Patent Publication Number: US-2016236431-A1

Title: Improvement of the Uniformity of a Tire Using Estimation of Transient Effects

Description:
FIELD 
     The present disclosure relates generally to systems and methods for improving tire uniformity, and more particularly to systems and methods for identifying contributions to tire uniformity from transient uniformity effects that evolve over time to obtain uniformity improvement. 
     BACKGROUND 
     Tire non-uniformity relates to the symmetry (or lack of symmetry) relative to the tire&#39;s axis of rotation in certain quantifiable characteristics of a tire. Conventional tire building methods unfortunately have many opportunities for producing non-uniformities in tires. During rotation of the tires, non-uniformities present in the tire structure produce periodically-varying forces at the wheel axis. Tire non-uniformities are important when these force variations are transmitted as noticeable vibrations to the vehicle and vehicle occupants. These forces are transmitted through the suspension of the vehicle and may be felt in the seats and steering wheel of the vehicle or transmitted as noise in the passenger compartment. The amount of vibration transmitted to the vehicle occupants has been categorized as the “ride comfort” or “comfort” of the tires. 
     Tire uniformity characteristics, or attributes, are generally categorized as dimensional or geometric variations (radial run out (RRO) and lateral run out (LRO)), mass variance, and rolling force variations (radial force variation, lateral force variation and tangential force variation, sometimes also called longitudinal or fore and aft force variation). Uniformity measurement machines often measure the above and other uniformity characteristics by measuring force at a number of points around a tire as the tire is rotated about its axis. 
     Many different factors can contribute to the presence of uniformity characteristics in tires. Uniformity dispersions in tires can result from both tire harmonic uniformity effects and process harmonic uniformity effects. Tire harmonic uniformity effects have periods of variation that coincide with the tire circumference (e.g. fit an integer number of times within the tire circumference). Tire harmonic uniformity effects can be attributable to tread joint width, out-of-roundness of the building drums, curing press effects, and other effects. Process harmonic uniformity effects have periods of variation that do not coincide with the tire circumference. Process harmonic effects are generally related to process elements rather than tire circumference. Typical process harmonic effects can be caused, for instance, in the preparation of a semi-finished product (e.g. a tread band), by thickness variations due to the extruder control system or by rollers that can deform the shape of softer products. The impact of the process harmonic effect can change from tire to tire depending on the rate of introduction of the process harmonic effect relative to the tire circumference. 
     Certain factors can contribute to transient uniformity effects that evolve over time. Because transient effects can have characteristics, (e.g., frequency of introduction, amplitude, and phase angle of maximum amplitude, etc.), that evolve over time, transient effects can be different from a process harmonic effect for which only the impact of the process harmonic changes from tire to tire. For instance, a curing membrane used during a curing process can contribute to tire harmonic uniformity effects on the uniformity of a tire, similar to a building drum. However, the actual effect of the curing membrane can be expected to change throughout its curing history. This change can be attributable to, for instance, a membrane joint that changes with each cure. Similar dynamic effects can be imparted through flexible and inflatable tooling elements, such as tire building drums and rollers. 
     It can be difficult to physically measure the time changing effects contributing to tire uniformity during a tire manufacturing process. Moreover, transient effects can share some characteristics with fixed tooling elements and some characteristics with process harmonics. As a result, current techniques for identifying and analyzing tire harmonics and/or process harmonics may not adequately identify or address transient effects. 
     Thus, a need exists for a system and method that can be used to improve the uniformity of a tire using estimation of transient uniformity effects, such as transient tire harmonic uniformity effects caused, for instance, by a curing membrane. 
     SUMMARY 
     Aspects and advantages of the invention will be set forth in part in the following description, or may be apparent from the description, or may be learned through practice of the invention. 
     One example aspect of the present disclosure is directed to a method for improving the uniformity of a tire. The method can include obtaining uniformity measurements of a uniformity parameter for each tire in a set of a plurality of tires and analyzing, with one or more processing devices, the uniformity measurements to identify a transient uniformity effect. The transient uniformity effect changes from tire to tire in the set of tires. The method can further include modifying manufacture of one or more tires based at least in part on the transient uniformity effect. For instance, the method can include modifying a process element (e.g. manufacture of the process element) used during tire manufacture contributing to the transient uniformity effect. In an example implementation, the transient uniformity effect can be attributable to a tire harmonic uniformity effect. For instance, the transient uniformity effect can include a membrane effect attributable to a curing membrane. 
     Another example aspect of the present disclosure is directed to a system for improving the uniformity of a tire. The system includes a measurement machine configured to obtain uniformity measurements for each tire in a set of a plurality of tires. The system can further include a computing system coupled to the measurement machine. The computing system can include one or more processors and at least one non-transitory computer-readable medium. The at least one non-transitory computer-readable medium stores computer-readable instructions that when executed by the one or more processors cause the one or more processors to perform operations. The operations can include analyzing the uniformity measurements to identify a transient uniformity effect. The transient uniformity effect changes from tire to tire in the set of 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  depicts an overview of an example tire manufacturing process. 
         FIG. 2  depicts a flow diagram of an example method for improving the uniformity of a tire according to an embodiment of the present disclosure. 
         FIG. 3  depicts a flow diagram of an example method for determining a membrane effect according to an embodiment of the present disclosure. 
         FIG. 4  depicts an example confection operator tooling signature to be removed from uniformity measurements according to an embodiment of the present disclosure.  FIG. 4  plots azimuth about the tire along the abscissa and magnitude of the uniformity parameter along the ordinate. 
         FIG. 5  depicts example residual waveforms for six consecutively cure tires according to an embodiment of the present disclosure.  FIG. 5  plots azimuth about the tire along the abscissa and magnitude of the uniformity parameter along the ordinate. 
         FIG. 6  depicts a graphical representation of membrane joint estimation for six consecutively cured tires according to an embodiment of the present disclosure.  FIG. 6  plots location on the curing membrane along the abscissa and height of the membrane joint along the ordinate. 
         FIG. 7  depicts a graphical representation of membrane joint estimation for six consecutively cured tires according to an embodiment of the present disclosure.  FIG. 7  plots location on the curing membrane along the abscissa and height of the membrane joint along the ordinate. 
         FIG. 8  depicts a graphical representation of monitoring a membrane effect to determine when to replace a curing membrane according to an example embodiment of the present disclosure.  FIG. 8  plots the particular tire along the abscissa and the magnitude of the membrane effect along the ordinate. 
         FIG. 9  depicts a vector representation of an example tire optimization process according to an example embodiment of the present disclosure. 
         FIG. 10  depicts an example system for improving the uniformity of a tire according to an embodiment of the present disclosure. 
     
    
    
     DETAILED DESCRIPTION 
     It is to be understood by one of ordinary skill in the art that the present discussion is a description of exemplary embodiments only, and is not intended as limiting the broader aspects of the present invention. Each example is provided by way of explanation of the invention, not limitation of the invention. In fact, it will be apparent to those skilled in the art that various modifications and variations can be made in the present invention without departing from the scope or spirit of the invention. For instance, features illustrated or described as part of one embodiment can be used with another embodiment to yield a still further embodiment. Thus, it is intended that the present invention covers such modifications and variations as come within the scope of the appended claims and their equivalents. 
     Overview 
     Generally, example aspects of the present disclosure are directed to improving tire uniformity through identification of transient effects contributing to the non-uniformity of a tire. Certain uniformity effects can be transient effects that evolve over time, such as an effect attributable to a curing membrane of a tire. Such transient effects can be difficult to analyze using techniques for identifying tire harmonic uniformity effects and process harmonic uniformity effects. Example aspects of the present disclosure solve the problem of identifying transient uniformity effects that evolve over time by analyzing readily available uniformity measurements of a tire. The identified transient uniformity effects can be used to improve the uniformity of a tire in various ways. For instance, the identified transient effects can be used to provide an indirect assessment of tooling elements contributing to the transient effect, which could be difficult to measure during a tire manufacturing process. 
     More particularly, uniformity measurements of a uniformity parameter for a set of tires can be obtained. The uniformity parameter can be radial run out, radial force variation, lateral run out, lateral force variation, static balance, tangential force variation or other suitable uniformity parameter. After optionally removing nuisance effects from the waveform, the transient effect can be identified by analyzing the uniformity measurements for an effect that varies from tire to tire. In one example, the uniformity measurements can be modeled as a sum of a non-transient effect term and a transient effect term. The transient effect term can be specified such that it can vary from tire to tire. Coefficients associated with the transient effect term can be identified using, for instance, a regression or programming analysis. The coefficients associated with the transient effect term can be used to assess one or more characteristics of the transient uniformity effect, such as the rate of change of the transient effect term from tire to tire. 
     One example transient effect that can be identified according to example aspects of the present disclosure is a membrane effect attributable to a curing membrane used to cure the set of tires. Aspects of the present disclosure will be discussed with reference to identification of a transient membrane effect for purposes of illustration and discussion. Those of ordinary skill in the art, using the disclosures provided herein, will understand that other suitable transient effects can be identified from the uniformity measurements without deviating from the scope of the present disclosure. 
     During tire manufacture, a curing membrane can be inflated to engage a tire as the tire is cured in a curing press. The curing membrane can include a membrane joint. As the curing membrane is inflated and re-inflated during sequential curing processes, the shape of the curing membrane joint can be altered. The altering of this curing membrane joint can lead to a transient uniformity effect on the tire. The membrane effect can have a period corresponding to the tire circumference and is thus a transient tire harmonic uniformity effect. A transient membrane effect caused by a curing membrane can be identified by analyzing uniformity waveforms measured for a set of tires, such as uniformity waveforms measured for the set of tires or based on uniformity summary data (e.g. magnitude and phase angle of one or more harmonic components of the uniformity effect) for the set of tires. 
     Tire manufacture can be modified based at least in part on the identified transient uniformity effect. For instance, the membrane effect can be used to determine when to replace a curing membrane during tire manufacture since it can provide a tire-by-tire estimation of the membrane radial run out. This is an advantage over attempting to measure the radial run out of the curing membrane during press operation, which can be difficult, expensive, and disruptive. 
     As another example, joint audits can be conducted on curing membrane joints using analysis of tire uniformity measurements in order to provide feedback correction of the membrane construction process. In addition, characteristics of a membrane joint in a curing membrane can be designed in a reverse engineering process using the observed transient effects of the curing membrane with the aim to reduce a membrane effect on the uniformity of a tire. The membrane effect can also be considered as a source of non-uniformity that can be used in a tire uniformity optimization process, for instance, by changing a loading angle of a green tire relative to the curing membrane in the press to best match its effect with effects from other components in the process. 
     Example Tire Manufacturing Process 
       FIG. 1  depicts a simplified depiction of an example tire manufacturing process. A tire carcass  100  is formed on a building drum element  105 . In a unistage manufacturing process, the carcass  100  remains on the drum element  105 . In a two-stage process, the carcass  100  can be removed from the drum element  105  and moved to a second stage finishing drum element. In either case, the carcass is inflated to receive a finished tread band  110  to produce a finished green tire  115 . The tread band  110  can be built on a form tooling element  112  before the tread band  110  is combined with the carcass to produce the finished green tire  115 . 
     The green tire  115  can then be loaded into a curing press  120  and cured to produce a cured tire  125 . The curing press  120  can include press elements and a curing membrane  122 . During cure of a tire, the curing membrane  122  can be inflated to engage the green tire  115  and press the green tire  115  against the press elements. Heat can be applied to the green tire  115  from the press elements and from the curing membrane  122  to produce the cured tire  125 . 
     Uniformity measurements of various uniformity parameters can be performed on the tire using uniformity measurement machines at various stages during the tire manufacturing process. For instance, the radial run out of the green tire  115  can be measured before loading the green tire  115  into the curing mold  120 . The radial force variation of the cured tire  125  can be measured after the cured tire has been cured in the curing mold  120 . An example system for performing uniformity measurements and analyzing uniformity parameters will be discussed in more detail with reference to  FIG. 10 . 
     Each of the above tooling elements can have an effect on the uniformity of a tire. For instance, out-of-roundness of the building drum element  105 , the form tooling element  110 , and/or the curing press  120  can affect the uniformity of a tire. The curing membrane  122  can also affect the uniformity of the tire. For instance, out-of-roundness of the curing membrane  122  due to, for instance, a membrane joint can affect the uniformity of a tire. Because the shape of the membrane joint can change with each cure, the uniformity effect caused by the curing membrane  122  can change from tire to tire and thus evolves over time. 
     Example Method for Improving the Uniformity of a Tire 
       FIG. 2  depicts a flow diagram of an example method ( 200 ) for improving the uniformity of a tire though identification of transient uniformity effects according to an embodiment of the present disclosure.  FIG. 2  can be implemented at least in part using a suitable uniformity improvement system, such as the system  600  depicted in  FIG. 10 .  FIG. 2  depicts steps performed in a particular order for purposes of illustrations and discussion. Those of ordinary skill in the art, using the disclosures provided herein, will understand that various steps of any of the methods disclosed herein can be omitted, expanded, adapted, rearranged, and/or modified in various ways without deviating from the scope of the present disclosure. 
     At ( 202 ), the method includes identifying a set of a plurality of tires for uniformity analysis. The set of tires can include tires that are subjected to the same transient uniformity effect. For instance, in the example of identifying a transient uniformity effect attributable to a curing membrane, the set of tires can include tires that are consecutively cured using the same curing membrane. Any number of tires can be selected for use in the set of tires. For instance, 5 to 10 tires consecutively cured using the same curing membrane can be identified for analysis. 
     At ( 204 ), uniformity measurements are obtained for the set of tires. As used herein, “obtaining uniformity measurements” can include actually performing the uniformity measurements or accessing the uniformity measurements stored in, for instance, a memory of a computing device. The uniformity measurements can be of any suitable uniformity parameter. For instance, the uniformity measurements can correspond, for example, to such uniformity parameters as radial run out (RRO), lateral run out (LRO), mass variance, balance, radial force variation (RFV), lateral force variation (LFV), tangential force variation (TFV), and other parameters. 
     In one implementation, the uniformity measurements can include uniformity waveforms for the set of tires. Alternatively, the uniformity measurements can include uniformity summary data. The uniformity summary data can include the magnitude and/or phase angle of one or more harmonics of a uniformity parameter of interest. For instance, the uniformity summary data can include the magnitude of the first four harmonics of radial force variation for each tire in the set of tires. 
     The uniformity measurements can include contributions from many different effects. For instance, the uniformity measurements can include contributions from tire harmonic uniformity effects (e.g. tooling effects) as well as process harmonic uniformity effects. To identify contributions from these various effects, the uniformity measurements for a tire can be modeled as a sum of tire harmonic terms, process harmonic terms, and a residual. 
     An example model is provided below: 
     
       
         
           
             
               w 
               i 
             
             = 
             
               
                 
                   ∑ 
                   
                     t 
                     = 
                     1 
                   
                   T 
                 
                  
                 
                     
                 
                  
                 
                   
                     ∑ 
                     
                       h 
                       = 
                       1 
                     
                     
                       N 
                       2 
                     
                   
                    
                   
                       
                   
                    
                   
                     
                       a 
                       th 
                     
                      
                     
                       cos 
                        
                       
                         ( 
                         
                           
                             2 
                              
                             π 
                              
                             
                                 
                             
                              
                             ih 
                           
                           N 
                         
                         ) 
                       
                     
                   
                 
               
               + 
               
                 
                   b 
                   th 
                 
                  
                 
                   sin 
                    
                   
                     ( 
                     
                       
                         2 
                          
                         π 
                          
                         
                             
                         
                          
                         ih 
                       
                       N 
                     
                     ) 
                   
                 
               
               + 
               
                 
                   ∑ 
                   
                     p 
                     = 
                     1 
                   
                   P 
                 
                  
                 
                     
                 
                  
                 
                   
                     a 
                     p 
                   
                    
                   
                     cos 
                      
                     
                       ( 
                       
                         
                           2 
                            
                           π 
                            
                           
                               
                           
                            
                           
                             ih 
                             p 
                           
                         
                         N 
                       
                       ) 
                     
                   
                 
               
               + 
               
                 
                   b 
                   p 
                 
                  
                 
                   sin 
                    
                   
                     ( 
                     
                       
                         2 
                          
                         π 
                          
                         
                             
                         
                          
                         
                           ih 
                           p 
                         
                       
                       N 
                     
                     ) 
                   
                 
               
               + 
               
                 ɛ 
                 i 
               
             
           
         
       
     
     w i  is the measured uniformity data for each data point i of N data points about the tire. The mathematical model models tire harmonic uniformity effects t=1 to T. h is the particular harmonic of the tire harmonic uniformity effect. The mathematical model also models process harmonics p=1 to P. h p  is the harmonic number of the particular process harmonic uniformity effect. The harmonic number provides a measure of the rate of introduction of the process harmonic uniformity effect relative to the tire circumference. a th  and b th  are coefficients associated with the tire harmonic terms. a p  and b p  are coefficients associated with the process harmonic terms. ε i  is a residual term. 
     Various tire harmonic uniformity effects and process harmonic uniformity effects can be determined from the model by estimating the coefficients associated with the tire harmonic terms and process harmonic terms. The coefficients can be estimated, for instance, using a regression analysis or a programming analysis. Under a regression approach, coefficients are estimated to best fit the mathematical model to the data points in the uniformity measurements. Under a programming approach, the coefficients are estimated to minimize the difference or error between the uniformity measurement and an estimated measurement using a model. 
     The coefficients associated with the tire harmonic terms and the process harmonic terms are generally constant and do not change from tire to tire. This is true for many tire harmonic uniformity effects and process harmonic uniformity effects. Tooling elements such as building drums and transfer rings are typically relatively rigid and thus tend to impart the same uniformity effects in continued usage. A process harmonic may have its impact change from tire to tire depending on the rate of introduction of the process harmonic relative to the tire circumference. However, the overall effect of the process harmonic remains relatively constant for the set of tires. 
     Unlike process harmonic and tire harmonic uniformity effects, transient uniformity effects evolve over time. Transient effects can be identified from uniformity measurements by expanding the model to include a term modeling the varying transient effects from tire to tire. An example mathematical model that includes transient effect terms used to model transient effect contributions to uniformity measurements is provided below: 
     
       
         
           
             
               w 
               i 
               k 
             
             = 
             
               
                 
                   ∑ 
                   
                     t 
                     = 
                     1 
                   
                   T 
                 
                  
                 
                     
                 
                  
                 
                   
                     ∑ 
                     
                       h 
                       = 
                       1 
                     
                     
                       N 
                       2 
                     
                   
                    
                   
                       
                   
                    
                   
                     
                       a 
                       th 
                     
                      
                     
                       cos 
                        
                       
                         ( 
                         
                           
                             2 
                              
                             π 
                              
                             
                                 
                             
                              
                             ih 
                           
                           N 
                         
                         ) 
                       
                     
                   
                 
               
               + 
               
                 
                   b 
                   th 
                 
                  
                 
                   sin 
                    
                   
                     ( 
                     
                       
                         2 
                          
                         π 
                          
                         
                             
                         
                          
                         ih 
                       
                       N 
                     
                     ) 
                   
                 
               
               + 
               
                 
                   ∑ 
                   
                     p 
                     = 
                     1 
                   
                   P 
                 
                  
                 
                     
                 
                  
                 
                   
                     a 
                     p 
                   
                    
                   
                     cos 
                      
                     
                       ( 
                       
                         
                           2 
                            
                           π 
                            
                           
                               
                           
                            
                           
                             ih 
                             p 
                           
                         
                         N 
                       
                       ) 
                     
                   
                 
               
               + 
               
                 
                   b 
                   p 
                 
                  
                 
                   sin 
                    
                   
                     ( 
                     
                       
                         2 
                          
                         π 
                          
                         
                             
                         
                          
                         
                           ih 
                           p 
                         
                       
                       N 
                     
                     ) 
                   
                 
               
               + 
               
                 
                   ∑ 
                   
                     h 
                     = 
                     1 
                   
                   
                     N 
                     / 
                     2 
                   
                 
                  
                 
                     
                 
                  
                 
                   
                     a 
                     h 
                     k 
                   
                    
                   
                     cos 
                      
                     
                       ( 
                       
                         
                           2 
                            
                           π 
                            
                           
                               
                           
                            
                           ih 
                         
                         N 
                       
                       ) 
                     
                   
                 
               
               + 
               
                 
                   b 
                   h 
                   k 
                 
                  
                 
                   sin 
                    
                   
                     ( 
                     
                       
                         2 
                          
                         π 
                          
                         
                             
                         
                          
                         ih 
                       
                       N 
                     
                     ) 
                   
                 
               
               + 
               
                 ɛ 
                 i 
                 k 
               
             
           
         
       
     
     w i   k  is the measured uniformity data for each tire k for each data point i of N data points about the tire. The mathematical model models tire harmonic uniformity effects t=1 to T. h is the particular harmonic of the tire harmonic uniformity effect. The mathematical model models process harmonics p=1 to P. h p  is the harmonic number of the particular process harmonic uniformity effect. a th  and b th  are coefficients associated with the tire harmonic uniformity effects. a p  and b p  are coefficients associated with the process harmonic uniformity effects. The model includes a transient effect term in addition to the tire harmonic uniformity effect and process harmonic uniformity effect terms. The transient effect term varies from tire to tire. a h   k  and b h   k  are coefficients associated with the transient effect term. k represents in index for the sequence of tires in the set (not an exponent). ε i   k  is a residual term. 
     A transient uniformity effect can be identified from uniformity measurements based at least in part on aspects of these models. More particularly at ( 206 ) of  FIG. 2 , the method can optionally include removing one or more uniformity effects from the uniformity measurements to identify residual uniformity measurements. The uniformity effects that are removed can be nuisance effects, such as process harmonic uniformity effects and non-transient tire uniformity effects attributable to certain tooling elements. In a particular implementation, the nuisance effects can be identified using a tooling signature analysis, such as the tooling signature analysis techniques disclosed in PCT Application No. PCT/US12/57864, which is incorporated herein by reference. 
     An example tooling signature analysis can model the uniformity measurements as a sum of tooling element terms and non-tooling element terms. The tooling element terms can be associated with effects resulting from tooling elements used during tire manufacture. The non-tooling element terms can be associated with all other harmonics (whether tire harmonics or process harmonics) that can contribute to the uniformity of the tire. Coefficients associated with the tooling element terms can be estimated using a regression analysis or a programming analysis. The tooling signature can then be generated based on the estimated coefficients associated with the tooling element terms using, for instance, an analysis of variance analysis (ANOVA analysis). 
     The ANOVA analysis technique can be performed in which waveform points for the tooling signature are fitted by a set of N offsets with N being the number of data points for the tooling signature, such as 256 data points. To perform this ANOVA analysis technique, there must be multiple measured uniformity waveforms for tires manufactured using the same tooling element. An example mathematical statement of the ANOVA method for a tooling element is provided below: 
     
       
         
           
             
               w 
               ji 
             
             = 
             
               α 
               + 
               
                 
                   ∑ 
                   
                     q 
                     = 
                     1 
                   
                   
                     Q 
                     c 
                   
                 
                  
                 
                     
                 
                  
                 
                   
                     ∑ 
                     
                       i 
                       = 
                       1 
                     
                     N 
                   
                    
                   
                       
                   
                    
                   
                     β 
                     qi 
                   
                 
               
               + 
               
                 ɛ 
                 ji 
               
             
           
         
       
     
     The w ji  is the ith waveform point for the jth tire. α is a constant term or intercept. β qi  is a fitted constant for each point of the tooling signature (1 to N) and each tooling element q. The β qi  terms are determined based on the estimated coefficients determined during the regression or programming analysis. The ANOVA analysis can determine the β qi  terms using a least squared analysis. In particular, a set of β qi  terms can be selected to minimize the sum of squared errors across all waveform points. There are in general N such β terms for each of the tooling elements that are fitted. In particular, this formulation allows for N (e.g. 256) possible unique coefficients (one for each of the tooling signature data points) for each of the tooling elements. These N unique coefficients provide the data points for the comprehensive tooling signature for a tooling element. 
     Once the tooling signatures for the various tooling elements are identified, the tooling signatures can be removed from the uniformity measurements to identify the residual uniformity measurements. The residual uniformity measurements can then be analyzed to separate transient uniformity effects from non-transient uniformity effects as shown at ( 208 ) of  FIG. 2 . In particular, the residual uniformity measurements can be analyzed to identify an effect that varies from tire to tire in the set of tires. In one implementation, the residual can be modeled as a sum of a non-transient term and a transient term. The transient term can vary from tire to tire in the model. Coefficients associated with the non-transient term and the transient term can be estimated, for instance, using a regression analysis or a programming analysis. The estimated coefficients can be determined based on an expected change (e.g. linear or other relations) of the transient term from tire to tire. One or more parameters (e.g. rate of change of the transient uniformity effect) transient uniformity effect can be identified based at least in part on the estimated coefficients associated with the transient term. 
     At ( 210 ), tire manufacture can be modified based at least in part on the identified transient uniformity effect. The dynamic effects can provide an indirect tire-by-tire assessment of the either the membrane radial run out or the membrane radial force which could be a very difficult or even impossible to measure directly during the curing process. This effect is also done with no disruption to the process that might make the estimates of the curing membrane effects to become biased. The transient effect can be used to determine when to repair or replace certain transient tools (e.g. a curing membrane, flexible building drum with inflatable element, etc.) used during tire manufacture to reduce the uniformity effects attributable to the tool. Because the transient effect often changes in a smooth and predictable pattern it can also be a useful piece of a tire uniformity optimization process. Examples of modifying tire manufacture to improve tire uniformity based at least in part on an identified dynamic uniformity effect are discussed in more detail below. 
     Example Analysis of Uniformity Measurements to Identify a Membrane Effect 
     Referring now to  FIG. 3 , an example method ( 300 ) for identifying a transient uniformity effect attributable to a curing membrane will now be set forth. At ( 302 ), the method includes obtaining uniformity waveforms for the set of tires. The set of tires can include a plurality of tires that have been consecutively cured using the same curing membrane. The uniformity waveforms can be obtained by measuring the uniformity waveforms using a uniformity measurement machine or by accessing previously measured uniformity waveforms stored, for instance, in a memory. 
     The uniformity waveforms can include a measured uniformity parameter for a plurality of data points about the azimuth of a tire. For instance, a waveform can be constructed from a number of data points measured in equally spaced points during one rotation of a tire according to a sampling resolution (e.g.,  128 ,  256 ,  512  or other number of data points per tire revolution). It should be appreciated that the uniformity waveforms can be obtained under a variety of conditions. The uniformity waveforms can be obtained for rotation of the tire in either direction (direct and/or indirect). In addition, the uniformity waveforms can be obtained under loaded or unloaded conditions. 
     At ( 304 ), one or more uniformity effects are optionally removed from the uniformity waveforms to obtain residual waveforms. More particularly, the uniformity waveforms can be cleaned of uniformity effects other than effects attributable to the curing membrane, such as process harmonic uniformity effects and tooling element effects attributable to other tooling elements used during tire manufacture. For example, tooling signatures can be identified for various tooling elements using a tooling signature analysis. This pre-treatment of the data to remove non-dynamic effects is optional but it can be beneficial in reducing dispersion that may affect the final estimates. 
       FIG. 4  depicts an example tooling signature  402  that can be obtained for a tooling element, such as a confection operator element.  FIG. 4  plots the tooling signature  402  with azimuth about the tooling element along the abscissa and contribution to the uniformity parameter along the ordinate. The tooling signature  402  can be representative of one or more tooling elements used during tire manufacture. 
     The identified tooling signatures and other uniformity effects (e.g. identified process harmonic uniformity effects) can be removed from the uniformity waveforms to identify residual waveforms associated with the curing membrane.  FIG. 5  plots six residual uniformity waveforms  404  obtained for a set of six tires.  FIG. 5  plots azimuth about the tire along the abscissa and magnitude of the uniformity parameter along the ordinate. 
     The residual waveforms can include contributions from non-transient effects as well as transient effects. For instance, the residual waveforms can include contributions from a press effect that remains fixed through consecutive cures and a membrane effect that is transient through consecutive cures. If the press effect is known, for instance from a tooling signature analysis, the press effect can be removed from the residual waveforms to identify the transient membrane effect for each tire. The transient effect for each tire can then be analyzed to asses one or more parameters of the transient effect, such as a rate of change of the transient effect. 
     If the press effect is not known, each residual waveform can be modeled as a sum of a press effect term and a membrane effect term as shown at ( 306 ) of  FIG. 3 . For instance, the residual waveforms can be modeled as follows: 
     
       
         
           
             
               r 
               i 
             
             = 
             
               
                 p 
                  
                 
                     
                 
                  
                 
                   cos 
                    
                   
                     ( 
                     
                       
                         2 
                          
                         π 
                          
                         
                             
                         
                          
                         i 
                       
                       N 
                     
                     ) 
                   
                 
               
               + 
               
                 q 
                  
                 
                     
                 
                  
                 
                   sin 
                    
                   
                     ( 
                     
                       
                         2 
                          
                         π 
                          
                         
                             
                         
                          
                         i 
                       
                       N 
                     
                     ) 
                   
                 
               
               + 
               
                 g 
                 * 
                 t 
                 * 
                 
                   cos 
                    
                   
                     ( 
                     
                       
                         2 
                          
                         π 
                          
                         
                             
                         
                          
                         i 
                       
                       N 
                     
                     ) 
                   
                 
               
               + 
               
                 h 
                 * 
                 t 
                 * 
                 
                   sin 
                    
                   
                     ( 
                     
                       
                         2 
                          
                         π 
                          
                         
                             
                         
                          
                         i 
                       
                       N 
                     
                     ) 
                   
                 
               
             
           
         
       
     
     r i  can be the uniformity parameter for a data point i of N data points of the residual waveform. p and q can represent coefficients associated with the press effect. The membrane effect can be captured by the coefficients g and h. Notice the dependence of the membrane effect on t which represents the tire order of cure of the curing membrane. g and h can be more complicated functions of t without deviating from the scope of the present disclosure. 
     At ( 308 ), one or more parameters of the membrane effect can be determined using the model. For instance, the rate of change of the membrane effect for the set of tires can be identified using a regression or a programming analysis. Since the precise value oft may not be known for a particular waveform, one can focus on the differences in the residual waveforms. This can subtract out the press effect (since it is fixed for all tires) and isolate the slope of the membrane change. This can be represented as follows: 
     
       
      
       d 
       t 
       =g*s+h*s  
      
     
     where d t  represents the point-by-point differences between consecutively cured tires s represents the interval of time between t+1 and t. The g and h coefficients represent the membrane effects as a function of the duration between time values (between cures). 
     In one particular implementation of the present disclosure, magnitudes of various harmonics of the individual residual waveforms can be identified, for instance, using a Fourier analysis. In particular, a set of harmonic magnitudes for harmonics 1-10 can be identified for each residual waveform. A model can be constructed in which the harmonic magnitude for each harmonic is modeled as a sum of a press effect term and a membrane effect term. One example model is provided below: 
     
       
      
       h 
       k 
       =c 
       k 
       +d 
       k 
       *t  
      
     
     where h k  is the harmonic magnitude for each harmonic k, c k  is the coefficient associated with the press effect magnitude for each harmonic k, and d k  is the coefficient associated with the membrane effect magnitude for each harmonic k. 
     Regression or programming techniques can be used to identify coefficients for the model. Similar to the case of the full waveform, the absolute value of the coefficient d k  cannot be obtained because the exact value of t is not known. Instead, differences can be taken in the harmonic magnitudes to estimate the change in magnitude of the membrane effect with continued use. The change in magnitude can be assumed to be linear or a more complicated model can be used. 
     Because the membrane effect can be produced by a membrane joint in the curing membrane, it can be useful to analyze the one or more parameters associated with the membrane effect to assess parameters of the membrane joint. For instance, at ( 310 ) the method can include constructing an estimate of membrane joint effects and/or joint shapes. For instance, the rates of change of the membrane effect contribution to the harmonic magnitude for a plurality of harmonics (e.g. the first  10  harmonics) can be identified as discussed above. These values can estimate the change in membrane effect through repeated cures. The rates of change may not be equal across the harmonics. This can imply that the joint shape is changing as well as its overall thickness. 
     According to particular aspects of the present disclosure, it is possible to estimate the joint shape changes by combining the results of all harmonics. For example one might estimate a change y h  for harmonic h. The overall change can be the sum of these terms as follows: 
     
       
         
           
             
               ∑ 
               
                 h 
                 = 
                 1 
               
               p 
             
              
             
                 
             
              
             
               
                 y 
                 h 
               
                
               
                 cos 
                  
                 
                   ( 
                   
                     
                       2 
                        
                       π 
                        
                       
                           
                       
                        
                       i 
                     
                     N 
                   
                   ) 
                 
               
             
           
         
       
     
     where y h  is the estimated associated with each harmonic h of p harmonics and i is each data point of N is the number of data points about the tire. The sum of these terms will be a waveform over the length of the tire but will tend to be show most movement near the membrane joint since only cosine curves are used. 
       FIG. 6  depicts a graphical representation  410  of the estimated joint shape changes of a curing membrane determined from a set of tires.  FIG. 6  plots location on the curing membrane along the abscissa and height of the membrane joint along the ordinate. As shown, the membrane joint is estimated to change shape with each cure. This shape change can be useful to infer membrane evolution over time. 
     The above example is discussed with reference to determining one or more parameters of a membrane effect using full uniformity waveforms measured for the set of tires. One or more parameters of the membrane effect can also be determined using uniformity summary data. The uniformity summary data can provide magnitude of one or more harmonic components of a uniformity parameter. For instance, the uniformity summary data can provide a magnitude of the first four harmonics of the uniformity parameter. 
     The membrane effect can be identified by analyzing each of the harmonics of the uniformity parameter individually. For instance, one or more uniformity effects can be removed from each harmonic to identify a plurality of residual harmonics associated with the set of tires. The residual harmonics can then be analyzed individually to identify one or more parameters of the membrane effect. 
     In one implementation, a model can be constructed in which the harmonic magnitude for each harmonic is modeled as a sum of a press effect term and a membrane effect term. One example model is provided below: 
     
       
      
       h 
       k 
       =c 
       k 
       +d 
       k 
       *t  
      
     
     where h k  is the harmonic magnitude for each harmonic k, c k  is the coefficient associated with the press effect magnitude for each harmonic k, and d k  is the coefficient associated with the membrane effect magnitude for each harmonic k. 
     A regression or programming analysis can be used to determine coefficients for the model. The absolute value of the coefficient d k  cannot be obtained because the exact value oft is not known. Instead, differences can be taken in the harmonic magnitudes to estimate the change in magnitude of the membrane effect with continued use. The change in magnitude can be assumed to be linear or a more complicated model can be used. The change of the magnitude of the membrane effect can be different for each harmonic in the uniformity summary data. As discussed above, this can be representative of potential changes in a membrane joint used in the curing membrane during tire manufacture. 
       FIG. 7  depicts a graphical representation  420  of the estimated curing membrane joint shape change for an example set of tires.  FIG. 7  plots location on the curing membrane along the abscissa and height of the membrane joint along the ordinate. As shown, the curing membrane joint is estimated to change shape with each cure using the curing membrane. 
     Example Modification of Tire Manufacture 
     The identification of a transient effect from uniformity measurements can achieve multiple benefits. For instance, the identification of membrane effects can have a direct impact on membrane performance, membrane design, and uniformity yields. According to aspects of the present disclosure, the manufacture of a tire can be modified based at least in part on the identified transient effect to improve tire uniformity. As used herein, modifying the manufacture of a tire can refer to modifying a component or design of the tire itself or modifying a process element (e.g. a curing membrane) used to manufacture the tire. 
     In one example embodiment, an identified transient membrane effect can be used to estimate the evolution of a joint shape of a membrane joint in the curing membrane. For instance, uniformity measurements associated with a first set of tires (e.g. forty tires) cured using a particular membrane can be analyzed according to aspects of the present disclosure to estimate the membrane effect size and evolution in time. Using the estimated trend, one can predict performance in time and establish a criterion for curing membrane change out or maintenance before its performance becomes unacceptable. 
     For instance,  FIG. 8  provides a graphical representation of an expected change  450  of a membrane effect from tire to tire.  FIG. 8  plots number of cures along the abscissa and magnitude of the membrane effect along the ordinate. As shown by the expected change  450 , the magnitude of the membrane effect in this example is expected to increase as more and more tires are cured using the curing membrane. When the magnitude of the membrane effect exceeds a threshold, such as threshold  452 , maintenance can be performed on the curing membrane or the curing membrane can be replaced. Since the change of a membrane under failure can be expensive this predictive maintenance approach can provide economic benefits. 
     According to another example, a membrane effect can be estimated using the uniformity measurements for a set of consecutively cured tires can be used to estimate joint shape. For instance, joint shape representations as shown in  FIGS. 6 and 7  can be generated based at least in part on the membrane effect identified for each tire. The determined joint shapes can be used as part of a quality audit to provide feedback on membrane performance. Extensive examination of patterns and other trends in the membrane effect can also be used to provide new designs of membrane shape and for the machinery and processes used to construct the curing membranes. Studies can also be performed with different compounds and treatments to determine improvement actions. Normally such studies would be indirect since it would be normally difficult or impossible to measure the membrane changes under use in a continuous fashion so this can drastically decrease the cost and improve the applicability of the results. 
     According to yet another example, an identified membrane effect can be considered as one of many potential sources of non-uniformity in a tire to be used in a tire optimization process. For example, it can be determined that the membrane effect on the first harmonic of radial force variation can be modeled as a vector that changes magnitude by a determined amount with each cure and shifts azimuth with each cure. This vector can be used to oppose some other effects (e.g. bandage variation) by purposely changing the loading angle of a green tire into the press for each cure. This can enhance the normal tire optimization process by allowing the membrane effect to change consecutively with each consecutive cure. Since the observed sizes of membrane effects can be on the order of 0.8 kgs force this can provide a substantial improvement in tire uniformity and an increase in yield perhaps on the order of 15%. 
     For instance,  FIG. 9  depicts a vector representation of an example tire optimization process for a uniformity parameter. Vector  462  can be representative of the first harmonic of radial force variation measured for a green tire. Vector  464  can be representative of a press effect on the first harmonic of radial force variation. Vector  466  can be representative of transient membrane effect on the first harmonic of radial force variation. Vector  466  can be expected to change magnitude and azimuth with each cure of the tire. The green tire can be loaded into the press such that the press effect vector  464  and membrane effect vector  466  oppose the vector  462 . The resultant vector  468  can be representative of the resulting first harmonic of radial force variation for the cured tire. As shown, the magnitude of the first harmonic of radial force variation is reduced. 
     Example System for Improving the Uniformity of a Tire 
     Referring now to  FIG. 10 , a schematic overview of example system components for implementing the above-described methods is illustrated. An example tire  600  is constructed in accordance with a plurality of respective manufacturing processes. Such tire building processes may, for example, include applying various layers of rubber compound and/or other suitable materials to form the tire carcass, providing a tire belt portion and a tread portion to form the tire summit block, positioning a green tire in a curing press, and curing the finished green tire, etc. Such respective process elements are represented as  602   a ,  602   b , . . . ,  602   n  in  FIG. 11  and combine to form exemplary tire  600 . It should be appreciated that a batch of multiple tires can be constructed from one iteration of the various processes  602   a  through  602   n.    
     Referring still to  FIG. 10 , a measurement machine  604  is provided to obtain the uniformity measurements of the tire  600 . The uniformity measurement machine  604  can be configured to measure radial run out and other uniformity parameters (e.g. radial force variation, lateral force variation, tangential force variation) of the tire  600 . In general, such a uniformity measurement machine  604  can include sensors (e.g. laser sensors) to operate by contact, non-contact or near contact positioning relative to tire  600  in order to determine the relative position of the tire surface at multiple data points (e.g., 128 points) as it rotates about a center line. The uniformity measurement machine  604  can also include a wheel used to load the tire to obtain force measurements as the tire  600  is rotated. 
     The measurements obtained by measurement machine  604  can be relayed such that they are received at one or more computing devices  606 , which may respectively contain one or more processors  608 , although only one computer and processor are shown in  FIG. 10  for ease and clarity of illustration. Processor(s)  608  may be configured to receive input data from input device  614  or data that is stored in memory  612 . Processor(s)  608 , can then analyze such measurements in accordance with the disclosed methods, and provide useable output such as data to a user via output device  616  or signals to a process controller  618 . Uniformity analysis may alternatively be implemented by one or more servers  610  or across multiple computing and processing devices. 
     Various memory/media elements  612   a ,  612   b ,  612   c  (collectively, “ 612 ”) may be provided as a single or multiple portions of one or more varieties of non-transitory computer-readable media, including, but not limited to, RAM, ROM, hard drives, flash drives, optical media, magnetic media or other memory devices. The computing/processing devices of  FIG. 10  may be adapted to function as a special-purpose machine providing desired functionality by accessing software instructions rendered in a computer-readable form stored in one or more of the memory/media elements. 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 one implementation, the processor(s)  608  can execute computer-readable instructions that are stored in the memory elements  612   a ,  612   b , and  612   c  to cause the processor to perform operations. The operations can include obtaining uniformity measurements of a uniformity parameter for each tire in a set of a plurality of tires and analyzing the uniformity measurements to identify a transient uniformity effect, such as a membrane effect. 
     Example Application Results 
     A set of 50 uniformity waveforms for a set of 50 consecutively manufactured tires were obtained. The uniformity waveforms each included 256 data points. In addition to the waveform data, other variables such as confection operators, finishing operators, curing press, and curing load angle, and the order of cure within a press were available for each tire in the set. From this data, there were approximately 7 tires that are consecutively cured in each of 7 different presses. 
     The uniformity waveforms were cleaned of uniformity effects caused by confection and finishing operators using a tooling signature analysis. The residual waveforms from the tooling signature analysis were decomposed using a Fourier analysis into the first  10  respective harmonic components. The magnitude of each of the first  10  harmonics was modeled as a sum of a press effect term and a transient membrane effect term. The rate of change in magnitude attributable to the transient membrane effect was determined for each harmonic. The results are provided in Table 1 below: 
     
       
         
           
               
               
               
             
               
                   
                 TABLE 1 
               
               
                   
                   
               
               
                   
                 harmonic 
                 Trend estimate 
               
               
                   
                   
               
             
            
               
                   
               
            
           
           
               
               
               
            
               
                   
                 1 
                 0.53131 
               
               
                   
                 2 
                 0.28859 
               
               
                   
                 3 
                 0.14185 
               
               
                   
                 4 
                 0.14327 
               
               
                   
                 5 
                 0.12345 
               
               
                   
                 6 
                 0.10149 
               
               
                   
                 7 
                 0.07786 
               
               
                   
                 8 
                 0.05184 
               
               
                   
                 9 
                 0.04219 
               
               
                   
                 10 
                 0.04271 
               
               
                   
                   
               
            
           
         
       
     
     The trend estimate provides the estimated change in the membrane effect through repeated cures. The rate of change of the membrane effect is not equal through all harmonics. This implies that the membrane joint shape is changing as well as its overall thickness.  FIG. 6  depicts an example plot of the changing joint shape determined based on the data provided in Table 1. 
     While the present subject matter has been described in detail with respect to specific exemplary embodiments and methods thereof, it will be appreciated that those skilled in the art, upon attaining an understanding of the foregoing may readily produce alterations to, variations of, and equivalents to such embodiments. Accordingly, the scope of the present disclosure is by way of example rather than by way of limitation, and the subject disclosure does not preclude inclusion of such modifications, variations and/or additions to the present subject matter as would be readily apparent to one of ordinary skill in the art using the teachings disclosed herein.