Design of Experiments and Sequential Analysis used as an Optimization Technique of a ...

24 Pages·2006·2.21 MB·English

by  Axel J. Ramm

Design of Experiments and Sequential Analysis used as
an Optimization Technique of a Refrigerator Cabinet
Axel J. Ramm
Whirlpool Corporation, Joinville, Santa Catarina, Brazil.

Abstract

Global competitive pressures are causing organizations to find ways to better meet the needs of their
costumers, to reduce costs, and to increase productivity.
Nowadays the appliance industry, particularly refrigeration, is inserted in a very competitive scenario and
there is a big effort to achieve cost reductions without causing quality degradation in order to survive in the
core business.
Regarding variability in manufacturing process, refrigeration cabinets are the most affected components.
Basically they are built of external sheet metal parts, plastic inner liners and the internal volume is filled with
polyurethane foam.
In this paper it will be presented some techniques to better represent refrigerator cabinets finite element
modeling. Statistical tools will be used to help in numerical model calibration and sources of variation
evaluation. Once having a calibrated model, an optimization analysis based on Design of Experiments
technique will be carried out in ANSYS. Therefore Design of Experiments and sequential analysis will be
directly compared to subproblem approximation method of ANSYS optimization routine using APDL
(ANSYS Parametric Design Language), which is an essential step in the optimization process.
The projected cost savings covered by this paper contents are about US$1.250.000,00 per year and the
generated knowledge will be extremely useful for refrigerator cabinet design guidelines.
Introduction

Reducing the time and cost of product and process development is a key concern of today’s competitive
industrial environment. Since there is increasing evidence in refrigerator cabinets cost reductions it is required
to plan a systematic and complete study to achieve its structural optimization – saving in the product cost
while not decreasing its quality.
The main reason for guaranteeing cabinet robustness is that the lack of stiffness can generate insulation loss
due to door misalignment and aesthetics degradation, affecting directly the perceived quality by the
consumers.
Concerning the cabinet robustness, the current production cabinets are approved under a “Product Test
Method” which establishes a distortion limit for a fully assembled refrigerator cabinet at specified angular
door openings of its fully loaded door. In the same manner, there is a specification limit for door deflection
relative to the cabinet (door drop). Once the door is loaded there occurs a cabinet distortion and the door ends
up moving downwards referentially to its original position. In long periods of time this phenomenon can be
increased by polyurethane foam viscoelastic behavior whose main consequence is the occurrence of creep,
that is, an increasing deformation under sustained load and the rate of strain depending on the stress.
Therefore, the main focus was given to the response variable “door drop”.
In the other hand it is very complicated to evaluate an accurate value of cabinet deflection or door drop since
there is a lot of variation between products of the same model. The manufacturing process is surrounded of a
great number of noises that affect directly the cabinet stiffness. In the same way, the product test conditions
can significantly influence in the structural assessment results.
The dispersal environment make it only possible to discern fairly changes in cabinet stiffnesses since the
differentiation will effectively occur if the data results for a modified design retain robust from all sources of
variation. The initial step of the proposed study will be focused in sources of variation appraisal in order to
determine data dispersion (standard deviation from the mean results under a reliability degree) and to provide
conditions to plan systematic laboratory tests to help in finite element model calibration.
Considering all the relevant structural components and fixations, it was carried out a modeling of an overall
refrigerator cabinet finite element. In addition, it was modeled the refrigerator and freezer doors with the
purpose to provide proper loading distribution and serve as reference to evaluate the door drop due to cabinet
distortion.
A proper finite element model validation is essential to start the cabinet optimization study because
knowledge about variation has been gained and now the numerical model structural behavior is quantitatively
in accordance with the real conditions.
The essential technique used to approach the study was the sequential strategy based on Design of
Experiments.
The Design of Experiments is a technique used to plan experiments, consisting in a series of tests of a system
carried out by changing levels of factors and background variables and an observation of the effect of that
change on the response variable.
The sequential nature of learning should be considered in planning experiments. As knowledge is gained
sequentially, experiments will be refined by using new levels for the factors (inference space), adding some
new factors or eliminating the negligible ones.
To set up a factorial design, the investigator determines the factors to be studied and the levels for each. A full
factorial design consists of all possible combinations of the factors and levels, making it possible to obtain the
maximum experiment resolution, since there are not any aliasing between main effects and higher-order
interactions.
The number of runs required by a full factorial design increases geometrically as the number of factors
increases and an increasing amount of the data is used to estimate higher-order interactions. These
interactions are usually negligible and therefore are of little interest to the experimenter. Fractional factorial
designs are an important class of experimental designs that allow the size of experiments to be kept practical
while still enabling the estimation of important effects. The negative point of using fractional factorials is the
confounding of factors and its interactions, depending on the experiment resolution.
All of the most important steps concerning Design of Experiments sequential analysis are presented in this
paper since fractional factorial designs and parameters selection up to the final optimum solution. Afterwards
ANSYS traditional optimization techniques specifically Subproblem Approximation Method will be used as a
comparison of the study based on sequential analysis.
Refrigerator Cabinet Geometry

The product considered in this analysis is a 450 liters double door refrigerator which has been in production
for over two years.
The refrigerator cabinet construction comprises basically external sheet metal parts, polyurethane foam filling
and internal plastic liners. The metal parts are: wrapper (with roll-formed reinforcements), back panel, bottom
deck, intermediary rail, front rail, compressor mounting plate, glider rails and hinges (upper, center and
bottom). The cabinet inner liners are made of plastic material adhering to the polyurethane foam with outer
layers and internally forming the refrigerator and freezer compartments.
Figures 01 and 02 show some of the refrigerator cabinet most important parts.
Figure 01. Cabinet Components – Front View
Figure 02. Cabinet and Doors Assembly – Opened and Closed Doors

Model Description and Modeling Techniques

The finite element model is composed of solid and shell elements. The polyurethane foam, EPS mullion,
hinges and levelers were modeled with solid tetrahedrons elements (Solid 45) and other parts, basically
composed of thin plates, were modeled with Shell 181 elements. For all the connections of clinch joints and
screws it was adopted the use of the element beam 181.
All the materials properties were considered as linear isotropic and the input data was picked from laboratory
tests and supplier technical reports. Particularly for polyurethane foam, once it is susceptible to a high level of
variation (position to position in the cabinet and due to injection process fluctuation), the elastic properties
were evaluated in a laboratory test device and elasticity modulus was included as a factor in the analysis
considering the levels as the mean of its minimum and maximum values.
In order to adequately represent the real loading conditions, it was evaluated the mass of all cabinet parts. All
the evaluated masses were distributed in its proper position and eventually the total mass and the gravity
center of the real fully assembled cabinet was very similar to the finite element model one.
On its bottom base the cabinet was constrained simulating a real operating condition. Considering that all
cabinet supports were able to rotate, only translations were restricted at three base locations. The figure 03
shows the constraints application.
Figure 03. Boundary Conditions.

The door attachments with the hinges were modeled with constraint equations which allowed controlling
translations and rotations to be correctly transferred from the doors to the cabinet. Thus, it was possible to
impose door support only at its bottom position and release rotations from hinge pins. Therefore it was
necessary to set two additional constraints at the upper liner of each door to eliminate rigid body motion
(figure 03).
Regarding the Product Test Method, the masses corresponding to the cabinet and doors loading were
distributed at each own particular location. The acceleration due to gravity was applied as load boundary
condition. The figure 04 shows the masses disposition in the cabinet and doors liners which were applied to
the finite element model.
Figure 04. Cabinet Loading (Mass) Distribution.

For the door drop assessment it was considered the analytical model with its doors at the closed position. The
response variable was established as the subtraction of door drop and cabinet drop with the purpose to
consider only the relative displacement between door and cabinet. The figures 05 and 06 show the evaluation
scheme of cabinet door drop.
Figure 05. Analyzed Finite Element Model: Cabinet Distortion due to Door Loading.

Figure 06. Cabinet Door Drop Evaluation.
Sources of Variation Evaluation

Only when a numerical model is calibrated it can be used to perform a correct assessment of its structural
performance and afterwards run an optimization analysis.
The first step of a model calibration was the definition of some possible sources of variation which could
generate errors to test data collection. From the Test Process Map it was elected four factors considered as the
most influencing ones: different products of the same model, test setup, door opening velocity, time to read
data and different measurements. The Sample Three Diagram is presented in figure 07.

Figure 07. Experiment Sample Tree Diagram.

The total sum of cabinet lateral displacement (sway X) was considered to be the response variable. Regarding
the test conditions, initially the doors were closed (zero position), thus the signal starts to be saved and hence
the doors were opened. The figure 08 shows an example a sample of signal collected from one experiment
run. The sum modulus of the signal peak and valley is considered to be the cabinet Sway X.

Figure 08. Signal Collected from a Laboratory Test.

In the Sample Three Diagram it can be realized that the data collection started with the random choice of four
products of the same model. Each product was tested under two different setups (put the cabinet at the test
position), two door opening velocities (fast and slow) and the time for reading the cabinets deflection was
computed at 15 seconds and 3 minutes respectively. Each configuration was measured three times, totaling a
number of 96 measures.
For the data collection analysis it was used an important statistical tool: Control Charts. Control Charts for
Averages and Ranges are a simple and effective way to present data for a use as a basis for process stability
evaluation, making it possible to track both the process level and process variation at the same time, as well as
detect the presence of special causes. The figure 09 shows the Sample Mean (Averages) and Sample Range
chart for displacement measurement at the cabinet upper lateral corner.

Xbar-R Chart of Sway X
5,0 1
1
n 4,8 1 1 1 1
a
e 1
M
ple 4,6 __UCL=4,6283
m X=4,5094
a
S 4,4 LCL=4,3904
1 1
1 1
4,2 1 1 1 1 1 1
1 4 7 10 13 16 19 22 25 28 31
Sample
0,3 UCL=0,2993
e
g
n 0,2
a
R
e _
pl R=0,1162
m 0,1
a
S
0,0 LCL=0
1 4 7 10 13 16 19 22 25 28 31
Sample
Figure 09. Sample Means Average and Sample Range Charts.

The process is said to be SPC (stable, predictable and consistent) if all the points existing in the Range Chart
are inside the control limits. Analyzing the Sample Range Chart in figure 09 it can be checked out the process
stability.
An important issue to carry out is the MSE (Measurement System Evaluation). The measurement system is
said to have enough discrimination if there are as much as required levels of resolution in the Range chart.
The capacity to evaluate measure between subgroups occurs if there are more than 50% of the points out of
the control limits in the Sample Mean chart. Looking at Sample Mean Chart in figure 09 it can be realized that
these requirements are also verified for the measurement process.
Figure 10 shows a very important graph - Variability Chart. Variability Chart plots the mean for each level
side by side. Along with the data, you can view the mean, range, and standard deviation of the data in each
category, seeing how they change across the categories.
This graph is also very helpful to look for systematic effects between factors and levels. A very interesting
thing to observe is that always at the time of 3 minutes the measures are greater than at the time of 15 seconds
– it can be explained by the creep effect of the polyurethane foam inside the cabinet.
Figure 10. Variability Chart and Components of Variation (COV) Calculation.

To quantify the contribution of each factor it is employed a variance components analysis (COV). Performing
a COV study it could be checked that the variation between products is the most significant over the other
selected factors. This issue indicates that no matter levels of setup, velocity, time and measure levels are
configured, always the product-by-product variation will stand out among them. Check that the bottom part of
figure 10 displays that 71,7% of total variation in the response variable is due to differences among products
(manufacturing).
With the purpose to assure better reliability in data for numerical model calibration it was decided that the
number of samples for different products of the same model had to be increased. Therefore 16 products were
randomly selected from the manufacturing line and tested considering only the factors: products and
measures. The figure 11 shows the control charts for the assigned experiment.