US20110146864A1 - Tire tread having balanced stiffness - Google Patents
Tire tread having balanced stiffness Download PDFInfo
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- US20110146864A1 US20110146864A1 US13/034,109 US201113034109A US2011146864A1 US 20110146864 A1 US20110146864 A1 US 20110146864A1 US 201113034109 A US201113034109 A US 201113034109A US 2011146864 A1 US2011146864 A1 US 2011146864A1
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- Prior art keywords
- circumferential
- lugs
- rib
- tire
- stiffness
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B60—VEHICLES IN GENERAL
- B60C—VEHICLE TYRES; TYRE INFLATION; TYRE CHANGING; CONNECTING VALVES TO INFLATABLE ELASTIC BODIES IN GENERAL; DEVICES OR ARRANGEMENTS RELATED TO TYRES
- B60C11/00—Tyre tread bands; Tread patterns; Anti-skid inserts
- B60C11/03—Tread patterns
- B60C11/0306—Patterns comprising block rows or discontinuous ribs
-
- B—PERFORMING OPERATIONS; TRANSPORTING
- B60—VEHICLES IN GENERAL
- B60C—VEHICLE TYRES; TYRE INFLATION; TYRE CHANGING; CONNECTING VALVES TO INFLATABLE ELASTIC BODIES IN GENERAL; DEVICES OR ARRANGEMENTS RELATED TO TYRES
- B60C99/00—Subject matter not provided for in other groups of this subclass
- B60C99/006—Computer aided tyre design or simulation
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/10—Geometric CAD
- G06F30/15—Vehicle, aircraft or watercraft design
Definitions
- the present application is directed to a tire design method. More particularly, the present application is directed to a method of designing a tire tread to reduce variation in stiffness.
- Tire stiffness is an amount of deflection produced for a given amount of load, or force divided by deflection.
- Tire designers have designed tire treads that produce varying stiffness in different parts of the tire, including varying stiffness in the sidewall, shoulder, and tire tread.
- the varying stiffness is a symptom of varying tread characteristics.
- a tire includes a first rib having a first circumferential shear stiffness, wherein the first rib has a first plurality of lugs. Each of the first plurality of lugs has a first length.
- the tire further includes a second rib having a second circumferential shear stiffness substantially equal to the first circumferential shear stiffness.
- the second rib has a second plurality of lugs, each of the second plurality of lugs having a second length different from the first length. Additionally, the first rib has a different number of lugs from the second rib.
- FIG. 1A illustrates a top view of a portion of a tread of a tire
- FIG. 1B illustrates a cross section of the tire tread along the line A-A of FIG. 1A ;
- FIG. 2 illustrates a top view of a portion of a tread of another tire
- FIG. 3 illustrates a top view of a portion of a tread of another tire
- FIG. 4 illustrates a top view of a portion of a tread of yet another tire
- FIG. 5 illustrates a top view of a portion of a tread of still another tire
- FIG. 6A illustrates a side view of a tire on a road
- FIG. 6B illustrates a close-up view of a free body diagram of a lateral view of a lug of the tire illustrated in FIG. 6A that is used to model circumferential shear stiffness
- FIG. 7 illustrates a flow chart of one embodiment of a method of designing a tire having balanced rib stiffness.
- Axial and “axially” refer to a direction that is parallel to the axis of rotation of a tire.
- “Circumferential” and “circumferentially” refer to a direction extending along the perimeter of the surface of the tire at a constant radius from the axis of rotation.
- Equatorial plane refers to the plane that is perpendicular to the tire's axis of rotation and passes through the center of the tire's tread.
- “Footprint” refers to the area of the tread of the tire that makes contact with the ground.
- “Lateral” refers to a direction along the tread of the tire going from one sidewall to the other sidewall.
- Modeling refers to making a drawing, either on paper or displayed by a computer, of a tire design and the design related attributes, including but not limited to, dimensions, material properties, application of standard modeling, including finite element analysis, and the like.
- Ring and radially refer to a direction perpendicular to the axis of rotation of the tire.
- “Sidewall” refers to that portion of the tire between the footprint of the tread and the bead, so the sidewall includes the buttress portion as defined above.
- Tire designer refers to at least one of the following: an engineer, a technician, a designer, a consultant, a manager, any person trained to model tires, a computer, and a computer program.
- Thread refers to that portion of the tire that comes into contact with the road under normal inflation and load.
- FIG. 1A is a schematic drawing of a top view of a tire 100 with a tread 105 and FIG. 1B illustrates a cross section of the tire tread 105 , along the line A-A of FIG. 1A , that is on a horizontal surface; e.g. a road.
- tire 100 further includes at least two circumferential ribs 110 that are laterally separated by at least one circumferential groove 115 .
- Each of the at least two circumferential ribs 110 include a series of lugs 120 , wherein each lug 120 is separated from another lug in the same circumferential rib 110 by a lateral groove 125 .
- the series of lugs 120 in each of the at least two circumferential ribs 110 are in an unlocked relationship, so there is a circumferentially continuous window 135 a - d (see FIG. 1B ; the axial length of the window is represented as dashed lines in FIG. 1A ) in the at least one circumferential groove 115 a - d between adjacent lateral edges 130 of each rib.
- the at least two circumferential ribs 110 include five circumferential ribs 110 a - e , each having the same number of lugs 120 a - e and the same number of lateral grooves 125 around the circumference of tire 100 .
- Each lug 120 a - e has the same circumferential length and the width of each rib 110 a - e is about the same.
- the width of each rib 110 a - e and the number of lugs 120 a - e vary.
- circumferential grooves 115 a - d separate the five circumferential ribs 110 a - e , e.g., circumferential groove 115 a separates circumferential rib 110 a laterally from circumferential rib 110 b and circumferential groove 115 b separates circumferential rib 110 b laterally from circumferential rib 110 c , etc.
- FIG. 2 illustrates a top view of a tire 200 with a tread 205 that will be used to demonstrate an exemplary tire before the balanced rib stiffness design method is applied.
- Tire 200 includes at least two circumferential ribs 210 that are laterally separated by at least one circumferential groove 215 .
- Each rib of the at least two circumferential ribs 210 comprises a series of lugs 220 , wherein each lug 220 is separated from another lug in the same circumferential rib 210 by a lateral groove 225 .
- the series of lugs 220 in each of the at least two circumferential ribs 210 are in an unlocked relationship, so there is a circumferentially continuous window (the axial length of the window is represented as dashed lines) in the at least one circumferential groove 215 between adjacent lateral edges 230 of each rib.
- the at least two circumferential ribs 210 include five circumferential ribs 210 a - e that each may have a different number of lugs 220 a - e .
- lugs 220 a - e can each have different circumferential lengths, different circumferential widths, and different shapes.
- circumferential grooves 215 a - d separate the five circumferential ribs 210 a - e , e.g., circumferential groove 215 a separates circumferential rib 210 a laterally from circumferential rib 210 b and circumferential groove 215 b separates circumferential rib 210 b laterally from circumferential rib 210 c , etc.
- FIG. 3 illustrates a top view of a tire 300 with a tread 305 that will be used to demonstrate an exemplary tire having balanced rib stiffness.
- Tire 300 is substantially the same as the tire 200 of FIG. 2 , except for the differences discussed below.
- Tire 300 includes a series of lugs 320 having varying lengths compared to the lengths of the series of lugs 220 in FIG. 2 .
- circumferential rib 210 b has from about 4 to about 5 lugs 220 b in the section of the tire shown in FIG. 2 and circumferential rib 310 b has about 3 lugs 320 b in the same section of the tire shown in FIG. 3 .
- circumferential rib 210 d has from about 5 lugs 220 d in the section of the tire shown in FIG. 2 and circumferential rib 310 d has about 3 lugs 320 b in the same section of the tire shown in FIG. 3 .
- Lugs 320 of any shape may be used. However, for two adjacent circumferential ribs 310 to have differing numbers of lugs 320 , the ribs are in an unlocked relationship.
- the tire 300 may include a greater or fewer number of the circumferential ribs 310 than what is illustrated in FIG. 3 .
- one or more of the circumferential ribs 310 may be circumferentially continuous, without any lateral grooves 325 .
- Tire 300 includes at least two circumferential ribs 310 that are laterally separated by at least one circumferential groove 315 .
- Each rib of the at least two circumferential ribs 310 comprises a series of lugs 320 , wherein each lug 320 is separated from another lug in the same circumferential rib 310 by a lateral groove 325 .
- the series of lugs 320 in each of the at least two circumferential ribs 310 are in an unlocked relationship, so there is a circumferentially continuous window (the axial length of the window is represented as an axial distance between dashed lines) in the at least one circumferential groove 315 between adjacent lateral edges 330 of each rib.
- the at least two circumferential ribs 310 include five circumferential ribs 310 a - e that each may have a different number of lugs 320 a - e .
- Lugs 320 a - e can each have different circumferential lengths, different circumferential widths, and different shapes.
- circumferential grooves 315 a - d separate the five circumferential ribs 310 a - e , e.g., circumferential groove 315 a separates circumferential rib 310 a laterally from circumferential rib 310 b and circumferential groove 315 b separates circumferential rib 310 b laterally from circumferential rib 310 c , etc.
- FIG. 4 illustrates a top view of a tire 400 with a tread 405 that demonstrates another exemplary tire before the balanced rib stiffness design method is applied to the tire design.
- Tire 400 includes at least two circumferential ribs 410 that are laterally separated by at least one circumferential groove 415 .
- Each rib of the at least two circumferential ribs 410 comprises a series of lugs 420 , wherein each lug 420 is separated from another lug in the same circumferential rib 410 by a lateral groove 425 .
- the at least two circumferential ribs 410 include six circumferential ribs 410 a - f that each may have a different number of lugs 420 a - f .
- Lugs 420 a - f can each have different circumferential lengths and different circumferential widths.
- Five circumferential grooves 415 a - e separate the six circumferential ribs 410 a - f , e.g., circumferential groove 415 a separates circumferential rib 410 a laterally from circumferential rib 410 b and circumferential groove 415 b separates circumferential rib 410 b laterally from circumferential rib 410 c.
- the series of lugs 420 in each of the at least two circumferential ribs 410 are in an unlocked relationship, except circumferential ribs 410 c and 410 d , so there is a circumferentially continuous window (the axial length of the window is represented as an axial distance between dashed lines) formed by circumferential grooves 415 a , 415 b , 415 d , and 415 e .
- Circumferential ribs 410 c and 410 d are in a locked relationship because the cross section of circumferential ribs 410 c and 410 d and circumferential groove 415 c do not form a circumferentially continuous window.
- FIG. 5 illustrates a top view of another tire 500 with a tread 505 that illustrates an embodiment of a tire having balanced rib stiffness.
- Tire 500 is substantially the same as the tire 400 of FIG. 4 , except for the differences discussed below.
- Tire 500 includes a series of lugs 520 having varying lengths compared to the lengths of the series of lugs 420 in FIG. 4 .
- circumferential rib 410 a has about 5 lugs 420 a in the section of the tire shown in FIG. 4 and circumferential rib 510 a has about 6 lugs 520 a in the same section of the tire shown in FIG. 5 .
- circumferential rib 410 f has about 5 lugs 420 f in the section of the tire shown in FIG. 4 and circumferential rib 510 f has about 6 lugs 520 f in the same section of the tire shown in FIG. 5 .
- Tire 500 includes a series of lugs 520 .
- Lugs 520 of any shape may be used.
- the ribs are in an unlocked relationship.
- two of the at least two circumferential ribs 510 are in an unlocked relationship because circumferential ribs 510 a , 510 b , 510 e , and 510 f are in an unlocked relationship.
- a tire designer For a given tire with at least two circumferential ribs and at least one circumferentially continuous groove, e.g., the tires illustrated in FIGS. 2 and 3 and the tires illustrated in FIGS. 4 and 5 , a tire designer includes in the tire design a number of lugs in each of the at least two circumferential ribs. The tire designer selects the number of lugs in each rib according to various performance characteristics or aesthetic characteristics that are desired. The tire designer then models a single lug of each rib to determine circumferential shear stiffness. A tire designer can model the circumferential shear stiffness of a single lug by using known modeling techniques, e.g., a computer finite element analysis modeling technique.
- FIG. 6A is a schematic of a side view of a tire 600 with a lug 620 on a road where the tire has a radius R and is rotating with a torque T.
- FIG. 6B illustrates a close-up view of a free body diagram of a lateral view of the lug 620 of the tire 600 that is illustrated in FIG. 6A .
- a lug force F L produced from the torque T of tire 600 causes a reactive road force F R and a resulting lug deflection A.
- the reactive road force F R and the lug force F L are opposite forces that can vary in magnitude.
- the lug deflection ⁇ in the circumferential direction is represented by a circumferential change in the lug position between an initial lug position (represented by solid lines) and a secondary lug position (represented by dashed lines).
- the tire designer may use finite element analysis modeling or some other modeling technique of the tire 600 to determine the reactive road force F R , the lug force F L , and the resulting lug deflection ⁇ to calculate a circumferential shear stiffness K L .
- K L F L ⁇ ⁇ ⁇ ( e . g . , units ⁇ ⁇ of ⁇ ⁇ Lb ⁇ / ⁇ in ⁇ ⁇ or ⁇ ⁇ kg ⁇ / ⁇ m ) . ( 1 )
- FIG. 7 illustrates a flow chart of one embodiment of a balanced rib stiffness tire design method 700 .
- a tire designer using the balanced rib stiffness tire design method 700 creates a tire model (e.g., a tire model with a tire tread as illustrated in FIGS. 2 and 3 and the tire tread illustrated in FIGS. 4 and 5 ), comprising a tread, sidewalls, and bead portions.
- the tire designer includes at least two unlocked circumferential ribs and at least one circumferential groove in the tread, each circumferential rib comprising an initial number of tread lugs separated by a number of lateral grooves in the circumferential direction of the tire. (Step 705 ).
- the tire designer models a circumferential shear stiffness K L of a single lug in each rib by a modeling technique described above and illustrated in FIG. 6 (Step 710 ).
- the tire designer calculates circumferential shear stiffness per unit length K Nx for each rib by dividing each circumferential shear stiffness K L by a length L of the lug modeled for each rib (Step 715 ).
- each rib stiffness K Rx is about equal to an average rib stiffness K AVG divided by a number of lugs N X in a rib x i (where i is equal to 1 to n), shown below in Equation (2):
- the average rib stiffness K AVG is equal to the circumferential shear stiffness per unit length K Nx multiplied by the average rib length L AVG , shown below in Equation (3):
- K AVG K N X *L AVG , (3)
- K R X K N X * ⁇ * D N X 2 , ( 5 )
- D is the diameter of the tire and N X is the number of lugs in a given rib x i .
- An approximation of ⁇ may be employed.
- the tire designer picks any rib as a reference rib x o and defines a number of lugs N o in the reference rib x o (Step 720 ).
- Equation (6) A tire designer can then solve Equation (6) for an ideal number of lugs N i in rib x i , to arrive at the following equation (9):
- rib x i is one of the at least two circumferential ribs, except the reference rib x o
- K R i is equal to the circumferential shear stiffness per unit length K N X for one of the at least two circumferential ribs x i , any of the ribs except the reference rib x o
- K R 0 is the circumferential shear stiffness per unit length K N X for the reference rib x o
- N 0 is the number of lugs selected by the tire designer in the reference rib x o .
- the tire designer determines the ideal number of rib lugs (Ideal N i )
- the tire designer calculates an optimal number of lugs (Optimal N) as the nearest integer number of lugs closest to the Ideal N i because a physical tire has a whole number of lugs in each rib (Step 735 ). For example, if the partial value of Ideal N i is less than 0.5, e.g., 0.466, then the tire designer rounds down to the closest integer. If the partial value of Ideal N i is equal to or greater than 0.5, e.g., 0.649, then the tire designer rounds up to the closest integer.
- a tire designer can produce tire designs using the balanced rib stiffness tire design method 700 where the optimal rib stiffness of the at least two ribs is within 5% of the optimal stiffness of the reference rib. In other embodiments, a tire designer can produce tire designs using the balanced rib stiffness tire design method 700 where the optimal rib stiffness of the at least two ribs is within about 3% or within about 1% of the optimal stiffness of the reference rib.
- Tables A and B illustrate examples of how a tire designer can use the balanced rib stiffness tire design method 700 and should not be construed as limiting the scope or spirit of the present application.
- the design method can be used on a tire of any diameter that includes at least two circumferential ribs and at least one circumferential groove. Further, the design method can use any rib position as the reference rib x o , can use any number of lugs N o for the initial rib x o , and can use any circumferential shear stiffness per unit length K N X for the reference rib x o and for each remaining rib to produce a tire design with balanced rib stiffness.
- Table A shown above, is a table that shows how a tire designer uses the design method to design a tire having balanced rib stiffness. For example, a tire designer picks a tire that is 557 millimeters in diameter and includes five circumferentially continuous ribs (rib #'s 1-5) that are each laterally separated by at least one circumferentially continuous groove, adjacent ribs are unlocked.
- a tire designer using the balanced rib stiffness design method 700 designs a tire with 5 ribs and models a lug in each rib by applying a load F to a lug in each rib to determine the deflection per lug and the circumferential shear stiffness K L .
- a force from about 50 Newtons to about 230 Newtons is applied to a lug in each rib, the length of the modeled lug in each rib is about 1 millimeter, and the deflection of the modeled lug in each rib is about 1 millimeter.
- the circumferential shear stiffness per unit length K N X is determined by dividing the circumferential shear stiffness K L , by the length L of the modeled lug.
- the tire designer selects any of the rib #'s 1-5, in this case rib #3, as the first rib x o and the number of ideal lugs N o is selected so an optimal stiffness can be determined.
- the optimal number of lugs is the same as the initial number of lugs, 70, and the circumferential shear stiffness for rib #3 is 177 N/mm, which produces an Ideal Stiffness of 177 N/mm and an equal Optimal Stiffness.
- the tire designer selects a second rib x 1 (here, rib #2) and then determines the number of ideal lugs Ideal N x , the number of optimal lugs Optimal N x , and the ideal stiffness and optimal stiffness for rib #2.
- the design model produces 43.2 ideal lugs and 43 optimal lugs with an ideal stiffness of 177 N/mm and an optimal stiffness of 178.8 N/mm, so the stiffness of rib #2 is 1.06% off from its ideal stiffness.
- the designer then completes these calculations for the remaining ribs (x 2 , x 3 , x 4 ) to determine an ideal and an optimal number of lugs that will give an approximately equal optimal stiffness in each of the ribs in the tire design.
- the number of lugs in each rib varies, including 39 lugs in rib #4, 43 lugs in rib #2, 62 lugs in rib #1, 70 lugs in rib #3, and 79 lugs in rib #5.
- the optimal stiffness in each rib varies relative to an ideal stiffness from about 0.20% to about 2.45%.
- Table B shown above, is a table that shows how a tire designer uses the design method to design a tire having balanced rib stiffness. For example, a tire designer picks a tire that is 557 millimeters in diameter and includes six circumferentially continuous ribs (rib #'s 1-6). In this example, the ribs are each laterally separated by at least one circumferentially continuous groove so adjacent ribs are unlocked, except ribs 3 and 4 are locked relative to one another and unlocked relative to other adjacent ribs.
- a tire designer using the balanced rib stiffness design method 700 designs a tire with 6 ribs and models a lug in each rib by applying a load F to a lug in each rib to determine the deflection per lug and the circumferential shear stiffness K L .
- a force from about 86 Newtons to about 142 Newtons is applied to a lug in each rib, the length of the modeled lug in each rib is about 1 millimeter, and the deflection of the modeled lug in each rib is about 1 millimeter.
- the circumferential shear stiffness per unit length K N X is determined by dividing the circumferential shear stiffness K L by the length L of the modeled lug.
- the tire designer selects any of the rib #'s 1-6, in this case ribs #3 and #4, as the first rib x o (both ribs are selected since they are in a locked relationship) and the number of ideal lugs N o is selected so an optimal stiffness can be determined.
- the optimal number of lugs is the same as the initial number of lugs, 70, and the circumferential shear stiffness for ribs #3 and #4 is 93 N/mm, which produces an Ideal Stiffness of 93 N/mm and an equal Optimal Stiffness.
- the tire designer selects a second rib x 1 (here, rib #2) and then determines the number of ideal lugs Ideal N x , the number of optimal lugs Optimal N x , and the ideal stiffness and optimal stiffness for rib #2.
- the design model produces 67.3 ideal lugs and 67 optimal lugs with an ideal stiffness of 93 N/mm and an optimal stiffness of 93.87 N/mm, so the stiffness of rib #2 is 0.94% off from its ideal stiffness.
- the designer then completes these calculations for the remaining ribs (x 2 , x 3 , x 4 ) to determine an ideal and an optimal number of lugs that will give an approximately equal optimal stiffness in each of the ribs in the tire design.
- the number of lugs in each rib varies, including 67 lugs in ribs #2 and #5, 70 lugs in ribs #3 and #4, and 86 lugs in ribs #1 and #6.
- the optimal stiffness in each rib varies relative to an ideal stiffness from about 0.66% to about 0.94%.
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Abstract
A tire includes a first rib having a first circumferential shear stiffness, wherein the first rib has a first plurality of lugs. Each of the first plurality of lugs has a first length. The tire further includes a second rib having a second circumferential shear stiffness substantially equal to the first circumferential shear stiffness. The second rib has a second plurality of lugs, each of the second plurality of lugs having a second length different from the first length. Additionally, the first rib has a different number of lugs from the second rib.
Description
- This application is a continuation of U.S. patent application Ser. No. 12/429,204 filed in the United States Patent and Trademark Office on Apr. 24, 2009, the entirety of which is fully incorporated herein.
- The present application is directed to a tire design method. More particularly, the present application is directed to a method of designing a tire tread to reduce variation in stiffness.
- Tire stiffness is an amount of deflection produced for a given amount of load, or force divided by deflection. Tire designers have designed tire treads that produce varying stiffness in different parts of the tire, including varying stiffness in the sidewall, shoulder, and tire tread. The varying stiffness is a symptom of varying tread characteristics.
- A tire includes a first rib having a first circumferential shear stiffness, wherein the first rib has a first plurality of lugs. Each of the first plurality of lugs has a first length. The tire further includes a second rib having a second circumferential shear stiffness substantially equal to the first circumferential shear stiffness. The second rib has a second plurality of lugs, each of the second plurality of lugs having a second length different from the first length. Additionally, the first rib has a different number of lugs from the second rib.
- In the accompanying drawings, embodiments of a method of designing a tire tread are illustrated that, together with the detailed description provided below, describe various embodiments of the design method. One of ordinary skill in the art will appreciate that a step may be designed as multiple steps or that multiple steps may be designed as a single step.
- Further, in the accompanying drawings and description that follow, like parts are indicated throughout the drawings and written description with the same reference numerals, respectively. Some figures may not be drawn to scale and the proportions of certain parts may have been exaggerated for convenience of illustration.
-
FIG. 1A illustrates a top view of a portion of a tread of a tire; -
FIG. 1B illustrates a cross section of the tire tread along the line A-A ofFIG. 1A ; -
FIG. 2 illustrates a top view of a portion of a tread of another tire; -
FIG. 3 illustrates a top view of a portion of a tread of another tire; -
FIG. 4 illustrates a top view of a portion of a tread of yet another tire; -
FIG. 5 illustrates a top view of a portion of a tread of still another tire; -
FIG. 6A illustrates a side view of a tire on a road; -
FIG. 6B illustrates a close-up view of a free body diagram of a lateral view of a lug of the tire illustrated inFIG. 6A that is used to model circumferential shear stiffness; and -
FIG. 7 illustrates a flow chart of one embodiment of a method of designing a tire having balanced rib stiffness. - The following definitions are provided to aid in the understanding of the invention. The definitions include various examples and/or forms of components that fall within the scope of a term and that may be used for implementation. The examples are not intended to be limiting. Both singular and plural forms of terms may be within the definitions.
- “Axial” and “axially” refer to a direction that is parallel to the axis of rotation of a tire.
- “Circumferential” and “circumferentially” refer to a direction extending along the perimeter of the surface of the tire at a constant radius from the axis of rotation.
- “Equatorial plane” refers to the plane that is perpendicular to the tire's axis of rotation and passes through the center of the tire's tread.
- “Footprint” refers to the area of the tread of the tire that makes contact with the ground.
- “Lateral” refers to a direction along the tread of the tire going from one sidewall to the other sidewall.
- “Modeling” refers to making a drawing, either on paper or displayed by a computer, of a tire design and the design related attributes, including but not limited to, dimensions, material properties, application of standard modeling, including finite element analysis, and the like.
- “Radial” and “radially” refer to a direction perpendicular to the axis of rotation of the tire.
- “Sidewall” refers to that portion of the tire between the footprint of the tread and the bead, so the sidewall includes the buttress portion as defined above.
- “Tire designer” refers to at least one of the following: an engineer, a technician, a designer, a consultant, a manager, any person trained to model tires, a computer, and a computer program.
- “Tread” refers to that portion of the tire that comes into contact with the road under normal inflation and load.
-
FIG. 1A is a schematic drawing of a top view of atire 100 with atread 105 andFIG. 1B illustrates a cross section of thetire tread 105, along the line A-A ofFIG. 1A , that is on a horizontal surface; e.g. a road. InFIG. 1A ,tire 100 further includes at least two circumferential ribs 110 that are laterally separated by at least one circumferential groove 115. Each of the at least two circumferential ribs 110 include a series of lugs 120, wherein each lug 120 is separated from another lug in the same circumferential rib 110 by alateral groove 125. The series of lugs 120 in each of the at least two circumferential ribs 110 are in an unlocked relationship, so there is a circumferentially continuous window 135 a-d (seeFIG. 1B ; the axial length of the window is represented as dashed lines inFIG. 1A ) in the at least one circumferential groove 115 a-d between adjacentlateral edges 130 of each rib. In other words, there is a circumferentially continuous window 135 formed by the at least one circumferential groove 115, adjacentlateral edges 130 of each rib, and the horizontal surface. - In
FIG. 1A , the at least two circumferential ribs 110 include five circumferential ribs 110 a-e, each having the same number of lugs 120 a-e and the same number oflateral grooves 125 around the circumference oftire 100. Each lug 120 a-e has the same circumferential length and the width of each rib 110 a-e is about the same. In another exemplary embodiment, the width of each rib 110 a-e and the number of lugs 120 a-e vary. Four circumferential grooves 115 a-d separate the five circumferential ribs 110 a-e, e.g.,circumferential groove 115 a separatescircumferential rib 110 a laterally fromcircumferential rib 110 b andcircumferential groove 115 b separatescircumferential rib 110 b laterally fromcircumferential rib 110 c, etc. -
FIG. 2 illustrates a top view of atire 200 with atread 205 that will be used to demonstrate an exemplary tire before the balanced rib stiffness design method is applied.Tire 200 includes at least two circumferential ribs 210 that are laterally separated by at least one circumferential groove 215. Each rib of the at least two circumferential ribs 210 comprises a series of lugs 220, wherein each lug 220 is separated from another lug in the same circumferential rib 210 by alateral groove 225. The series of lugs 220 in each of the at least two circumferential ribs 210 are in an unlocked relationship, so there is a circumferentially continuous window (the axial length of the window is represented as dashed lines) in the at least one circumferential groove 215 between adjacentlateral edges 230 of each rib. In the illustrated embodiment, the at least two circumferential ribs 210 include five circumferential ribs 210 a-e that each may have a different number of lugs 220 a-e. Further, lugs 220 a-e can each have different circumferential lengths, different circumferential widths, and different shapes. Four circumferential grooves 215 a-d separate the five circumferential ribs 210 a-e, e.g.,circumferential groove 215 a separatescircumferential rib 210 a laterally fromcircumferential rib 210 b andcircumferential groove 215 b separatescircumferential rib 210 b laterally fromcircumferential rib 210 c, etc. -
FIG. 3 illustrates a top view of atire 300 with atread 305 that will be used to demonstrate an exemplary tire having balanced rib stiffness.Tire 300 is substantially the same as thetire 200 ofFIG. 2 , except for the differences discussed below.Tire 300 includes a series of lugs 320 having varying lengths compared to the lengths of the series of lugs 220 inFIG. 2 . For example,circumferential rib 210 b has from about 4 to about 5lugs 220 b in the section of the tire shown inFIG. 2 andcircumferential rib 310 b has about 3lugs 320 b in the same section of the tire shown inFIG. 3 . Further,circumferential rib 210 d has from about 5lugs 220 d in the section of the tire shown inFIG. 2 andcircumferential rib 310 d has about 3lugs 320 b in the same section of the tire shown inFIG. 3 . - Lugs 320 of any shape may be used. However, for two adjacent circumferential ribs 310 to have differing numbers of lugs 320, the ribs are in an unlocked relationship. In an alternative embodiment (not shown), the
tire 300 may include a greater or fewer number of the circumferential ribs 310 than what is illustrated inFIG. 3 . In another alternative embodiment, one or more of the circumferential ribs 310 may be circumferentially continuous, without anylateral grooves 325. -
Tire 300 includes at least two circumferential ribs 310 that are laterally separated by at least one circumferential groove 315. Each rib of the at least two circumferential ribs 310 comprises a series of lugs 320, wherein each lug 320 is separated from another lug in the same circumferential rib 310 by alateral groove 325. The series of lugs 320 in each of the at least two circumferential ribs 310 are in an unlocked relationship, so there is a circumferentially continuous window (the axial length of the window is represented as an axial distance between dashed lines) in the at least one circumferential groove 315 between adjacentlateral edges 330 of each rib. In the illustrated embodiment, the at least two circumferential ribs 310 include five circumferential ribs 310 a-e that each may have a different number of lugs 320 a-e. Lugs 320 a-e can each have different circumferential lengths, different circumferential widths, and different shapes. Four circumferential grooves 315 a-d separate the five circumferential ribs 310 a-e, e.g.,circumferential groove 315 a separatescircumferential rib 310 a laterally fromcircumferential rib 310 b andcircumferential groove 315 b separatescircumferential rib 310 b laterally fromcircumferential rib 310 c, etc. -
FIG. 4 illustrates a top view of atire 400 with atread 405 that demonstrates another exemplary tire before the balanced rib stiffness design method is applied to the tire design.Tire 400 includes at least two circumferential ribs 410 that are laterally separated by at least one circumferential groove 415. Each rib of the at least two circumferential ribs 410 comprises a series of lugs 420, wherein each lug 420 is separated from another lug in the same circumferential rib 410 by alateral groove 425. - In the illustrated embodiment, the at least two circumferential ribs 410 include six circumferential ribs 410 a-f that each may have a different number of lugs 420 a-f. Lugs 420 a-f can each have different circumferential lengths and different circumferential widths. Five circumferential grooves 415 a-e separate the six circumferential ribs 410 a-f, e.g.,
circumferential groove 415 a separatescircumferential rib 410 a laterally fromcircumferential rib 410 b andcircumferential groove 415 b separatescircumferential rib 410 b laterally fromcircumferential rib 410 c. - The series of lugs 420 in each of the at least two circumferential ribs 410 are in an unlocked relationship, except
circumferential ribs circumferential grooves Circumferential ribs circumferential ribs circumferential groove 415 c do not form a circumferentially continuous window. -
FIG. 5 illustrates a top view of anothertire 500 with atread 505 that illustrates an embodiment of a tire having balanced rib stiffness.Tire 500 is substantially the same as thetire 400 ofFIG. 4 , except for the differences discussed below.Tire 500 includes a series of lugs 520 having varying lengths compared to the lengths of the series of lugs 420 inFIG. 4 . For example,circumferential rib 410 a has about 5lugs 420 a in the section of the tire shown inFIG. 4 andcircumferential rib 510 a has about 6lugs 520 a in the same section of the tire shown inFIG. 5 . Further,circumferential rib 410 f has about 5lugs 420 f in the section of the tire shown inFIG. 4 andcircumferential rib 510 f has about 6lugs 520 f in the same section of the tire shown inFIG. 5 . -
Tire 500 includes a series of lugs 520. Lugs 520 of any shape may be used. However, for two circumferential ribs 510 to have differing number of lugs 520, the ribs are in an unlocked relationship. In the illustrated embodiment, two of the at least two circumferential ribs 510 are in an unlocked relationship becausecircumferential ribs - For a given tire with at least two circumferential ribs and at least one circumferentially continuous groove, e.g., the tires illustrated in
FIGS. 2 and 3 and the tires illustrated inFIGS. 4 and 5 , a tire designer includes in the tire design a number of lugs in each of the at least two circumferential ribs. The tire designer selects the number of lugs in each rib according to various performance characteristics or aesthetic characteristics that are desired. The tire designer then models a single lug of each rib to determine circumferential shear stiffness. A tire designer can model the circumferential shear stiffness of a single lug by using known modeling techniques, e.g., a computer finite element analysis modeling technique. -
FIG. 6A is a schematic of a side view of atire 600 with alug 620 on a road where the tire has a radius R and is rotating with a torque T.FIG. 6B illustrates a close-up view of a free body diagram of a lateral view of thelug 620 of thetire 600 that is illustrated inFIG. 6A . In the close-up view ofFIG. 6B , a lug force FL produced from the torque T oftire 600 causes a reactive road force FR and a resulting lug deflection A. For a tire with a radius R that is running at a torque T, the force F is equal to the torque T divided by the tire radius R (F=T/R). In the illustrated embodiment, the reactive road force FR and the lug force FL are opposite forces that can vary in magnitude. In the illustration, the lug deflection Δ in the circumferential direction is represented by a circumferential change in the lug position between an initial lug position (represented by solid lines) and a secondary lug position (represented by dashed lines). The tire designer may use finite element analysis modeling or some other modeling technique of thetire 600 to determine the reactive road force FR, the lug force FL, and the resulting lug deflection Δ to calculate a circumferential shear stiffness KL. - For a
representative lug 620 in each rib (not shown) where thelug 620 has a length L, the circumferential shear stiffness is calculated using Equation (1): -
-
FIG. 7 illustrates a flow chart of one embodiment of a balanced rib stiffnesstire design method 700. A tire designer using the balanced rib stiffnesstire design method 700 creates a tire model (e.g., a tire model with a tire tread as illustrated inFIGS. 2 and 3 and the tire tread illustrated inFIGS. 4 and 5 ), comprising a tread, sidewalls, and bead portions. The tire designer includes at least two unlocked circumferential ribs and at least one circumferential groove in the tread, each circumferential rib comprising an initial number of tread lugs separated by a number of lateral grooves in the circumferential direction of the tire. (Step 705). - The tire designer models a circumferential shear stiffness KL of a single lug in each rib by a modeling technique described above and illustrated in
FIG. 6 (Step 710). The tire designer calculates circumferential shear stiffness per unit length KNx for each rib by dividing each circumferential shear stiffness KL by a length L of the lug modeled for each rib (Step 715). - The tire designer can model each rib stiffness as a series of springs, with each lug in the rib represented as a spring, so the rib stiffness KRx is about equal to an average rib stiffness KAVG divided by a number of lugs NX in a rib xi (where i is equal to 1 to n), shown below in Equation (2):
-
- The average rib stiffness KAVG is equal to the circumferential shear stiffness per unit length KNx multiplied by the average rib length LAVG, shown below in Equation (3):
-
K AVG =K NX *L AVG, (3) - where the average rib length LAVG is equal to the circumference of the rib (π times diameter) divided by the number of lugs NX, shown below in Equation (4):
-
- Combining Equations (2), (3), and (4) results in:
-
- where D is the diameter of the tire and NX is the number of lugs in a given rib xi. An approximation of π may be employed.
- The tire designer picks any rib as a reference rib xo and defines a number of lugs No in the reference rib xo (Step 720). The tire designer calculates an ideal number of lugs (Ideal Nx) in each remaining rib xi by equating KR
i =KR0 and employing equation (5): -
- A tire designer can then solve Equation (6) for an ideal number of lugs Ni in rib xi, to arrive at the following equation (9):
-
- where rib xi is one of the at least two circumferential ribs, except the reference rib xo, where KR
i is equal to the circumferential shear stiffness per unit length KNX for one of the at least two circumferential ribs xi, any of the ribs except the reference rib xo, where KR0 is the circumferential shear stiffness per unit length KNX for the reference rib xo, and where N0 is the number of lugs selected by the tire designer in the reference rib xo. - Once the tire designer determines the ideal number of rib lugs (Ideal Ni), the tire designer then calculates an optimal number of lugs (Optimal N) as the nearest integer number of lugs closest to the Ideal Ni because a physical tire has a whole number of lugs in each rib (Step 735). For example, if the partial value of Ideal Ni is less than 0.5, e.g., 0.466, then the tire designer rounds down to the closest integer. If the partial value of Ideal Ni is equal to or greater than 0.5, e.g., 0.649, then the tire designer rounds up to the closest integer.
- The above steps are repeated for the remaining ribs xi (
Steps Step 750 and 755). - In one embodiment, a tire designer can produce tire designs using the balanced rib stiffness
tire design method 700 where the optimal rib stiffness of the at least two ribs is within 5% of the optimal stiffness of the reference rib. In other embodiments, a tire designer can produce tire designs using the balanced rib stiffnesstire design method 700 where the optimal rib stiffness of the at least two ribs is within about 3% or within about 1% of the optimal stiffness of the reference rib. - Tables A and B illustrate examples of how a tire designer can use the balanced rib stiffness
tire design method 700 and should not be construed as limiting the scope or spirit of the present application. As is illustrated in the tables below, the design method can be used on a tire of any diameter that includes at least two circumferential ribs and at least one circumferential groove. Further, the design method can use any rib position as the reference rib xo, can use any number of lugs No for the initial rib xo, and can use any circumferential shear stiffness per unit length KNX for the reference rib xo and for each remaining rib to produce a tire design with balanced rib stiffness. -
TABLE A Step 705 rib # 1 2 3 4 5 705 Xi 2 1 0 3 4 705 Outside Diameter(D) (mm) 557 557 557 557 557 705 NOP 70 70 70 70 70 705 Pitch 25 25 25 25 25 710 Deflection (Delta) (mm) 1 1 1 1 1 710 Force (F) (N) 137.6 67.5 177 53.6 225.9 710 Modeled Lug Length (L) 1 1 1 1 1 (mm) 710 Circumferential Shear 137.60 67.50 177.00 53.60 225.90 Stiffness (KL) (N/mm) 715 Circumferential Shear 137.60 67.50 177.00 53.60 225.90 Stiffness per Unit Length (KNX) (N/mm/mm) 720 No 70 KNX/KNO 0.777 0.381 1.000 0.303 1.276 730 Ideal Ni (partial lugs)) 61.7 43.2 70.0 38.5 79.1 735 Optimal Ni (whole # of lugs) 62 43 70 39 79 725, Ideal Rib Stiffness (partial 177.0 177.0 177.0 177.0 177.0 730 lugs) 725, Optimal Rib Stiffness (whole 175.4 178.8 177.0 172.7 177.4 735 # of lugs) — Optimal Rib Stiffness/Ideal 99.10% 101.06% 100.00% 97.55% 100.20% Rib Stiffness (%) - Table A, shown above, is a table that shows how a tire designer uses the design method to design a tire having balanced rib stiffness. For example, a tire designer picks a tire that is 557 millimeters in diameter and includes five circumferentially continuous ribs (rib #'s 1-5) that are each laterally separated by at least one circumferentially continuous groove, adjacent ribs are unlocked. A tire designer using the balanced rib
stiffness design method 700 designs a tire with 5 ribs and models a lug in each rib by applying a load F to a lug in each rib to determine the deflection per lug and the circumferential shear stiffness KL. In this example, a force from about 50 Newtons to about 230 Newtons is applied to a lug in each rib, the length of the modeled lug in each rib is about 1 millimeter, and the deflection of the modeled lug in each rib is about 1 millimeter. For each rib, the circumferential shear stiffness per unit length KNX is determined by dividing the circumferential shear stiffness KL, by the length L of the modeled lug. Next, the tire designer selects any of the rib #'s 1-5, in this case rib #3, as the first rib xo and the number of ideal lugs No is selected so an optimal stiffness can be determined. For this first rib, the optimal number of lugs is the same as the initial number of lugs, 70, and the circumferential shear stiffness for rib #3 is 177 N/mm, which produces an Ideal Stiffness of 177 N/mm and an equal Optimal Stiffness. The tire designer then selects a second rib x1 (here, rib #2) and then determines the number of ideal lugs Ideal Nx, the number of optimal lugs Optimal Nx, and the ideal stiffness and optimal stiffness for rib #2. The design model produces 43.2 ideal lugs and 43 optimal lugs with an ideal stiffness of 177 N/mm and an optimal stiffness of 178.8 N/mm, so the stiffness of rib #2 is 1.06% off from its ideal stiffness. The designer then completes these calculations for the remaining ribs (x2, x3, x4) to determine an ideal and an optimal number of lugs that will give an approximately equal optimal stiffness in each of the ribs in the tire design. As can be seen in the table above, the number of lugs in each rib varies, including 39 lugs in rib #4, 43 lugs in rib #2, 62 lugs in rib #1, 70 lugs in rib #3, and 79 lugs in rib #5. As a result, the optimal stiffness in each rib varies relative to an ideal stiffness from about 0.20% to about 2.45%. -
TABLE B Step 705 rib # 1 2 3 4 5 6 705 Xi 2 1 0 0 3 4 705 Outside Diameter(D) (mm) 557 557 557 557 557 557 705 NOP 70 70 70 70 70 70 705 Pitch 25 25 25 25 25 25 710 Deflection (Delta) (mm) 1 1 1 1 1 1 710 Force (F) (N) 141.30 86.00 93.00 93.00 86.00 141.30 710 Modeled Lug Length (L) 1 1 1 1 1 1 (mm) 710 Circumferential Shear 141.30 86.00 93.00 93.00 86.00 141.30 Stiffness (KL) (N/mm) 715 Circumferential Shear 141.3 86.0 93.00 93.00 86.0 141.3 Stiffness per Unit Length (KNX) (N/mm/mm) 720 No 70 70 KNX/KNO 1.519 0.925 1.000 1.000 0.925 1.519 730 Ideal Ni (partial lugs)) 86.3 67.3 70.0 70.0 67.3 86.3 735 Optimal Ni (whole # of lugs) 86 67 70 70 67 86 725, Ideal Rib Stiffness (partial 93.0 93.0 93.0 93.0 93.0 93.0 730 lugs) 725, Optimal Rib Stiffness 93.61 93.87 93.0 93.0 93.9 93.6 735 (whole # of lugs) — Optimal Rib Stiffness/ 100.66% 100.94% 100.00% 100.00% 100.94% 100.66% Ideal Rib Stiffness (%) - Table B, shown above, is a table that shows how a tire designer uses the design method to design a tire having balanced rib stiffness. For example, a tire designer picks a tire that is 557 millimeters in diameter and includes six circumferentially continuous ribs (rib #'s 1-6). In this example, the ribs are each laterally separated by at least one circumferentially continuous groove so adjacent ribs are unlocked, except ribs 3 and 4 are locked relative to one another and unlocked relative to other adjacent ribs. A tire designer using the balanced rib
stiffness design method 700 designs a tire with 6 ribs and models a lug in each rib by applying a load F to a lug in each rib to determine the deflection per lug and the circumferential shear stiffness KL. In this example, a force from about 86 Newtons to about 142 Newtons is applied to a lug in each rib, the length of the modeled lug in each rib is about 1 millimeter, and the deflection of the modeled lug in each rib is about 1 millimeter. For each rib, the circumferential shear stiffness per unit length KNX is determined by dividing the circumferential shear stiffness KL by the length L of the modeled lug. The tire designer selects any of the rib #'s 1-6, in this case ribs #3 and #4, as the first rib xo (both ribs are selected since they are in a locked relationship) and the number of ideal lugs No is selected so an optimal stiffness can be determined. For these ribs, the optimal number of lugs is the same as the initial number of lugs, 70, and the circumferential shear stiffness for ribs #3 and #4 is 93 N/mm, which produces an Ideal Stiffness of 93 N/mm and an equal Optimal Stiffness. The tire designer then selects a second rib x1 (here, rib #2) and then determines the number of ideal lugs Ideal Nx, the number of optimal lugs Optimal Nx, and the ideal stiffness and optimal stiffness for rib #2. The design model produces 67.3 ideal lugs and 67 optimal lugs with an ideal stiffness of 93 N/mm and an optimal stiffness of 93.87 N/mm, so the stiffness of rib #2 is 0.94% off from its ideal stiffness. The designer then completes these calculations for the remaining ribs (x2, x3, x4) to determine an ideal and an optimal number of lugs that will give an approximately equal optimal stiffness in each of the ribs in the tire design. As can be seen in the table above, the number of lugs in each rib varies, including 67 lugs in ribs #2 and #5, 70 lugs in ribs #3 and #4, and 86 lugs in ribs #1 and #6. As a result, the optimal stiffness in each rib varies relative to an ideal stiffness from about 0.66% to about 0.94%. - To the extent that the term “includes” or “including” is used in the specification or the claims, it is intended to be inclusive in a manner similar to the term “comprising” as that term is interpreted when employed as a transitional word in a claim. Furthermore, to the extent that the term “or” is employed (e.g., A or B) it is intended to mean “A or B or both.” When the applicants intend to indicate “only A or B but not both” then the term “only A or B but not both” will be employed. Thus, use of the term “or” herein is the inclusive, and not the exclusive use. See, Bryan A. Garner, A Dictionary of Modern Legal Usage 624 (2d. Ed. 1995). Also, to the extent that the terms “in” or “into” are used in the specification or the claims, it is intended to additionally mean “on” or “onto.” Furthermore, to the extent the term “connect” is used in the specification or claims, it is intended to mean not only “directly connected to,” but also “indirectly connected to” such as connected through another component or components.
- While the present application illustrates various embodiments, and while these embodiments have been described in some detail, it is not the intention of the applicant to restrict or in any way limit the scope of the appended claims to such detail. Additional advantages and modifications will readily appear to those skilled in the art. Therefore, the invention, in its broader aspects, is not limited to the specific details, the representative embodiments, and illustrative examples shown and described. Accordingly, departures may be made from such details without departing from the spirit or scope of the applicant's general inventive concept.
Claims (20)
1. A tire having a circumferential tread, the tire comprising:
a plurality of circumferential grooves disposed in the circumferential tread, including at least a first circumferential groove and a second circumferential groove;
a plurality of circumferential ribs at least partially defined by the plurality of circumferential grooves, the plurality of circumferential ribs including at least a first circumferential rib, a second circumferential rib, and a third circumferential rib;
a first plurality of lugs formed in the first circumferential rib;
a second plurality of lugs formed in the second circumferential rib, wherein a total number of lugs in the second plurality of lugs is different from a total number of lugs in the first plurality of lugs; and
a third plurality of lugs formed in the third circumferential rib,
wherein the first circumferential rib has a first circumferential shear stiffness, the second circumferential rib has a second circumferential shear stiffness that is within 5-percent of the first circumferential shear stiffness, and the third circumferential rib has a third circumferential shear stiffness that is within 5-percent of the first circumferential shear stiffness.
2. The tire of claim 1 , wherein at least a portion of the first plurality of lugs have a first length and at least a portion of the second plurality of lugs have a second length different from the first length.
3. The tire of claim 2 , wherein each of the first plurality of lugs has the first length and each of the second plurality of lugs has the second length.
4. The tire of claim 1 , wherein at least a portion of the first plurality of lugs have a first geometric shape and at least a portion of the second plurality of lugs have a second geometric shape different from the first geometric shape.
5. The tire of claim 4 , wherein each of the first plurality of lugs has the first geometric shape and each of the second plurality of lugs has the second geometric shape.
6. The tire of claim 4 , wherein at least a portion of the third plurality of lugs have a third geometric shape different from the first geometric shape and different from the second geometric shape.
7. The tire of claim 1 , wherein a total number of lugs in the third plurality of lugs is different from the total number of lugs in the first plurality of lugs.
8. A tire comprising:
a circumferential tread;
at least one circumferential groove disposed in the circumferential tread, the at least one circumferential groove at least partially defining a first circumferential rib and a second circumferential rib;
a first plurality of lugs formed in the first circumferential rib, at least a portion of the first plurality of lugs having a first geometric shape;
a second plurality of lugs formed in the second circumferential rib, at least a portion of the second plurality of lugs having a second geometric shape different from the first geometric shape,
wherein a total number of lugs in the first plurality of lugs is different from a total number of lugs in the second plurality of lugs, and
wherein the first circumferential rib has a first circumferential shear stiffness and the second circumferential rib has a second circumferential shear stiffness that is within 5-percent of the first circumferential shear stiffness.
9. The tire of claim 8 , wherein the second circumferential shear stiffness is within 3-percent of the first circumferential shear stiffness.
10. The tire of claim 8 , wherein the second circumferential shear stiffness is within 1-percent of the first circumferential shear stiffness.
11. The tire of claim 8 , wherein the at least one circumferential groove includes at least a first circumferential groove and a second circumferential groove, which at least partially define the first circumferential rib, the second circumferential rib, and a third circumferential rib.
12. The tire of claim 11 , further comprising a third plurality of lugs formed in the third circumferential rib, at least a portion of the third plurality of lugs having a third geometric shape different from the first geometric shape and different from the second geometric shape.
13. The tire of claim 12 , wherein a total number of lugs in the third plurality of lugs is different from the total number of lugs in the first plurality of lugs, and different from the total number of lugs in the second plurality of lugs.
14. The tire of claim 13 , wherein the third circumferential rib has a third circumferential shear stiffness that is within 5-percent of the first circumferential shear stiffness and within 5-percent of the second circumferential shear stiffness.
15. A tire comprising:
a first rib having a first circumferential shear stiffness, wherein the first rib has a first plurality of lugs, at least a portion of the first plurality of lugs having a first length; and
a second rib having a second circumferential shear stiffness substantially equal to the first circumferential shear stiffness, wherein the second rib has a second plurality of lugs, at least a portion of the second plurality of lugs having a second length different from the first length,
wherein the first rib has a different number of lugs from the second rib.
16. The tire of claim 15 , wherein the second circumferential shear stiffness is within 5-percent of the first circumferential shear stiffness.
17. The tire of claim 15 , further comprising a third rib having a third circumferential shear stiffness substantially equal to the first circumferential shear stiffness.
18. The tire of claim 17 , wherein the third circumferential shear stiffness is within 5-percent of the first circumferential shear stiffness.
19. The tire of claim 17 , wherein the third rib has a third plurality of lugs, at least a portion of the third plurality of lugs having a third length different from the first length.
20. The tire of claim 19 , wherein the third length is different from the second length.
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US13/034,109 US20110146864A1 (en) | 2009-04-24 | 2011-02-24 | Tire tread having balanced stiffness |
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US12/429,204 US8170839B2 (en) | 2009-04-24 | 2009-04-24 | Method of designing a tire tread |
US13/034,109 US20110146864A1 (en) | 2009-04-24 | 2011-02-24 | Tire tread having balanced stiffness |
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US20160001604A1 (en) * | 2013-02-25 | 2016-01-07 | The Yokohama Rubber Co., Ltd. | Pneumatic Tire |
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US8170839B2 (en) * | 2009-04-24 | 2012-05-01 | Bridgestone Americas Tire Operations, Llc | Method of designing a tire tread |
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US9884518B2 (en) * | 2013-02-25 | 2018-02-06 | The Yokohama Rubber Co., Ltd. | Pneumatic tire |
Also Published As
Publication number | Publication date |
---|---|
CA2759219A1 (en) | 2010-10-28 |
WO2010124173A4 (en) | 2011-04-21 |
WO2010124173A2 (en) | 2010-10-28 |
JP5608733B2 (en) | 2014-10-15 |
EP2421717A2 (en) | 2012-02-29 |
US8170839B2 (en) | 2012-05-01 |
WO2010124173A3 (en) | 2011-03-03 |
US20100274533A1 (en) | 2010-10-28 |
MX2011011192A (en) | 2011-11-18 |
JP2012524694A (en) | 2012-10-18 |
EP2421717A4 (en) | 2014-03-12 |
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