Abstract:
A tire having a modified geodesic belt is described. The ideal geodesic belt path is modified to select the centerline belt angle and to avoid excessive build up of the belt at the belt edges. The method includes the step of calculating the minimum three dimensional distance from one belt edge to the other belt edge preferably using dynamic successive approximation.

Description:
FIELD OF THE INVENTION 
     The invention is directed to the field of tire manufacturing and tire construction. 
     BACKGROUND OF THE INVENTION 
     It is known in the art to utilize zigzag belts in aircraft tires and truck tires. Zigzag belts are typically continuously woven from one belt edge to the other belt edge at a constant angle, with a turn around at the belt edges. A zigzag belt results in two layers of cord interwoven together with no cut belt edges. However, depending upon the tire size and other factors, the angle of the zigzag belt in the crown area is typically 10-14 degrees, with the turnaround angle at the belt edges typically around 90 degrees. It is however desired to have a higher angle at the centerline in order to improve wear, typically in the range of 15-45 degrees. 
     A geodesic belt construction has the belt cords arranged on a geodesic line on the tire&#39;s curved surface. On a curved surface the geodesic path is the least curvature or shortest distance between two points on a curved surface. A true geodesic path follows the special mathematical law: pcosα=constant. A true geodesic belt has the advantage of a higher crown angle at the centerline as compared to the zigzag belt. The true geodesic belt also has the advantage of no shear stress, because it is the minimum path. Unlike the zigzag belt construction, the geodesic belt angle continuously varies such that the angle is high at the centerline, typically around 45 degrees, and is 180 degrees at the belt edges. Both the zigzag belt and the geodesic belt have an issue at the belt edges of accumulation. It is thus desired to provide an improved belt design which modifies the geodesic path to overcome the disadvantages of the geodesic belt. Thus for the foregoing reasons, it is desired to provide an tire having a belt with a modified geodesic path without the above described disadvantages. 
     DEFINITIONS 
     “Aspect Ratio” means the ratio of a tire&#39;s section height to its section width. 
     “Axial” and “axially” means the lines or directions that are parallel to the axis of rotation of the tire. 
     “Bead” or “Bead Core” means generally that part of the tire comprising an annular tensile member, the radially inner beads are associated with holding the tire to the rim being wrapped by ply cords and shaped, with or without other reinforcement elements such as flippers, chippers, apexes or fillers, toe guards and chafers. 
     “Bias Ply Tire” means that the reinforcing cords in the carcass ply extend diagonally across the tire from bead-to-bead at about 25-65° angle with respect to the equatorial plane of the tire, the ply cords running at opposite angles in alternate layers 
     “Breakers” or “Tire Breakers” means the same as belt or belt structure or reinforcement belts. 
     “Carcass” means a layer of tire ply material and other tire components. Additional components may be added to the carcass prior to its being vulcanized to create the molded tire. 
     “Circumferential” means lines or directions extending along the perimeter of the surface of the annular tread perpendicular to the axial direction; it can also refer to the direction of the sets of adjacent circular curves whose radii define the axial curvature of the tread as viewed in cross section. 
     “Cord” means one of the reinforcement strands, including fibers, which are used to reinforce the plies. 
     “Inner Liner” means the layer or layers of elastomer or other material that form the inside surface of a tubeless tire and that contain the inflating fluid within the tire. 
     “Inserts” means the reinforcement typically used to reinforce the sidewalls of runflat-type tires; it also refers to the elastomeric insert that underlies the tread. 
     “Ply” means a cord-reinforced layer of elastomer-coated cords. 
     “Radial” and “radially” mean directions radially toward or away from the axis of rotation of the tire. 
     “Sidewall” means a portion of a tire between the tread and the bead. 
     “Laminate structure” means an unvulcanized structure made of one or more layers of tire or elastomer components such as the innerliner, sidewalls, and optional ply layer. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The invention will be described by way of example and with reference to the accompanying drawings in which: 
         FIG. 1  is a cross-sectional view of one half of a symmetrical aircraft tire. 
         FIG. 2  is a perspective view of a tire illustrating an ideal geodesic line  3  on the outer surface. 
         FIGS. 3   a ,  3   b  are front views of a tire with a modified geodesic belt. 
         FIG. 4  is a schematic view of a modified geoline from ψ=0 to ψ=360 degrees. 
         FIG. 5  is a side view simplified schematic of a tire building drum illustrating angle of drum rotation: ψ=0 to ψ=AG. 
         FIG. 6  is a process flow chart showing method steps of invention. 
         FIG. 7  illustrates the minimum path L in rectangular coordinates. 
         FIG. 8  is a cross-sectional view of one half of a symmetrical belt package. 
     
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
       FIG. 1  illustrates a cross-sectional view of one half of a radial aircraft tire  10  of the present invention. The tire is symmetrical about the mid-circumferential plane so that only one half is illustrated. As shown, the aircraft tire comprises a pair of bead portions  110  each containing a bead core  120  embedded therein. One example of a bead core suitable for use in an aircraft tire is shown in U.S. Pat. No. 6,571,847. The bead core  120  preferably has an aluminum, aluminum alloy or other light weight alloy in the center portion surrounded by a plurality of steel sheath wires (not shown). A person skilled in the art may appreciate that other bead cores may also be utilized. 
     The aircraft tire further comprises a sidewall portion  116  extending substantially outward from each of the bead portions  110  in the radial direction of the tire, and a tread portion  130  extending between the radially outer ends of the sidewall portions  116 . Furthermore, the tire  10  is reinforced with a carcass  22  toroidally extending from one of the bead portions  12  to the other bead portion  12 . The carcass  22  is comprised of inner carcass plies  22  and outer carcass plies  24 , preferably oriented in the radial direction. Among these carcass plies, typically four inner plies  22  are wound around the bead core  120  from inside of the tire toward outside thereof to form turnup portions, while typically two outer plies  24  are extended downward to the bead core  120  along the outside of the turnup portion of the inner carcass ply  22 . Each of these carcass plies  22 , 24  may comprise any suitable cord, typically nylon cords such as nylon-6,6 cords extending substantially perpendicular to an equatorial plane EP of the tire (i.e., extending in the radial direction of the tire). Preferably the nylon cords have an 1890 denier/2/2 or 1890 denier/3 construction. One or more of the carcass plies  22 ,  24  may also comprise an aramid and nylon cord structure, for example, a hybrid cord, a high energy cord or a merged cord. Examples of suitable cords are described in U.S. Pat. No. 4,893,665, U.S. Pat. No. 4,155,394 or U.S. Pat. No. 6,799,618. 
     The aircraft tire  10  further comprises a belt package  150  arranged between the carcass  22  and the tread rubber  130 .  FIG. 8  illustrates a first embodiment of one half of a belt package  150  suitable for use in the aircraft tire. The belt package  150  is symmetrical about the mid-circumferential plane so that only one half of the belt package is illustrated. The belt package  150  as shown comprises a first belt layer  50  located adjacent the carcass. The first belt layer  50  is preferably formed of cords having an angle of 5 degrees or less with respect to the mid-circumferential plane. Preferably, the first belt layer  50  is formed of a rubberized strip  43  of two or more cords made by spirally or helically winding the cords at an angle of plus or minus 5 degrees or less relative to the circumferential direction. The first belt layer  50  is the narrowest belt structure of the belt package  150 , and has a width in the range of about 13% to about 100% of the rim width (width between flanges), and more particularly in the range of about 20% to about 70% of the rim width (width between flanges), and most particularly in the range of about 30% to about 42% of the rim width (width between flanges). 
     The belt package  150  further comprises a second belt layer  60  located radially outward of the first belt layer  50 . The second belt layer  60  is preferably formed of cords having an angle of 5 degrees or less with respect to the mid-circumferential plane. Preferably, the second belt layer  60  is formed of a rubberized strip  43  of two or more cords made by spirally or helically winding the cords at an angle of plus or minus 5 degrees or less relative to the circumferential direction. The first belt  100  is the radially innermost belt, and has a width Bw s . The first belt  50  is the narrowest belt of all the belts. The second belt  60  is located radially outward of the first belt, and has a slightly larger width than the first belt. The embodiment further includes a third  70  and fourth belt  80 , having a low angle of 5 degrees or less with respect to the circumferential plane. The third and fourth belts are preferably helically wound. The third belt  110  is located radially outward of the second belt, and is substantially wider than the first and second belts. The third belt has a width bw3 and is the widest belts of the first, second and fourth belts  50 ,  60 ,  80 . The fourth belt  80  is located radially outward of the third belt, and is the widest of the low angle belts. The fourth belt has a width slightly less than the third belt. The embodiment further includes a first  120  and second  130  modified geodesic belt structure that are both located radially outward of the first through fourth belts. The first geodesic belt  120  is located radially outward of the fourth belt  80 , and has the widest width BwZ of all of the belts  50 , 60 , 70 , 80 , 130 . The ratio of the geodesic belt width BWg to the narrowest cut belt Bws is as follows:
 
0.3&lt;BWs/BWg&lt;0.6, and more preferably in the range of 0.3&lt;BWs/BWg&lt;0.5  (1)
 
     In the above embodiment, it is additionally preferred that the ply be made of nylon and that the belt be made of an aramid/nylon blend, such that the ply cord % elongation is greater than the belt cord % elongation at break. It is additionally preferred that the maximum belt cord elongation at break be less than 18%. 
     The belt package has at least one modified geodesic belts made as described in more detail, below. It is helpful to understand that a true geodesic line on a curved surface is the shortest 3 dimensional distance between two points in space or the least curvature.  FIG. 2  illustrates line  3  which illustrates a belt having a true geodesic line. Note that the cord is tangent to the belt edge at point A. A true geodesic ply pattern follows the mathematical equation exactly: ρcos α=ρ 0  cos α 0 , wherein ρ is the radial distance from the axis of rotation to the cord at a given location; α is the angle of the cord at a given location with respect to the mid-circumferential plane; and ρ is the radial distance from the axis of rotation of the core to the crown, and ρ 0 , α 0  is the radius and angle at the midcircumferential plane. 
       FIGS. 3   a  and  3   b  each illustrate a front view of a tire on a belt making machine constructed with a modified geodesic belt  120 , 130  of the present invention. The angle of the belt at the edges is slightly less than 180 degrees. Each belt looks different due to the selection of different parameters such as desired centerline angle θs. The geodesic belt is applied using a belt applier on a rotating B&amp;T drum. The belt applier utilizes a mechanical arm applier (not shown) that translates in an axial direction from one belt edge shoulder to the other belt edge shoulder. A computer controller controls the arm position (x axis) coordinated with the speed of the B&amp;T drum (ψ). The modified geodesic belt path  120 , 130  is determined from the following steps. 
       FIGS. 4 and 7  illustrates a modified geodesic path  151  according to the teachings of the invention.  FIG. 4  illustrates the path for 1 revolution from 0 degrees to Phi=360 degrees. For a true geodesic path, at each belt edge (W/2) the angle α=0 degrees so that the cord is tangent at the belt edge. The modified geodesic path of the invention deviates from an angle of zero at the belt edges in order to avoid excessive build up at the belt edges. The modified geodesic path also deviates from the angle at the centerline, so that a desired centerline angle θs may be obtained. For purposes of illustration, for an exemplary tire size, it is known that there are 20 geolines formed in 9 revolutions. Thus a geoline is formed in 0.45 revolutions for a true geodesic path. At each belt edge, the geoline is tangent to the belt edges (α=0), and the belt angle at the centerline is about 15.5 degrees. A geoline is defined as the three dimensional minimum path from one belt edge (point A on  FIG. 4 ) to the opposite belt edge (point D,  FIG. 4 ). Thus a belt would require multiple geolines in order to completely cover the tire belt surface, typically 80 geolines. 
     AG is defined as the change in angle ψ from the starting point A to the ending point D of the geoline as shown in  FIG. 5 . AG is set to have an initial value by specifying an initial NR value of 20, and an NG value of 30. The value of NG, AG will change as the iterative series of calculations are performed.
 
 AG= 360* NR/NG,  
 
     Where NR=number of revolutions to form NG geolines 
     NG=number of geolines in the set, all sets are equal 
       FIG. 6  illustrates the flow chart for outlining the steps to calculate a modified geoline  150  for a belt. For step  10 , the belt width, strip width and desired centerline angle θs are input. For step  20 , θs is set to the input value θs, and NR is set to 20, NG is set to 30. These values were determined from experience. 
     Where NR=number of revolutions in one set of geolines 
     NG=number of geolines in a set that have a starting point and ending point of zero degrees phi 
     For step  30 , AG is determined from the following calculation:
 
 AG= 360* NR/NG,  
 
     In step  40 , the three dimensional minimum distance path L is determined for a geoline from the equation below, over the range from, X=−W/2 to W/2, phi=0 to AG
 
L=σ( SQRT ( X   2   +Y   2   +Z   2 )), for i=1 to k
 
     Where Z=R*δψ 
     In step  50 , the angle θ is calculated at the centerline and compared with the input value θs. For step  60 , if θ=θs? is not true, then step  70  is performed wherein NG is increased by the following formula:
 
 NG=NG+ΔNG  
 
     Steps  30 - 70  are repeated until θ=θs. 
     Once θ=θs, then the remaining geolines for the set are determined using equations from step  40 . Alternatively, once a geoline is calculated, the other remaining geolines can be determined by adding AG to the Phi values of the geoline data set. 
     A first data set is now known, wherein NR=20, and NG=70 was determined in this example. The first set of data points describing the minimal path are known in X, Y, Ψ coordinates. In order to fill the belt surface sufficiently, several sets are needed, typically in the range of 2 to 5 sets. Assume in this example four data sets are needed. In order to determine the starting point of sets two through four, the value K is computed from the equation below. 
     For four data sets, the first data set is preferably modified by a factor K in order to completely cover the belt area by the cords and to ensure that the second data set begins where the first data set ends. For four specified data sets, the ending point of the first data set will occur precisely at Ψ=90 degrees. Thus our first data set will start at Phi=0 and end at Phi=90 degrees. Set two will start at 90 degrees and end at 180 degrees. Set three will start at 180 degrees and end at 270 degrees. Set four will start at 270 degrees and end at 0/360 degrees.
 
 K=[ 360 *NR+ 360 /NS ])/ NR  
 
     Where NS is number of data sets to be generated, in the example 4 
     In order to fill the belt, it is desired to have at least 4 data sets generated. 
     For the first data set, Ψ′=K*Ψ 
     Thus, the first data set has 70 geolines formed in 20 revolutions, wherein the data set begins at Ψ=0 and ends at Ψ=90. K is a multiplier which slightly stretches the data set to end precisely at an even interval such as 90 degrees. The second data set begins at Ψ=90 and ends at Ψ=180. This data set can be derived from the first data set by adding Ψ=Ψ+90, while the other data values stay the same. The third data set begins at Ψ=180 and ends at Ψ=270 degrees. This data set can be derived from the first data set by adding Ψ=Ψ+180, while the other data values stay the same. The fourth data set begins at Ψ=270 degrees and ends at Ψ=360 degrees. This data set can be derived from the first data set by adding Ψ=Ψ+270, while the other data values stay the same. 
     Cord Construction 
     The cord may comprise one or more rubber coated cords which may be polyester, nylon, rayon, steel, flexten or aramid. 
     Variations in the present invention are possible in light of the description of it provided herein. While certain representative embodiments and details have been shown for the purpose of illustrating the subject invention, it will be apparent to those skilled in this art that various changes and modifications can be made therein without departing from the scope of the subject invention. It is, therefore, to be understood that changes can be made in the particular embodiments described which will be within the full intended scope of the invention as defined by the following appended claims.