Abstract:
A powered massaging assembly includes a handle and a massage head each having an enclosure that presents a chamber. The massage head includes a drive shaft that extends into and out of the chamber. The massage head also includes a driven massage element drivingly attached to the drive shaft and mounted outside the chamber to manipulate tissue. The enclosures include connectors rotatably attached to each other to provide a swivel joint that rotatably interconnects the handle and head.

Description:
FIELD OF THE INVENTION 
     The present invention relates to methods for determining sidewall aggression performance parameters that indicate the ability of a tire to resist sidewall aggression and therefore damage to the sidewall. 
     BACKGROUND OF THE INVENTION 
     While a tire tread is designed to be in contact with the ground surface and is therefore constructed from compositions intended for this purpose, the sidewalls are generally not designed to be ground contacting. Instead, the sidewalls of a tire typically include a layer of rubber material that covers certain structural elements, such as e.g., the cords of a tire carcass, which extend between and through the sidewalls of the tire. This rubber material is conventionally created from a composition not designed for ground contact but rather for flexibility so that the sidewalls can withstand the repeated flexing of the tire that occurs as it rotates through the contact patch. In addition, this sidewall rubber is typically not as thick as the tread rubber. As such, the sidewalls generally have less resistance than the tread to puncture damage that can occur when the tire is contacted with another object in or along the ground surface. 
     Certain tires are intended for more rugged applications where encounters with objects that may puncture or otherwise damage the sidewall can be frequent. For example, for recreational and emergency off-road applications, tires may be subjected to contact with rocks, trees, and other objects that can puncture and deflate a pneumatic tire. Of course, for such tires it is generally desirable to increase their capability to resist sidewall aggression—i.e., to increase their resistance to puncture, rupture, or other sidewall damaging events caused by contact during tire use. Features can be added at, for example, the shoulder region of the tire to help resist certain sidewall aggressions. More particularly, lugs or blocks can be added about the shoulder to protect the sidewall from shoulder aggression by remaining between a dangerous object and the sidewall as the tire rolls over the object. 
     While testing tires under actual conditions such as off road environments can provide important information about a tire&#39;s ability to resist sidewall aggression, the repeatability of such testing in harsh conditions so that different tires may be compared accurately is very difficult. Even operating the same vehicle over the same path of rocky terrain does not ensure that the tires will be subjected to the same sidewall aggression events on each pass. Rocks and other debris can be moved or affected by each pass of the vehicle, thereby ensuring that different conditions will be presented even if the vehicle can be operated along the same path for each pass. A rock that does not present a sharp point during one pass may be repositioned in a manner that becomes more of a sidewall damage threat for the next pass or vice versa. As such, it can be difficult to compare different tires with such testing. 
     Accordingly, specific methods for testing a tire&#39;s ability to resist damage from sidewall aggression are desirable. More particularly, methods for determining particular performance parameters that characterize a tires resistance to sidewall aggression under conditions that can be repeated among multiple tests would be very useful. These and other useful aspects of the present invention will be apparent from the description that follows. 
     SUMMARY OF THE INVENTION 
     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 general, aspects of the present invention concern methods for evaluating tire resistance to sidewall aggression. In accordance with such methods, one or more test tires may be subjected to contact with a damage tool. The height and depth of the damage tool can be selectively varied by adjusting the respective vertical and lateral dimensions of the damage tool relative to a tire sidewall surface. 
     In a more particular exemplary embodiment, a method for testing the resistance of a tire to sidewall damage involves subjecting one or more test tires to contact with a damage tool. The lowest height of the damage tool at which a given type of damaging event (e.g., rupture, puncture, splitting, cutting) occurs in each test tire is measured. A first performance parameter based at least in part on the measured lowest height of the damage tool at which the given type of damaging event occurs in each test tire is calculated. Such first performance parameter provides information about a tire&#39;s ability to drive over an object while resisting sidewall damage. 
     In some embodiments, the measured lowest height of the damage tool at which a given type of damaging event occurs is determined for different types of tire features (j=1, . . . , J), for example—lugs and voids along a tire sidewall. Characteristic dimensions 
     a j  for each different type of tire feature (j=1, . . . , J) may also be determined and used in the calculation of the first performance parameter. A particular example in which the first performance parameter for the one or more test tires (T 1 ) may be determined is in keeping with the formula 
                 P   ⁢           ⁢     1     T   ⁢           ⁢   1         =       1       ∑     j   =   1     J     ⁢     a   j         ⁡     [       ∑     j   =   1     J     ⁢       a   j     ⁢     h   ⁡     (     T   ⁢           ⁢     1     j   ⁢   _   ⁢   low         )           ]         ,         
where h(T 1   j   _   low ) is the measured lowest height of the damage tool at which a given type of damaging event occurs at each type of tire feature j within the test tire (T 1 ). Such first performance parameter also optionally may be related to a reference value, such as but not limited to a threshold value or a value similar to the first performance parameter calculated for one or more reference tires.
 
     In another more particular exemplary embodiment, a method for testing the resistance of a tire to sidewall damage involves subjecting one or more test tires to contact with a damage tool. The depth of the damage tool at which a given type of damaging event occurs in the test tire while the damage tool is fixed at one or more predetermined heights (k) is measured. A second performance parameter based at least in part on the measured depth of the damage tool at which the given type of damaging event occurs in the test tire (T 1 ) at each of the one or more predetermined heights (k) is then determined. Such second performance parameter provides information about the strength of a tire sidewall to resist damage from protruding objects encountered along the sidewall. 
     In some embodiments, the measured depths of the damage tool at which a given type of damaging event occurs is determined for different types of tire features (j=1, . . . , J), for example—lugs and voids along a tire sidewall. Characteristic dimensions a j  for each different type of tire feature (j=1, . . . , J) may also be determined and used in the calculation of the second performance parameter. A particular example in which the second performance parameter (P 2 ) for the one or more test tires (T 1 ) may be determined is in keeping with the formula 
                 P   ⁢           ⁢     2     T   ⁢           ⁢   1         =       1       ∑     j   =   1     J     ⁢     a   j         ⁡     [       ∑     j   =   1     J     ⁢         a   j     K     ⁡     [       ∑     k   =   1     K     ⁢     d   ⁡     (     T   ⁢           ⁢     1     j   ⁢   _   ⁢   k         )         ]         ]         ,         
where d(T 1   j   _   k ) is the measured depth of the damage tool at which the given type of damaging event occurs at each of the one or more predetermined heights (k=1, . . . , K) and for each type of tire feature (j=1, . . . , J) within the test tire (T 1 ). Such second performance parameter also optionally may be related to a reference value, such as but not limited to a threshold value or a value similar to the first performance parameter calculated for one or more reference tires.
 
     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 and constitute a part of this specification, illustrate embodiments of the invention and, together with the description, serve to explain the principles of the invention. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       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  illustrates an elevation view of an exemplary embodiment of an apparatus that may be used to test the resistance of a tire to sidewall aggression while the tire is mounted on the vehicle. 
         FIG. 2  illustrates a top view of the exemplary embodiment of  FIG. 1 . 
         FIG. 3  illustrates a top view of a vehicle placed into the tire guide of the apparatus of  FIG. 1  and in a ready position for testing. 
         FIG. 4  illustrates a tire as it drives over an exemplary embodiment of a damage tool. 
         FIG. 5  illustrates a detailed view of a test tire relative to a sidewall testing apparatus. 
         FIG. 6  illustrates a graphical representation of various height (h) versus depth (d) data points determined for different iterations of sidewall testing in which a damage tool interacts with a first type of tire sidewall feature (j=1). 
         FIG. 7  illustrates a graphical representation of various height (h) versus depth (d) data points determined for different iterations of sidewall testing in which a damage tool interacts with a second type of tire sidewall feature (j=2). 
         FIG. 8  provides a flow chart of exemplary steps in a method of calculating a first sidewall performance parameter (P 1 ) for one or more test tires. 
         FIG. 9  provides a flow chart of exemplary steps in a method of calculating a second sidewall performance parameter (P 2 ) for one or more test tires. 
         FIG. 10  provides a schematic block diagram of exemplary hardware components used for implementing selected steps of the present technology. 
     
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     The present invention relates a tire&#39;s resistance to sidewall aggression—i.e. the ability of a tire to avoid puncture, rupture, cutting, or other damage to the sidewall when contacting an object in the roadway. More particularly, the present invention relates to methods for determining sidewall aggression performance parameters that indicate the ability of a tire to resist sidewall aggression and therefore damage to the sidewall. The present invention provides for repeatability of test conditions between various tests and may also be used to provide quantitative data from such testing that can be used, for example, to compare the performance of different tires and/or further develop existing tire designs. 
     For purposes of describing the invention, reference now will be made in detail to embodiments and methods 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 and steps 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. 
       FIGS. 1 and 2  provide elevation and top views of a test vehicle  100  onto which a tire  105  has been mounted for testing with an exemplary apparatus  120  of the present invention. Apparatus  120  allows tire  105  to be tested on the actual vehicle application intended for a particular tire. In this way, test conditions that may be unique to a particular vehicle, such as e.g., the vehicle weight and suspension, can be applied and replicated during the tests. While many types of tires may be tested using the present invention, tire  105  could be considered as an “off road” tire that is equipped with various features  110  that can help tire  105  resist damage to its sidewall  115  ( FIG. 4 ) when contacting an object in the travel path. 
     As best seen in  FIGS. 2 and 3 , apparatus  120  includes a guide  160  constructed from a pair of rails  170  and  175 . Guide  160  defines a longitudinal travel path for vehicle  100 . As will be further described below, in order to provide consistency between tests, guide  160  operates to maintain the movement of vehicle  100  along the direction of arrow A as tire  105  is rolled into contact with a damage tool  125  on each test. Rails  170  and  175  maintain the orientation of the tires along one side of vehicle  100  opposite from the side having test tire  105 . Depending upon e.g., the width of vehicle  100 &#39;s tires and the distance between rails  170  and  175 , the tires may rub or catch on rails  170  and  175  and thereby induce unwanted lateral (defined as perpendicular to the longitudinal travel path defined by guide  160 ) movement. Accordingly, rails  170  and  175  can be lubricated to help prevent or minimize such an effect. Rails  170  and  175  are provided by way of example only. Guide  160  may be constructed from other features such as raised concrete, a recess in the road or contact surface, and others. 
     On the opposite side from rails  170  and  175 , apparatus  120  includes a tray  165  that receives two tires from vehicle  100  including test tire  105 . Tray  165  serves to position tire  105  at the proper height for contact with damage tool  125 . Tray  165  may also be constructed in a variety configurations including raised concrete, wood, and others. The configuration (e.g., material) chosen for tray  165  may be based on the intended surface characteristics of test tire  105 , such as but not limited to friction factor and the like. 
     As indicated, apparatus  120  also includes a damage tool  125  that appears in the figures as a wedge-shaped device. Damage tool  125  is intended to replicate sidewall aggression—i.e. contact with features that could puncture, rupture, or otherwise damage the sidewall of tire  105 . The present invention is not limited to the particular shape illustrated in the figures and other shapes may be used with apparatus  120 . Regardless, the consistent application of the same shape for damage tool  125  allows for accurate comparison between tests. 
     As indicated by arrow L in  FIG. 1 , damage tool  125  can be advanced along this lateral direction and into the longitudinal travel path defined by guide  160 . More particularly, the lateral position of damage tool  125  relative to the predetermined path for tire  105  can be selected by moving damage tool  125  within rails  155  using handle  150 . A locking device (not shown) can be provided to fix the position of damage tool  125  once a lateral position has been selected. For example, to selectively fix the position of damage tool  125 , rails  155  could include mechanical fasteners, a rack and pinion, or other mechanisms that hold tool  125  in place as tire  105  makes contact. Similarly, the height of damage tool  125  relative to tire  105  can also be selected by movement along the direction of arrow W, and a locking device (not shown) can also be provided to fix the height of damage tool  125  once selected. 
     Even with guides  160  and lubrication of rails  170  and  175 , the lateral position of vehicle  100  within guides  160  may vary as vehicle  100  moves along the longitudinal travel path defined by guides  160 . In a manner to be more fully described, damage tool  125  will be incrementally advanced into the longitudinal travel path during testing of tire  105 . For purposes of comparing test results between tires, it is desirable to know the position of tool  125  relative to tire  105 . More particularly, it is desirable to know the actual amount by which damage tool  125  projects into the path of tire  105  so that different tests can be accurately compared. 
     Accordingly, referring specifically to  FIG. 1 , apparatus  120  includes a sensing device  130  that determines the lateral movement of vehicle  100  as it moves along the longitudinal travel path. For example, in one exemplary embodiment, sensing device  130  includes a laser that is reflected off the vehicle by placing a reflector on the wheel hub. As vehicle  100  passes by, light is reflected and changes in the reflecting intensity can be used to determine whether vehicle  100  has shifted laterally i.e. towards or away from sensor  130 . Position sensor  140  provides information about the location of damage tool  125 . Therefore, by calibrating position sensor  140  and sensing device  130  and using the information provided by sensor  130  to adjust for lateral movement, the actual amount by which damage tool  125  is projected into the path of tire  105  can be determined even though vehicle  100  may drift along the lateral direction as it moves along the longitudinal travel path provided by guide  160 . This positional information (i.e. depth) for damage tool  125  allows for a more accurate comparison of results between various tests despite variations in the lateral movement of vehicle  100  during testing. 
     For example, in order to set up apparatus  120  for testing, tire  105  is positioned immediately adjacent to damage tool  125 . Damage tool  125  is then positioned laterally and vertically to a position where the tip  180  ( FIG. 1 ) of tool  125  makes contact with the widest part of tire  105  such as e.g., the equator along the sidewall  115 . This position is defined as the “zero” for tool  125  and all incremental movements of tool  125  along lateral direction L are measured with reference to this starting point. While tire  105  is in this same position, sensor  130  also provides a reading that is defined as the zero point for the lateral position of tire  105 . It should be appreciated that the widest part of the tire  105  (e.g., the equator) is only one example of a reference location for determining relative placement of the tool  125 . The location of tool  125  in lateral, vertical or other directions may be obtained relative to any particular reference location(s) established during a test. 
     Accordingly, during testing, vehicle  100  will pass sensor  130 . Any lateral movement detected by sensor  130  will be used in to determine the “true” amount by which tool  125  is projecting into the path of tire  110 . If during a given test run, for example, damage tool  125  has been laterally advanced by 5 mm from its “zero” position, but sensor  130  records lateral movement of tire  105  towards the sensor of 2 mm, then the actual projection of tool  125  into the tire path is only 3 mm. This adjusting for the lateral movement of vehicle  100  is performed constantly as vehicle  100  is moved down the longitudinal travel path defined by guide  160 . 
     An exemplary method for use with apparatus  120  will now be described beginning with  FIG. 3 . A vehicle  100  of choice is placed onto apparatus  120  with a selected test tire  105  mounted on the vehicle and positioned upon tray  165 . Wheels on the opposite side of vehicle  100  from test tire  105  are placed into guide  160  and, more specifically, between rails  170  and  175 . 
     After calibration and zeroing of damage tool  125  and sensor  130  as previously described, damage tool  125  is placed at is lowest height. Knowing the “zero” of damage tool  125  as previously described, tool  125  is now advanced laterally along the direction of arrow L into the longitudinal travel path by a chosen incremental amount, and the lateral and vertical position of tool  125  is then fixed or locked in preparation for contact with tire  105  as vehicle  100  passes by. The lateral position and height of damage tool  125  is recorded. 
     Vehicle  100  is then backed in the direction of arrow A along the longitudinal travel path defined by guide  160 . As tire  105  passes sensor  130 , display  135  indicates the amount by and which damage tool  125  extends into the path of tire  105 . For example, display  135  may indicate that damage tool  125  extends 5 mm into the path of tire  105 . In the event vehicle  100  drifts laterally, sensor  130  determines the amount of this drift and an adjustment is automatically made so that display  135  provides the actual amount by which tool  125  projects into the path of tire  105  at any given point during the test. 
     In the event tire  105  is not ruptured or punctured from contact with damage tool  125  during a given pass, vehicle  100  is then returned to its original position (as shown in  FIG. 3 ). Damage tool  125  is now advanced by a predetermined amount along the lateral direction of arrow L so as to increase the amount by which damage tool  125  projects into the path of tire  105 . This position is recorded and vehicle  100  is again backed along the direction of the longitudinal travel path so that tire  105  is again rolled into contact with damage tool  125  and then past damage tool  125 . As tire  105  passes, sensor  130  again determines whether there is any movement of vehicle  100  along the lateral direction so that the actual amount of projection of damage tool  125  into the path of tire  105  may be indicated from display  135 . 
     If the sidewall of tire  105  is not damaged by damage tool  125 , the process of advancing damage tool  125  laterally by an incremental amount and backing vehicle  100  along guide  160  is repeated. “Damage” to the sidewall as used herein includes cutting, puncturing, rupturing, splitting or otherwise damaging the sidewall of the tire. For example, the test can be operated until only one or a combination of these events occurs, whichever event(s) is selected for the test. 
     During each pass of tire  105  and lateral advancement of damage tool  125 , the wedge-shaped element of tool  125  will project farther and farther into the path of tire  105 . Each time tire  105  rolls into contact with tool  125 , there is an opportunity for tool  125  to damage sidewall  115  of tire  105 . If sidewall  115  is damaged, then the test is terminated and the lateral position (depth) and vertical position (height) of damage tool  125  at the time of such damage (e.g., a puncture) is recorded for tire  105 . Alternatively, if tire  105  is not damaged as damage tool  125  is increasingly advanced laterally for each pass of vehicle  100 , then tire  105  will eventually begin to either roll over damage tool  125  or slide off tool  125  without damaging sidewall  115 . For example,  FIG. 4  shows the deformation of tire  105  as it rolls over damage tool  125  without damage, such as e.g., a puncture, to sidewall  115 . Once this condition is reached, damage tool  125  is retracted laterally back to its original zero position and the height of damage tool  125  is increased by an incremental amount. Now, the entire process of advancing damage tool  125  along lateral direction L by incremental amounts for a given height are repeated until tire  105  is either damaged or begins rolling over or sliding off damage tool  125 , at which point the vertical height of tool  125  is increased and the lateral advancement process is repeated. Camera system  145  ( FIGS. 1 and 2 ), preferably a high speed system, can be used to record any puncture of tire  105  and provide information for later study. Information provided by display  135  can also be recorded electronically for later use if desired. 
     Eventually, for each tire that is tested, a lateral and vertical position will be reached at which a given tire will experience damage to its sidewall  115 . By repeating this test for different tires, apparatus  120  provides a valuable and repeatable test by which the resistance of different tires to sidewall aggression may be evaluated. For example, some tires may not be able to resist sidewall puncture even when damage tool  125  is set at a relatively low height and minimal projection into the tire path along lateral direction L. Conversely, other designs may be able to stand deeper projections into the tire path and at greater heights. Both tire architecture and tread design may be evaluated and developed through comparison testing. Accordingly, apparatus  120  provides a repeatable, reliable method of comparing tires of different design and manufacture for resistance to sidewall aggression. 
     While general reference has been made to methods of testing tires using an apparatus  120 ,  FIGS. 5-10  present additional aspects of particular performance parameters for use in sidewall aggression evaluation for tires. In particular, methods are presented herein for determining a first exemplary performance parameter (P 1 ) referred to herein as a “Drive Over Performance Parameter.” Parameter P 1  generally characterizes the ability of a tire to drive over an object while experiencing no amount or a minimum or acceptable amount of sidewall damage. Parameter P 1  specifically identifies the lowest estimated sidewall height at which a tire is susceptible to a particular type of damaging event. 
     In addition, methods are presented herein for determining a second exemplary performance parameter (P 2 ) referred to herein as a “sidewall Strength Performance Parameter.” Parameter P 2  generally characterizes the ability of a tire to deal with protrusion into the tire sidewall while experiencing no amount or a minimum or acceptable amount of sidewall damage. Parameter P 2  specifically identifies the lowest estimated sidewall depth at which a tire is susceptible to a particular type of damaging event. 
     The introduction of the specific types of parameters P 1  and P 2  described herein is advantageous for several reasons. First, the realization of at least two different types of parameters to assess overall tire sidewall aggression performance provides more meaningful results for assessing tire fitness. In addition, the methods described herein account for different tire geometries by addressing how to evaluate tire sidewall fitness when different types of tire features are present along a tire sidewall (e.g., various combinations of one or more types of lugs, blocks, voids, grooves, etc.). The inventors have identified that the damage tool within a testing apparatus has the possibility to damage a tire with different severities depending on how and where it interacts with a tire sidewall (e.g., interaction at a lug versus a void). For this reason, the disclosed parameters account for such phenomenon by extrapolating the performance parameter based on an understanding of the tire geometry and the weighted probabilities of where the damage tool might happen to land along a tire sidewall. 
     Referring now to  FIG. 8 , an exemplary method  800  is presented for calculating the Drive Over Performance Parameter (P 1 ). In accordance with a first step in such method, an initial step  805  involves subjecting one or more test tires (T 1 ) to a sidewall testing apparatus that includes a damage tool, wherein the damage tool is configured at different combinations of vertical position (i.e., height—h) and lateral position (i.e., depth—d) until each test tire (T 1 ) experiences a given type of damaging event upon exposure of the damage tool to one or more types of tire features (e.g., lugs and voids). Ultimately, a determination is made in step  810  identifying h(T 1   j   _   low )—the lowest average height of the damage tool at which the given type of damaging event occurs in each test tire (T 1 ) when the damage tool interacts with each type of tire feature (j=1, . . . , J). 
     More particular aspects of step  805  may be appreciated with reference to  FIG. 5 , in which a test tire  105  is subjected to sidewall testing apparatus  120 , including damage tool  125 . For each iteration of the test, i.e., each different combination of height and depth of damage tool  125 , the relative location of damage tool  125  in both lateral and vertical dimensions is determined. Such dimensional locations can be measured relative to any reference locations. For example, as shown in  FIG. 5 , height (h) can be measured from a ground surface to the top edge (or other outermost location) of damage tool  125 . In some embodiments, the height of the tray  165  is subtracted out from the measured height (h) value. The depth (d) can be measured from an initial depth to another varied level. For example, the damage tool  125  can be adjusted laterally inward towards the sidewall surface of tire  105  until it is just touching the surface but not exerting any force to cause protrusion into the sidewall surface. This location can be set as the initial depth, and all measured depth values (d) can be measured as respective lateral distances at which damage tool  125  protrudes into the sidewall of tire  105  from such initial depth. 
     The respective height (h) and depth (d) values can be determined during specific interaction at different types of tire features. For example, the methods disclosed herein may be concerned with interaction of the damage tool  125  at the location of sidewall lugs  185  as well as at the location of sidewall voids  190 , realizing that different levels of damage could occur at such different types of tire features. Generally, lugs are considered to be the outermost portion of the tread design. When found along the crown portion of the tire, lugs correspond to that portion of the tread design that contacts the road surface. Voids are spaces between the lugs that allow the lugs to flex. 
     Referring again to steps  805  and  810 , it should be appreciated that the types of damaging events may include, without limitation, puncture, rupture, splitting, cutting, occurrence of one or more of the above instances to some threshold level (e.g., a cut of at least 5 min) or other predefined damage to the sidewall. The number of test tires (T 1 ) may vary from one test tire to many test tires. The total number of test tires (T 1 ) is often chosen in a way that balances the preference for meaningful average performance results with the cost realization that every test tire normally experiences irreparable harm during testing. In a nonlimiting example, the total number of test tires (T 1 ) is in a range of between about three tires and about twenty tires. 
     The height (h) and depth (d) of the damage tool  125  is successively varied in order to determine the lowest height (h) of the damage tool  125  at which a given type of damaging event occurs in each test tire (T 1 ). In one example, this value can be determined by starting the damage tool at a fixed initial height (e.g., a low initial height) and gradually incrementing the depth of the damage tool to see if the damaging event occurs. If the depth is incremented to a given point and either no damage occurs to the tire sidewall or the tire begins to literally drive over the damage tool, then the height can be incremented to a next fixed level where the depth of the damage tool is again incrementally increased while the tire sidewall is observed to detect damage. This process can be repeated by gradually incrementing the height and depth of the damage tool until a damaging event occurs. 
     With further respect to steps  805  and  810 , it should be appreciated that the process of repeatedly subjecting one or more test tires to different combinations of height and depth of a damage tool may be repeated for different types of tire features if a tire sidewall includes a total number (J) of one or more types of tire features. For example, some tire sidewalls may be outfitted with a first type of feature such as lugs (j=1) and a second type of tire feature such as voids (j=2). In another example, some tire sidewalls may be provided with a first type of lug (j=1), a first type of void (j=2), a second type of lug (j=3) and a second type of void (j=4). An unlimited number of combinations of tire features is possible along a tire sidewall. Ultimately, the resultant lowest height (h) of the damage tool at which a given damaging event occurs for a given type of tire feature j, averaged across all test tires (T 1 ), is referred to herein as h(T 1   j   _   low ). The h(T 1   j   _   low ) values may be determined for all types of tire features (j=1, . . . , J). 
     By separately performing the disclosed sidewall aggression tests with specific interaction at each different type of tire feature, the disclosed methods can account for such variation in features across a tire sidewall. Then, the results of performance for each particular type of tire feature can be qualified by each type of feature&#39;s respective characteristic dimension (e.g., length, width, surface area, etc.) so that a global performance score for a tire accounts for the probabilities that a damage tool will interact with the various types of tire features. As such, exemplary step  815  in method  800  involves measuring the average characteristic dimension (a j ) for each type of tire feature (j=1, . . . , J) for the plurality of test tires (T 1 ). For example, in a tire sidewall that includes two types of tire features, lugs (j=1) and voids (j=2), the average length of the lugs (a 1 ) and the average length of the voids (a 2 ) along a particular cross-section of the tire sidewall can be measured as part of step  815 . In same embodiments, every pitch length combination is measured to assure that the aspect ratio is consistent along the entire circumference of the tire. In other embodiments, a characteristic dimension is measured only for the types of tire features which specifically interact with the damage tool in each test run. Some or all of these measured dimensions can then be used to obtain an appropriate ratio for determining the global performance scores disclosed herein. 
     Once the height values h(T 1   j   _   low ) and characteristic dimension values a j  for all types of tire features j=1, . . . , J are obtained per steps  805 - 815 , a first performance score (P 1   T1 ) that generally indicates the Drive Over Performance for a tire can be electronically calculated in step  820  for the set of one or more test tires (T 1 ). More particularly, the first performance score (P 1   T1 ) for the plurality of test tires (T 1 ) can be calculated by the following equation: 
     
       
         
           
             
               
                 
                   
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     In some embodiments of the above technology, the above parameter P 1   T1  is more meaningful when compared with a reference value. In some embodiments, such a reference value may correspond to a predetermined threshold identified as an acceptable score for P 1 . In other embodiments, such a reference value corresponds to a similar drive over performance parameter determined for a second set of tires including one or more reference or comparison tires. In other words, it may be useful to compare the first performance score (P 1   T1 ) to a similar performance score (P 1   T2 ) for one or more reference tires (T 2 ). In such instance, similar data obtained in steps  805 - 815  are obtained and averaged over all reference tires T 2  having characteristic dimensions b j  for all j=1, . . . , J such that P 1   T2  can be calculated by: 
     
       
         
           
             
               
                 
                   
                     P 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       1 
                       
                         T 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         2 
                       
                     
                   
                   = 
                   
                     
                       
                         1 
                         
                           
                             ∑ 
                             
                               j 
                               = 
                               1 
                             
                             J 
                           
                           ⁢ 
                           
                             b 
                             j 
                           
                         
                       
                       ⁡ 
                       
                         [ 
                         
                           
                             ∑ 
                             
                               j 
                               = 
                               1 
                             
                             J 
                           
                           ⁢ 
                           
                             
                               b 
                               j 
                             
                             ⁢ 
                             
                               h 
                               ⁡ 
                               
                                 ( 
                                 
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                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   
                                     2 
                                     
                                       j 
                                       ⁢ 
                                       _ 
                                       ⁢ 
                                       low 
                                     
                                   
                                 
                                 ) 
                               
                             
                           
                         
                         ] 
                       
                     
                     . 
                   
                 
               
               
                 
                   ( 
                   2 
                   ) 
                 
               
             
           
         
       
     
     In one example, P 1   T1  is related to P 1   T2  by calculating a global P 1  value (P 1   global ), where P 1   global =ΔP 1 =P 1   T1 −P 1   T2 . In another example, P 1   T1  is related to P 1   T2  by considering the percentage of the above ΔP 1  global score. In other words, (P 1   global )=ΔP 1 /P 1   T1 =P 1   T1 −P 1   T2 /P 1   T1 . 
     An example of the measured values used to obtain the first performance parameter (P 1 ) described relative to  FIG. 8  is represented by part of the exemplary data set shown in  FIGS. 6 and 7 , both of which provide graphical representations of different data points associated with various sets of tires, where depth (d) is plotted along the abscissa and height (h) is plotted along the ordinate. The open circular data points in  FIGS. 6 and 7  represent measurements obtained for a first set of tires, test tires (T 1 ). The solid circular data points in  FIGS. 6 and 7  represent measurements obtained for a second set of tires, reference tires (T 2 ). 
     In the example of  FIGS. 6 and 7 , the total number of types of tire features (J) is two.  FIG. 6  illustrates data points (various height and depth combinations) for sidewall damage testing performed at a first type of tire feature—lugs (j=1). In particular, the data points measured in accordance with this particular example correspond to T 1   1   _   low  and T 2   1   _   low . The height and depth at each data point are typically available via sensing device  130  and position sensor  140  associated with testing apparatus  120 . However, the specific values used in determining P 1   T1  and P 1   T2  will be h(T 1   1   _   low ) and h(T 2   1   _   low ). Similarly,  FIG. 7  illustrates data points for sidewall damage testing performed at a second type of tire feature—voids (j=2). In particular, the data points correspond to T 1   2   _   low  and T 2   2   _   low , and the particular values used in determining P 1   T1  and P 1   T2  will be h(T 1   2   _   low ) and h(T 2   2   _   low ). Characteristic dimensions a 1  and a 2  are also measured so that the formula for P 1  for the test tires (T 1 ) can be determined from equation (1) above as: 
               P   ⁢           ⁢     1     T   ⁢           ⁢   1         =         1       ∑     j   =   1     J     ⁢     a   j         ⁡     [       ∑     j   =   1     J     ⁢       a   j     ⁢     h   ⁡     (     T   ⁢           ⁢     1     j   ⁢   _   ⁢   low         )           ]       =             a   1     ⁢     h   ⁡     (     T   ⁢           ⁢     1     1   ⁢     _   ⁢   low           )         +       a   2     ⁢     h   ⁡     (     T   ⁢           ⁢     1     2   ⁢     _   ⁢   low           )               a   1     +     a   2         .             
Characteristic dimensions b 1  and b 2  are measured for the reference tires (T 2 ), so that the formula for P 1  for the reference tires (P 1   T2 ) can be similarly determined from equation (2) above as:
 
               P   ⁢           ⁢     1     T   ⁢           ⁢   2         =         1       ∑     j   =   1     J     ⁢     b   j         ⁡     [       ∑     j   =   1     J     ⁢       b   j     ⁢     h   ⁡     (     T   ⁢           ⁢     2     j   ⁢   _   ⁢   low         )           ]       =             b   1     ⁢     h   ⁡     (     T   ⁢           ⁢     2     1   ⁢     _   ⁢   low           )         +       b   2     ⁢     h   ⁡     (     T   ⁢           ⁢     2     2   ⁢     _   ⁢   low           )               b   1     +     b   2         .             
A meaningful result might compare the test and reference tires by determining a parameter P 1   global =ΔP 1 =P 1   T1 −P 1   T2 .
 
     Referring now to  FIG. 9 , an exemplary method  900  is presented for calculating the Sidewall Strength Performance Parameter (P 2 ). In accordance with a first step in such method, an initial step  905  involves subjecting one or more test tires (T 1 ) to a sidewall testing apparatus that includes a damage tool. The configuration of the damage tool at different combinations of vertical position (i.e., height—h) and lateral position (i.e., depth—d) is similar to the process described above relative to method  800 , and is repeated until damaging events occur at each different type of tire feature (j=1, . . . , J) in a tire sidewall. 
     In contrast to the Drive Over Performance Parameter (P 1 ), P 2  provides more specific information on acceptable depth levels associated with potential sidewall aggression (i.e., the strength of the sidewall against protrusion). As such, the height (h) and depth (d) of the damage tool  125  is successively varied in order to determine the average depth of the damage tool  125  at which a given type of damaging event occurs in each test tire (T 1 ). In one example, this value can be determined by fixing the damage tool at one or more predetermined height levels (for K total number of heights), and gradually incrementing the depth of the damage tool to determine when the damaging event occurs. Ultimately, the resultant depth values of the damage tool at which a given damaging event occurs for a given type of tire feature (j), averaged across all test tires (T 1 ) and determined at a given height (k), is referred to herein as d(T 1   j   _   k ). The d(T 1   j   _   k ) values are determined as indicated in step  910  for all tire features (j=1, . . . , J) and all predetermined test heights (k=1, . . . , K). In addition, the respective characteristic dimensions (a j ) are measured in step  915  for each type of tire feature (j=1, . . . , J) for the plurality of test tires (T 1 ), similar to step  815 . 
     The total number of different heights (K) at which a depth damage value is obtained can vary from one to many. In one example, K=2 such that the above depth parameters d(T 1   j   _   k ) are obtained for k=1 and k=2—i.e., d(T 1   j   _   1 ) and d(T 1   j   _   2 ) are determined. The values for the K different heights used in determining the Sidewall Strength Performance Parameter (P 2 ) may also be specifically chosen. In some examples, at least one iteration of testing is performed while the height of the damage tool is fixed at the level of the tire rim (e.g., height  195  represented in  FIG. 5 .) This causes the damage tool to interact with the tire sidewall closer towards where the tire bead is seated on the rim. In other examples, the depth information is determined while the damage tool is at the lowest susceptible height identified in step  810  above—h(T 1   j   _   low ). This means that some of the data required by process  900  could come from process  800 , thus reducing the total amount of tire testing required. In other examples, testing is performed while the height of the damage tool is fixed at a height corresponding to the lowest susceptible height identified in step  810  above plus some predetermined value. In other words, h(T 1   j   _   k ) for some k=h(T 1   j   _   low )+y, for some value of y (e.g., y=10 mm). 
     Once the depth values d(T 1   j   _   k ) and characteristic dimension values a j  for all types of tire features j=1, . . . , J are obtained at each test height k=1, . . . , K, per steps  905 - 915 , a second performance score (P 2   T1 ) that generally indicates the Sidewall Strength Performance for a tire can be electronically calculated in step  920  for the set of one or more test tires (T 1 ). More particularly, the second performance score (P 2   T1 ) for the plurality of test tires (T 1 ) can be calculated by the following equation: 
     
       
         
           
             
               
                 
                   
                     P 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       2 
                       
                         T 
                         ⁢ 
                         
                             
                         
                         ⁢ 
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                   = 
                   
                     
                       
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                                 a 
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                                     k 
                                     = 
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                                 ⁢ 
                                 
                                   d 
                                   ⁡ 
                                   
                                     ( 
                                     
                                       T 
                                       ⁢ 
                                       
                                           
                                       
                                       ⁢ 
                                       
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                         ] 
                       
                     
                     . 
                   
                 
               
               
                 
                   ( 
                   3 
                   ) 
                 
               
             
           
         
       
     
     In some embodiments of the above technology, the above parameter P 2   T1  is more meaningful when compared with a reference value. In some embodiments, such a reference value may correspond to a predetermined threshold identified as an Acceptable score for P 2 . In other embodiments, such a reference value corresponds to a similar sidewall strength performance parameter determined for a second set of tires including one or more reference or comparison tires. In other words, it may be useful to compare the first performance score (P 2   T1 ) to a similar performance score (P 2   T2 ) for one or more reference tires (T 2 ). In such instance, similar data obtained in steps  905 - 915  are obtained and averaged over all reference tires T 2  having characteristic dimensions b j  for all j=1, . . . , J such that P 2   T2  can be calculated by: 
     
       
         
           
             
               
                 
                   
                     P 
                     ⁢ 
                     
                         
                     
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                       2 
                       
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                         ⁢ 
                         
                             
                         
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                         2 
                       
                     
                   
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                     . 
                   
                 
               
               
                 
                   ( 
                   4 
                   ) 
                 
               
             
           
         
       
     
     In one example, P 2   T1  is related to P 2   T2  by calculating a global P 2  value (P 2   global ), where P 2   global =ΔP 2 =P 2   T1 −P 2   T2 . In another example, P 2   T1  is related to P 2   T2  by considering the percentage of the above ΔP 2  global score. In other words, (P 2   global )=ΔP 2 /P 2   T1 . 
     An example of the measured values used to obtain the second performance parameter (P 2 ) described relative to  FIG. 9  is represented by part of the exemplary data set shown in  FIGS. 6 and 7 . Again, the open circular data points in  FIGS. 6 and 7  represent measurements obtained for a first set of tires, test tires (T 1 ). The solid circular data points in  FIGS. 6 and 7  represent measurements obtained for a second set of tires, reference tires (T 2 ). 
     In the example of  FIGS. 6 and 7 , the total number of tire features (J) is two.  FIG. 6  illustrates data points (various height and depth combinations) for sidewall damage testing performed at a first type of tire feature—lugs (j=1), while  FIG. 7  illustrates data points for sidewall damage testing performed at a second type of tire feature—voids (j=2). In addition, the total number of test heights (K) at which a damage value d(T 1   j   _   k ) is obtained corresponds to two. In one example, the first test height (k=1) corresponds to the height of the rim (e.g., height  195  in  FIG. 5 ), and the second test height (k=2) corresponds to the lowest susceptible height at which a test tire experiences damage (T 1   j   _   low )+y, for some value of y (e.g., y=10 mm). 
     In particular, where j=1,2 and k=1,2, the data points measured in accordance with the particular example of  FIGS. 6 and 7  correspond to T 1   1   _   2 , T 1   2   _   2 , T 1   2   _   1 , and T 1   2   _   2  as well as T 2   1   _   2 , T 2   2   _   2 , T 2   2   _   1 , and T 2   2   _   2 . Again, the height and depth at each data point are typically available via sensing device  130  and position sensor  140  associated with testing apparatus  120 . However, the values from  FIG. 6  used in determining P 2   T1  and P 2   T2  will be d(T 1   1   _   1 ), d(T 1   1   _   2 ), d(T 2   1   _   1 ) and d(T 2   1   _   2 ). Similarly, the values from  FIG. 7  used in determining P 2   T1  and P 2   T2  will be d(T 1   2   _   1 ), d(T 1   2   _   2 ), d(T 2   2   _   1 ) and d(T 2   2   _   2 ). Characteristic dimensions a 1  and a 2  are also measured so that the formula for P 1  for the test tires (T 1 ) can be determined from equation (3) above as: 
               P   ⁢           ⁢     2     T   ⁢           ⁢   1         =         1       ∑     j   =   1     J     ⁢     a   j         ⁡     [       ∑     j   =   1     J     ⁢         a   j     K     ⁡     [       ∑     k   =   1     K     ⁢     d   ⁡     (     T   ⁢           ⁢     1     j   ⁢   _   ⁢   k         )         ]         ]       =               a   1     2     ⁡     [       d   ⁡     (     T   ⁢           ⁢     1     1   ⁢   _   ⁢   1         )       +     d   ⁡     (     T   ⁢           ⁢     1     1   ⁢   _   ⁢   2         )         ]       +         a   2     2     ⁡     [       d   ⁡     (     T   ⁢           ⁢     1     2   ⁢   _   ⁢   1         )       +     d   ⁡     (     T   ⁢           ⁢     1     2   ⁢   _   ⁢   2         )         ]             a   1     +     a   2         .             
Characteristic dimensions b 1  and b 2  are measured for the reference tires (T 2 ), so that the formula for P 2  for the reference tires (P 2   T2 ) can be similarly determined from equation (4) above as:
 
               P   ⁢           ⁢     2     T   ⁢           ⁢   2         =         1       ∑     j   =   1     J     ⁢     b   j         ⁡     [       ∑     j   =   1     J     ⁢         b   j     K     ⁡     [       ∑     k   =   1     K     ⁢     d   ⁡     (     T   ⁢           ⁢     2     j   ⁢   _   ⁢   k         )         ]         ]       =               b   1     2     ⁡     [       d   ⁡     (     T   ⁢           ⁢     2     1   ⁢   _   ⁢   1         )       +     d   ⁡     (     T   ⁢           ⁢     2     1   ⁢   _   ⁢   2         )         ]       +         b   2     2     ⁡     [       d   ⁡     (     T   ⁢           ⁢     2     2   ⁢   _   ⁢   1         )       +     d   ⁡     (     T   ⁢           ⁢     2     2   ⁢   _   ⁢   2         )         ]             b   1     +     b   2         .             
A meaningful result might compare the test and reference tires by determining a parameter P 2   global =ΔP 2 =P 2   T1 −P 2   T2 .
 
     In some embodiments of the present technology, it is also helpful to optionally provide one or more additional statistical parameters that help qualify the reliability of the exemplary performance parameters (e.g., P 1  and P 2 ). For example, the power of each test (Px) may be determined by the following formula: 
                       Power   Px     =       1   -   β     =     1   -     [         ζ   ⁢     N         2   *     σ     Px   ⁢           ⁢   global           -     α   2       ]           ,           (   5   )               
where ζ is the resolution of the test Px, α/2 is the Type I error rate, β is the Type II error rate, N is the total number of test tires (e.g., T 1 ) and σ Pxglobal  is the standard deviation of the calculated Px global  parameter calculated across the N different test tires. The Power Px  value can be reported to a user in order to provide the probability that the real difference in means is at least as big as the observed difference.
 
     The power of the test can help a user determine whether or not the chosen sample size used in a study that determines the parameters P 1  and/or P 2  described herein is ideal or should be modified in the future. For example, the strength of the data used in determining such parameters can be relayed in part by two sources of information—the Type I Error rate and the Type II Error rate, respectively. The Type I error rate is the probability that one falsely concludes a statistical difference, say between two averages, when there really is no statistical difference in the averages. This is analogous to a false positive. The Type II error rate is the probability that one falsely concludes no statistical difference, say between two averages, when there really is a statistical difference in the averages. This is analogous to a false negative. 
     Referring now to  FIG. 10 , exemplary apparatuses that may be used to implement various aspects of the disclosed methodology are now disclosed. It should be evident from the present disclosure that the subject methods are tied to a testing apparatus such as apparatus  120  shown in  FIGS. 1 and 5 . Specific components within apparatus  120  may provide electronic data that are used for subsequent electronic calculations. For example, the sensing device  130  and position sensor  140  may provide electronic data indicating the respective height and depth coordinates for different data points in a test procedure. Such electronic data may be relayed to a computer control system  610  for subsequent analysis in accordance with the steps disclosed herein. Any other additional data required for electronic processing (e.g., characteristic dimensions for each tire or set of tires, identification parameters, or other variables) may be provided to computer control system  610  via data input device  625 . Exemplary input devices may include but are not limited to a keyboard, touch-screen monitor, microphone, mouse and the like. 
     Computer control system  610  generally may include such components as at least one memory/media element or database for storing data and software instructions as well as at least one processor. In the particular example of  FIG. 10 , a processor(s)  615  and associated memory/media elements  620   a ,  620   b  and  620   c  are configured to perform a variety of computer-implemented functions (i.e., software-based data services), including the electronic calculation of the performance parameters described herein. At least one memory/media element (e.g., element  620   b  in  FIG. 10 ) is dedicated to storing software and/or firmware in the form of computer-readable and executable instructions that will be implemented by the one or more processor(s)  615 . Other memory/media elements (e.g., memory/media elements  620   a ,  620   c ) are used to store data which will also be accessible by the processor(s)  615  and which will be acted on per the software instructions stored in memory/media element  620   b . As such, computing/processing device(s)  615  may be adapted to operate as a special-purpose machine by executing the software instructions rendered in a computer-readable form stored in memory/media element  620   b . When software is used, any suitable programming, scripting, or other type of language or combinations of languages may be used to implement the teachings contained herein. In other embodiments, the methods disclosed herein may alternatively be implemented by hard-wired logic or other circuitry, including, but not limited to application-specific circuits. 
     The various memory/media elements of  FIG. 10  may be provided as a single or multiple portions of one or more varieties of non-transitory computer-readable media, such as but not limited to any combination of volatile memory (e.g., random access memory (RAM, such as DRAM, SRAM, etc.) and nonvolatile memory (e.g., ROM, flash, hard drives, magnetic tapes, CD-ROM, DVD-ROM, etc.) or any other memory devices including diskettes, drives, other magnetic-based storage media, optical storage media and others. Although  FIG. 10  shows three separate memory/media elements  620   a ,  620   b  and  620   c , the content dedicated to such devices may actually be stored in one memory/media element or in multiple elements, any such possible variations and other variations of data storage will be appreciated by one of ordinary skill in the art. 
     In one particular embodiment of the present subject matter, a first portion of memory/media  620   a  is configured to store input data for the subject sidewall performance parameter determination methods. Input data stored in memory/media element  620   a  may include raw measurement data obtained from sensing device  130  and position sensor  140  associated with apparatus  120  as well as characteristic dimensions measured for the various test tires. Second memory element  620   b  includes computer-executable software instructions that can be read and executed by processor(s)  615  to act on the data stored in memory/media element  620   a  to create new output data (e.g., performance parameters, alarm signals, graphical outputs and/or control signals for improving or modifying a set of tires) for storage in a third memory/media element  620   c . Such output data may be provided to info display  135  or to another peripheral output device  630 , such as monitor, printer or other device for visually depicting the output data, or as control signals to still further components. 
     Additional steps subsequent to the calculation of performance parameters via the system of  FIG. 10  include sorting or grading tires based on the determined performance parameters, modifying a tire by grinding, removing mass or adding mass to a tire, and/or changing one or more steps in the manufacturing process of a tire to improve the tires in response to the determined performance parameters. 
     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. For example, an exemplary method of the present invention has been described in which the vehicle was driven in reverse over a damage tool. However, the test could be performed driving the vehicle in a forward gear as well. 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 using the teachings disclosed herein.