Patent Publication Number: US-11376776-B2

Title: Method of measuring true shear viscosity profile of molding material in capillary and molding system performing the same

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application claims the benefit of prior-filed provisional application with application Ser. No. 63/070,566, filed Aug. 26, 2020, which is incorporated by reference in its entirety. 
    
    
     TECHNICAL FIELD 
     The present disclosure relates to a measurement method, and more particularly, to a method of measuring the shear viscosity. 
     DISCUSSION OF THE BACKGROUND 
     In injection molding process, the flow behavior of a molding material in the capillary is simulated based on several assumptions, such as constant melt temperature, Weissenberg-Rabinowitsch correction, and generalized Newtonian fluids without viscoelasticity. However, these assumptions are inappropriate in some situations. For example, when the molding material has a temperature change, the flow behavior of the molding material will be simulated inaccurately. Consequently, the result of the injection molding will deviate from the simulation which makes the injection molding process inefficient. Therefore, the accuracy of the simulation of the molding material has become a critical issue in this field. 
     This Discussion of the Background section is provided for background information only. The statements in this Discussion of the Background are not an admission that the subject matter disclosed in this section constitutes prior art to the present disclosure, and no part of this Discussion of the Background section may be used as an admission that any part of this application, including this Discussion of the Background section, constitutes prior art to the present disclosure. 
     SUMMARY 
     One aspect of the present disclosure provides a method of measuring a true shear viscosity profile of a molding material in a capillary. The method includes the operations of: determining a setpoint temperature of the molding material before injecting into the capillary; obtaining an initial shear viscosity profile at the setpoint temperature with respect to a shear rate of the molding material; fitting an initial temperature profile with respect to the shear rate according to the initial shear viscosity based on a Cross William-Landel-Ferry (Cross-WLF) model; fitting a first shear viscosity profile and a first temperature profile with respect to the shear rate according to the initial temperature profile based on the Cross-WLF model; and setting the first shear viscosity profile as the true shear viscosity profile when a difference between the first temperature profile and the initial temperature profile is not greater than a predetermined threshold. 
     In some embodiments, the method further includes the operations of: fitting a second shear viscosity profile and a second temperature profile with respect to the shear rate according to the first temperature profile based on the Cross-WLF model when a difference between the first temperature profile and the initial temperature profile is greater than the predetermined threshold; and setting the second shear viscosity profile to be the true shear viscosity profile when a difference between the second temperature profile and the first temperature profile is not greater than the predetermined threshold. 
     In some embodiments, the method further includes simulating a plurality of flow behaviors of the molding material injecting into a cavity with respect to a plurality of parameter sets according to the true shear viscosity profile. 
     In some embodiments, the method further includes the operations of: comparing the plurality of flow behaviors to a predetermined flow behavior to select one of the plurality of flow behaviors closest to the predetermined flow behavior; determining one of the plurality of parameter sets corresponding to the selected one of the plurality of flow behavior to be an actual parameter set; and injecting the molding material into the cavity by applying the actual parameter set. 
     In some embodiments, the operation of obtaining the initial shear viscosity profile at the setpoint temperature with respect to the shear rate of the molding material includes the operations of: obtaining a wall stress; obtaining the shear rate; and obtaining the initial shear viscosity profile by dividing the wall stress by the shear rate. 
     In some embodiments, the operation of obtaining the initial shear viscosity profile at the setpoint temperature with respect to the shear rate of the molding material further includes the operations of measuring a radius of the capillary; determining a volumetric flow rate of the molding material; measuring a longitudinal length of the capillary; measuring an inlet pressure at an inlet of the capillary; and measuring an outlet pressure at an outlet of the capillary. 
     In some embodiments, the wall stress is obtained according to the inlet pressure, the outlet pressure, the radius, and the longitudinal length. 
     In some embodiments, the initial shear rate is obtained according to the volumetric flow rate, the radius, and the wall stress. 
     In some embodiments, the operation of fitting the initial temperature profile with respect to the shear rate according to the initial shear viscosity based on the Cross-WLF model includes the operations of: measuring a density, a velocity vector, a stress tensor, a specific heat, and a thermal conductivity of the molding material; calculating the initial temperature profile and a capillary temperature profile according to the density, the velocity vector, the stress tensor, the specific heat, the thermal conductivity, and the shear rate; and obtaining the initial temperature profile according to the capillary temperature profile. 
     In some embodiments, the initial temperature profile is obtained according to a temperature at a predetermined position from an inlet of the capillary of the capillary temperature profile. 
     In some embodiments, a distance between the predetermined position and the inlet of the capillary is about ⅓ of a longitudinal length of the capillary. 
     In some embodiments, the operation of fitting the first shear viscosity profile and the first temperature profile with respect to the shear rate according to the initial temperature profile based on the Cross-WLF model includes the operations of: calculating the first temperature profile and updating the capillary temperature profile according to the density, the velocity vector, the stress tensor, the specific heat, the thermal conductivity, and the shear rate; and obtaining the first temperature profile according to the updated capillary temperature profile. 
     In some embodiments, the first temperature profile is obtained according to a temperature at a predetermined position from an inlet of the capillary of the capillary temperature profile. 
     In some embodiments, a distance between the predetermined position and the inlet of the capillary is about ⅓ of a longitudinal length of the capillary. 
     In some embodiments, the first temperature profile is obtained according to an average temperature among the capillary temperature profile. 
     In some embodiments, the true shear viscosity profile is measured by a rheometer. 
     Another aspect of the present disclosure provides a molding system. The molding system includes a dispenser and a rheometer. The rheometer is configured to perform the method of measuring a true shear viscosity profile of a molding material in a capillary of the dispenser. 
     The foregoing has outlined rather broadly the features and technical advantages of the present disclosure in order that the detailed description of the disclosure that follows may be better understood. Additional features and advantages of the disclosure will be described hereinafter, and form the subject of the claims of the disclosure. It should be appreciated by those skilled in the art that the conception and specific embodiment disclosed may be readily utilized as a basis for modifying or designing other structures or processes for carrying out the same purposes of the present disclosure. It should also be realized by those skilled in the art that such equivalent constructions do not depart from the spirit and scope of the disclosure as set forth in the appended claims. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       A more complete understanding of the present disclosure may be derived by referring to the detailed description and claims when considered in connection with the Figures, where like reference numbers refer to similar elements throughout the Figures. 
         FIG. 1  is a schematic diagram of a molding system according to some embodiments of the present disclosure. 
         FIG. 2  is a schematic diagram of a dispenser according to some embodiments of the present disclosure. 
         FIG. 3  is a schematic diagram of a portion of the dispenser according to some embodiments of the present disclosure. 
         FIG. 4  is a flowchart of a method according to some embodiments of the present disclosure. 
         FIG. 5  is a flowchart of an operation of the method shown in  FIG. 4  according to some embodiments of the present disclosure. 
         FIG. 6  is a flowchart of an operation of the method shown in  FIG. 4  according to some embodiments of the present disclosure. 
         FIG. 7  is a flowchart of an operation of the method shown in  FIG. 4  according to some embodiments of the present disclosure. 
         FIG. 8  is a flowchart of the method according to other embodiments of the present disclosure. 
         FIG. 9  is a flowchart of the method according to alternative embodiments of the present disclosure. 
         FIG. 10  is a flowchart of the method according to various embodiments of the present disclosure. 
     
    
    
     DETAILED DESCRIPTION 
     Embodiments, or examples, of the disclosure illustrated in the drawings are now described using specific language. It shall be understood that no limitation of the scope of the disclosure is hereby intended. Any alteration or modification of the described embodiments, and any further applications of principles described in this document, are to be considered as normally occurring to one of ordinary skill in the art to which the disclosure relates. Reference numerals may be repeated throughout the embodiments, but this does not necessarily mean that feature(s) of one embodiment apply to another embodiment, even if they share the same reference numeral. 
     It shall be understood that, although the terms first, second, third, etc. may be used herein to describe various elements, components, regions, layers or sections, these elements, components, regions, layers or sections are not limited by these terms. Rather, these terms are merely used to distinguish one element, component, region, layer or section from another element, component, region, layer or section. Thus, a first element, component, region, layer or section discussed below could be termed a second element, component, region, layer or section without departing from the teachings of the present inventive concept. 
     The terminology used herein is for the purpose of describing particular example embodiments only and is not intended to be limiting to the present inventive concept. As used herein, the singular forms “a,” “an” and “the” are intended to include the plural forms as well, unless the context clearly indicates otherwise. It shall be further understood that the terms “comprises” and “comprising,” when used in this specification, point out the presence of stated features, integers, steps, operations, elements, or components, but do not preclude the presence or addition of one or more other features, integers, steps, operations, elements, components, or groups thereof. 
       FIG. 1  is a schematic diagram of a molding system  10  according to some embodiments of the present disclosure. The molding system  10  includes a dispenser  100  and a rheometer  200 . The dispenser  100  is configured to dispense a molding material MM into a cavity  301  of a device  300 . The rheometer  200  is coupled to the dispenser  100 , and configured to measure the behavior of the molding material MM in the dispenser  100 . 
     In some embodiments, the device  300  includes a chip  310  bonded with a substrate  320 , and the cavity  301  is formed between the chip  310  and the substrate  320 . The molding material MM is configured to encapsulate the cavity  301  so as to protect the chip  310  and the substrate  320 . The device  300  is provided for illustration purposes. The present disclosure is not limited thereto. Various devices suitable for being dispensed the molding material MM are within the contemplated scope of the present disclosure. 
     Reference is made to  FIG. 2 .  FIG. 2  is a schematic diagram of the dispenser  100  according to some embodiments of the present disclosure. The dispenser  100  includes barrel  110 , a piston  120 , a capillary  130 , and a pressure transducer  140 . 
     The barrel  110  has a space therein configured to contain the molding material MM. The capillary  130  is coupled to the barrel  110 , and configured to receive the molding material MM from an inlet  131  of the capillary  130  and dispense the molding material MM from an outlet  132  of the capillary  130 . The piston  120  is configured to provide a force F to the molding material MM in the space. When the piston  120  is controlled to push the molding material MM in the barrel  110 , the molding material MM is pushed toward the inlet  131  of the capillary  130 . The molding material MM has a volumetric flow rate Q at the outlet  132  of the capillary  130  according to the force F. In some embodiments, the force F of the piston  120  is controlled by the rheometer  200 . 
     As illustrated in  FIG. 2 , the pressure transducer  140  is coupled to the barrel  110  close to the inlet  131  of the capillary  130 . The pressure transducer  140  is configured to measure a pressure P 1  of the molding material MM at the inlet  301  of the capillary  300 . In some embodiments, the measured value of the pressure P 1  is transmitted to the rheometer  200  for measuring the shear viscosity of the molding material MM. 
     In some conventional approaches, the injection molding process is performed with simulating the shear viscosity of the molding in which the simulated shear viscosity is independent of the temperature. However, when the melt is transmitted through the capillary, the temperature of the melt increases due to the friction between the melt and the wall of the capillary. In this situation, the melt temperature rise is also referred to as the viscous heating and/or the shear heating. In some embodiments, the shear viscosity is a function of temperature. Therefore, the simulated shear viscosity is not accurate when the temperature changes in the above conventional approaches. Consequently, the result of the injection molding process may not be acceptable. 
     Compared to the conventional approaches, the present disclosure provides a method of measuring the shear viscosity of the molding material MM. More specifically, the method takes the temperature dependence into account so as to obtain a much accurate flow behavior of the molding material MM in the capillary  130 . Please see the details below. 
     Reference is made to  FIG. 3  and  FIG. 4 .  FIG. 3  is a schematic diagram of a portion of the dispenser  100  according to some embodiments of the present disclosure.  FIG. 4  is a flowchart of a method  40  according to some embodiments of the present disclosure. To facilitate understanding, the method  40  is described with the same reference numerals shown in  FIG. 1 ,  FIG. 2 , and  FIG. 3 . The method is configured to measure a true shear viscosity η TRUE ({dot over (γ)}) of the molding material MM in the capillary  130 . In some embodiments, the rheometer  200  is configured to perform the method  40 . The method  40  includes operations S 41 , S 42 , S 43 , S 44 , and S 45 . 
     In operation S 41 , a setpoint temperature Ts of the molding material MM before the molding material MM injected into the capillary  130  is determined. In some embodiments, the setpoint temperature Ts is a temperature of the molding material MM in the barrel  110  before being pushed into the capillary  130 . In other words, the molding material MM has the setpoint temperature Ts in the barrel  110 . In some embodiments, the setpoint temperature Ts is determined by the rheometer  200 . 
     In operation S 42 , an initial shear viscosity profile η 0 ({dot over (γ)}) at the setpoint temperature Ts with respect to a shear rate {dot over (γ)} of the moding material MM is obtained. The initial shear viscosity profile η 0 ({dot over (γ)}) is obtained according to a wall stress τ w  of the molding material MM in the capillary  130  and the shear rate {dot over (γ)}. The shear rate {dot over (γ)} used in the operation S 42  is independent of the temperature. 
     Please refer to  FIG. 5  together.  FIG. 5  is a flowchart of the operation S 42  of the method  40  according to some embodiments of the present disclosure. The operation S 42  includes operations S 421 , S 422 , S 423 , S 424 , S 425 , S 426 , S 427 , and S 428 . 
     In operation S 421 , a radius R of the capillary  130  is measured. 
     In operation S 422 , the volumetric flow rate Q of the molding material MM is determined. In some embodiments, when the force F provided by the piston  120  is determined, a moving speed v m  of the molding material MM can be obtained. The volumetric flow rate Q can be obtained by an equation (1).
 
 Q=πR   2   v   m   (1)
 
     In operation S 423 , a longitudinal length L of the capillary  130  is measured. The longitudinal length is measured from the inlet  131  to the outlet  132 . 
     In operation S 424 , the pressure P 1  at the inlet  131  of the capillary  130  is measured. 
     In operation S 425 , a pressure P 2  at the outlet  132  of the capillary  130  is measured. In some embodiments, the pressure P 2  is the pressure outside of the dispenser  100 . 
     In operation S 426 , the wall stress τ w  of the molding material MM is obtained. In some embodiments, the wall stress τ w  is obtained according to an equation (2). 
                     τ   w     =           Δ   ⁢   P     cap     ·   R       2   ⁢   L               (   2   )               
The pressure difference ΔP cap  represents a pressure difference between the pressure P 1  and the pressure P 2 .
 
     In operation S 427 , the shear rate {dot over (γ)} is obtained. In some embodiments, the shear rate {dot over (γ)} is obtained according to an equation (3). In some embodiments, the equation (3) is also referred to as Weissenberg-Rabinowitsch correction. 
     
       
         
           
             
               
                 
                   
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     In operation S 428 , the initial shear viscosity profile η 0 ({dot over (γ)}) is obtained by dividing the wall stress τ w  by the shear rate {dot over (γ)}. The initial shear viscosity profile η 0 ({dot over (γ)}) can be expressed as an equation (4). 
     
       
         
           
             
               
                 
                   
                     
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     As mentioned above, in order to obtain a more accurate shear viscosity, the temperature dependence is taken into account. 
     Please refer to  FIG. 4  again. In operation S 43 , an initial temperature profile T 0 ({dot over (γ)}) is fitted according to the initial shear viscosity profile η 0 ({dot over (γ)}) based on a Cross William-Landel-Ferry (Cross-WLF) model. In some embodiments, the Cross-WLF model can be expressed as the following equations (5) and (6). 
                       η   0     ⁡     (     γ   .     )       =       η   r       1   +       (       η   r     ⁢       γ   .     /     τ   *         )       1   -   n                   (   5   )                 η   r     =       D   1     ⁢     exp   ⁡     [       -       A   1     ⁡     (     T   -     T   r       )             A   2     +     (     T   -     T   r       )         ]                 (   6   )               
In the equations (5) and (6), η r  is the zero-shear rate viscosity, n is the power-law index, D 1  is the viscosity at a reference temperature T r , and A 1  and A 2  are fitting constants. The shear rate {dot over (γ)} can be obtained when the operation S 43  is performed. In Some embodiment, the shear rate {dot over (γ)} is obtained according to the velocity gradient of the molding material MM.
 
     Please refer to  FIG. 6  for details of the operation S 43 .  FIG. 6  is a flowchart of the operation S 43  of the method  40  according to some embodiments of the present disclosure. The operation S 43  includes operations S 431 , S 432 , and S 433 . 
     In operation S 431 , a density ρ, a velocity vector ν, a stress tensor τ, a specific heat C p , and a thermal conductivity κ of the molding material MM are measured. 
     In operation S 432 , the initial temperature profile T 0 ({dot over (γ)}) and a capillary temperature profile T cap (z) are calculated according to the density ρ, the velocity vector ν, the stress tensor τ, the specific heat C p , the thermal conductivity κ, and the shear rate {dot over (γ)}. 
     In some embodiments, the initial temperature profile T 0 ({dot over (γ)}) and the capillary temperature profile T cap (z) are calculated further according to the governing equation, in which the governing equation has the limitations associated with the following equations (7), (8), (9), and (10). 
                         ∂   ρ       ∂   t       +     ∇     ·     ρ   ⁢   v           =   0           (   7   )                     ∂     ∂   t       ⁢     (     ρ   ⁢   v     )       +     ∇     ·     (       ρ   ⁢   vv     +   τ     )           =       -     ∇   p       +   ρg             (   8   )                   pC   p     ⁡     (         ∂     T   cap         ∂   t       +     v   ·     ∇     T   cap           )       =       ∇     ·     (     κ   ⁢     ∇     T   cap         )         +       η   0     ⁢       γ   .     2                 (   9   )               τ   =     -       η   0     ⁡     (       ∇   v     +     ∇     v   T         )                 (   10   )               
In the equations (7)-(10), t is time, p is pressure, and g is acceleration vector of gravity.
 
     In operation S 433 , the initial temperature profile T 0 ({dot over (γ)}) is obtained according to the capillary temperature profile T cap (z). In some embodiments, the capillary profile T cap (z) is a temperature  1   o  profile at the wall of the capillary  130  along a Z-axis, and the initial temperature profile T 0 ({dot over (γ)}) is a temperature profile with respect to the shear rate {dot over (γ)} in the capillary  130  at a predetermined position  133  as shown in  FIG. 3 . In some embodiments, the predetermined position  133  and the inlet  131  has a distance aL therebetween, and the predetermined position  133  and the outlet  132  has a distance (1−a)L therebetween. In some embodiments, the distance aL is substantially equal to ⅓ of the distance L. In some embodiments, the capillary temperature profile T cap (z) has an average temperature among the capillary temperature profile T cap (z) at the predetermined position  133 . 
     Based on the operations S 431 -S 433 , the operation S 43  is performed according to the Cross-WLF model rather than the power-law model. However, the present disclosure is not limited thereto. In some embodiments, the operation S 43  is performed according to the Carreau model. In some other embodiments, the operation S 43  is performed according to the Carreau-Yasuda model, in which the Carreau-Yasuda model is further able to obtain the shear rate γ at the second Newtonian plateau. In various embodiments, the operation S 43  is performed according to the Herschel-Bulkley model, in which the Herschel-Bulkley model is further able to obtain the yielding behavior of fluids when the shear rate {dot over (γ)} is low. In alternative embodiments, the operation S 43  is performed according to the Cross-WLF model, the Carreau model, the Carreau-Yasuda model, the Herschel-Bulkley model, or the combinations thereof. 
     In addition, because the operation S 43  is performed according to the Cross-WLF model, the shear viscosity profile can be obtained over a wider temperature range or a wider shear rate range than some conventional approaches, such as the Arrhenius equation or the Power-law model. The Arrhenius equation is merely valid when the temperature is about 100° C. higher than the glass transition temperature or over a narrow temperature range. The Power-law model is merely valid when the molding material MM is in fast flows. 
     Furthermore, because the operation S 43  is performed according to the Cross-WLF model, the shear viscosity is obtained with respect to the temperature without dividing into different flow regimes. In some conventional approaches, the flow speed is divided into different regimes according to the Cameron number. Therefore, an abrupt temperature change occurs between two adjacent regimes. Compared to the above conventional approaches, the shear viscosity obtained in operation S 43  is smooth and more accurately. 
     Please refer to  FIG. 4  again. In operation S 44 , a first shear viscosity profile η 1 ({dot over (γ)}) and a first temperature profile T 1 ({dot over (γ)}) are fitted according to the initial temperature profile T 0 ({dot over (γ)}) based on the Cross-WLF model. The fitting operation in the operation S 44  is similar to the fitting operation in the operation S 43 . 
     Please refer to  FIG. 7  for details of the operation S 44 .  FIG. 7  is a flowchart of the operation S 44  of the method  40  according to some embodiments of the present disclosure. The operation S 44  includes operations S 441  and S 442 . 
     In operation S 441 , the first temperature profile T 1 ({dot over (γ)}) is calculated, and the capillary temperature profile T cap (z) is updated. The operation S 441  is performed according to the density ρ, the velocity vector ν, the stress tensor τ, the specific heat C p , the thermal conductivity κ, and the shear rate {dot over (γ)}. 
     Similar to the operation S 432 , the first temperature profile T 1 ({dot over (γ)}) and the updated capillary temperature profile T cap (z) are obtained according to the governing equation, and the governing equation has the limitations associated with the equations (7)-(10). More specifically, the initial temperature profile T 0 ({dot over (γ)}) is replaced by the first temperature profile T 1 ({dot over (γ)}) to obtain the updated capillary temperature profile T cap (z). 
     In operation S 442 , the first temperature profile T 1 ({dot over (γ)}) is obtained according to the updated capillary temperature profile T cap (z). Similar to the operation S 433 , the first temperature profile T 1 ({dot over (γ)}) is a temperature profile at the predetermined position  133  according to the updated capillary temperature profile T cap (z). 
     Please refer to  FIG. 4  again. In operation S 45 , the first shear viscosity η 1 ({dot over (γ)}) is set as the true shear viscosity profile η TRUE ({dot over (γ)}) when a difference between the first temperature profile T 1 ({dot over (γ)}) and the initial temperature profile T 0 ({dot over (γ)}) is not greater than a predetermined threshold TOL. In other words, the method  40  further includes an operation S 45   a  configured to comparing the difference between the first temperature profile T 1 ({dot over (γ)}) and the initial temperature profile T 0 ({dot over (γ)}) to the predetermined threshold TOL, and the operation S 45   a  is performed between the operation S 44  and the operation S 45 . In some embodiments, the predetermined threshold TOL is about 0.1° C. 
     Reference is made to  FIG. 8 .  FIG. 8  is a flowchart of the method  40  according to other embodiments of the present disclosure. As illustrated in  FIG. 8 , the method  40  further includes operations S 46  and S 47 . 
     In operation S 45   a , when the difference between the first temperature profile T 1 ({dot over (γ)}) and the initial temperature profile T 0 ({dot over (γ)}) is greater than the predetermined threshold TOL, the method  40  proceeds to the operation S 46 . 
     In operation S 46 , a second viscosity profile  72 ( f ) and a second temperature profile T 2 ({dot over (γ)}) are fitted according to the first temperature profile T 1 ({dot over (γ)}) based on the Cross-WLF model when the difference between the first temperature profile T 1 ({dot over (γ)}) and the initial temperature profile T 0 ({dot over (γ)}) is greater than the predetermined threshold TOL. The operation S 46  is similar to the operation S 44 . 
     In operation S 47 , the second viscosity profile η 2  ({dot over (γ)}) is set to be the true viscosity profile η TRUE ({dot over (γ)}) when the difference between the second temperature profile T 2 ({dot over (γ)}) and the first temperature profile T 1 ({dot over (γ)}) is not greater than the predetermined threshold TOL. Similar to the operation S 45 , the method  40  further includes an operation S 47   a  configured to compare the difference between the second temperature profile T 2 ({dot over (γ)}) and the first temperature profile T 1 ({dot over (γ)}) to the predetermined threshold TOL, and the operation S 47   a  is performed between the operation S 46  and the operation S 47 . 
     Based on  FIG. 4  to  FIG. 8 , the method  40  can be rewritten as a flowchart shown in  FIG. 9 . In  FIG. 9 , when a viscosity profile η i ({dot over (γ)}) and a temperature profile T i ({dot over (γ)}) are obtained, a viscosity profile η i+1 ({dot over (γ)}) and a temperature profile T i+1 ({dot over (γ)}) are fitted according to the viscosity profile η i ({dot over (γ)}) and the temperature profile T i ({dot over (γ)}). Next, the temperature profile T i+1 ({dot over (γ)}) is compared to the temperature profile T i ({dot over (γ)}) to determine whether the viscosity profile η i+1 ({dot over (γ)}) is accurate enough to be the true viscosity profile η TRUE ({dot over (γ)}). When the difference between the temperature profile T i+1 ({dot over (γ)}) and the temperature profile T i ({dot over (γ)}) is not greater than the predetermined threshold TOL, the viscosity profile η i+1 ({dot over (γ)}) is set to be the true viscosity profile η TRUE  ({dot over (γ)}) In contrast, when the difference between the temperature profile T i+1 ({dot over (γ)}) and the temperature profile T i ({dot over (γ)}) is greater than the predetermined threshold TOL, a next iteration is performed to obtain a viscosity profile η i+2 ({dot over (γ)}) and a temperature profile T i+2 ({dot over (γ)}). 
     After the true viscosity profile η TRUE ({dot over (γ)}) is obtained, the rheometer  200  is able to simulate the flow behaviors of the molding material MM accurately. Moreover, due to the accurate simulations, the performance of the injection molding process can be investigated faster and more accurately. Therefore, the injection molding process can be performed more efficiently. 
     Reference is made to  FIG. 10 .  FIG. 10  is a flowchart of the method  40  according to various embodiments of the present disclosure. In various embodiments, the method  40  further includes S 48 , S 49 , S 50 , and S 51 . 
     In operation S 48 , the plurality of behaviors of the molding material MM injected into the cavity  301  with respect to a plurality of parameter sets are simulated according to the true viscosity profile η TRUE  ({dot over (γ)}). The parameters in each parameter set includes the force F, the setpoint temperature Ts, the properties of the molding material MM, and/or the dimension of the capillary  130 . However, the present disclosure is not limited thereto, the parameters in each parameter set further includes other suitable parameters in other embodiments. 
     In operation S 49 , the plurality of flow behaviors are compared to a predetermined flow behavior to select one of the flow behaviors closest to the predetermined flow behavior. 
     In operation S 50 , one of the parameter sets corresponding to the selected one of the flow behaviors is determined to be an actual parameter set. 
     In operation S 51 , the molding material MM is injected into the cavity  301  by applying the actual parameter set. The injected molding material MM has a flow behavior as the predetermined flow behavior. Alternatively stated, the measurement of the true shear viscosity profile η TRUE  ({dot over (γ)}) is transformed to an actual injection result on the device  300 , in which the measurement improves the efficiency of the injection molding process. 
     Reference is made to  FIG. 3  again. In some embodiments, the rheometer  200  is further configured to build a digital twin model as shown in  FIG. 3 . The digital twin model has a geometric dimension identical to the dispenser  100 . Further, the digital twin model has the true shear viscosity profile η TRUE ({dot over (γ)}) to estimate the flow behaviors of the molding material MM. 
     In some embodiments, the pressure transducer  140  is not exactly installed at the inlet  131  of the capillary  130 . Therefore, the pressure (denoted as P 0 ) measured by the pressure transducer  140  differs from the pressure P 1 . Therefore, the pressure difference ΔP cap  becomes (P 0 −P 2 ), in which the pressure difference ΔP cap  is defined as (P 1 −P 2 ). According to the equation (2), the wall stress r, is deviated due to the approximation. In order to compensate the deviation, the rheometer  200  is further configured to perform a correction based on Bagley end correction to calculate a pressure difference (P 0 −P 1 ) so as to obtain the pressure difference (P 1 −P 2 ). 
     In various embodiments, the method  40  is able to be applied in a molding system other than the molding system  10  shown in  FIG. 1  and  FIG. 2 . For example, the method  40  can be applied in a molding system having dispenser with a slit die rather than the capillary. However, the present disclosure is not limited thereto. Various configurations of the dispenser in the molding system  10  are within the contemplated scope of the present disclosure. 
     One aspect of the present disclosure provides a method of measuring a true shear viscosity profile of a molding material in a capillary. The method includes the operations of: determining a setpoint temperature of the molding material before injecting into the capillary; obtaining an initial shear viscosity profile at the setpoint temperature with respect to a shear rate of the molding material; fitting an initial temperature profile with respect to the shear rate according to the initial shear viscosity based on a Cross-WLF model; fitting a first shear viscosity profile and a first temperature profile with respect to the shear rate according to the initial temperature profile based on the Cross-WLF model; and setting the first shear viscosity profile as the true shear viscosity profile when a difference between the first temperature profile and the initial temperature profile is not greater than a predetermined threshold. 
     Another aspect of the present disclosure provides a molding system. The molding system includes a dispenser and a rheometer. The rheometer is configured to perform the method of measuring a true shear viscosity profile of a molding material in a capillary of the dispenser. 
     Although the present disclosure and its advantages have been described in detail, it should be understood that various changes, substitutions and alterations can be made herein without departing from the spirit and scope of the disclosure as defined by the appended claims. For example, many of the processes discussed above can be implemented in different methodologies and replaced by other processes, or a combination thereof. 
     Moreover, the scope of the present application is not intended to be limited to the particular embodiments of the process, machine, manufacture, composition of matter, means, methods and steps described in the specification. As one of ordinary skill in the art will readily appreciate from the present disclosure, processes, machines, manufacture, compositions of matter, means, methods, or steps, presently existing or later to be developed, that perform substantially the same function or achieve substantially the same result as the corresponding embodiments described herein, may be utilized according to the present disclosure. Accordingly, the appended claims are intended to include within their scope such processes, machines, manufacture, compositions of matter, means, methods, and steps.