chaotic function is adopted.

(15) Irregularity Index Vr The irregularity index Vr confirms that the pitch train has no specific periodicity, and is performed up to the 8th order. As shown in Table 2, the periodicity is checked up to the 8th order. As shown in Table 2, the vibration and noise generated due to each order component of the radial force change (RFV) during rolling of the tire are almost 8th order. Up to. This is because if there is no specific periodicity up to the 8th order, it is considered that no problem will occur.

[0107]

[Table 2]

In the present specification, the irregularity index Vr means a value defined by the following equations 13 to 15,
The irregularity index Vr is smaller than 2.

[0109]

(Equation 13)

Here,

[0111]

[Equation 14]

[0112]

(Equation 15)

Dj is the j-th dimensionless pitch in the pattern constitutional unit sequence. dj = Pj / average pitch Pj: pitch of the j-th pattern constituent unit in the pattern constituent unit row Average pitch: tire entire circumference length CL / total number of pitches NN in the pattern constituent unit row (see FIG. 24) Xj: jth pitch Position of.

The irregularity index Vr is an index indicating the degree of periodicity of the r-order component, as described above. Irregularity index V
It is shown that the r-th order periodicity increases as r increases. Further, as shown in FIG. 25, the irregularity index Vr
And the magnitude of the r-th order component of the RFV has a positive correlation.
In order to prevent vibration and noise caused by the RFV,
It was found that the irregularity index Vr should be smaller than 2. More preferably 1.7 or less, still more preferably 1.
5 or less is good. However, in general, it does not become 0, and Vr is
Greater than zero.

(16) Autocorrelation coefficient Ru The autocorrelation function Ru means the coefficient defined by the equation 16 in this specification.

[0116]

[Equation 16]

Here,

[0118]

[Equation 17]

In the above equation 16, the pitches of the pattern constituent units are P1, P2, ... Ps in ascending order, and the integers 1, 2, ... S are assigned to these pitches. A pitch array in the pattern unit row is represented by such an integer and 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
... means that. The variable u is the amount of deviation of the reference pitch array PQ (j) from j.

In the equation 16, the numerator is a generally called autocorrelation function, and the denominator is a normalization constant. The reason for dividing by the normalization constant is that it is impossible to judge the degree of irregularity of the period in the general autocorrelation function due to the magnitude of the amplitude.

Note that the autocorrelation coefficient Ru is Ru when the change in the pitch sequence is sinusoidal (having complete periodicity) and the deviation amount u matches the period length. 1
Becomes The periodicity decreases, the irregularity increases, and the shift amount u
Ru becomes closer to 0 as becomes larger. This means that distant pitches are uncorrelated and the arrangement is irregular.

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

(16) 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 values obtained by the equation 18.

[0124]

(Equation 18)

Here,

[0126]

[Formula 19]

[0127]

(Equation 20)

CL represents the entire circumference of the tire, and Xj represents the j-th pitch position.

The variance of the pitch sound (white noise conversion) is PSDrmax when the pitch array is analyzed by the order of Equation 18.
Related to value. When PSDrmax becomes large, the sound dispersion becomes poor and the sound approaches a pure tone, so that the sensory test score (sensory score) becomes poor as shown in FIG.
On the other hand, PSDrmax depends on the ratio (Ps / P1) of the shortest pitch P1 and the longest pitch Ps, and the total number Np of pitches. Therefore, Ps / P1 is set to 1.1 for every 0.1, for example.
In the range of to 1.7, Rn (= Np / 60) is set to 0.6
Three kinds of values of 7, 1.17, and 1.67 were set, and the pitch arrangement was obtained by using a chaotic function for each combination. The calculation was performed by computer processing to obtain 50 pitch arrays for each combination. Further, PSDrmax was calculated from the pitch arrangement by the above-mentioned formula 18. 5 for each combination
The smallest PSD among PSDrmax of 0 pitch array
The value of rmax is extracted and described in FIG. FIG. 27 shows each obtained value and a curve that gives a preferable margin range to each value.

The test for PSDrmax with respect to the pitch arrangement is to satisfy the following equation which is determined by taking the above curve, for example into consideration. By this test, a relatively small PSDrmax pitch arrangement is selected according to each combination. That is, given Ps / P
For 1, Rn (= Np / 60), PSDrmax is tested by the following formula, and this formula 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.

(17) A ratio SQ between the number SQ max of the pattern constituent units in which the pattern constituent units of the same pitch are continuous and the total number Np of pitches of the 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 should be arranged appropriately and continuously. However, if the same pitch is excessively continuous, a pulsating sound such as “wow wow” called a wah sound is generated, which is annoying.
FIG. 28 shows the relationship between the maximum number SQ max of consecutive numbers having the same pitch as the wah sound and the ratio of the number Np of pitches. It was found that when SQ max / Np increased, the wah sound deteriorated and the sensory evaluation deteriorated, and therefore, the range of SQ max / Np ≦ 0.15 was found to be good. Note that SQmax / Np is larger than 0.

(18) As described above, in the pneumatic tire of the present invention, the arrangement of pattern constituent units is obtained by the following procedure. A sequence is generated by a chaotic function. Converts a sequence of numbers into a pitch array of pattern constituent units. The suitability of Vr, Ru, PSDr max, SQ max / Np is confirmed and tested.

If the above test does not match, the process returns to and the 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 flow chart of the program shown in FIG.

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 of types s has a pitch of 4, the total number Np of pattern constituent units in the pattern constituent unit row is 6
4 and the number Np1 of each pitch P1, P2, P3, P4
When a condition such as setting Np4 to 16 is added, the calculation is repeated until the condition is satisfied. At that time, the initial value may be sequentially changed. It is also possible to change the chaotic function and constant used.

Further, in the above-mentioned embodiment, when converting from the numerical sequence to the pitch arrangement, an integer value is assigned to each of the division lines K0 to Ks, and the divisions on the horizontal axis and the vertical axis have the same length. However, it is also possible to change the length of each section such that the section having the shortest pitch and the section having the longest pitch are both smaller or larger than others. By this work, for example, when the total number Np of pitches of the pattern constituent unit row is 64, while satisfying the requirements of the present invention,
Number N of pattern constituent units at each pitch P1, P2, P3, P4
p1 = 19, Np2 = 13, Np3 = 13, Np4 = 1
It becomes possible to adjust to 9 or the like. This is shown in FIG.
This corresponds to the necessity of changing the parameters in the program chart of No. 9. As described above, the values of K0 to Ks are set so that the distribution number of each pitch is most likely to occur.
For example, when the number of types s = 3, and when there are 21 pattern constituent units for each pitch, K0 = 0, K1 = 1.13, K2
= 1.87 and K3 = 3.0. On the other hand, when the numbers are 18, 27 and 18, K0 = 0 and K1 = 1.0
5, K2 = 1.95 and K3 = 3.0.

As shown in FIG. 30, the pneumatic tire has a plurality of types s of pattern constituent units 1A, 1B, 1C having different pitches P in the circumferential direction (collectively referred to as pattern constituent unit 1) ... The pattern constituent unit rows 2A, 2A, 2B, 2B (arranged in the tire circumferential direction) (collectively referred to as the pattern constituent unit row 2) are symmetrically arranged on the tire tread and on both sides of the center rib 3 passing through the tire equator. It is arranged.

Further, in this embodiment, the pattern constituent unit 1A,
1B, 1C ... Have a block pattern composed of blocks. However, it may be a rib pattern, a lug pattern, or a combination thereof. At that time, one peak portion of the zigzag rib groove, a space between the lug grooves, and the like form the pattern constituent unit 1. Further, the pneumatic tire may be configured as a radial tire, a bias tire, a tire for passenger cars, a tire for trucks / buses, a tire for motorcycles, or the like.

In the block pattern shown in FIG. 30,
In the present embodiment, the pattern constituent unit columns 2A and 2A and the pattern constituent unit columns 2B and 2B have the same total number of pattern constituent units and the same arrangement of pattern constituent units, and are different only in phase.
However, the total number of pattern constituent units in the tire circumferential direction may be the same, and the arrangement of the pattern constituent units may be different.

Further, as shown in FIG. 31, the total number of pattern constituent units in the tire circumferential direction can be different between the pattern constituent unit rows 2A and 2A and the pattern constituent unit rows 2B and 2B.
Further, the number of the pattern constitutional unit rows 2 can be freely changed by about 3 to 7.

Further, as described above, each of the pattern constitutional unit rows 2 is formed as an optimum pitch arrangement by repeating the following procedure using the computer, and as shown in the drawing, for example, pitches P1, P2, P3. , P2, P
The array is set like 1, P2 .... A sequence is generated by a chaotic function. Converts a sequence of numbers into a pitch array of pattern constituent units. Confirm the compatibility of Vr, Ru, PSDr max, SQ max / Np.

The pitch is the length of the pattern constituent unit 1 in the tire circumferential direction, and in the case of a block pattern,
It is defined as the total length of the block and one lateral groove.

[0143]

【Example】

1) A radial tire having a tire size of 205 / 65R15, in which the pattern constituent unit columns 2A and 2A and the pattern constituent unit columns 2B and 2B of FIG. 30 have the same total number of pattern constituent units and the same arrangement of pattern constituent units, Tires in which only the phase differed by about 1/3 of the average pitch were prototyped according to the present invention according to the specifications shown in Tables 3-5. Further, with respect to the comparative example products 1 and 2 shown in Table 6, the irregularity index Vr, the autocorrelation coefficient Ru, the maximum dispersion coefficient PSDr max, and SQ max / Np were tested, and the order analysis of RFV was performed, and the pitch tone was measured. The sensory evaluation was carried out. The results are summarized in Table 6
(In each table, the pattern constituent unit is described as pitch).

As a precaution, the above-mentioned Japanese Examined Japanese Patent Publication 58-284.
Regarding a tire having a tread pattern shown in FIG. 3 of JP-A No. 4 (Japanese Patent Application Laid-Open No. 55-8904), prototypes were made with the same specifications as the tire with respect to the tire size, and the results of the same sensory evaluation and each test were performed. It is shown in Comparative Example 3 in Table 6. A tire based on the invention described in JP-B-3-23366 (Japanese Patent Laid-Open No. 54-115801) is shown in Table 6 as Comparative Example 4.

[0145]

[Table 3]

[0146]

[Table 4]

[0147]

[Table 5]

[0148]

[Table 6]

Even in the repetitive calculation by the computer program described above, the comparative example 3 shown in FIG. 3 of JP-B-58-2844 (JP-A-55-8904) and JP-B-3-23366 (JP-A-3-23366). 54-115801
No pitch train of Comparative Example 4 based on the invention described in No. 1) did not occur. Further, in the tire of Comparative Example 3, Vr was as high as 2.46, and therefore the third-order component of RFV was 1.92 kg.
The irregularity is small and Ru is as large as 0.76. Comparative Example 4 has a high Vr of 2.16, and therefore RF
The fifth component of V is also 1.72 kg, which is not preferable.

As described above, the pneumatic tire of the present invention is
It can be distinguished by the conventional tire and tread pattern.

2) The pattern constituent unit rows 2A, 2A and the pattern constituent unit rows 2B, 2B with the same tire size have the same total number of pattern constituent units in the tire circumferential direction, and the arrangement is different (1). Table 7 shows the results of similar trials of different tires.

3) Further, the pattern composition unit sequence 2 in FIG.
A, 2A, and the pattern constitutional unit rows 2B and 2B, in which the total number of the pattern constitutional units in the tire circumferential direction was made different, were made on a trial basis, and the results of the same examination are shown in Table 8.

[0153]

[Table 7]

[0154]

[Table 8]

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

In each sensory evaluation, the tire of the above size was mounted on a 2.5-liter FR vehicle and the air pressure was 200 kp.
Used in a. The sensory evaluation of the sound inside the vehicle is based on the 5-point method, and 3 or more is a good level. Moreover, the engine was turned off from 100 kph to evaluate. RFV measurement is JASO
It carried out according to C607.

[0157]

As described above, the pneumatic tire of the present invention utilizes one or more pitches in the order of length while utilizing the characteristics of the chaotic function in the pattern constituent units having three or more pitch lengths. The pattern constituent unit sequence is defined including the skipped array. Thus, in addition to having a chaotic arrangement, the disorder index Vr, the autocorrelation coefficient Ru, the maximum variance coefficient PSDr max, and SQ max / Np are tested to obtain the unpleasant sound factor. This makes it possible to reduce the noise of the tire and to provide a tire with excellent uniformity because it becomes a pattern constituent unit sequence of the tested object. Further, the definition region of the chaotic function is defined by setting the pitch ratio of the horizontal axis and the vertical axis to be 1.5 or less, and as described above, includes an array of pattern constituent units in which the pitch is changed by one or more. By this, the degree of freedom in the arrangement is further increased, the arrangement can be made more irregular, and the pitch sound is dispersed (white noise is improved).
In addition, such a configuration can easily set the arrangement easily even when the number of types of pitch is large, and can be useful for reducing the noise of the tire.

[Brief description of drawings]

FIG. 1 is a diagram showing an example of a chaotic 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 3.

FIG. 3 is a diagram showing a definition area of a chaotic function in which the number s of pattern constituent units is 4;

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

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

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 noise and the ratio of the total number of long- and short-pitch pattern constituent units to the number of independent long- and short-pitch pattern constituent units.

FIG. 11 is a diagram illustrating a chaotic function when the number of types of pattern constituent units is three.

FIG. 12 is a diagram illustrating a chaotic function when the number of types of pattern constituent units is four.

FIG. 13 is a diagram illustrating a chaotic function when the number of types of pattern constituent units is five.

FIG. 14 is a diagram illustrating a chaotic function when the number of types of pattern constituent units is five.

FIG. 15 is a diagram illustrating a chaotic function when the number of types of pattern constituent units is three.

FIG. 16 is a diagram illustrating a chaotic function when the number of types of pattern constituent units is four.

FIG. 17 is a diagram illustrating a chaotic function when the number of types of pattern constituent units is 5.

FIG. 18 is a diagram illustrating a chaotic function when the number of types of pattern constituent units is 5.

FIG. 19 is a diagram illustrating a chaotic function when the number of types of pattern constituent units is three.

FIG. 20 is a diagram illustrating a chaotic function when the number of types of pattern constituent units is four.

FIG. 21 is a diagram illustrating a chaotic function when the number of types of pattern constituent units is 5.

FIG. 22 is a diagram illustrating a chaotic function when the number of types of pattern constituent units is five.

FIG. 23 is a diagram illustrating a method of obtaining a sequence using a chaotic function.

FIG. 24 is a diagram illustrating Xj of irregularity index Vr.

FIG. 25 is a diagram showing the results of sensory evaluation of irregularity index Vr and pitch sound.

FIG. 26 is a diagram showing the results of sensory evaluation of PSDr max and pitch sound.

FIG. 27 is a diagram illustrating the relationship between the minimum values of PSDrmax in the combination of Ps / P1 and Rn.
It is a diagram which shows the result of the sensory evaluation of PSDr max and a pitch sound.

FIG. 28 is a diagram showing the results of sensory evaluation of Sq max and wah sound.

FIG. 29 is a flowchart of a computer program for obtaining a sequence of numbers.

FIG. 30 is a plan view showing a tread pattern according to an embodiment of the present invention.

FIG. 31 is a plan view showing a tread pattern of another embodiment of the present invention.

[Explanation of symbols]

 1, 1A, 1B, 1C pattern constituent unit 2, 2A, 2B pattern constituent unit sequence P, P1, P2, P3, P4 ... Ps pitch s maximum number of types of pattern constituent unit

─────────────────────────────────────────────────── ───

[Procedure amendment]

[Submission date] August 23, 1995

[Procedure Amendment 1]

[Document name to be amended] Statement

[Name of item to be corrected] Claim 1

[Correction method] Change

[Correction content]

[Procedure Amendment 2]

[Document name to be amended] Statement

[Correction target item name] 0021

[Correction method] Change

[Correction content]

In the chaotic function, “values in the neighborhood are continuously
“Variable” means the “pitch” of the arrangement of the pattern constituent units.
Continuity of length change (relationship between neighboring pitches) "
Corresponding. In addition, there is no correlation between the separated values of the chaotic function.
"There is" is the above-mentioned "irregularity" in the arrangement of pattern constituent units.
"Regularity (no periodicity)". Furthermore, "the initial value is
"To be separated even if they are close to each other" is in the arrangement of the pattern constituent units.
It is equivalent to "the similar arrangement is unlikely to occur". This
This is the arrangement of pattern constituent units in the arrangement of pattern constituent units.
It means that it can interfere with the repetition of In this regard
However, the arrangement of the pattern constituent units is determined based on the chaos function.
By distributing the pitch sound,
It is possible to reduce the peak noise that feels
You could think so. Thus, the basic idea of chaos function
By adopting the
It was expected that the sequence of such structural units could be obtained.

[Procedure 3]

[Document name to be amended] Statement

[Correction target item name] 0026

[Correction method] Change

[Correction content]

[0026]

SUMMARY OF THE INVENTION According to the present invention, a pattern constitutional unit row in which three or more kinds of pattern constitutional units s having different pitches P in the circumferential direction are arranged in the tire circumferential direction, A pneumatic tire forming a tread pattern of a tire tread, wherein the coordinates are obtained by dividing the horizontal axis and the vertical axis in the right-angled coordinate with the horizontal axis and the vertical axis at each right angle and in one direction from the origin to the number of types s. A vertical dividing line and a horizontal dividing line that form a plurality of rectangular areas on the surface are provided.
Further, the pattern constituent units from the origin are assigned to the sections on the horizontal axis and the vertical axis in ascending order of pitch, and the horizontal axis is Xn and the vertical axis is X (n + 1), and X (n +
1) = Definition area of the chaotic function fc represented by fc (Xn) for each section on the horizontal axis is assigned in the vertical axis direction among all areas arranged in the vertical direction in each section on the horizontal axis And the pitch assigned to the horizontal axis is the denominator of the smaller pitch, and the larger pitch is the numerator, the ratio of the pitches is the sum of the areas that are 1.5 or less. In each section of the horizontal axis in, and the following,
Based on the sequence of the function values of X (n + 1) sequentially obtained by the chaotic function satisfying the requirement of 1), and further including the pattern constituent units arranged at intervals of one or more pitches adjacent in the order of length. The pneumatic tire is characterized in that it is composed of the above-mentioned pattern constituent unit sequence, and that the pattern constituent unit sequence is provided with a pattern constituent unit sequence to be tested obtained by performing the following tests. The chaotic function fc is the derivative f′c ≧ 1 in each section on the horizontal axis. In the section in which the shortest pitch and the longest pitch are defined, at the start point (Xc) on the small side of the section and at the end point (Xe) on the large side, f'c (Xe)>f'c in the section of the shortest pitch (X
c) In the section with the longest pitch, f'c (Xc)>f'c (X
e) The irregularity index Vr is smaller than 2. The autocorrelation coefficient Ru is smaller than 0.5 when u> 5. The maximum dispersion coefficient PSDrmax satisfies the following formula. PSDrmax ≦ {100 / (Ps / P1) ¹⁰ } × (1
/ R n ) + 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 arrangement of the pattern constituent units in the tire circumferential direction. Ratio SQmax / Np of 0.15 or less.

[Procedure amendment 4]

[Document name to be amended] Statement

[Correction target item name] 0104

[Correction method] Change

[Correction content]

The irregularity index Vr is smaller than 2 (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
/ R n ) + 5 × {(1 / Rn) +1} where Rn is a dimensionless value of the total pitch number Np, and Rn = Np / 60 as described above. The ratio SQ max / Np of the number SQ max of the pattern constituent units in which the pattern constituent units of the same pitch are continuous and the total number Np of the pitches in the tire circumferential direction of the pattern constituent units is 0.15 or less (claim) Equivalent to 1).

[Procedure Amendment 5]

[Document name to be amended] Statement

[Correction target item name] 0130

[Correction method] Change

[Correction content]

The test for PSDrmax with respect to the pitch arrangement is to satisfy the following equation which is determined by taking the above curve, for example into consideration. By this test, a relatively small PSDrmax pitch arrangement is selected according to each combination. That is, given Ps / P
For 1, Rn (= Np / 60), PSDrmax is tested by the following formula, and this formula 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.

Claims (5)

[Claims] 1. A tread pattern of a tire tread is formed by a pattern constituent unit row in which three or more kinds of pattern constituent units of different number s having different pitches P which are circumferential lengths are arranged in the tire circumferential direction. A pneumatic tire having a plurality of rectangular regions on the coordinate plane by dividing the abscissa and the ordinate in the right-angled coordinate with the abscissa and ordinate at right angles and in one direction from the origin to the number of types s. Forming vertical division lines and horizontal division lines, and assigning pattern constituent units from the origin to each division of the horizontal axis and the vertical axis in ascending order of pitch, and setting the horizontal axis to Xn, the vertical axis. The axis is X (n + 1), and X
Of the chaotic function fc represented by (n + 1) = fc (Xn),
The definition area for each section of the horizontal axis is defined as the smaller of the pitches assigned in the vertical axis direction and the pitches assigned in the horizontal axis direction, of all the areas lined up vertically in each section of the horizontal axis. When the pitch is the denominator and the larger pitch is the numerator, the ratio of the pitches is the sum of the areas that are 1.5 or less. In this defined area, it is determined for each section on the horizontal axis, and Based on the sequence of the function values of X (n + 1) sequentially obtained by the chaotic function satisfying the requirement, and further including the pattern constituent units arranged in the order of the length by skipping one or more adjacent pitches. A pneumatic tire comprising a pattern constitutional unit sequence, and the pattern constitutional unit sequence including a pattern constitutional unit sequence to be tested obtained by performing the following tests. The chaotic function fc is the derivative f′c ≧ 1 in each section on the horizontal axis. In the section in which the shortest pitch and the longest pitch are defined, at the start point (Xc) on the small side of the section and at the end point (Xe) on the large side, f'c (Xe)>f'c in the section of the shortest pitch (X
c) In the section with the longest pitch, f'c (Xc)>f'c (X
e) The irregularity index Vr is smaller than 2. The autocorrelation coefficient Ru is smaller than 0.5 when u> 5. The maximum dispersion coefficient PSDrmax satisfies the following formula. PSDrmax ≦ {100 / (Ps / P1) 10} ×
(1 / Ra) + 5 × {(1 / Rn) +1} where P1 is the shortest pitch, Ps is the longest pitch, and R is
n is Np / 60, Np is the total number of pattern constituent units in the pattern constituent unit row, the maximum number SQmax of the pattern constituent units in which the pattern constituent units with the same pitch are continuous, and the total number of arrangements of the pattern constituent units in the tire circumferential direction. The ratio SQmax / Np with Np is 0.1
Must be 5 or less. 2. The chaotic function intersects with a horizontal imaginary line passing through a vertical intermediate height point of the defined area on the left and right in each of the sections other than the sections having the shortest and longest pitches on the horizontal axis. The pneumatic tire according to claim 1, wherein each of two chaotic functions including a left chaotic function Fcu passing through and a right chaotic function Fcd is set. 3. The left chaotic function Fcu passes through a horizontal imaginary line passing through a vertical intermediate height point of the defined area, crossing the origin on a side closer to a central point Xa in the horizontal axis direction of the section. , And the right chaotic function Fcd intersects with each other on the opposite side, and within the same section on the horizontal axis, the previously defined function value X (n
+1) occurs in the right or left chaotic functions Fcu and Fcd, the next function value X (n + 2) is also the same as the previously determined function value X (n + 1) in the right or left chaotic function Fcu. , Fcd, and when the previously determined function value X (n + 1) occurs in a section on the side with a smaller pitch on the horizontal axis or is an initial value, the left chaotic function Fcu is used to determine the previously determined function. The right chaotic function Fcd when the value X (n + 1) occurs in the section with the larger pitch on the horizontal axis
3. The pneumatic tire according to claim 2, wherein the following function values X (n + 2) are generated respectively. 4. The tire tread is provided with two or more types of pattern constituent unit rows having the same total number of pattern constituent units in the tire circumferential direction but different arrangements of the pattern constituent units. 1. The pneumatic tire according to 1. 5. The pneumatic tire according to claim 1, wherein the tire tread includes two or more types of pattern constituent unit rows having different total numbers of pattern constituent units in the tire circumferential direction.