Mathematical Equations used in PET Preform Design {Part I}

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 PET (Polyethylene Terephthalate) preform design involves creating a mold for manufacturing PET bottles. Mathematical equations are used in PET preform design to ensure that the preform has the correct dimensions, weight, and properties that are necessary for the final product.

One important equation used in PET preform design is the equation for calculating the weight of the preform. The weight of the preform is important because it determines the amount of PET material required for each bottle. The equation for calculating the weight of the preform is:
                      Weight of Preform = Volume of Preform x Density of PET

The volume of the preform is calculated using the following equation:
                   Volume of Preform = π x (Neck Diameter/2) ^2 x (Preform Height - Neck Height)
Where
 π is the mathematical constant pi, Neck Diameter is the diameter of the neck of the bottle, Preform Height is the height of the preform, and Neck Height is the height of the neck of the bottle.
Another important equation used in PET preform design is the equation for calculating the wall thickness of the preform. The wall thickness of the preform is important because it affects the strength and stability of the final product. The equation for calculating the wall thickness of the preform is:
                                       Wall Thickness = (Preform Diameter - Neck Diameter)/2

Where Preform Diameter is the diameter of the preform.
These equations, along with other mathematical calculations and simulations, are used in PET preform design to optimize the design for various factors such as the desired bottle shape, production efficiency, and material properties. For example, mathematical simulations can be used to predict the behavior of the PET material during the injection molding process, helping to optimize the preform design for minimal defects and maximum strength. Overall, mathematical equations play an important role in PET preform design by providing a quantitative way to ensure that the preform design meets the desired specifications and performance requirements.

1- Injection Force Equation:
The injection force equation relates the injection pressure to the injection force, considering the projected area of the cavity.
                      Injection force = Injection pressure * Projected area of the cavity
where the projected area is the area of the cavity's cross-section in the direction of the injection.
2- Axial Strain Equation:
The axial strain equation relates the preform's axial strain to the stretch ratio and the preform's original and final lengths.
                                             εa = ln(Lf / Lp)
where 
  1. εa is the axial strain
  2.  Lf is the final bottle length
  3. Lp is the preform length
3- Hoop Strain Equation:
The hoop strain equation relates the preform's hoop strain to the stretch ratio and the preform's original and final diameters.
                                                             εh = ln(Df / Dp)
where 
  • εh is the hoop strain, 
  • Df is the final bottle diameter, 
  • Dp is the preform diameter.
4- Conditioning Time Equation:
The conditioning time equation relates the preform's conditioning time to the conditioning temperature and the activation energy of PET.
                                                                 t = exp((Tc - T0) / Q)
where 
  • t is the conditioning time, 
  • Tc is the conditioning temperature, 
  • T0 is the initial preform temperature
  •  Q is the activation energy of PET.
5-Intrinsic Viscosity Equation:
The intrinsic viscosity equation relates the intrinsic viscosity of PET to its molecular weight.
                                                        ln(IV) = -k * ln(Mw) + b
where 
  • IV is the intrinsic viscosity, 
  • Mw is the molecular weight,
  •  k and b are constants.
These equations are essential in the PET preform design process to ensure that the preform's dimensions and mechanical properties meet the bottle's requirements.

This was prepared and written by
     Eng/ Mohamed Bayoumi 
   Mobile +201550289138


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