# Estimation of Density Distribution in a Rigid PU Foam Block Manufactured in a Sealed Mold

## TL;DR

This study estimates the density distribution in rigid polyurethane foam blocks made in sealed molds using experimental data and mathematical modeling.

## Contribution

A mathematical model using polynomial approximations to estimate density distribution in rigid PU foam blocks is developed.

## Key findings

- Density distribution was calculated and visualized with color charts and equidensity lines.
- The center of elliptical equidensity lines is asymmetrically located ≈17 mm above the geometric center.
- Density gradients were calculated in directions parallel and perpendicular to the foams’ rise direction.

## Abstract

Rigid polyurethane foams are often manufactured in sealed molds, so knowledge of the density distribution in the molded blocks is essential. A study was conducted with the aim to estimate density distribution within a rigid polyurethane foam block (average core density of ≈96 kg/m3) manufactured in a rectangular sealed mold. The density of 150 rectangular samples was determined experimentally. Characteristic locations of the foams’ columns in the block were outlined, having similar foaming conditions. Averaged density in the characteristic columns was calculated for each characteristic location. A mathematical model was developed based on density data of characteristic columns, approximated with second- and third-degree polynomials. Density distribution was calculated, and corresponding color charts with density zones and equidensity lines were constructed for six horizontal and two vertical sections of the block. It was found that the common center of the elliptical equidensity lines is located asymmetrically, ≈17 mm above the geometric center of the untrimmed block. Density gradients were calculated in directions parallel and perpendicular to the foams’ rise direction. The developed mathematical model allowed us to estimate density distribution within the rigid polyurethane foam block manufactured in a rectangular sealed mold.