Abstract:
A method for testing a tire of a vehicle that includes the steps of creating a first condition comprising a first slip angle of the tire, obtaining a first set of data regarding performance of the tire under the first condition, creating a second condition comprising either a second slip angle or lateral displacement of the tire, obtaining a second set of data regarding performance of the tire under the second condition, and determining the transient response of the lateral force and aligning moment of the tire, using the first set of data and the second set of data.

Description:
TECHNICAL FIELD 
     The present invention generally relates to the field of vehicles and, more specifically, to methods and systems for testing tires of vehicles to determine transient force and moment responses. 
     BACKGROUND OF THE INVENTION 
     For today&#39;s vehicles, tires are generally tested as they are designed and manufactured, along with various other points during the lifespan of the tire. For example, tires may be tested during the development of the tires or the vehicles to which the tires belong, for example to evaluate vehicular performance and use of the tires going forward and to further improve future tire composition. Typically, tires are tested under quasi-steady state conditions. However, in certain circumstances it may be desirable to conduct tests on tires in a manner that simulates dynamic conditions. 
     Accordingly, it is desirable to provide an improved method for conducting tests of tires of a vehicle that simulate dynamic conditions of the tire. It is also desirable to provide an improved program product for conducting such tire tests on vehicles. It is further desirable to provide an improved system for conducting such tire tests on vehicles. Furthermore, other desirable features and characteristics of the present invention will be apparent from the subsequent detailed description and the appended claims, taken in conjunction with the accompanying drawings and the foregoing technical field and background. 
     SUMMARY OF THE INVENTION 
     In accordance with an exemplary embodiment of the present invention, a method for testing a tire of a vehicle is provided. The method comprises the steps of creating a first condition comprising a first slip angle of the tire, obtaining a first set of data regarding performance of the tire under the first condition, creating a second condition comprising a second slip angle of the tire, obtaining a second set of data regarding performance of the tire under the second condition, and determining relationships of the forces and moments of the tire, using the first set of data and the second set of data. 
     In accordance with another exemplary embodiment of the present invention, a program product for testing a tire of a vehicle is provided. The program product comprises a program and a computer-readable signal bearing media. The program is configured to at least facilitate creating a first condition comprising a first slip angle of the tire, obtaining a first set of data regarding performance of the tire under the first condition, creating a second condition comprising a second slip angle of the tire, obtaining a second set of data regarding performance of the tire under the second condition, and determining the relationships of the forces and moments of the tire, using the first set of data and the second set of data. The computer-readable signal bearing media bears the program. 
     In accordance with a further exemplary embodiment of the present invention, a system for testing a tire of a vehicle is provided. The system comprises a memory and a processor. The memory is configured to store a program that is configured to at least facilitate creating a first condition comprising a first slip angle of the tire, obtaining a first set of data regarding performance of the tire under the first condition, creating a second condition comprising a second slip angle of the tire, obtaining a second set of data regarding performance of the tire under the second condition, and determining the relationships of the forces and moments of the tire, using the first set of data and the second set of data. The processor is coupled to the memory, and is configured to at least facilitate executing the program. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The present invention will hereinafter be described in conjunction with the following drawing figures, wherein like numerals denote like elements, and wherein: 
         FIG. 1  is a flowchart of a method for testing a tire of a vehicle, in accordance with an exemplary embodiment of the present invention; 
         FIG. 2  is a flowchart of a first test sequence, namely a yaw imposed test sequence, that can be used in connection with the method of  FIG. 1 , in accordance with an exemplary embodiment of the present invention; 
         FIG. 3  is a flowchart of a second test sequence, namely a side movement imposed via side velocity test sequence, that can be used in connection with the method of  FIG. 1 , in accordance with an exemplary embodiment of the present invention; 
         FIG. 4  is a flowchart of a third test sequence, namely a side movement imposed via lateral displacement test sequence, that can be used in connection with the method of  FIG. 1 , in accordance with an exemplary embodiment of the present invention; 
         FIG. 5  is a flowchart of a method for removing tire non-uniformity related force and moment variations, and that can be used in connection with the method of  FIG. 1 , in accordance with an exemplary embodiment of the present invention; 
         FIG. 6  is a flowchart of a data fitting method for fitting data to general functions with non-uniformity terms, and that can be used in connection with the method of  FIG. 1 , in accordance with an exemplary embodiment of the present invention; 
         FIG. 7  is an exemplary illustration of a tire and wheel test assembly and test machine, depicted along with representations of spin angle, lateral force, relative lateral displacement, relative slip angle, vertical load, loaded radius, direction of tire heading, and direction of tire travel pertaining to the process of  FIG. 1 , the first test sequence of  FIG. 2 , the second test sequence of  FIG. 3 , the third test sequence of  FIG. 4 , the non-uniformity removal method of  FIG. 5 , and the data fitting method of  FIG. 6 , in accordance with an exemplary embodiment of the present invention; 
         FIG. 8  is a functional block diagram of a computer and data acquisition system  800  for testing a tire of a vehicle, and that can be used in connection with the process of  FIG. 1 , the first test sequence of  FIG. 2 , the second test sequence of  FIG. 3 , the third test sequence of  FIG. 4 , the non-uniformity removal method of  FIG. 5 , and the data fitting method of  FIG. 6 , in accordance with another exemplary embodiment of the present invention; 
         FIG. 9  depicts lateral force and aligning moment general fit equations for use in the process of  FIG. 1 , in accordance with an exemplary embodiment of the present invention; and 
         FIG. 10  depicts lateral force and aligning moment general fit equations with non-uniformity terms for use in the process of  FIG. 1 , in accordance with an exemplary embodiment of the present invention. 
     
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     The following detailed description is merely exemplary in nature, and is not intended to limit the invention or the application and uses of the invention. Furthermore, there is no intention to be bound by any expressed or implied theory presented in the preceding technical field, background, brief summary or the following detailed description. 
       FIG. 1  is a flowchart of a process  100  for testing a tire of a vehicle, in accordance with an exemplary embodiment of the present invention. In the depicted embodiment, the process  100  begins with the step of mounting a tire and wheel test assembly on a test machine (step  102 ). A test sequence is then conducted for the tire and wheel assembly on the test machine while acquiring data (step  104 ). In all cases, relative movement, simulating forward travel on vehicle, between the tire and the roadbed is accomplished at low speeds, preferably in the range of 3-8 km/hr. In a preferred embodiment, the acquired data includes a lateral force, an aligning moment, and a distance travelled for the tire and wheel test assembly. Also in a preferred embodiment, data is not acquired during sequence steps in which the wheel test assembly is not rotating. 
     Various test sequences may be utilized in step  104  in various embodiments of the present invention. An exemplary first test sequence  200  comprises a yaw imposed test sequence, and is depicted in  FIG. 2  and described further below in connection therewith. An exemplary second test sequence  300  comprises a side movement imposed via side velocity test sequence, and is depicted in  FIG. 3  and described further below in connection therewith. An exemplary third test sequence  400  comprises a side movement imposed via lateral displacement test sequence, and is depicted in  FIG. 4  and described further below in connection therewith. 
     Next, in one preferred embodiment, the process proceeds along a first path  106 , and a lateral force (F y ) and an aligning moment (M z ) are fit to their respective general fit equations with non-uniformity terms (step  110 ). An exemplary embodiment of a data fitting method  600  for implementing step  110  is depicted in  FIG. 6  and described further below in connection therewith in accordance with an exemplary embodiment of the present invention. In addition,  FIG. 10  depicts the lateral force and aligning moment general fit equations for step  110  in accordance with a preferred embodiment. Specifically, as depicted in  FIG. 10 , in the distance-travelled domain, the lateral force equation for a transient function is set forth as follows: 
     
       
         
           
             
               
                 
                   
                     
                       
                         a 
                         3 
                       
                       ⁢ 
                       
                         
                           ⅆ 
                           3 
                         
                         
                           ⅆ 
                           
                             x 
                             3 
                           
                         
                       
                       ⁢ 
                       
                         F 
                         y 
                       
                     
                     + 
                     
                       
                         a 
                         2 
                       
                       ⁢ 
                       
                         
                           ⅆ 
                           2 
                         
                         
                           ⅆ 
                           
                             x 
                             2 
                           
                         
                       
                       ⁢ 
                       
                         F 
                         y 
                       
                     
                     + 
                     
                       
                         a 
                         1 
                       
                       ⁢ 
                       
                         ⅆ 
                         
                           ⅆ 
                           x 
                         
                       
                       ⁢ 
                       
                         F 
                         y 
                       
                     
                     + 
                     
                       F 
                       y 
                     
                   
                   = 
                   
                     
                       b 
                       0 
                     
                     ⁢ 
                     
                       α 
                       ⁡ 
                       
                         ( 
                         x 
                         ) 
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     1 
                   
                   ) 
                 
               
             
           
         
       
     
     Also as depicted in  FIG. 10 , in the distance-travelled domain, the lateral force equation including non-uniformities is set forth as follows: 
     
       
         
           
             
               
                 
                   
                     F 
                     
                       y 
                       , 
                       measured 
                     
                   
                   = 
                   
                     
                       F 
                       y 
                     
                     + 
                     
                       
                         ∑ 
                         
                           n 
                           = 
                           1 
                         
                         N 
                       
                       ⁢ 
                       
                         
                           c 
                           n 
                         
                         ⁢ 
                         
                           cos 
                           ⁡ 
                           
                             ( 
                             
                               n 
                               ⁡ 
                               
                                 ( 
                                 
                                   θ 
                                   - 
                                   
                                     θ 
                                     cn 
                                   
                                 
                                 ) 
                               
                             
                             ) 
                           
                         
                       
                     
                   
                 
               
               
                 
                   
                     ( 
                     
                       Equation 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       2 
                     
                     ) 
                   
                   ⁢ 
                   
                       
                   
                 
               
             
           
         
       
     
     In addition, in the distance travelled domain, the aligning moment equation for a transient function is set forth as follows: 
     
       
         
           
             
               
                 
                   
                     
                       
                         g 
                         3 
                       
                       ⁢ 
                       
                         
                           ⅆ 
                           3 
                         
                         
                           ⅆ 
                           
                             x 
                             3 
                           
                         
                       
                       ⁢ 
                       
                         M 
                         z 
                       
                     
                     + 
                     
                       
                         g 
                         2 
                       
                       ⁢ 
                       
                         
                           ⅆ 
                           2 
                         
                         
                           ⅆ 
                           
                             x 
                             2 
                           
                         
                       
                       ⁢ 
                       
                         M 
                         z 
                       
                     
                     + 
                     
                       
                         g 
                         1 
                       
                       ⁢ 
                       
                         ⅆ 
                         
                           ⅆ 
                           x 
                         
                       
                       ⁢ 
                       
                         M 
                         z 
                       
                     
                     + 
                     
                       M 
                       z 
                     
                   
                   = 
                   
                     
                       
                         h 
                         3 
                       
                       ⁢ 
                       
                         
                           ⅆ 
                           3 
                         
                         
                           ⅆ 
                           
                             x 
                             3 
                           
                         
                       
                       ⁢ 
                       
                         α 
                         ⁡ 
                         
                           ( 
                           x 
                           ) 
                         
                       
                     
                     + 
                     
                       
                         h 
                         2 
                       
                       ⁢ 
                       
                         
                           ⅆ 
                           2 
                         
                         
                           ⅆ 
                           
                             x 
                             2 
                           
                         
                       
                       ⁢ 
                       
                         α 
                         ⁡ 
                         
                           ( 
                           x 
                           ) 
                         
                       
                     
                     + 
                     
                       
                         h 
                         1 
                       
                       ⁢ 
                       
                         ⅆ 
                         
                           ⅆ 
                           x 
                         
                       
                       ⁢ 
                       
                         α 
                         ⁡ 
                         
                           ( 
                           x 
                           ) 
                         
                       
                     
                     + 
                     
                       
                         h 
                         0 
                       
                       ⁢ 
                       
                         α 
                         ⁡ 
                         
                           ( 
                           x 
                           ) 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     3 
                   
                   ) 
                 
               
             
           
         
       
     
     Also, in the distance travelled domain, the aligning moment equation including non-uniformities is set forth as follows 
     
       
         
           
             
               
                 
                   
                     M 
                     
                       z 
                       , 
                       measured 
                     
                   
                   = 
                   
                     
                       M 
                       z 
                     
                     + 
                     
                       
                         ∑ 
                         
                           n 
                           = 
                           1 
                         
                         N 
                       
                       ⁢ 
                       
                         
                           d 
                           n 
                         
                         ⁢ 
                         
                           cos 
                           ⁡ 
                           
                             ( 
                             
                               n 
                               ⁡ 
                               
                                 ( 
                                 
                                   θ 
                                   - 
                                   
                                     θ 
                                     dn 
                                   
                                 
                                 ) 
                               
                             
                             ) 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     4 
                   
                   ) 
                 
               
             
           
         
       
     
     Also as depicted in  FIG. 10 , in the spatial frequency domain, the lateral force equation is set forth as follows: 
                       F   y     ⁡     (   s   )       =           b   0           a   3     ⁢     s   3       +       a   2     ⁢     s   2       +       a   1     ⁢   s     +   1       ⁢     α   ⁡     (   s   )         +       ∑     n   =   1     N     ⁢       c   n     ·     ⅇ     ⅈ   ·   n   ·     θ   cn         ·     δ   ⁡     (     ω   -     n   ·     ω   0         )                     (     Equation   ⁢           ⁢   5     )               
For practical implementation, this and subsequent equations can be used with conveniently selected tire-rotation synchronized sampling.
 
     In addition, in the spatial frequency domain, the aligning moment equation is set forth as follows: 
     
       
         
           
             
               
                 
                   
                     
                       M 
                       z 
                     
                     ⁡ 
                     
                       ( 
                       s 
                       ) 
                     
                   
                   = 
                   
                     
                       
                         
                           
                             
                               h 
                               3 
                             
                             ⁢ 
                             
                               s 
                               3 
                             
                           
                           + 
                           
                             
                               h 
                               2 
                             
                             ⁢ 
                             
                               s 
                               2 
                             
                           
                           + 
                           
                             
                               h 
                               1 
                             
                             ⁢ 
                             s 
                           
                           + 
                           
                             h 
                             0 
                           
                         
                         
                           
                             
                               g 
                               3 
                             
                             ⁢ 
                             
                               s 
                               3 
                             
                           
                           + 
                           
                             
                               g 
                               2 
                             
                             ⁢ 
                             
                               s 
                               2 
                             
                           
                           + 
                           
                             
                               g 
                               1 
                             
                             ⁢ 
                             s 
                           
                           + 
                           1 
                         
                       
                       ⁢ 
                       
                         α 
                         ⁡ 
                         
                           ( 
                           s 
                           ) 
                         
                       
                     
                     + 
                     
                       
                         ∑ 
                         
                           n 
                           = 
                           1 
                         
                         N 
                       
                       ⁢ 
                       
                         
                           d 
                           n 
                         
                         · 
                         
                           ⅇ 
                           
                             ⅈ 
                             · 
                             n 
                             · 
                             
                               θ 
                               dn 
                             
                           
                         
                         · 
                         
                           δ 
                           ⁡ 
                           
                             ( 
                             
                               ω 
                               - 
                               
                                 n 
                                 · 
                                 
                                   ω 
                                   0 
                                 
                               
                             
                             ) 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     6 
                   
                   ) 
                 
               
             
           
         
       
     
     Care must be exercised in estimates for the coefficients of the non-uniformities in the above equations in order to assure convergence of solution. Coefficients for these terms, especially those of phase, must be sufficiently near representative values for the test tire. Use of arbitrary initial estimates can result in divergence of the fitting techniques, and is well known to those skilled in the art. 
     By way of reference, In Equations 1-6 above:
         F y =Lateral Force from Tire Transient Response (N)   F y,measured =Measured Lateral Force with Non-Uniformity and Tire Transient Response (N)   M z =Aligning Moment from Tire Transient Response (Nm)   M z,measured =Measured Aligning Moment with Non-Uniformity and Tire Transient Response (Nm)   α=Tire Slip Angle (deg)   s=Spatial Frequency, ω (rad/m) times (−i), where i=square-root(−1)   ω 0 =First Harmonic Spatial Frequency of Assembly (rad/m)   n=Harmonics of Assembly (n=1, 2, . . . N)   N=Highest Assembly Harmonic accounted for in non-uniformity   a j , b 0 , g j , h j  are all scalar coefficients in which j=0, 1, 2, 3   c n , θ cn , d n , θ dn  are all scalar coefficients in which n=1, . . . N   δ=Delta function   x=Distance travelled (m)   θ=Angular orientation of tire (radians)       

     Returning now to  FIG. 1 , in an alternate preferred embodiment, the process may proceed instead along a second path  108 , in which assembly non-uniformities are removed from lateral force (Fy) and aligning moment (Mz) data (step  112 ). This is accomplished, for example, by referencing Equations (2) &amp; (4), and assuming superposition of invariant non-uniformities throughout the individual test condition. An exemplary non-uniformity removal method  500  for removing these non-uniformities is depicted in  FIG. 5  and described further below in connection therewith. 
     The lateral force and aligning moment are then fit to their respective general fit equations (step  114 ).  FIG. 9  depicts the lateral force and aligning moment general fit equations for step  114  in accordance with a preferred embodiment. Specifically, as depicted in  FIG. 9 , in the distance-travelled domain, the lateral force equation is set forth as follows: 
     
       
         
           
             
               
                 
                   
                     
                       
                         a 
                         3 
                       
                       ⁢ 
                       
                         
                           ⅆ 
                           3 
                         
                         
                           ⅆ 
                           
                             x 
                             3 
                           
                         
                       
                       ⁢ 
                       
                         F 
                         y 
                       
                     
                     + 
                     
                       
                         a 
                         2 
                       
                       ⁢ 
                       
                         
                           ⅆ 
                           2 
                         
                         
                           ⅆ 
                           
                             x 
                             2 
                           
                         
                       
                       ⁢ 
                       
                         F 
                         y 
                       
                     
                     + 
                     
                       
                         a 
                         1 
                       
                       ⁢ 
                       
                         ⅆ 
                         
                           ⅆ 
                           x 
                         
                       
                       ⁢ 
                       
                         F 
                         y 
                       
                     
                     + 
                     
                       F 
                       y 
                     
                   
                   = 
                   
                     
                       b 
                       0 
                     
                     ⁢ 
                     
                       α 
                       ⁡ 
                       
                         ( 
                         x 
                         ) 
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     7 
                   
                   ) 
                 
               
             
           
         
       
     
     In addition, in the distance travelled domain, the aligning moment equation is set forth as follows: 
     
       
         
           
             
               
                 
                   
                     
                       
                         g 
                         3 
                       
                       ⁢ 
                       
                         
                           ⅆ 
                           3 
                         
                         
                           ⅆ 
                           
                             x 
                             3 
                           
                         
                       
                       ⁢ 
                       
                         M 
                         z 
                       
                     
                     + 
                     
                       
                         g 
                         2 
                       
                       ⁢ 
                       
                         
                           ⅆ 
                           2 
                         
                         
                           ⅆ 
                           
                             x 
                             2 
                           
                         
                       
                       ⁢ 
                       
                         M 
                         z 
                       
                     
                     + 
                     
                       
                         g 
                         1 
                       
                       ⁢ 
                       
                         ⅆ 
                         
                           ⅆ 
                           x 
                         
                       
                       ⁢ 
                       
                         M 
                         z 
                       
                     
                     + 
                     
                       M 
                       z 
                     
                   
                   = 
                   
                     
                       
                         h 
                         3 
                       
                       ⁢ 
                       
                         
                           ⅆ 
                           3 
                         
                         
                           ⅆ 
                           
                             x 
                             3 
                           
                         
                       
                       ⁢ 
                       
                         α 
                         ⁡ 
                         
                           ( 
                           x 
                           ) 
                         
                       
                     
                     + 
                     
                       
                         h 
                         2 
                       
                       ⁢ 
                       
                         
                           ⅆ 
                           2 
                         
                         
                           ⅆ 
                           
                             x 
                             2 
                           
                         
                       
                       ⁢ 
                       
                         α 
                         ⁡ 
                         
                           ( 
                           x 
                           ) 
                         
                       
                     
                     + 
                     
                       
                         h 
                         1 
                       
                       ⁢ 
                       
                         ⅆ 
                         
                           ⅆ 
                           x 
                         
                       
                       ⁢ 
                       
                         α 
                         ⁡ 
                         
                           ( 
                           x 
                           ) 
                         
                       
                     
                     + 
                     
                       
                         h 
                         0 
                       
                       ⁢ 
                       
                         α 
                         ⁡ 
                         
                           ( 
                           x 
                           ) 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     8 
                   
                   ) 
                 
               
             
           
         
       
     
     Also as depicted in  FIG. 9 , in the spatial frequency domain, the lateral force equation is set forth as follows: 
     
       
         
           
             
               
                 
                   
                     
                       F 
                       y 
                     
                     ⁡ 
                     
                       ( 
                       s 
                       ) 
                     
                   
                   = 
                   
                     
                       
                         b 
                         0 
                       
                       
                         
                           
                             a 
                             3 
                           
                           ⁢ 
                           
                             s 
                             3 
                           
                         
                         + 
                         
                           
                             a 
                             2 
                           
                           ⁢ 
                           
                             s 
                             2 
                           
                         
                         + 
                         
                           
                             a 
                             1 
                           
                           ⁢ 
                           s 
                         
                         + 
                         1 
                       
                     
                     ⁢ 
                     
                       α 
                       ⁡ 
                       
                         ( 
                         s 
                         ) 
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     9 
                   
                   ) 
                 
               
             
           
         
       
     
     In addition, in the spatial frequency domain, the aligning moment equation is set forth as follows: 
     
       
         
           
             
               
                 
                   
                     
                       M 
                       z 
                     
                     ⁡ 
                     
                       ( 
                       s 
                       ) 
                     
                   
                   = 
                   
                     
                       
                         
                           
                             h 
                             3 
                           
                           ⁢ 
                           
                             s 
                             3 
                           
                         
                         + 
                         
                           
                             h 
                             2 
                           
                           ⁢ 
                           
                             s 
                             2 
                           
                         
                         + 
                         
                           
                             h 
                             1 
                           
                           ⁢ 
                           s 
                         
                         + 
                         
                           h 
                           0 
                         
                       
                       
                         
                           
                             g 
                             3 
                           
                           ⁢ 
                           
                             s 
                             3 
                           
                         
                         + 
                         
                           
                             g 
                             2 
                           
                           ⁢ 
                           
                             s 
                             2 
                           
                         
                         + 
                         
                           
                             g 
                             1 
                           
                           ⁢ 
                           s 
                         
                         + 
                         1 
                       
                     
                     ⁢ 
                     
                       α 
                       ⁡ 
                       
                         ( 
                         s 
                         ) 
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     10 
                   
                   ) 
                 
               
             
           
         
       
     
     In Equations 7-10 above, F y  denotes lateral force (N), M z  represents aligning moment (Nm), s represents the product of spatial frequency (rad/m) times i, where i=square-root(−1), and a n , b 0 , g n , each represent scalar coefficients in which n=0, 1, 2, 3. In a preferred embodiment, the same general fit equations are utilized in step  114  as in step  110  discussed above. 
     Returning again to  FIG. 1 , next, regardless of whether the process is following the first path  106  or the second path  108 , reduced fit coefficients are generated in order to obtain tire transient metrics (step  116 ). The tire transient metrics can then be used to quantify and/or improve the tire and/or the manufacture and/or use thereof (step  118 ). It will be appreciated that certain steps of the process  100  of  FIG. 1  may vary from those depicted in  FIG. 1  and/or described herein in connection therewith. It will similarly be appreciated that certain of the steps of the process  100  of  FIG. 1  may occur simultaneously or in a different order than that depicted in  FIG. 1  and/or described herein. 
       FIG. 2  is a flowchart of the above-referenced first test sequence  200  that can be used in implementing step  104  of the process  100  of  FIG. 1 , in accordance with an exemplary embodiment of the present invention. As noted above, the first test sequence comprises a yaw imposed test sequence. 
     In the depicted embodiment, the first test sequence  200  begins with the step of setting the mounted tire and wheel test assembly&#39;s vertical load (F z ) or Loaded Radius (RL) along with the slip angle (α) (step  202 ). The above-referenced data acquisition of step  104  of  FIG. 1  is begun (step  204 ), and the tire and wheel test assembly is rolled on the test machine until a steady state equilibrium is established (step  206 ). 
     Then, in one preferred embodiment, the process proceeds along a first path  208  following step  206 . As part of the first path  208 , the forward movement of the tire and wheel test assembly is stopped while data acquisition continues (step  212 ). The tire and wheel test assembly is then rapidly steered to a new slip angle (step  214 ). The tire and wheel test assembly is then rolled on the test machine until a steady state equilibrium is reached (step  216 ). The data acquired during stopped movement of the of the tire and wheel test assembly is then removed (step  218 ). 
     In another preferred embodiment, the process proceeds instead along a second path  210  following step  206 . As part of the second path  210 , forward movement of the tire and wheel test assembly is stopped, and the data acquisition is also stopped (step  220 ). The tire and wheel test assembly is then steered rapidly to a new slip angle (step  222 ). Data acquisition is then restarted (step  223 ). The tire and wheel test assembly is then rolled on the test machine until a steady state equilibrium is reached (step  226 ). 
       FIG. 3  is a flowchart of the above-referenced second test sequence  300  that can be used in implementing step  104  of the process  100  of  FIG. 1 , in accordance with an exemplary embodiment of the present invention. As noted above, the second test sequence comprises a side movement imposed via the side velocity test sequence. 
     In the depicted embodiment, the second test sequence  300  begins with the step of setting the mounted tire and wheel test assembly&#39;s slip angle while the tire and wheel test assembly is unloaded (step  302 ). The tire and wheel test assembly&#39;s vertical load (F z ) is then set (step  304 ). The above-referenced data acquisition of step  104  of  FIG. 1  is begun (step  306 ), and the tire and wheel test assembly is rolled on the test machine until a steady state equilibrium is established (step  308 ). 
     Forward movement of the tire and wheel test assembly is stopped, and the data acquisition is also stopped (step  310 ). The vertical load (F z ) is set equal to zero (step  312 ), and care is taken to make sure that there is no contact with the test machine surface. The tire and wheel test assembly is then steered to a new slip angle (step  314 ), and the tire and wheel test assembly&#39;s vertical load (Fz) is set (step  316 ). The above-referenced data acquisition of step  104  of  FIG. 1  then begins again (step  318 ). The tire and wheel test assembly is then rolled again on the test machine until a steady state equilibrium is again reached (step  320 ). 
       FIG. 4  is a flowchart of the above-referenced third test sequence  400  that can be used in implementing step  104  of the process  100  of  FIG. 1 , in accordance with an exemplary embodiment of the present invention. As noted above, the third test sequence comprises a side movement imposed via lateral displacement test sequence. 
     In the depicted embodiment, the third test sequence  400  begins with the step of setting the mounted tire and wheel test assembly&#39;s vertical load (F z ) and slip angle (α) (step  402 ). The above-referenced data acquisition of step  104  of  FIG. 1  is begun (step  404 ), and the tire and wheel test assembly is rolled on the test machine until a steady state equilibrium is established (step  406 ). Forward movement of the tire and wheel test assembly is stopped, and the data acquisition is also stopped (step  408 ). The tire and wheel assembly is then displaced rapidly to a new lateral position (step  410 ). The above-referenced data acquisition of step  104  of  FIG. 1  then begins again (step  412 ). The tire and wheel test assembly is then rolled again to resume movement on the test machine until a steady state equilibrium is again reached (step  414 ). 
       FIG. 5  is a flowchart of a non-uniformity removal method  500  for removing tire uniformity that can be used in implementing step  112  of the process  100  of  FIG. 1 , in accordance with an exemplary embodiment of the present invention. In the depicted embodiment, the non-uniformity removal method  500  is performed for each nominal vertical load (F z ) and slip angle (α) at which the tire and wheel test assembly is tested. For each such nominal vertical load (F z ) and slip angle (α), the mounted tire and wheel test assembly&#39;s vertical load (F z ) and slip angle (α) are set accordingly (step  502 ). The tire and wheel test assembly is then rolled on the test machine until a steady state equilibrium is reached (step  504 ). Data acquisition is begun (step  506 ). A lateral force (F y ), an aligning moment (M z ), and a spindle angle (θ) are then each measured for a predetermined number of revolutions (step  508 ). 
     Then, in one preferred embodiment, the non-uniformity removal method  500  continues along a first path  512  after step  510 . During the first path  512 , initial estimates are determined of coefficients for non-uniformity terms in the general response equations (step  516 ). In a preferred embodiment, these initial estimates of the coefficients for the non-uniformity terms are determined using a fast Fourier transform (FFT) on the acquired data. Also in a preferred embodiment, the above-described lateral force (Fy) and aligning moment (Mz) general fit equations with non-uniformity terms of  FIG. 10  are preferably utilized in this step. 
     In an alternate preferred embodiment, the non-uniformity removal method  500  continues along a second path  514  after step  510 . During the second path  514 , the uniformity functions of the tire and wheel assembly are determined (step  518 ). Preferably uniformity functions are determined using piece-wise analysis of the steady state data and the above-described equations of  FIG. 9 . In addition, in certain embodiments, the steady state data before, during and after the steer event may be used to determine the uniformity functions either separately or averaged together using one or more weighting techniques (step  520 ). The functions are then subtracted from any data measured on the tire and wheel test assembly at this specific nominal vertical load (F z ) and slip angle (α) condition (step  522 ). In the case of non-uniformities that are substantial and significantly contaminating the transient evaluation, other methods may be likewise employed to minimize these interferences. One such method involves multiple transient test runs each starting at different angular orientations of the tire resulting in asynchronous superposition of the two sources, viz, non-uniformities and the transient responses. Decomposition of the two constituent responses from these multiple test runs is then possible by suitable synchronous averaging techniques known and practiced by those skilled in the art in other analogous applications. 
     Initial estimates are determined for non-uniformity terms in the general response equations (step  516 ). In a preferred embodiment, these initial estimates of the coefficients for the non-uniformity terms are determined using a fast Fourier transform (FFT) on the acquired data. Also in a preferred embodiment, the above-described lateral force (Fy) and aligning moment (Mz) general fit equations with non-uniformity terms of  FIG. 10  are preferably utilized in this step. 
       FIG. 6  is a flowchart of a data fitting method  600  for fitting data to general functions with non-uniformity terms, and that can be used in implementing step  110  of the process  100  of  FIG. 1 , in accordance with an exemplary embodiment of the present invention. In the depicted embodiment, the data fitting method  600  begins with use of coefficient estimates obtained from previous analyses as an initial coefficients guess (step  602 ). 
     Response values are then calculated from the appropriate general transient function from  FIG. 10  (step  604 ). Response values are then also calculated from the appropriate general non-uniformity function from  FIG. 10  (step  606 ). 
     The response values from the general functions are then added together (step  608 ), and the response values from the measured values are then subtracted in order to obtain error values (step  610 ). All of the error values are then squared and added together (step  612 ), and the summed square error value is compared with the value of the summed square error value in a prior iteration (step  614 ). 
     A determination is then made as to whether the summed squared error value has decreased below a predetermined threshold (step  616 ). If it is determined that the summed squared error value has not decreased below the predetermined threshold, then the coefficients are modified accordingly (step  618 ), and the process returns to step  604 . Steps  604 - 618  then repeat with iterations until a determination is made in a subsequent iteration of step  616  that the summed squared error value has decreased below the predetermined threshold. Once it is determined in any iteration of step  616  that the summed squared error value has decreased below a predetermined threshold, the data fitting method  600  is deemed to be complete. Many such iterative techniques, commonly referred to as “Minimization” or “Least-Squares” approaches are available, recognized by those skilled in the art, and can be implemented in this step. 
       FIG. 7  depicts, for further ease of reference, an illustration  700  of the tire and wheel test assembly  702  and the test machine  704  referenced in  FIGS. 1-6  above, in accordance with an exemplary embodiment of the present invention.  FIG. 7  also depicts spin angle (θ)  706 , lateral force (F y )  708 , relative lateral displacement (Y)  709 , relative slip angle (α)  710 , vertical load (Fz)  712 , loaded radius (RL)  713 , direction of tire heading  714 , and direction of tire travel  716 , as also referenced in  FIGS. 1-6 . Further definition of these terms may be found in the Society of Automotive Engineers (SAE) standards document J670. 
       FIG. 8  is a functional block diagram of a computer and data acquisition system  800  for testing a tire of a vehicle, that can be used in connection with the process  100  of  FIG. 1 , the first test sequence  200  of  FIG. 2 , the second test sequence  300  of  FIG. 3 , the third test sequence  400  of  FIG. 4 , the non-uniformity removal method  500  of  FIG. 5 , and the data fitting method  600  of  FIG. 6 , in accordance with another exemplary embodiment of the present invention. 
     In the embodiment depicted in  FIG. 8 , the computer and data acquisition system  800  includes a central processing unit or processor  802 , a random access memory  804 , a read only memory  806 , a computer bus  810 , and a storage device  808 . The central processing unit or processor  802  performs the computation and control functions of the computer and data acquisition system  800  or portions thereof, preferably in executing a program  807  that performs the steps of the process  100  of  FIG. 1 , the first test sequence  200  of  FIG. 2 , the second test sequence  300  of  FIG. 3 , the third test sequence  400  of  FIG. 4 , the non-uniformity removal method  500  of  FIG. 5 , and the data fitting method  600  of  FIG. 6  and described above in connection therewith. 
     The central processing unit or processor  802  may comprise any type of processor or multiple processors, single integrated circuits such as a microprocessor, or any suitable number of integrated circuit devices and/or circuit boards working in cooperation to accomplish the functions of a processing unit. During operation, the central processing unit or processor  802  executes one or more programs  807  preferably stored within the random access memory  804  and, as such, controls the general operation of the computer and data acquisition system  800 . 
     The read only memory  806  stores a program or programs  807  that execute one or more embodiments of processes such as the steps of the process  100  of  FIG. 1 , the first test sequence  200  of  FIG. 2 , the second test sequence  300  of  FIG. 3 , the third test sequence  400  of  FIG. 4 , the non-uniformity removal method  500  of  FIG. 5 , and the data fitting method  600  of  FIG. 6  and described above in connection therewith. 
     The random access memory  804  can be any type of suitable memory. This would include various types of dynamic random access memory (DRAM) such as SDRAM (synchronous DRAM), various types of static RAM (SRAM-static random access memory), and various types of non-volatile memory (PROM-programmable read only memory, EPROM-erasable programmable read only memory, and flash). 
     The computer bus  810  serves to transmit programs, data, status, and other information or signals between the various components of the computer and data acquisition system  800 . The computer bus  810  can be any suitable physical or logical means of connecting computer systems and components. This includes, but is not limited to, direct hard-wired connections, fiber optics, and infrared and wireless bus technologies. 
     The storage device  808  can be any suitable type of storage apparatus, including direct access storage devices such as hard disk drives, flash systems, floppy disk drives and optical disk drives. In one exemplary embodiment, the storage device  808  is a program product from which read only memory  806  can receive a program  807  that executes (and/or that the central processing unit or processor  802  executes and/or causes to execute) one or more embodiments of the process  100  of  FIG. 1 , the first test sequence  200  of  FIG. 2 , the second test sequence  300  of  FIG. 3 , the third test sequence  400  of  FIG. 4 , the non-uniformity removal method  500  of  FIG. 5 , and the data fitting method  600  of  FIG. 6  and described above in connection therewith. As one exemplary implementation, the computer and data acquisition system  800  may also utilize an Internet website, for example for providing, storing, or maintaining data or performing operations thereon. 
     In addition, as shown in  FIG. 8 , in certain embodiments the computer and data acquisition system  800  also includes a converter  815 . In certain embodiments, the converter  815  receives analog signals from the test machine and converts the analog signals to digital signals for use by the computer and data acquisition system  800 . Those skilled in the art also recognize the need for protecting the acquired data from such effects commonly referred to as “Aliasing”. Protection analog circuits, over-sampling, or other methods can be used to avoid Aliasing. Aliasing is the contamination of data that occurs when signal content exists at frequencies in excess of a threshold frequency. The establishment of threshold frequencies includes setting an upper limit for acceptable signal content by frequency, said frequency being related to the sampling frequency. These techniques are known to those skilled in the art and need to be considered for successful implementation. 
     It will be appreciated that while this exemplary embodiment is described in the context of a fully functioning computer system, those skilled in the art will recognize that the mechanisms of the present invention are capable of being distributed as a program product in a variety of forms, and that the present invention applies equally regardless of the particular type of computer-readable signal bearing media used to carry out the distribution. Examples of signal bearing media include: recordable media such as floppy disks, hard drives, memory cards and optical disks, and transmission media such as digital and analog communication links. It will similarly be appreciated that the computer and data acquisition system  800  may also otherwise differ from the embodiment depicted in  FIG. 8 , for example in that the computer and data acquisition system  800  may be coupled to or may otherwise utilize one or more remote computer systems and/or other control systems. 
     It will likewise be appreciated that the process  100  of  FIG. 1 , the first test sequence  200  of  FIG. 2 , the second test sequence  300  of  FIG. 3 , the third test sequence  400  of  FIG. 4 , the non-uniformity removal method  500  of  FIG. 5 , and the data fitting method  600  of  FIG. 6 , the computer and data acquisition system  800  and associated program products and programs of  FIG. 8 , and/or the parts and/or components thereof, may vary in various embodiments of the present invention. 
     Accordingly, improved methods, program products, and systems are provided for testing tires of vehicles. The improved methods, program products, and systems allow for improved testing of tires under dynamic conditions. Specifically, the improved methods, program, products, and systems provide for determination of relationships between tire forces and moments under different slip angles for the tire. This allows for improved testing of tires as well as improved fine-tuning of how the particular types of tires are manufactured, how the tires are aligned, managed, controlled, and/or utilized in the vehicle, how and when the tires are maintained, and/or how and when the tires are replaced, among other possible applications of the methods, program products, and systems provided herein. 
     It will be appreciated that, in various embodiments, the disclosed methods, program products, and systems may vary from those depicted in the figures and described herein. For example, the imposition of slip angles and lateral displacements are described in the preceding as movements of the tire; the relevant conditions, however, are only relative movements between the tire and the roadbed. Such relative motions can also be achieved with stationary wheel spindles and articulated roadbeds, thereby achieving equivalent imposed conditions between the tire and the roadbed by movements of the roadbed and not the tire. Any combination of tire and roadbed movements, furthermore, can also be implemented in order to achieve the equivalent conditions of relative movements. It will similarly be appreciated that, while the disclosed methods, program products, and systems are described above as being used in connection with automobiles such as sedans, trucks, vans, sports utility vehicles, and cross-over vehicles, the disclosed methods, program products, and systems may also used in connection with any number of different types of vehicles, and in connection with any number of different systems thereof and environments pertaining thereto. 
     While at least one exemplary embodiment has been presented in the foregoing detailed description, it should be appreciated that a vast number of variations exist. It should also be appreciated that the exemplary embodiment or exemplary embodiments are only examples, and are not intended to limit the scope, applicability, or configuration of the invention in any way. Rather, the foregoing detailed description will provide those skilled in the art with a convenient road map for implementing the exemplary embodiment or exemplary embodiments. It should be understood that various changes can be made in the function and arrangement of elements without departing from the scope of the invention as set forth in the appended claims and the legal equivalents thereof.