Thursday, February 6, 2014

Rubber State-of-Cure vs Time and Position

Rubber state of cure generally depends on the temperature time history during the mold cycle.  It can be a complex thermal kinetics problem due to the transient nature of the cure and temperature in time and position.  The attached MS Excel Macro is a temperature and state-of-cure calculator that has 5 molding configurations:  1) planar with one heated side; 2) planar with two heated sides; 3) cylindrical with a heated inner surface; 4) heated outer surface and 5) both inner and outer surfaces heated.  For these configurations it is assumed that the molded shape has a high length-to-thickness ratio allowing the problem to be treated 2-dimensionally.

The dashboard looks like this with a worksheet tab for each configuration.

Rubber State-of-Cure Calculator Dashboard.
The calculator uses the user input cure curve information for the rubber and the calculator solves the time/position/temperatures and the resulting state-of-cure versus time and position.

This section was added on 2/22/2014:

The implicit finite difference formulation is used to solve the for the temperatures in time and position. The implicit method is unconditionally stable in time, although this does not preclude using a small time step for improved accuracy.  Progressively decreasing the time step until convergence is always good practice.  The same is true for the spatial size. In this case the number of nodes.  Any number of good references are available that describe the methodology including Fundamentals of Heat and Mass Transfer by Incropera and DeWitt, 4th Edition.

This module assumes that the thermal properties (conductivity and specific heat) do not change over the temperature range and state-of-cure.  It also assumes there is no significant additional heating from the curing kinetics.

The MS Excel Macro has been code signed with a 3rd party code signing certificate to allow higher macro security settings.

A version enabling a larger range of shapes is underway.


  1. Have you tested the accuracy of this simulation against real world data?

    I am trying to use this but do not understand how I determine when the component has reached T90.

  2. We have some actual part data that we have roughly checked this against and it appears to be relatively close.

    The model has two basic calculation elements: 1) the transient heat transfer and 2) the state-of-cure. The heat transfer is primarily a subject of the thermal conductivity of the rubber. The model currently assumes it stays constant over the cure range. This is probably is the most uncertain portion of the model.

    The cure calculation needs the Ts2 and Tc 90 values which usually are obtained from an MDR or ODR cure test.

  3. what is FDM method that you solve T(x,t)?