Meaning
Scalar sensitivity measures compute the ratio of relative output error to relative input perturbation for a linear mapping or numerical matrix. In numerical process modelling and polymer tooling simulation, the condition number of a stiffness or conductivity matrix indicates whether small variations in boundary measurements produce outsized errors in predicted displacements or temperatures. Values close to unity signify stable, well-posed systems where roundoff noise or measurement tolerance does not corrupt the output.
As values climb toward infinity, small changes in clamping force or measured displacement cause large shifts in calculated residual stress or warpage profiles. The definition ceases to apply when a governing operator becomes nonlinear or cannot be reduced to a singular-value decomposition.
Numerical Sensitivity
Inversion routines fail when ill-conditioned systems amplify floating-point truncation. A high condition number in polymer filling simulations frequently arises from aspect-ratio distortion in thin-walled finite elements. When element thickness drops to a fraction of a millimetre while planar dimensions span tens of millimetres, the governing equations generate stiffness matrices with disparate eigenvalues.
Calculating warpage fields from these assemblies yields numerical divergence or artificial deflections that do not originate from mould shrinkage. Regularisation techniques or double-precision linear solvers damp these artifacts.
Moulding Distortion
Process engineers map measured part deflections back to cavity pressure distributions through inverted sensitivity equations. The condition number of this inverse formulation determines whether tool repositioning calculations converge reliably during multi-cavity balancing. If two pressure transducers sit too close to one another along a runner, their response vectors become nearly parallel.
That spatial alignment inflates the ratio, causing the optimization algorithm to suggest extreme steel adjustments for minimal flow imbalances. Correct transducer placement reduces the ratio and stabilizes tooling corrections.
Process Stability
Physical variation in feedstocks alters the practical limits of mathematical process controllers. Batches containing regrind show fluctuating melt flow indices, altering shear heating and pressure loss through gates. If the predictive algorithm governing pack-and-hold pressures possesses an elevated condition number, standard five-percent shifts in polymer viscosity cause wild swings in commanded barrel pressure.
Flashing or short shots follow directly from these erratic machine corrections. Linear controllers run reliably when the operator matrix maintains a low value across the full operating window.
