Parametric FEM model optimization for a pyrolitic Indesit oven

2009 Ecohitech Award: Recently, Indesit Company has won the prestigious Ecohitech Award and thus earned itself an “eco-virtuous enterprise" status.

By examining only the internal glass of the pyrolitic oven which consists of visco-elastic material, the optimization process obtained the minimum stress distribution and stress gradient.
To successfully finalize the work and to deliver the best possible technical results insuring highest quality standards are met, the following analyses have been performed by Indesit and EnginSoft:

1. Parametric FEM model creation with ANSYS
   
2. Creation of workflow in modeFRONTIER and ANSYS integration into Frontier’s loop
   
3. Optimization of the clamping system by an automated routine defined within modeFRONTIER
   
4. Results analysis and optimum design extraction according to the given objectives

The present device belongs to a new type of the Indesit domestic oven range, called Pyrolitics.
Indesit’s new technology allows a fast cleaning of oven cavity, by means of a pyrolysis process that burns encrustation caused by cooking. The Pyrolysis process starts at temperatures close to 500°C which are extremely high for a traditional device considering an external temperature of 20°C. This environment produces an high thermal gradient which considerably deforms the glass.

Picture 2.2.1 - Temperature measuring point on internal glass

The door structure of the oven is made of a triple-glass system, whereas each is separated by an air wall to guarantee rapid heat dissipation and to respect the safety regulations which limit the allowed external glass temperature to 60°C.
Glass stresses are derived from the thermal gradient, established between its surfaces, and produce a consequent deformation; an inappropriate glass clamping system would probably increase internal stresses and cause rupture.
From experimental tests, we have learned that the internal glass is exposed to the highest stresses; in fact, this is the component with higher thermal gradients between its faces. The aim of this work was to develop a methodology that allows to simulate the real working conditions of the glass and to find an optimal glass clamping solution that minimizes the stresses.

2 Structure of the model
2.1 Solid model
The model provided by Indesit has been made of a 3D door model of the oven with the actual glass clamping system. The door is composed of a 3 glass system, mounted on a specific structure that keeps them parallel and separated in order to allow the passage of the air cooling flow. This model has been simplified in order to obtain a complete glass clamp system to reproduce the real door-clamping solution.
The provided material included some elements, such as, chamfer and a non-functional fillet that have been deleted in order to create a simplified model far easier to analyze. Constraints characteristics and glass geometry have been maintained in order to produce a suitable approximated model.

2.2 Experimental measures
After some experimental measures, a series of grid-organized values of temperatures on the internal glass of the oven, was provided by the user.
These glass temperatures were obtained by some thermocouple probes on the point highlighted in picture 2.2.1.

Many repeated tests were performed in order to minimize the error of measure, and an average value of each measuring point was taken into account.
In this verification, we have considered the maximum measured values to reproduce the worst working condition.

3 Glass modeling
3.1 Thermal modeling of the glass

Picture 3.1.1. - Approximating function and error graph (relative and absolute errors respectively)

In order to perform a FEM analysis, it was necessary to assign to each node its temperature, but we had only eight measured points, that is why, the available value was modeled by using a RSM application. In fact, we used the eight measuring points to build an opportune RSM that reproduces the glass-temperature distribution with a good approximation.
A Response Surface, also called meta-model, is a post-processing tool of modeFRONTIER; in this application an approximate RSM was chosen, because all measuring points may be affected by a measuring error, due to uncontrollable thermal effects (e.g.: radiation and convection).
In picture 3.1.1, an approximate function and relative approximation error graph are shown.
Apart from obtaining a continuous tool able to estimate temperatures of all values including a variable space definition, using modeFRONTIER allows to obtain an analytical form of this surface.This expression will be used in the FEM modeler (ANSYS) to assign temp value on each node.

The next step is the application of the analytical expression to the FEM model. In picture 3.1.2 we observe the glass with the applied temperature.

Picture 3.1.2 - Constraint system of the glass

3.2 FEM Model
During the FEM modeling process, free glass deformation was evaluated firstly, or the maximum deformation reached without any constraint.
During the next step, a series of constraints was applied on the glass, in order to compare the real glass deformation with the simulation and to estimate the model reliability.

3.2.1 Free glass deformation
By using ANSYS Multiphysics as finite element solver, only a corner was bonded and thermal field was applied in order to allow any deformation due to the thermal gradient.
The thermal gradient originates from a difference in temperatures between contiguous areas; to perform the analysis we should know the values on both glass sides.
The door of the oven is composed of three glass sheets spaced by few millimeters to allow an air cooling passage, this eliminates the installation of probes on the internal sides of the glass.
To obtain all necessary temperature values and to perform our analysis, we had to model the whole multiple glass system, considering convecting effects; the known temperatures were from the measured set on the first internal glass face and a reference temperature of 60°C was established.
Once the estimated necessary temperature values were defined, we have modeled a single bond on an edge of the glass. We knew that this was an unfeasible solution but it was necessary to understand the entity of the maximum glass deformation with this temperature field.
By applying the calculated temperature function on the first glass, simulating heat transfer from the oven cavity to the room and calculating the thermal gradient on the component, we were able to obtain the maximum deformation of the glass in free conditions.
The results show that the maximum deformation is concentrated in the center of the glass, as expected. The value of this deformation is aligned to the experimental results.

3.2.2 Constrained glass deformation
The initial complete model has been simplified in order to speed up the simulation, as detailed in par. 2.1.
The constraints applied to the internal glass for the simulation of the real condition are:

• Upper support
  
• Side support
  
• Back support
  
• Lower support

Picture 3.1.2 - Glass surface with the applied node-temperature

Picture 3.1.2 illustrates the constraint system with and without glass. The upper support block YZ glass displacement, the side support block XZ displacement and the lower support block XY displacement. The constraint conditions have to be understood with a little tolerance in displacement. In fact, every constraint allows a clearance to avoid stress concentration due to an over- constrained condition.
Applying the temperature field to the modeled system as described before, we continue with the structural simulation to calculate the stress on and the deformation of the examined
component.

In order to avoid value distortion, due to mesh problems, instead of considering maximum and minimum values, we have taken into account a mean value of this quantity close to the glass constraints.

4 Optimization of the glass support
The initial model described previously has been parametrized to allow the management by modeFRONTIER; the described parameters refer to the dimensions of the upper and lower glass constraints. While we focused on these constraints, the distances from the left and right glass edges and their width were parametrized.

Picture 4.1.1 - modeFRONTIER's workflow

The aim of this step was to define an optimum set-up of the constraint system that minimizes the glass deformations in pyrolysis conditions.

4.1 Project set-up in modeFRONTIER
Variables used in this first optimization sub-step are therefore four and each couple refers to the dimension of a constraint. The constraints on the glass are four, symmetrical, and hence it is sufficient to modify the dimensions of only one to modify the couple: these will be the variables of the optimization.
Lower and upper bounds of all the variables were set according to the customer’s requirements.
By using modeFRONTIER, we want to manage the entire FEM (ANSYS) process automatically, to obtain the desired results.
To interface the FEM model with the optimizer, some macros were built, or rather a series of pre- and post-processing instructions to modify the geometry of the model during each simulation.

Picture 4.2.1 - History chart SX

During the set-up of the optimization, some factors, such as time for each calculation or maximum available time have to be taken into account in order to define the best strategy.
In this project, the time for each calculation was about 75 minutes, not negligible; this made us choose a genetic algorithm that has a good robustness to find the optimum.
The objectives were:

• Minimization SXZ shear stress;
  
• Minimization SX normal stress;
  
• Minimization SZ normal.

The chosen algorithm was the MOGA (Multi Objective Genetic Algorithm), starting from an initial random population (DOE) of the input variables domain.
Simulation parameters:

• MOGA iterations: 10
  
• DOE dimensions: 12 - variables number multiplied for objectives

With these settings we have to do 120 runs for a total run time of 150 hours

4.2 Optimization results
After the optimization process, a good convergence of results was achieved: values of shear and stresses decreased up to 40% with respect to the original configuration.
Picture 4.2.1 shows an example of the history charts of stresses SX.

Picture 4.2.2 - Displacement sun

As this is a multi-objective optimization, optimum results are more than one: in fact, we could have some designs which achieve the first objective, but are very far from the other objectives. Hence we are looking for the best tradeoff!
In this job, all three objective are very correlated, so the convergence is parallel, which allows us to choose two optimal designs.
From the obtained results we can extract some important information about the component behavior in real working conditions, especially with regard to the glass constraints dimension and their dispersion across the oven door:

• Distance of the lower constraint from the edge of the glass seems to have no influence on stresses;
  
• Width of lower constraint should be bigger than original;
  
• Distance of the upper constraint from the edge of the glass seems to have no influence on stresses;
  
• Width of upper constraint should be smaller than original;

In summary, for an optimal solution, the constraints layout should encompass the upper constraint going more close with the opposite behavior for the lower constraints. In the following picture the optimal solution is graphically represented.

Picture 4.2.3 - Elongation due to the shear SXZ

For the stresses, without having sufficient information about the glass characteristics, it is more opportune to present the deformation chart of the glass, during the pyrolysis phase.

5 Conclusions
The provided model is composed of an assembled system of three glasses, mounted on a chassis that keeps them separated to allow an air passage between them, in accordance with the regulations for this appliance.
Experimental tests performed by Indesit are focused on temperature measurement of pre-determined points located on the internal side of the first glass, in pyrolysis conditions, when the internal temperature of the oven rises to 500°C.
Punctual values of temperature, were computed with response surface modeling in modeFRONTIER in order to obtain a function that describes the temperature distribution on the entire glass, and assigns a relative value on each FEM model node.
The built map is related to the hot side of the considered glass. To calculate temperature distribution on the cold side, the entire glass system was modeled by thermal analysis. Knowing the internal cavity temperature distribution, the safety temperature on the external side of the outdoor glass and convex thermal coefficients, we were able to obtain the temperature distribution on the coldest side of the most stressed glass and hence also the thermal gradient applied to this component.

The focus of the first simulation was on examining the free constraint condition of the glass, or to verify the maximum deformation of the glass, without constraint.
In the subsequent simulations, the initial configuration, as described in the initial 3D model, was modeled with the dual purpose to validate the FEM model with experimental results, and to determine stress and deformation values of the initial configuration.

The aim of the optimization process was to find an optimal layout of the constraint system that minimizes stresses on the internal glass. To achieve this result, the FEM model was
parametrized by means of a series of instructions named “macros”, to allow modeFRONTIER to manage the geometry of the model.

The task of modeFRONTIER is to modify the model geometry on each run and to drive the input variables to the best set.
The modified parameters are referred to as the upper and lower glass constraints dimension, and in particular, the reciprocal distance and the width of each constraints are verified.

The results were the values of stress and deformation on the model, due to the thermal gradient applied. Due to imperfections in the mesh, the mean value of stresses close to constraints, was taken into account.
Obviously, the selected area for the calculation of this mean, was related to the area affected by higher stress values, to be precautionary.

The obtained results meet our expectations: a sensible decrease of stresses was registered nearby 30-40% with respect to the customer configuration, and a good conversion of results was achieved, highlighting the good quality of the work performed by modeFRONTIER.
The deformations of the optimized configuration are bigger than the original ones, which is an indication that the obtained design provides room for a better movement for the glass.

Finally, we are certain that the obtained results are sufficient and correct, and that this work has delivered further information and details about the system behavior to the modeFRONTIER users at Indesit Company.

For more information:
Ing. Nicola Baldecchi
info@enginsoft.it