US20150053319A1 - Tire with tread profile having continuous curvature and method for forming tire - Google Patents
Tire with tread profile having continuous curvature and method for forming tire Download PDFInfo
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- US20150053319A1 US20150053319A1 US14/529,308 US201414529308A US2015053319A1 US 20150053319 A1 US20150053319 A1 US 20150053319A1 US 201414529308 A US201414529308 A US 201414529308A US 2015053319 A1 US2015053319 A1 US 2015053319A1
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- Prior art keywords
- tread
- tire
- splines
- control points
- tread profile
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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
- B60C11/0083—Tyre tread bands; Tread patterns; Anti-skid inserts characterised by the curvature of the tyre tread
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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
- B60C11/0008—Tyre tread bands; Tread patterns; Anti-skid inserts characterised by the tread rubber
- B60C2011/0016—Physical properties or dimensions
- B60C2011/0033—Thickness of the tread
Definitions
- the present invention relates to a tire with a tread profile having a continuous curvature and a method for forming the tire, and more particularly to a tire with a tread profile that utilizes splines to develop a continuous curvature.
- the design of the tread profile for a tire is an important factor in the performance of the tire. For example, when a tire rolls across a surface, the tire is subject to cyclical compressive forces.
- the design of the tread profile for the tire may have a significant impact on the pressure distributions that are developed in the tire tread due to these compressive forces. Portions of the tread that are subjected to relatively higher contact pressures may fatigue faster than other portions of the tread, thereby resulting in unacceptable performance.
- the shoulder rib may have a tendency to wear during typical use. Further, the shoulder rib may be subjected to increased forces when, for example, the tire is turned during use. Specifically, when a vehicle utilizing the tire turns during use, the tread, and specifically one of the shoulder ribs of the tread, may be subjected to suddenly increased forces. Thus, the potential for fatigue and failure of the tire at the shoulder ribs may be one area of concern in the design of tread profiles.
- Conventional tread profile designs utilize arcs to define and model the tread profile.
- arcs may be formed between the shoulder of the tire or the edge of contact of the tread and the top center point of the tread.
- the tread profile may be modeled based on these arcs.
- the use of arcs to define and model a tread profile has disadvantages.
- the curvature of the arcs at the intersections of adjacent arcs may have different curvatures. These varying curvatures may cause difficulties in controlling the pressure distributions at the arc intersections.
- FIG. 3 provides a data plot illustrating one example of the pressures across a tire tread formed utilizing arcs.
- the tire tread formed and tested according to FIG. 3 was designed using five arcs between the top center point of the tread and the intersection between the tread and the sidewall.
- the relative pressure distribution along this tread is undesirably high in important areas of the tread.
- the pressure distribution on the exterior portions of the shoulders ribs may be undesirably high.
- the pressures in the region between an axial position of approximately ⁇ 90 and an axial position of approximately ⁇ 75, and in the region between an axial position of approximately 75 and an axial position of approximately 90 may be undesirably high.
- a tread profile and a method for forming the tread profile that helps to control pressure distributions in a tire tread would be useful. Further, a tread profile having a continuous curvature throughout the profile and a method for forming the tread profile would be useful.
- the present invention provides a tire.
- the tire includes a tread defining an inferior tread profile and a superior tread profile, the superior tread profile having a generally continuous curvature between an edge of contact and a top center point.
- the superior tread profile includes a plurality of control points and a plurality of splines. Each of the plurality of splines extends between at least two of the plurality of control points. Curvatures of adjacent splines are generally equal at each of the plurality of control points.
- the present invention provides a method for forming a tire tread, the tire comprising the tread and a sidewall.
- the method includes defining an inferior profile of the tread.
- the method further includes defining a plurality of control points spaced from the inferior profile.
- Each of the plurality of control points is spaced from the inferior profile by a depth parameter.
- Each of the plurality of control points is spaced from adjacent control points of the plurality of control points by a width parameter.
- the method further includes forming a plurality of splines, each of the plurality of splines extending between at least two of the plurality of control points.
- the method includes adjusting each of the plurality of splines at each of the control points such that the curvatures of adjacent splines are generally equal at each of the plurality of control points.
- FIG. 1 provides a cross-sectional view, along the meridian plane, of a tire schematic according to one exemplary embodiment of the present disclosure
- FIG. 2 illustrates one exemplary embodiment of the various splines and control points utilized to model a tire tread in accordance with the present disclosure
- FIG. 3 provides a data plot illustrating the pressures across a tire tread developed according to prior art methods utilizing arcs.
- FIG. 4 provides a data plot illustrating the pressures across a tire tread developed according to one exemplary embodiment of the present disclosure.
- “Meridian Plane” means a plane that passes through and includes the axis of rotation of a tire.
- FIG. 1 illustrates an exemplary embodiment of a tire 100 of the present disclosure. More particularly, the tire 100 includes a tread 102 and sidewalls 104 . The tread 102 and each of the sidewalk 104 may define an intersection 106 therebetween. The tread 102 may define a plurality of grooves 110 . Each of the grooves 110 may extend generally circumferentially around the tire 100 . The grooves 110 may at least partially define a plurality of ribs 112 . The ribs 112 may also extend circumferentially around the tire 100 . Further, the ribs 112 may include shoulder ribs 114 defining the shoulders of the tire 100 , as is generally known in the art.
- An inferior tread profile I may be defined by the bottom of at least one of the grooves 110 .
- the inferior tread profile l may have any suitable shape.
- the inferior tread profile I may be a curve of constant radius or a line that is tangent to the groove bottom of at least one groove 110 defined in the tread 102 of the tire 100 .
- the inferior tread profile I may have a varying radius and/or other suitable characteristics.
- a superior tread profile S may be at least partially defined by the tops of the ribs 112 and the grooves 110 , as discussed below. Thus, each of the ribs 112 and grooves 110 may be defined between the inferior tread profile I and the superior tread profile S.
- the tread 102 may further define a top center point 120 .
- the top center point 120 may generally be defined on the superior tread profile S, and may define the center of the tread 102 as viewed along the meridian plane.
- the top center point 120 may be defined on one of the plurality of ribs 112 or in one of the plurality of grooves 110 , depending on the number and positioning of the ribs 112 and grooves 110 .
- the tread 102 may further define an edge of contact 122 or edges of contact 122 .
- the edge of contact 122 may generally be a point on the tread 102 that, when the tire 100 is disposed on a surface, generally defines where the tread 102 ceases to contact the surface.
- the superior tread profile S may have a generally continuous curvature between the edge of contact 122 and the top center point 120 . As discussed below, this generally continuous curvature of the superior tread profile S allows the pressure distributions across the tread 102 to be reduced and controlled. Specifically, the use of splines to develop the continuous curvature of the superior tread profile S, as discussed below, allows the pressure distributions across the tread 102 to be reduced and controlled.
- the superior profile S may, in exemplary embodiments, include and be defined by a plurality of splines 130 .
- Each of the splines 130 may extend between control points 132 .
- each of the plurality of control points 132 may be spaced front the inferior profile I, and may further define the superior profile S.
- Each control point 132 may be defined on one of the plurality of ribs 112 , such as on the top of the rib 112 , or in one of the plurality of grooves 110 , such as in the top of the groove 110 .
- control points 132 may be defined on, for example, the top center point 120 , the edge of contact 122 , and/or the intersection 106 , as desired.
- Each of the plurality of splines 130 may extend between at least two of the control points 132 .
- the curvatures of adjacent splines 130 are generally equal at each of the control points 132 .
- the generally continuous curvature of the superior tread profile S may be developed through the use of splines 130 with curvatures that are generally equal at control points 132 .
- the intersection 106 may define one of the control points 132 , such as a first control point 134 .
- An adjacent control point 132 may further be defined as a second control point 136 .
- one of the plurality of splines 130 may extend between the first and second control points 134 , 136 .
- the superior tread profile S may further include a line 138 extending between the first control point 134 and the second control point 136 .
- the line 138 may have a tangency parameter
- the adjacent spline 130 extending from the second control point 136 may additionally have a tangency parameter.
- the tangency parameters of the line 138 and the adjacent spline 130 may be generally equal at the second control point 136 .
- the superior tread profile S may comprise six splines 130 .
- six splines 130 may be formed to comprise the superior tread profile S between the top center point 120 and edge of contact 122 .
- the present disclosure is not limited to six splines. Rather, any number of splines 130 less than six or greater than six is also within the scope and spirit of the present disclosure.
- FIG. 4 provides a data plot illustrating one example of the pressures across a tread 102 formed utilizing six splines 130 and a line 138 .
- the six splines 130 extend between the top center point 120 and the edge of contact 122
- the line 138 extends between the edge of contact 122 and the intersection 106 .
- the relative pressure distributions along this tread 102 may be desirably lower and better controlled in critical areas of the tread 102 .
- the pressure distribution on the exterior portions of the shoulder ribs 114 may be lower and better controlled.
- the pressures in the region between an axial position of approximately ⁇ 100 and an axial position of approximately ⁇ 80, and in the region between an axial position of approximately 65 and an axial position of approximately 85 may be lower and better controlled than the pressure distributions shown in FIG. 3 , as discussed above.
- This decrease in the relative pressures on the exterior portions of the shoulder ribs 114 and the better control of the pressure distributions throughout the tread 102 are advantageously due to the use of splines 130 in the design and formation of the tread 102 .
- the present disclosure is not limited to embodiments wherein the pressure distributions on the exterior portions of the shoulder ribs 114 are controlled. Rather, any embodiments wherein pressure distributions on any portion of a tread 102 are controlled through the use of a superior tread profile S having a generally continuous curvature, and through the use of splines 130 to create that generally continuous curvature, are within the scope and spirit of the present disclosure.
- the present disclosure is further directed to a method for forming a tread 102 of a tire 100 .
- the resulting tread 102 and specifically the superior tread profile S of the tread 102 , may have a generally continuous curvature between the edge of contact 122 and the top center point 120 .
- the present method for forming a tread 102 may be performed utilizing any suitable software for modeling a tread 102 .
- a suitable software program for performing the method of the present disclosure is CATIA by DASSAULT SYST ⁇ MES.
- Other examples of suitable software include any suitable virtual or computer-aided design software programs, any suitable finite element analysis software programs, and any suitable programs capable of performing the mathematical formulas described herein.
- the present method for forming a tread 102 is directed to both the design and development of a tire 100 and to the design and development of a tire mold for manufacturing the tire 100 .
- the present disclosure encompasses the use of the present method for forming a tread 102 with regard to both the tire 100 and the tire mold.
- the method includes the step of defining an inferior profile I of the tread 102 .
- the method further includes the step of defining a plurality of control points 132 spaced from the inferior profile I.
- the control points 132 may at least partially define the superior tread profile S, and each control point 132 may define the top of one of the plurality of ribs 112 or one of the plurality of grooves 110 .
- Each of the plurality of control points 132 may be spaced from the inferior tread profile I by a depth parameter 150 .
- the depth parameter 150 for each control point 132 may define the height of the rib 112 or the depth of the groove 110 associated with the control point 132 .
- the depth parameters 150 may thus be chosen or controlled as desired to control the heights of the ribs 112 and/or the depths of the grooves 110 .
- Each of the plurality of control points 132 may further be spaced from adjacent control points 132 by a width parameter 152 .
- the width parameter 152 may be defined between the adjacent control points 132 , or may be defined for each control point 132 with respect to a reference point such as, for example, the top center point 120 or the edge of contact 122 .
- the width parameters 152 may further define the width of the tread 102 , and may thus be chosen or controlled as desired to control the width of the tread 102 .
- the method according to the present disclosure may further include the step of forming a plurality of splines 130 .
- each of the plurality of splines 130 may extend between at least two of the plurality of control points 132 .
- the method may include the step of adjusting each of the plurality of splines 130 at each of the plurality of control points 132 such that the curvatures of adjacent splines 130 are generally equal at each of the plurality of control point 132 .
- the adjusting step may include adjusting the curvature of each of the plurality of splines 130 at each of the plurality of control points 132 .
- the curvature of a spline 130 at any point on the spline 130 is the second derivative of the equation of the spline 130 at that point.
- the second derivatives of the equations of the splines 130 that meet at that control point 132 may be adjusted to be generally equal.
- the curvatures of the splines 130 may be adjusted through the use of mathematical formulas.
- the above equation or a similar equation may be utilized to adjust the splines 130 .
- the curvatures may be adjusted manually or semi-manually through the use of suitable software, as discussed above.
- the adjusting step may include, for example, adjusting a tangency parameter for each of the splines 130 at each of the control points 132 .
- the tangency parameter may generally be the parameter that establishes the slope and tangent line for a given spline 130 at a given point, such as at a control point 132 .
- the slope of a spline 130 at any point on the spline 130 is the first derivative of the equation of the spline 130 at that point.
- the first derivatives of the equations of the splines 130 that meet at that control point 132 may be adjusted to be generally equal.
- the tangency parameters may be adjusted in accordance with the present method through the use of mathematical formulas.
- the above equation or a similar equation may be utilized to adjust the splines 130 .
- the tangency parameter may be adjusted manually or semi-manually through the use of suitable software, as discussed above.
- the adjusting step may further include, for example, adjusting a tension parameter for each of the control points 132 .
- the tension parameter defines how sharply the splines 130 bend as the splines 130 extend from a control point 132 .
- the concept of a tension parameter was derived from the physics of an elastic beam subjected to lateral forces and pulled under tension.
- the tension parameter for each control point 132 may be adjusted in accordance with the present method through the use of a suitable mathematical formula. Additionally or alternatively, the tension parameter may be adjusted manually or semi-manually through the use of suitable software, as discussed above.
- the forming step may further include forming a line 138 between a first control point 134 and a second control point 136 .
- the first control point 134 may be defined at the intersection 106
- the second control point 136 may be the control point 132 adjacent to the first control point 134 .
- the line 138 may extend between the first and second control points 134 , 136 .
- the adjusting step may include adjusting a tangency parameter for the spline 130 adjacent the line 138 at the second control point 136 such that the tangency parameter for the spline 130 at the second control point 136 is generally equal to a tangency parameter of the line 138 .
- the tangency parameter may generally be the parameter that establishes the slope and tangent line for a given spline 130 at a given point, such as at a control point 132 .
- the tangency parameter of the line 138 may similarly generally be the parameter that establishes the slope and tangent line for the line 138 at a given point, such as at a control point 132 .
- the slope of the line 138 at any point on the line 138 is the first derivative of the equation of the line 138 at that point.
- the first derivatives of the equations of the line 138 and adjacent spline 130 may be adjusted to be generally equal.
- the forming step may include forming six splines 130 .
- six splines 130 may be formed between the top center point 120 and edge of contact 122 .
- the present disclosure is not limited to the formation of six splines. Rather, the formation of any number of splines 130 less than six or greater than six is also within the scope and spirit of the present disclosure.
- a tread 102 and a method for forming a tread 102 with reference to one half of the tread, between the top center point 120 and the edge of contact 122 , intersection 106 , and/or sidewall 104
- the methods and apparatus herein may further apply to the other half of the tread extending from the top center point 120 to the opposing edge of contact 122 , intersection 106 , and/or sidewall 104 .
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Abstract
Description
- The present application is a divisional application that claims priority to U.S. application Ser. No. 12/895,239 filed on Sep. 30, 2010, which is incorporated by reference in its entirety herein.
- The present invention relates to a tire with a tread profile having a continuous curvature and a method for forming the tire, and more particularly to a tire with a tread profile that utilizes splines to develop a continuous curvature.
- The design of the tread profile for a tire is an important factor in the performance of the tire. For example, when a tire rolls across a surface, the tire is subject to cyclical compressive forces. The design of the tread profile for the tire may have a significant impact on the pressure distributions that are developed in the tire tread due to these compressive forces. Portions of the tread that are subjected to relatively higher contact pressures may fatigue faster than other portions of the tread, thereby resulting in unacceptable performance.
- One portion of the tread that may be of concern is the shoulder rib. In many tires, the shoulder rib may have a tendency to wear during typical use. Further, the shoulder rib may be subjected to increased forces when, for example, the tire is turned during use. Specifically, when a vehicle utilizing the tire turns during use, the tread, and specifically one of the shoulder ribs of the tread, may be subjected to suddenly increased forces. Thus, the potential for fatigue and failure of the tire at the shoulder ribs may be one area of concern in the design of tread profiles.
- Conventional tread profile designs utilize arcs to define and model the tread profile. For example, a variety of arcs may be formed between the shoulder of the tire or the edge of contact of the tread and the top center point of the tread. The tread profile may be modeled based on these arcs. However, the use of arcs to define and model a tread profile has disadvantages. For example, the curvature of the arcs at the intersections of adjacent arcs may have different curvatures. These varying curvatures may cause difficulties in controlling the pressure distributions at the arc intersections.
- In particular, the pressure distributions across the shoulder ribs may be difficult to control when arcs are utilized to define and model a tread profile. For example,
FIG. 3 provides a data plot illustrating one example of the pressures across a tire tread formed utilizing arcs. The tire tread formed and tested according toFIG. 3 was designed using five arcs between the top center point of the tread and the intersection between the tread and the sidewall. As illustrated byFIG. 3 , the relative pressure distribution along this tread is undesirably high in important areas of the tread. For example, the pressure distribution on the exterior portions of the shoulders ribs may be undesirably high. Specifically, with reference to the X-axis inFIG. 3 , the pressures in the region between an axial position of approximately −90 and an axial position of approximately −75, and in the region between an axial position of approximately 75 and an axial position of approximately 90, may be undesirably high. - Therefore, a tread profile and a method for forming the tread profile that helps to control pressure distributions in a tire tread would be useful. Further, a tread profile having a continuous curvature throughout the profile and a method for forming the tread profile would be useful. These and other advantages will be apparent from the description of the present invention that follows below.
- Aspects and advantages of the invention will be set forth in part in the following description, or may be obvious from the description, or may be learned through practice of the invention.
- In one exemplary embodiment, the present invention provides a tire. The tire includes a tread defining an inferior tread profile and a superior tread profile, the superior tread profile having a generally continuous curvature between an edge of contact and a top center point. The superior tread profile includes a plurality of control points and a plurality of splines. Each of the plurality of splines extends between at least two of the plurality of control points. Curvatures of adjacent splines are generally equal at each of the plurality of control points.
- In another exemplary embodiment, the present invention provides a method for forming a tire tread, the tire comprising the tread and a sidewall. The method includes defining an inferior profile of the tread. The method further includes defining a plurality of control points spaced from the inferior profile. Each of the plurality of control points is spaced from the inferior profile by a depth parameter. Each of the plurality of control points is spaced from adjacent control points of the plurality of control points by a width parameter. The method further includes forming a plurality of splines, each of the plurality of splines extending between at least two of the plurality of control points. Further, the method includes adjusting each of the plurality of splines at each of the control points such that the curvatures of adjacent splines are generally equal at each of the plurality of control points.
- These and other features, aspects and advantages of the present invention will become better understood with reference to the following description and appended claims. The accompanying drawings, which are incorporated in arid constitute a part of this specification, illustrate embodiments of the invention and, together with the description, serve to explain the principles of the invention.
- A full and enabling disclosure of the present invention, including the best mode thereof, directed to one of ordinary skill in the art, is set forth in the specification, which makes reference to the appended figures, in which:
-
FIG. 1 provides a cross-sectional view, along the meridian plane, of a tire schematic according to one exemplary embodiment of the present disclosure; -
FIG. 2 illustrates one exemplary embodiment of the various splines and control points utilized to model a tire tread in accordance with the present disclosure; -
FIG. 3 provides a data plot illustrating the pressures across a tire tread developed according to prior art methods utilizing arcs; and -
FIG. 4 provides a data plot illustrating the pressures across a tire tread developed according to one exemplary embodiment of the present disclosure. - For purposes of describing the invention, reference now will be made in detail to embodiments of the invention, one or more examples of which are illustrated in the drawings. Each example is provided by way of explanation of the invention, not limitation of the Invention. In fact, it will be apparent to those skilled in the art that various modifications and variations can be made in the present invention without departing from the scope or spirit of the invention. For instance, features illustrated or described as part of one embodiment, can be used with another embodiment to yield a still further embodiment. Thus, it is intended that the present invention covers such modifications and variations as come within the scope of the appended claims and their equivalents. For example, in the description that follows, exemplary embodiments of the present invention will be described in conjunction with an exemplary tire and a method for forming the tire. Using the teaching disclosed herein, however, it will be understood by one of ordinary skill in the art that other exemplary tires and methods for forming the tires are within the scope of the present invention and claims that follow.
- “Meridian Plane” means a plane that passes through and includes the axis of rotation of a tire.
-
FIG. 1 illustrates an exemplary embodiment of atire 100 of the present disclosure. More particularly, thetire 100 includes atread 102 andsidewalls 104. Thetread 102 and each of thesidewalk 104 may define anintersection 106 therebetween. Thetread 102 may define a plurality ofgrooves 110. Each of thegrooves 110 may extend generally circumferentially around thetire 100. Thegrooves 110 may at least partially define a plurality ofribs 112. Theribs 112 may also extend circumferentially around thetire 100. Further, theribs 112 may includeshoulder ribs 114 defining the shoulders of thetire 100, as is generally known in the art. - An inferior tread profile I may be defined by the bottom of at least one of the
grooves 110. The inferior tread profile l may have any suitable shape. For example, in some embodiments, the inferior tread profile I may be a curve of constant radius or a line that is tangent to the groove bottom of at least onegroove 110 defined in thetread 102 of thetire 100. In other embodiments, the inferior tread profile I may have a varying radius and/or other suitable characteristics. Further, a superior tread profile S may be at least partially defined by the tops of theribs 112 and thegrooves 110, as discussed below. Thus, each of theribs 112 andgrooves 110 may be defined between the inferior tread profile I and the superior tread profile S. - The
tread 102 may further define atop center point 120. Thetop center point 120 may generally be defined on the superior tread profile S, and may define the center of thetread 102 as viewed along the meridian plane. Thetop center point 120 may be defined on one of the plurality ofribs 112 or in one of the plurality ofgrooves 110, depending on the number and positioning of theribs 112 andgrooves 110. - The
tread 102 may further define an edge ofcontact 122 or edges ofcontact 122. The edge ofcontact 122 may generally be a point on thetread 102 that, when thetire 100 is disposed on a surface, generally defines where thetread 102 ceases to contact the surface. - The superior tread profile S according to the present disclosure may have a generally continuous curvature between the edge of
contact 122 and thetop center point 120. As discussed below, this generally continuous curvature of the superior tread profile S allows the pressure distributions across thetread 102 to be reduced and controlled. Specifically, the use of splines to develop the continuous curvature of the superior tread profile S, as discussed below, allows the pressure distributions across thetread 102 to be reduced and controlled. - As shown in
FIG. 2 , the superior profile S may, in exemplary embodiments, include and be defined by a plurality ofsplines 130. Each of thesplines 130 may extend between control points 132. As discussed below, each of the plurality ofcontrol points 132 may be spaced front the inferior profile I, and may further define the superior profile S. Eachcontrol point 132 may be defined on one of the plurality ofribs 112, such as on the top of therib 112, or in one of the plurality ofgrooves 110, such as in the top of thegroove 110. Additionally, control points 132 may be defined on, for example, thetop center point 120, the edge ofcontact 122, and/or theintersection 106, as desired. Each of the plurality ofsplines 130 may extend between at least two of the control points 132. In the exemplary embodiment, the curvatures ofadjacent splines 130 are generally equal at each of the control points 132. Thus, the generally continuous curvature of the superior tread profile S may be developed through the use ofsplines 130 with curvatures that are generally equal at control points 132. - As mentioned, the
intersection 106 may define one of the control points 132, such as afirst control point 134. Anadjacent control point 132 may further be defined as asecond control point 136. In some embodiments, one of the plurality ofsplines 130 may extend between the first and second control points 134, 136. In other embodiments, however, the superior tread profile S may further include aline 138 extending between thefirst control point 134 and thesecond control point 136. Further, as discussed below, theline 138 may have a tangency parameter, and theadjacent spline 130 extending from thesecond control point 136 may additionally have a tangency parameter. In exemplary embodiments, the tangency parameters of theline 138 and theadjacent spline 130 may be generally equal at thesecond control point 136. - In an exemplary embodiment, as discussed below with regard to
FIG. 4 , the superior tread profile S may comprise sixsplines 130. For example, sixsplines 130 may be formed to comprise the superior tread profile S between thetop center point 120 and edge ofcontact 122. However, it should be understood that the present disclosure is not limited to six splines. Rather, any number ofsplines 130 less than six or greater than six is also within the scope and spirit of the present disclosure. -
FIG. 4 provides a data plot illustrating one example of the pressures across atread 102 formed utilizing sixsplines 130 and aline 138. The sixsplines 130 extend between thetop center point 120 and the edge ofcontact 122, while theline 138 extends between the edge ofcontact 122 and theintersection 106. As illustrated byFIG. 4 and in comparison toFIG. 3 , the relative pressure distributions along thistread 102 may be desirably lower and better controlled in critical areas of thetread 102. For example, the pressure distribution on the exterior portions of theshoulder ribs 114 may be lower and better controlled. Specifically, with reference to the X-axis inFIG. 4 , the pressures in the region between an axial position of approximately −100 and an axial position of approximately −80, and in the region between an axial position of approximately 65 and an axial position of approximately 85, may be lower and better controlled than the pressure distributions shown inFIG. 3 , as discussed above. This decrease in the relative pressures on the exterior portions of theshoulder ribs 114 and the better control of the pressure distributions throughout thetread 102 are advantageously due to the use ofsplines 130 in the design and formation of thetread 102. - It should be understood that the present disclosure is not limited to embodiments wherein the pressure distributions on the exterior portions of the
shoulder ribs 114 are controlled. Rather, any embodiments wherein pressure distributions on any portion of atread 102 are controlled through the use of a superior tread profile S having a generally continuous curvature, and through the use ofsplines 130 to create that generally continuous curvature, are within the scope and spirit of the present disclosure. - The present disclosure is further directed to a method for forming a
tread 102 of atire 100. As discussed above, the resultingtread 102, and specifically the superior tread profile S of thetread 102, may have a generally continuous curvature between the edge ofcontact 122 and thetop center point 120. - In exemplary embodiments, the present method for forming a
tread 102 may be performed utilizing any suitable software for modeling atread 102. One example of a suitable software program for performing the method of the present disclosure is CATIA by DASSAULT SYSTÈMES. Other examples of suitable software include any suitable virtual or computer-aided design software programs, any suitable finite element analysis software programs, and any suitable programs capable of performing the mathematical formulas described herein. - It should be understood that the present method for forming a
tread 102 is directed to both the design and development of atire 100 and to the design and development of a tire mold for manufacturing thetire 100. Thus, the present disclosure encompasses the use of the present method for forming atread 102 with regard to both thetire 100 and the tire mold. - The method includes the step of defining an inferior profile I of the
tread 102. The method further includes the step of defining a plurality ofcontrol points 132 spaced from the inferior profile I. As discussed above, the control points 132 may at least partially define the superior tread profile S, and eachcontrol point 132 may define the top of one of the plurality ofribs 112 or one of the plurality ofgrooves 110. - Each of the plurality of
control points 132 may be spaced from the inferior tread profile I by adepth parameter 150. Thedepth parameter 150 for eachcontrol point 132 may define the height of therib 112 or the depth of thegroove 110 associated with thecontrol point 132. Thedepth parameters 150 may thus be chosen or controlled as desired to control the heights of theribs 112 and/or the depths of thegrooves 110. - Each of the plurality of
control points 132 may further be spaced fromadjacent control points 132 by awidth parameter 152. Thewidth parameter 152 may be defined between the adjacent control points 132, or may be defined for eachcontrol point 132 with respect to a reference point such as, for example, thetop center point 120 or the edge ofcontact 122. Thewidth parameters 152 may further define the width of thetread 102, and may thus be chosen or controlled as desired to control the width of thetread 102. - The method according to the present disclosure may further include the step of forming a plurality of
splines 130. As discussed above, each of the plurality ofsplines 130 may extend between at least two of the plurality of control points 132. Further, the method may include the step of adjusting each of the plurality ofsplines 130 at each of the plurality ofcontrol points 132 such that the curvatures ofadjacent splines 130 are generally equal at each of the plurality ofcontrol point 132. - In one embodiment, the adjusting step may include adjusting the curvature of each of the plurality of
splines 130 at each of the plurality of control points 132. The curvature of aspline 130 at any point on thespline 130, as is generally understood in the art, is the second derivative of the equation of thespline 130 at that point. Thus, in accordance with the present method, for eachcontrol point 132, the second derivatives of the equations of thesplines 130 that meet at thatcontrol point 132 may be adjusted to be generally equal. - In one embodiment, the curvatures of the
splines 130 may be adjusted through the use of mathematical formulas. For example, the curvatures ofadjacent splines 130 having equal curvatures at acontrol point 132 may be represented by the equation fi″(xi+1)=fi+1″(xi+1), wherein i represents thecontrol point 132. Thus, the above equation or a similar equation may be utilized to adjust thesplines 130. Additionally or alternatively, the curvatures may be adjusted manually or semi-manually through the use of suitable software, as discussed above. - In an alternative embodiment, the adjusting step may include, for example, adjusting a tangency parameter for each of the
splines 130 at each of the control points 132. The tangency parameter may generally be the parameter that establishes the slope and tangent line for a givenspline 130 at a given point, such as at acontrol point 132. For example, the slope of aspline 130 at any point on thespline 130, as is generally understood in the art, is the first derivative of the equation of thespline 130 at that point. Thus, in accordance with the present method, for eachcontrol point 132, the first derivatives of the equations of thesplines 130 that meet at thatcontrol point 132 may be adjusted to be generally equal. - In one embodiment, the tangency parameters may be adjusted in accordance with the present method through the use of mathematical formulas. For example, the slopes of
adjacent splines 130 having equal slopes at acontrol point 132 may be represented by the equation fi′(xi+1)=fi+1′(xi+1), wherein i represents acontrol point 132. Thus, the above equation or a similar equation may be utilized to adjust thesplines 130. Additionally or alternatively, the tangency parameter may be adjusted manually or semi-manually through the use of suitable software, as discussed above. - The adjusting step may further include, for example, adjusting a tension parameter for each of the control points 132. In general, the tension parameter defines how sharply the
splines 130 bend as thesplines 130 extend from acontrol point 132. The concept of a tension parameter, as is generally known in the art, was derived from the physics of an elastic beam subjected to lateral forces and pulled under tension. In one embodiment, the tension parameter for eachcontrol point 132 may be adjusted in accordance with the present method through the use of a suitable mathematical formula. Additionally or alternatively, the tension parameter may be adjusted manually or semi-manually through the use of suitable software, as discussed above. - The forming step according to various embodiments of the present disclosure may further include forming a
line 138 between afirst control point 134 and asecond control point 136. As discussed above, thefirst control point 134 may be defined at theintersection 106, and thesecond control point 136 may be thecontrol point 132 adjacent to thefirst control point 134. Theline 138 may extend between the first and second control points 134, 136. - Further, the adjusting step may include adjusting a tangency parameter for the
spline 130 adjacent theline 138 at thesecond control point 136 such that the tangency parameter for thespline 130 at thesecond control point 136 is generally equal to a tangency parameter of theline 138. As discussed above, the tangency parameter may generally be the parameter that establishes the slope and tangent line for a givenspline 130 at a given point, such as at acontrol point 132. Further, the tangency parameter of theline 138 may similarly generally be the parameter that establishes the slope and tangent line for theline 138 at a given point, such as at acontrol point 132. For example, the slope of theline 138 at any point on theline 138, as is generally understood in the art, is the first derivative of the equation of theline 138 at that point. Thus, in accordance with the present method and as discussed above with regard to thesplines 130, for thesecond control point 136, the first derivatives of the equations of theline 138 andadjacent spline 130 may be adjusted to be generally equal. - In an exemplary embodiment, as discussed above with regard to
FIG. 4 , the forming step may include forming sixsplines 130. For example, sixsplines 130 may be formed between thetop center point 120 and edge ofcontact 122. However, it should be understood that the present disclosure is not limited to the formation of six splines. Rather, the formation of any number ofsplines 130 less than six or greater than six is also within the scope and spirit of the present disclosure. - It should further be understood that, while the present disclosure generally discusses a
tread 102 and a method for forming atread 102 with reference to one half of the tread, between thetop center point 120 and the edge ofcontact 122,intersection 106, and/orsidewall 104, the methods and apparatus herein may further apply to the other half of the tread extending from thetop center point 120 to the opposing edge ofcontact 122,intersection 106, and/orsidewall 104. - While the present subject matter has been described in detail with respect to specific exemplary embodiments and methods thereof, it will be appreciated that those skilled in the art, upon attaining an understanding of the foregoing may readily produce alterations to, variations of, and equivalents to such embodiments. Accordingly, the scope of the present disclosure is by way of example rather than by way of limitation, and the subject disclosure does not preclude inclusion of such modifications, variations and/or additions to the present subject matter as would be readily apparent to one of ordinary skill in the art.
Claims (5)
Priority Applications (1)
Application Number | Priority Date | Filing Date | Title |
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US14/529,308 US20150053319A1 (en) | 2010-09-30 | 2014-10-31 | Tire with tread profile having continuous curvature and method for forming tire |
Applications Claiming Priority (2)
Application Number | Priority Date | Filing Date | Title |
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US12/895,239 US8900388B2 (en) | 2010-09-30 | 2010-09-30 | Tire with tread profile having continuous curvature and method for forming tire |
US14/529,308 US20150053319A1 (en) | 2010-09-30 | 2014-10-31 | Tire with tread profile having continuous curvature and method for forming tire |
Related Parent Applications (1)
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US12/895,239 Division US8900388B2 (en) | 2010-09-30 | 2010-09-30 | Tire with tread profile having continuous curvature and method for forming tire |
Publications (1)
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US20150053319A1 true US20150053319A1 (en) | 2015-02-26 |
Family
ID=45888770
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US12/895,239 Active 2033-06-07 US8900388B2 (en) | 2010-09-30 | 2010-09-30 | Tire with tread profile having continuous curvature and method for forming tire |
US14/529,308 Abandoned US20150053319A1 (en) | 2010-09-30 | 2014-10-31 | Tire with tread profile having continuous curvature and method for forming tire |
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US12/895,239 Active 2033-06-07 US8900388B2 (en) | 2010-09-30 | 2010-09-30 | Tire with tread profile having continuous curvature and method for forming tire |
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US (2) | US8900388B2 (en) |
Citations (3)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
JPH09226323A (en) * | 1996-02-29 | 1997-09-02 | Bridgestone Corp | Pair of pneumatic tires |
US5710718A (en) * | 1993-01-27 | 1998-01-20 | Bridgestone Corporation | Method of designing a pneumatic tire to achieve a best mode under given conditions |
US20060118220A1 (en) * | 2004-12-06 | 2006-06-08 | The Goodyear Tire & Rubber Company | Pneumatic tire with elliptical shoulder |
Family Cites Families (2)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
US6073668A (en) | 1997-04-16 | 2000-06-13 | Sumitomo Rubber Industries, Inc. | Vehicle tire including tread portion having profile |
JP4393603B2 (en) * | 1998-08-12 | 2010-01-06 | 株式会社ブリヂストン | Pneumatic tire design method, pneumatic tire vulcanization mold design method, pneumatic tire manufacturing method, and recording medium recording a pneumatic tire design program |
-
2010
- 2010-09-30 US US12/895,239 patent/US8900388B2/en active Active
-
2014
- 2014-10-31 US US14/529,308 patent/US20150053319A1/en not_active Abandoned
Patent Citations (3)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
US5710718A (en) * | 1993-01-27 | 1998-01-20 | Bridgestone Corporation | Method of designing a pneumatic tire to achieve a best mode under given conditions |
JPH09226323A (en) * | 1996-02-29 | 1997-09-02 | Bridgestone Corp | Pair of pneumatic tires |
US20060118220A1 (en) * | 2004-12-06 | 2006-06-08 | The Goodyear Tire & Rubber Company | Pneumatic tire with elliptical shoulder |
Non-Patent Citations (1)
Title |
---|
machine translation for Japan 09-226223 (no date) * |
Also Published As
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US8900388B2 (en) | 2014-12-02 |
US20120080128A1 (en) | 2012-04-05 |
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