Runner Balance derivation

Runner balancing is performed as a conditional minimization of a criterion function, which is calculated by using the results of a simplified analysis.

A runner system with dimensions that satisfy the criterion function is considered to be a balanced system.

The criterion function

The criterion function is the weighted sum of the following factors:

• Volume, whose value indicates the fraction of the final runner volume in the full shot volume
• Pressure, whose value indicates how close the maximal injection pressure is to the maximum allowed value
• Pressure imbalance, whose value indicates the difference between the average pressure required to fill the most difficult cavity and the average pressure required to fill the easiest cavity
• Shear heating, whose value indicates the intensity of shear heating in the runners
• Runner size ratio, whose value indicates the change in runner size throughout the feed system
• Temperature, whose value indicates the minimum flow front temperature encountered
• Frozen layer, whose value indicates the maximum frozen layer fraction

The optimization stops when the value of the criterion function for an iteration is less than a set value, or when the limit for the number of iterations is reached.