Cross Machine Caliper Profile Control on High Speed Coated Packaging Lines
Cross-machine caliper control demands real-time induction calender profiling to maintain stiffness and prevent high-speed converting line jams.
Euler Bernoulli Beam Theory
Structural Mechanics
A classical mathematical model calculates the deflection and internal stresses of structural elements under transverse loads. When applying euler bernoulli beam theory, the model assumes that cross sections perpendicular to the neutral axis remain plane and perpendicular after bending occurs. This simplification allows for the analysis of stiffness and bending resistance in paperboard packaging during transport and storage.
The formulation is restricted to slender beams where shear deformation does not influence the overall deflection.
Deflection Analysis
The calculation relies on the relationship between the applied bending moment, the elastic modulus of the paperboard, and the area moment of inertia of the sheet profile. For multi-ply paperboard, the elastic properties of each individual layer must be integrated to determine the overall bending stiffness of the composite board. Using these mathematical formulas helps designers optimize the thickness and density of outer plies to resist buckling under top load.
By placing high stiffness fibres in the outer layers, the overall resistance of the carton to compression increases without adding excess weight.
Stress Prediction
Predicting the maximum load before crease failure or folding resistance limit relies on these stress profiles. The model is useful for determining the stacking strength of corrugated containers in humid environments. It provides the analytical basis for standard stiffness tests used throughout the packaging industry.