Meaning
Statistical metrics that evaluate the goodness of fit for mathematical models applied to experimental data points determine the accuracy of polymer melt equations. Simulation engineers utilize the reduced chi-square to assess how well a viscosity model matches raw capillary rheometer measurements. The calculation divides the chi-square statistic by the number of degrees of freedom in the data set.
A value close to unity indicates a highly accurate fit that can be safely used in flow simulations.
Model Validation
Fitting complex curves to viscosity data requires robust statistical tools to avoid overfitting the material data points. Calculating the reduced chi-square tells the analyst whether the model captures the true shear thinning behavior or merely fits the measurement noise. If the value is much greater than one, the model fails to represent the material flow correctly.
Rheological Accuracy
Polymer flow behaviors in injection moulds are highly non-linear and require precise modeling to predict pressure drops during filling. Utilizing the reduced chi-square ensures that the Cross or Carreau viscosity parameters used in the software are mathematically valid. This step reduces the discrepancy between simulated fill times and actual press performance.
Process Simulation
Inaccurate material models lead to incorrect tool design decisions and wrong machine selections. When the reduced chi-square of the viscosity fit is minimized, the simulation results reflect the real-world behavior of the flowing plastic. The resulting flow front predictions help optimize the placement of gates and cooling lines.