December 5, 2017
Optimization of pultrusion of glass-fiber reinforced profile
Based on the article "Optimizing Pultrusion of Glass-Fiber Reinforced Plastic Components" by Bruce Jenkins, Digital Engineering
Structural components made of glass-fiber reinforced plastic (GFRP) fabricated into complex-profile linear shapes are widely used today in aerospace, civil infrastructure and other industries. Pultrusion (pull + extrusion) is one of the most efficient processes for producing polymer composite materials with complex structural profiles. It is a continuous molding process in which reinforcing fibers are saturated with a liquid polymer resin, then pulled through a heated forming die to create the desired part. In pultrusion of GFRP products, a continuous reinforcement consisting of glass fiber roving and tapes is pulled through an impregnation bath containing a thermoset resin, then fed into a heated die that shapes the pultruded profile cross-section into the required geometry and cures the resin.
Pultrusion process: (1) creels with reinforcement, (2) resin impregnation bath, (3) folding unit, (4) forming die, (5) control panel, (6) pulling unit, (7) cutoff unit.
In this case study, DATADVANCE worked with Skoltech (Skolkovo Institute of Science and Technology) to develop methods for numerical optimization and sensitivity analysis of pultrusion process parameters for a C-section glass-fiber profile with dimensions 400mm X 120mm X 18mm used in bridge construction. The main goal of optimizing the pultrusion process parameters is to maximize the pulling speed in order to achieve maximum production rate while satisfying temperature, stress, deformation and quality constraints.
The challenge was to maximize pulling speed – the rate of production – while minimizing the product’s tendency to deform when critical process parameters are exceeded. Numerous phenomena had to be taken into account in order to accurately characterize the changes that occur as the preformed product passes through the heated die, including:
- Transfer of heat into the composite material
- The chemical reaction of the curing process
- The internal release of energy during this reaction
- Temperature and chemical deformations within the preformed product
- Thermal and mechanical contact with die surfaces
- Changes in thermal and mechanical properties of the composite material that result from phase transformations in the resin
In simulating the behavior of composite materials that incorporate thermoset resins, there is a need to determine the phase state changes in the resin over time. To characterize the phase state changes, a cure degree (changing within a range from 0 to 1) was used. The simulation of cure processes in thermoset composite materials was carried out using the Abaqus Standard implicit solver.
For stress determination, a model of transversely isotropic material was used. This model was implemented in Abaqus by means of a user subroutine mechanism. Thermal conductivity equations were solved using standard Abaqus tools.
Temperature in the pultruded profile
Degree of curing in the pultruded profile
As a relatively large air gap is formed between the pultruded profile and the die surfaces due to temperature deformations and chemical shrinkage, evaluation of the gap influence on the stress-strain state in a pultruded profile required an additional calculation step.
For numerical optimization and sensitivity analysis of process parameters, a simulation scheme was developed in pSeven, with 4 optimization parameters:
- Initial temperature of resin, T0
- Die first-zone temperature (where forming takes place), T1
- Die second-zone temperature (where resin curing takes place), T2
- Pulling speed, U
Table 1: Process parameters and bounds
|Parameter||Initial value||Lower bound||Upper bound||Description|
|T0, C||50||20||50||Initial temperature of material|
|T1, C||150||120||160||Temperature of die zone 1|
|T2, C||190||150||190||Temperature of die zone 2|
|U, mm/s||1.0||0.75||1.25||Pulling speed|
And 3 constraints to be considered:
- Maximum temperature of the material, Tmax
- Minimal degree of curing at the end of the die zone, α
- Maximum transverse stress in pultruded profile, Smax
Table 2: Constraint values
|Tmax, C||< 190||Prevent thermal decay|
|α||> 0.95||Provide material quality|
|Smax, MPa||< 11||Prevent from cracking|
The study was performed in two steps.
A uniform design of experiment (DOE) was conducted to study the model behavior and sensitivities. A sample of 45 points was obtained with the Latin hypercube sampling method. Sensitivity analysis was conducted on this data to estimate how variations in the model output can be attributed to variations in the model inputs.
An approximation model based on Gaussian processes was built with maximum RRMS error (based on training sample) of 0.04. Since one of the optimization goals is to reduce deformation of the pultruded part, the springback angle distribution over the parameter space was studied. Springback angle was shown to be only 0.5 degree at maximum, and less than 0.25 degree for almost half of all possible configurations. Increase in pulling speed does not lead to significant deformation; this finding allowed investigators to expect a flat Pareto frontier in carrying out the Pareto (multi-objective) optimization of springback angle vs. pulling speed.
The approximation model allows visualization of the areas for different constraint violations. Such areas are presented in coordinates T1 vs. T2 with ranges for the different initial temperatures and pulling speeds in Table 1.
This study showed it is possible to obtain configurations that satisfy all constraints. However, the allowed solution area is quite small.
Constraint violation areas
A two-criteria optimization problem was solved: the two goals were to minimize springback angle while maximizing pulling speed. The problem was solved using multi-objective surrogate-based optimization (MSBO) algorithm. A key feature of the MSBO algorithm’s implementation in pSeven is the ability to define the computational budget (number of model evaluations allowed). Together with an initial 45 data points, only 80 evaluations were made to discover the Pareto frontier, as shown below:
Optimization results (Pareto frontier) zoomed in
All configurations on the Pareto boundary were shown to have very small values for springback angle, so the problem effectively turned into a one-criterion (pulling speed) optimization problem.
Comparison between the initial configuration and the optimized configuration with maximum pulling speed is shown below. The comparison shows that not only was the pulling speed increased by 18%, but in addition, the temperature constraint is now satisfied.
|Parameters and goals||Initial configuration||Optimal configuration|
|Springback angle, deg||0.24||0.13|
|Stress in, MPa||11||11|
|Stress out, MPa||9||8|