Pneumatic tire including pitch sequence

• US 5,996,660 A
• Filed: 04/18/1996
• Issued: 12/07/1999
• Est. Priority Date: 08/18/1994
• Status: Expired due to Term

• Current Assignee: Sumitomo Rubber Industries Limited
• Original Assignee: Sumitomo Rubber Industries Limited
• Inventors: Aoki, Chieko, Kakumu, Kiichiro
• Primary Examiner(s): Maki, Steven D.
• Application Number:
  US08/632,446
• Time in Patent Office: 1,328 Days
• Field of Search: 152/209 R, 152/209 D
• US Class Current: 152/209.1
• CPC Class Codes: B60C 11/0318 irregular patterns with particular pitch sequence

Abstract

A tread pattern of tire tread is formed by an alignment (sequence) of pattern composing units of s types different in pitch P that is a circumferential length. The pattern composing units are allocated to sections of the axes of abscissa and ordinate from the origin in the order of lower pitch P. Out of all regions present in a certain section of the axis of abscissa and aligned in the longitudinal direction, a defined region defining a chaotic function is determined for respective sections of abscissa. The chaotic function is represented by X(n+1)=fc(Xn), where Xn is the axis of abscissa, and X(n+1) the axis of ordinate. An alignment of pattern composing units is obtained according to a sequence of numbers sequentially obtained by the chaotic function. The alignment of pattern composing units is further verified before employment. In such manner, discomfort due to noises caused by a tire during a travel is reduced.

Claims

1. A pneumatic tire having a tire tread including a pattern formed by a verified sequence of pattern composing units of different pitch P of number S, each pitch being a circumferential length, wherein lateral and longitudinal sectioning lines are provided in a coordinate plane for forming plural rectangular regions by dividing axes of abscissa and ordinate perpendicularly thereto in a positive direction from an origin of the coordinate plane into s sections, respectively, in a rectangular system of coordinates;

the pattern composing units are allocated in the order of lower pitches to larger pitches from the origin to the sections of the axes of abscissa and ordinate;

defined regions of a chaotic function fc represented by X(n+1)=fc(Xn) are defined for the sections of the axis of abscissa, where Xn is the abscissa and X(n+1) is the ordinate; and

the pattern composing units are arranged in order of a sequence of functional values of X(n+1) sequentially obtained using chaotic functions that are defined for the sections of the axis of abscissa in the defined regions, and satisfy requirements (1) and (2), and said verified sequence satisfies verifications (3) to (7) below, and the number S is two;

(1) a chaotic function fc is a derivative f'"'"'c>

1 in all sections of the axis of abscissa;

(2) at a starting point (Xc) of lower side and a terminal point (Xe) of higher side of sections with lowest and highest pitches defined,

space="preserve" listing-type="equation">f'"'"'c(Xe)>

f'"'"'c(Xc) in the section of the lowest pitch;

and

space="preserve" listing-type="equation">f'"'"'c(Xc)>

f'"'"'c(Xe) in the section of the highest pitch;

(3) an irregularity index Vr is less than 2, index Vr being defined as follows;

##EQU1## and where dj=Pj/mean pitch,

Pj is a pitch of jth pattern composing unit in a sequence of pattern forming units,

mean pitch is an entire circumferential length CL of tire/total number Np of pitches of a sequence of pattern composing units, and

Xj is the position of a jth pitch;

(4) an autocorrelation coefficient Ru is lower than 0.5 at u>

5, Ru being defined as follows;

##EQU2## and where the variable u represents an amount of offset of PQ(j) from j wherein PQ(j) is an integer corresponding to a pitch of a pattern composing unit in the sequence;

##EQU3## (5) a maximum variance coefficient PSDrmax satisfies the following formula

space="preserve" listing-type="equation">PSDrmax≦

{100/(Ps/P1).sup.10 }×

(1/Rn)+5×

{(1/Rn)+1}

where P1 is a shortest pitch, Ps is a longest pitch, Rn is Np/60, and Np is total number of pattern composing units in pattern composing unit row;

(6) the ratio SQmax/Np between the number SQmax of pattern composing units of an identical pitch sequentially disposed and the total number of pattern composing units in the sequence of pattern composing units of tire is 0.15 or less, the sequence has different pitches P1 and P2, a pitch ratio P2/P1 is 1.05 to 1.50, and each of said defined regions of two sections of the axis of abscissa is sums of two regions aligned in the longitudinal direction; and

(7) the ratio Rsp/Np between the total number Rsp of individual pattern composing units without continuing of the pattern composing units of an identical pitch and the total number of pattern composing units in the sequence of pattern composing units of the tire is 0.1 or less.

2. The pneumatic tire according to claim 1, wherein two chaotic functions, a left chaotic function Fcu passing in a side closer to the origin and a right chaotic function Fcd are set for each two sections of the axis of the abscissa.

3. The pneumatic tire according to claim 2, wherein in the section of pitch P1 of the axis of abscissa, a next functional value X(n+2) is provided by the left chaotic function Fcu, when a preceding defined functional value X(n+1) is provided in the section of pitch P1 of the axis of abscissa, or is at an initial value, and a next functional value X(n+2) is provided by the right chaotic function Fcd, when the a preceding defined functional value X(n+1) is provided in the section of pitch P2 of the axis of abscissa;

in the section of pitch P2 of the axis of abscissa, a next functional value X(n+2) is provided by the right chaotic function Fcd, when a preceding defined functional value X(n+1) is provided in the section of pitch P2 of the axis of abscissa, and a next functional value X(n+2) is provided by the left chaotic function Fcu, when the preceding defined functional value X(n+1) is provided in the section of pitch P1 of the axis of abscissa.

4. A pneumatic tire having a tire tread including a pattern formed by a verified sequence of pattern composing units of different pitch P of number S, each pitch being a circumferential length, wherein lateral and longitudinal sectioning lines are provided in a coordinate plane for forming plural rectangular regions by dividing axes of abscissa and ordinate perpendicularly thereto in a positive direction from an origin of the coordinate plane into s sections, respectively, in a rectangular system of coordinates;

the pattern composing units are allocated in the order of lower pitches to larger pitches from the origin to the sections of the axes of abscissa and ordinate;

defined regions of a chaotic function fc represented by X(n+1)=fc(Xn) are defined for the sections of the axis of abscissa, where Xn is the abscissa and X(n+1) is the ordinate; and

the pattern composing units are arranged in order of a sequence of functional values of X(n+1) sequentially obtained using chaotic functions that are defined for the sections of the axis of abscissa in the defined regions, and satisfy requirements (1) and (2), said verified sequence satisfies verifications (3) to (6) below and the number S is three or more;

(1) a chaotic function fc is a derivative f'"'"'c≧

1 in all sections of the axis of abscissa;

(2) at a starting point (Xc) of lower side and a terminal point (Xe) of higher side of sections with lowest and highest pitches defined,

space="preserve" listing-type="equation">f'"'"'c(Xe)>

f'"'"'c(Xc) in the section of the lowest pitch;

and

space="preserve" listing-type="equation">f'"'"'c(Xc)>

f'"'"'c(Xe) in the section of the highest pitch;

(3) an irregularity index Vr is less than 2, index Vr being defined as follows;

##EQU4## and where dj=Pj/mean pitch,

Pj is a pitch of jth pattern composing unit in a sequence of pattern forming units,

mean pitch is an entire circumferential length CL of tire/total number Np of pitches of a sequence of pattern composing units, and

Xj is the position of a jth pitch;

(4) an autocorrelation coefficient Ru is lower than 0.5 at u>

5, Ru being defined as follows;

##EQU5## and where the variable u represents an amount of offset of PQ(j) from j wherein PQ(j) is an integer corresponding to a pitch of a pattern composing unit in the sequence;

##EQU6## and (5) a maximum variance coefficient PSDrmax satisfies the following formula

space="preserve" listing-type="equation">PSDrmax≦

{100/(Ps/P1).sup.10 }×

(1/Rn)+5×

{(1/Rn)+1}

where P1 is a shortest pitch, Ps is a longest pitch, Rn is Np/60, and Np is total number of pattern composing units in pattern composing unit row;

(6) the ratio SQmax/Np between the number SQmax of pattern composing units of an identical pitch sequentially disposed and the total number of pattern composing units in the sequence of pattern composing units of tire is 0.15 or less; and

each defined region is a sum of regions at 1.5 or less in the ratio of higher to lower pitches allocated to a region aligning longitudinally in each said section of the axis of abscissa, and includes the pattern composing units arranged by skipping over a pitch or more adjacently disposed in the order of length.

5. The pneumatic tire according to claim 4, wherein two chaotic functions, left and right chaotic functions Fcu and Fcd intersecting a lateral virtual line Ha that passes a longitudinally intermediate level height of the defined region in left and right sides, are set for each section except those with the lowest and highest pitches of the axis of abscissa;

in the same section of the axis of abscissa, a next functional value X(n+2) is provided by the right or left chaotic function Fcu, Fcd that is identical to a preceding functional value X(n+1) in the section defined by the right or left chaotic function Fcu, Fcd;

the next functional value X(n+2) is provided by the left chaotic function Fcu, when the preceding functional value X(n+1) is provided in a section in a side of a lower pitch of the axis of abscissa, or is at an initial value; and

the next functional value X(n+2) is provided by the right chaotic function Fcd, when the preceding defined functional value X(n+1) is provided in a section in a side of a higher pitch.

6. The pneumatic tire according to claim 5, wherein the left chaotic function Fcu intersects a lateral virtual line Ha that passes a longitudinally intermediate height point of a defined range in a side closer to the origin than a middle point Xa in the direction of the axis of abscissa of the section and the right chaotic function Fcd intersects the line in the opposite side.

7. A pneumatic tire having a tire tread including a pattern formed by a verified sequence of pattern composing units of different pitch P of number S, each pitch being a circumferential length, wherein lateral and longitudinal sectioning lines are provided in a coordinate plane for forming plural rectangular regions by dividing axes of abscissa and ordinate perpendicularly thereto in a positive direction from an origin of the coordinate plane into s sections, respectively, in a rectangular system of coordinates;

the pattern composing units are allocated in the order of lower pitches to larger pitches from the origin to the sections of the axes of abscissa and ordinate;

defined regions of a chaotic function fc represented by X(n+1)=fc(Xn) are defined for the sections of the axis of abscissa, where Xn is the abscissa and X(n+1) is the ordinate; and

the pattern composing units are arranged in order of a sequence of functional values of X(n+1) sequentially obtained using chaotic functions that are defined for the sections of the axis of abscissa in the defined regions, and satisfy requirements (1) and (2), and said verified sequence satisfies verifications (3) to (6) below, and the number s is three or more;

(1) a chaotic function fc is a derivative f'"'"'c≧

1 in all sections of the axis of abscissa;

(2) at a starting point (Xc) of lower side and a terminal point (Xe) of higher side of sections with lowest and highest pitches defined,

space="preserve" listing-type="equation">f'"'"'c(Xe)>

f'"'"'c(Xc) in the section of the lowest pitch;

and

space="preserve" listing-type="equation">f'"'"'c(Xc)>

f'"'"'c(Xe) in the section of the highest pitch;

(3) an irregularity index Vr is less than 2, index Vr being defined as follows;

##EQU7## and where dj=Pj/mean pitch,

Pj is a pitch of jth pattern composing unit in a sequence of pattern forming units,

mean pitch is an entire circumferential length CL of tire/total number Np of pitches of a sequence of pattern composing units, and

Xj is the position of a jth pitch;

(4) an autocorrelation coefficient Ru is lower than 0.5 at u>

5, Ru being defined as follows;

##EQU8## and where the variable u represents an amount of offset of PQ(j) from j wherein PQ(j) is an integer corresponding to a pitch of a pattern composing unit in the sequence;

##EQU9## and (5) a maximum variance coefficient PSDrmax satisfies the following formula

space="preserve" listing-type="equation">PSDrmax≦

{100/(Ps/P1).sup.10} ×

(1/Rn)+5×

{(1/Rn)+1}

where P1 is a shortest pitch, Ps is a longest pitch, Rn is Np/60, and Np is total number of pattern composing units in pattern composing unit row;

(6) the ratio SQmax/Np between the number SQmax of pattern composing units of an identical pitch sequentially disposed and the total number of pattern composing units in the sequence of pattern composing units of tire is 0.15 or less; and

each said defined region has a sequence of pattern composing units arranged without skipping over a pitch adjacently disposed in the order of length of the pitch by setting the defined region as defined in (a), (b) and (c) below for the sections of the axis of abscissa;

(a) in a section with the lowest pitch of the axis of abscissa, the defined region is a sum of regions with an identical pitch and those with pitches adjacently disposed thereto in the longitudinal direction in a higher side out of all regions aligned longitudinally in the lowest section of the axis of abscissa;

(b) in a section with the highest pitch of the axis of abscissa, the defined region is a sum of regions with an identical pitch and those with pitches adjacently disposed thereto in the longitudinal direction in a lower side out of all regions aligned longitudinally in the highest section of the axis of abscissa; and

(c) in sections with an intermediate pitch of the axis of abscissa, the defined region is a sum of regions with an identical pitch and those with pitches adjacently disposed thereto in the longitudinal direction in higher and lower sides out of all regions aligned longitudinally in the sections of the axis of abscissa.

8. The pneumatic tire according to claim 7, wherein two chaotic functions, left and right chaotic functions Fcu and Fcd intersecting lateral virtual line Ha that passes a longitudinally intermediate level height of the defined region in left and right sides, are set for each section except those with the lowest and highest pitches of the axis of abscissa;

in the same section of the axis of abscissa, a next functional value X(n+2) is provided by the right or left chaotic functions Fcu, Fcd that is identical to a preceding functional value X(n+1) in the section defined by the right or left chaotic function Fcu, Fcd;

the next functional value X(n+2) is provided by the left chaotic function Fcu, when the first defined functional value X(n+1) is provided in a section in a side of a lower pitch of the axis of abscissa, or is at an initial value; and

the next functional value X(n+2) is provided by the right chaotic function Fcd, when the first defined functional value X(n+1) is provided in a section in a side of a higher pitch.

9. The pneumatic tire according to claim 8, wherein the left chaotic function Fcu intersects the lateral virtual line Ha that passes a longitudinally intermediate level height of a defined region in a side closer to the origin than a middle point Xa in the direction of the axis of abscissa of the section and the right chaotic function Fcd intersects the lateral virtual line Ha in the opposite side.