1. 1
SAE TECHNICAL 2008-36-0101
PAPER SERIES E
The Use of QFD and TRIZ in the Component Mathematics
Modeling for Virtual Durability Simulation
Silas Luis Sartori Paschoal da Silva Rosa
MSX International The Smart Alternative
Cristiano Vasconcellos Ferreira
SENAI CIMATEC
3. 3
MODELLING FOR VIRTUAL DURABILITY
SIMULATION
The method used to optimize the durability
computational simulation component searches to use the
tools of project of the QFD and the TRIZ. The considered
method was used to define the best element to attach the
hard points of the component in its base.
To carry through the computational simulation it was
used MSC_Nastran software 2004 R2, Sol 103 (normal
modes with option: design sensitivity – modes) and Sol
112 (modal transient response). [17].
As tool of support to this process the First Matrix of
the QFD was used. The identified necessities are listed
below. After the customer’s necessities, it was classified.
Initially, the necessities of the involved customers
were identified, and then the project requirements had been
listed, as listed to the Tab1.
Primary
requisite
Secondary necessities of the customers Tertiary Necessities of the customers
To minimize the time of elaboration of
the mathematical model
Low index breaks
Easiness of use
Modeling optimization
Standardization of the Corporative
specifications of materials
Compatibility of the results gotten with
the physical tests carried through with
the vehicles
Not to allow to incorrect modeling
Repeatability of the modeling
Topresentvirtualresultsthat
faithfulrepresenttheresultsofthe
durabilityofthevehicle
Economic
Use
Corporative
Tab1. Customers Necessities.
Based on these necessities, the strategies
simulations were evaluated on the modified morphologic
matrix, according to Tab 2.
1 Squared elements on mesh
Previous experiences on
works Elements normalization Use auto-mesh program
2 Avoid elements distortion
Use elements with small
variation base x height
Use similar forms on
elements Use similar size elements
3 Warpage
Use one plane for
element Avoid deformed surfaces Use auto-mesh program
4 Confection time mesh Use auto-mesh program Elements normalization
Use similar forms on
elements
5 Trustworthiness model
Previous experiences on
works Use auto-mesh program
Use elements with small
variation base x height
6 Repeatability Elements normalization
Previous experiences on
works
Use similar forms on
elements
7 Set time model Use auto-mesh program Elements normalization
Use elements with small
variation base x height
Principle 1
Principle 2
Principle 3
Principle 4
Solution Principles
Functions
Tab 2 – Modified morphologic matrix.
The objective of this article is to determine the
best modeling and simulation strategy component
mathematics modeling for virtual durability simulation [11]
[12]. To generate these strategies, the modified
morphologic matrix (according to Tab2) was used to
describe in the line the design requirements and in the
columns the possible solutions for the project
requirements. These possible solutions had been developed
based on the inventive principles of TRIZ. Each principle
represents one modeling and simulation strategy.
The strategies simulations shown on the modeling
generated had been combined giving origin to the possible
solutions of the simulation problem. In this case, is
proposed the use of Matrix of Pugh [5] to evaluate the best
solution strategy. Tab 3 shows the evaluation of the
generated solutions.
Requirements of Project Peso
Use of elements squared in the mesh 5 4 2 4 3
To prevent distortion of the elements 6 1 1 1 1
Warpage 5 3 3 2 4
Confection time mesh 5 1 1 1 1
Trustworthiness of the model 6 4 2 4 3
Model repetibility 5 1 1 1 1
Confection time mesh 5 1 1 1 1
10 7 9 9
1 - Bad
2 - Reasonable
3 - Good
4 - Excellent
Soluction principles
Tab 3. Pugh Matrix [5] [2]
Each symbol shown in the Tab 2 represents a
solution principle. After the analyzes of the Pugh Matrix,
the best solution is the Principle 1. In this case the best
modeling and simulation strategy is the first one (square):
Principle 1: Squared elements on mesh (Previous
experiences on works), Avoid elements distortion (Use
similar forms on elements), Warpage (Avoid deformed
surfaces), Confection time mesh (Use auto-mesh program),
Trustworthiness model (Use elements with small variation
base x height), Repeatability (Previous experiences on
works) and Set time model (Use auto-mesh program).
2. QFD
Quality function deployment (QFD) was originally
developed by Yoji Akao in 1966 when the author
combined his work in quality assurance and quality control
points with function deployment used in Value
Engineering. According to Akao [1] [10] QFD is a method
to transform using demands into design quality, to deploy
the functions forming quality, and to deploy methods for
achieving the design quality into subsystems and
component parts, and ultimately to specific elements of the
manufacturing process.”
QFD is designed to help planners focus on
characteristics of a new or existing product or service from
the viewpoints of market segments, company, or
technology-development needs.
QFD can be applied in a wide variety of services,
consumer products, military needs and emerging
technology products. The technique is also used to identify
and document competitive marketing strategies and tactics.
QFD is considered a key practice of Design for Six Sigma
4. 4
(DFSS). [3] It is also implicated in the new NBR ISO 9000
standard which focuses on customer satisfaction.
Results of QFD have been applied in many
companies into deploying the high-impact controllable
factors in strategic planning and strategic management,
including the U.S. automobile manufacturers (GM, Ford,
Daimler, Chrysler) and their suppliers, IBM, Raytheon,
General Electric, Boeing, Lockheed Martin, and many
others. [6] [8] [9].
The use of the First Matrix of QFD, House of
Quality, in the development of CAE solutions for product,
specially in the determination of boundary restriction,
performance parameters and other variables during the
CAE simulation.
House of Quality is a graphic tool for defining the
relationship between customer desires and the firm/product
capabilities. It is part of the Quality Function Deployment
(QFD) and it utilizes a planning matrix to relate what the
customer wants to how affirm (that produce the products)
is going to meet those wants. It looks like a House of
Quality with correlation matrix as its roof, customer wants
versus product features as the main part, competitor
evaluation as the porch etc. It is based on "the belief that
products should be designed to reflect customer's desires
and tastes" [3]. It also is reported to increase cross
functional integration within organizations using it,
specially between marketing, engineering and
manufacturing.
The basic structure is a table with "Whats" as the
labels on the left and "Hows" across the top. The roof is a
diagonal matrix of "Hows vs. Whats" (correlation matrix)
and the body of the house is a relationships matrix of
"Whats vs. Hows". Both of these matrices are filled with
indicators of whether the interaction of the specific item is
a strong positive, or a strong negative, or somewhere in
between. Additional annexes on the right side and bottom
hold the "Whys" (market research, etc.) and the "How
Much". Rankings based on the Whys and the correlations
can be used to calculate priorities for the "Hows".
The signals that they represent how much bigger,
better and that it represents how much lesser better for
each requirement. “Ranking” of the RP´s was carried
through the addition of the degree of relationship with the
values attributed to each necessity. Thus, they had started
to have an importance order, see in the end of each
column. The figure 4 represents de House of Quality of
QFD.
In this paper, the correlation matrix of the QFD will
be presented in a different way like shown on Tab4.
The signals ++++++++ means strongly positive relationship,
++++ means positive relationship, O means no relationship,
−−−− −−−− means strongly negative relationship and −−−− means
negative relationship.
The symbol identify the conflicts of the matrix
and to solve them will be used the TRIZ, presented in the
next sub-heading.
Custumers necessities
Quantitativeevaluation
(importance)
Useofelements
squaredinthemesh
Topreventelements
distortion
Warpage
Timemeshconfection
Reliabilityofthemodel
Modelingrepeatability
Resultstime
Loaddistribution
component/Element
type(RBE2)
Loaddistribution
component/Element
type(RBE3)
1 2 3
To minimize the time of elaboration of
the mathematical model
3,9 5 3 5 5 3 3 3 4 5 5 5 5
Low index of in addition the evaluated 3,0 1 5 3 3 5 3 1 4 4 4 4 4
Easiness using 2,9 5 3 1 2 5 3 1 4 5 2 2 3
Optimization of the modeling 3,9 5 5 3 5 5 3 1 4 5 4 5 3
Standardization of the specifications of
materials
1,6 1 1 1 1 3 3 1 5 5 5 5 4
Compatibility of the results gotten with
the physical tests carried through with
the vehicles
3,9 5 5 5 3 3 3 3 5 5 3 2 5
Not to allow to incorrect modeling 3,9 5 5 5 3 3 3 3 5 5 5 4 3
Repeatability of the modeling 1,6 1 1 1 1 1 3 3 5 5 3 4 4
3,5 3,5 3,0 2,9 3,5 3,0 2,0 4,5 4,9 4 4 4
97,6 96,1 84,4 79,6 89,6 73,3 50,7 108,6 119,1
3 4 6 7 5 8 9 2 1
Average
Softwares
competitors
Weightened importance
Ranking
Tab 4. QFD Quality House.
House of Quality analysis can also be cascaded,
with "Hows" from one level becoming the "Whats" of a
lower level; as these progresses the decisions get closer to
the engineering/manufacturing details.
With the necessities of the customers and the
requirements of projects identified, had been carried
through the relationships between both in order to identify
the requirements of more important project.
It is important to stand out the job of the roof in
the Matrix of the QFD, where the contradictions between
the project requirements are identified. In this case, they
identified the conflicts points in which occurrence.
According to the QFD House of Quality, the best
element to be used to fix the shock absorber and the spring
on the base are the RBE3 element. The optimization of
5. 5
product engineering parameters is a complex activity, since
during its execution, contradictions and conflicts with the
other engineering parameters can appear. Thus, to solve
these contradictions and conflicts it is necessary to look for
an inventive principle. For this, Altshuller (1946) [16]
developed a Matrix of Contradiction presented in figure 5.
In the case of the simulation process (CAE), the
involved team searches the “use of elements squared for
the mesh”, however, in view of the complex geometry of
the products, this solution is not possible. In this in case
that, the team must search solutions alternative, which can
cause distortion of elements, situation that also is not
desirable.
In view of identified these conflicts suggests to
use of the TRIZ to solve them.
3. TRIZ
The Theory of Inventive Problem Solving (TRIZ),
was developed by Genrich Altshuller [16], at the end of the
40’s. To do this, the author examined approximately,
1,500,000 patents of products, and observed the existence
of a series of 40 inventive principles, which are technical
indications and orientations for solving problems; and, he
also observed 39 engineering parameters, which
characterize and define the product from the engineering
point of view [4].
According to Altshuller (1946) [16], the activity of
product design can be defined as a search process for a
"ideal solution" for customer needs. Hence, product design
can be seen as a process of optimizing engineering
parameters and a search for solutions through the inventive
principle [4].
The 39 engineering parameters of TRIZ are now
presented:
1. Weight of moving object;
2. Weight of non-moving object;
3. Length of moving object;
4. Length of non-moving object;
5. Area of moving object;
6. Area of non-moving object;
7. Volume of moving object;
8. Volume of non-mobving object;
9. Speed;
10. Force;
11. Tension, pressure;
12.Shape;
13. Stability of object;
14. Strength;
15. Durability of moving object;
16. Durability of non-moving object;
17. Temperature;
18. Brightness;
19. Energy spent by moving object;
20. Energy spent by non-moving object;
21. Power;
22. Waste of energy;
23. Waste of substance;
24. Loss of information;
25. Waste of time;
26. Amount of .substance;
27. Reliability; 28. Accuracy of measurement;
29. Accuracy of manufacturing;
30. Harmful factors acting on object;
31. Harmful side effects;
32. Manufacturability;
33. Convenience of use;
34. Reparability;
35. Adaptability;
36. Complexity of device;
37. Complexity of control;
38. Level of automation;
39. Productivity.
The 40 Inventive Principles of TRIZ are now
presented [7]:
1. Division;
2. Extraction;
3. Local Quality;
4. Asymmetry;
5. Combining / Merging;
6. Universality;
7. Nesting;
8. Counterweight;
9. Preliminary Counteraction;
10. Preliminary Action;
11. Compensation;
12. Equipotentiality;
13. Reverse;
14. Sphericity;
15. Dynamism;
16. Partial or excessive actions;
17. Change Dimension;
18. Oscillation / Mechanical vibration;
19. Periodic Actions;
20. Continuity of useful action;
21. Skipping;
22. Turn a Minus into a Plus;
23. Feedback;
24. Intermediary;
25. Self Service;
26. Copying;
27. Cheap Short;
28. Mechanics substitution;
29. Pneumatics and hydraulics;
30. Flexible Membranes;
31. Porous Materials;
32. Changing Color;
33. Homogeneity;
34. Discarding and recovering;
35. Changing Properties;
36. Phase transitions;
37. Thermal Expansion;
38. Oxidant;
6. 6
39. Inert atmosphere;
40. Composite Materials.
In the case studied, for the conflicts identified, "time
mesh confection" and "to prevent distortion of the
elements", as well as, "time mesh confection" and "use of
elements squared in the mesh", can be used the following
inventive principles to solve them, proceeding from the
Matrix of Contradiction of the TRIZ:
"Local quality" – in order to avoid the distortion in
the quality of the elements, the risk can be assumed to
increase the time of confection of the mesh.
In the case of the conflict "reliability of the model”
and "time mesh confection" enters the project
requirements, the solution can be searched using the
beginning of the Triz:
“To convert damage into benefit” – time mesh
confection can be processed with this also increasing the
reliability in the model.
In the case of the conflict "time mesh confection" and
“Reliability of the model”, can be solved using itself the
beginning of the TRIZ:
“Combining” – it is possible to manage the time of
confection of the mesh in function of the time spent to run
the model and the reliability of the model.
To use Matrix of Contradiction the design team
should analyze the design in terms of the subject and
identify the engineering parameters that must be optimized
and those one that cause conflicts or contradiction with the
first ones. For example, suppose that there is a design of a
cylindrical tank and an engineering parameter to be
optimized, such as a length of movable object. The
engineering parameter, for example, that causes conflict
with the first one is strength.
Considering the TRIZ philosophy, this application is
possible to define the best strategy to solve the simulation
problem, including the definition of boundary variables,
the best optimization strategy for the problem and
simulations results precision is possible.
According to the approach of QFD and TRIZ the
design team can use these tools to establish the best
simulation strategy, to indicate an orientation about
constrains and the boundary condition, as well as the
engineers needs. These guidelines will be used to support
the design team in the establishment of component
mathematics modeling for virtual durability simulation.
The requirements identified of project in the QFD
had been associates to the 39 parameters of the TRIZ. As
result, the respective parameters of engineering of the
TRIZ to be optimized and the conflicting ones had been
identified.
The parameters of engineering of the TRIZ had been
used in the Matrix of Contradiction of the TRIZ to identify
the inventive principles that can identify a possible solution
for the project.
4. COMPONENT MATHEMATICS MODELLING
TO VIRTUAL DURABILITY’ SIMULATION –
PROPOSED MODEL APPLICATION
The objective of this simulation is to show that, bases
on the results of proposed methodology (described in
section 3), the element type RBE3 is better than RBE2 to
be used in this work. Initially, it will be described the
application results using RBE2 elements and in the
sequence the results using RBE3 elements.
In the process of simulation of components it presents
a complex nature in view of the large number of involved
variables. One of the main critical points involves the
definition of the most adjusted type of mesh element to be
used in the project. [13] [14] [15].
Virtual durability simulation is a process that
represents the real durability of the vehicle running in the
test track of the proving ground, but in this case, was used
over road loads in order to have better results. So, the
results presented here are not real values of the
vehicle/part.
Figure 1 shows the mathematical modeling of the
component.
Figure 1 – Mathematical component model.
For the two presented simulations, the base will be
attached (welded) in the body car with the element type
RBE2. These elements should transmit all the forces from
the road load to the component.
RBE2 definition: define a rigid body with
independent degrees of freedom that are specified in the
elements nodes of the part and with dependent degrees of
freedom specified in arbitrary numbers of nodes, that is, all
the forces and/or displacements that will be applied in we
will be transmitted integrally for the posterior node.
RBE2
Weld points of the
part in the body car.
Elements
7. 7
Finite Element definition: each one of the small
entities shown in the figure above.
4.1) First model – First simulation.
For the first simulation, RBE2 elements type will
be used to attach all the points: the part welding in the
body vehicle and the spring and shock absorber in the base,
as figure 1 and 2.
Two Rigids RBE2:
1) Coil Spring: one row nodes.
2) Shock Absorber and Jounce Bumper
on three row nodes.
RBE2: application forces in two rigids.
One with the coil springs forces and
another with the shock absorber
and jounce bumper.
Figure 2 – Attachment points of the spring and the shock
absorber.
4.1.1) Principal Stress Range
The principal stress range for the virtual durability
simulation is presented below:
Figure 3 – Principal Stress Range with RBE2 element.
* Observation: this value will be taken by the reference to
compare the results.
4.1.2) Maximum Von Misses Stress
The max Von Misses stress for the virtual
durability simulation is presented below:
Figure 4 – Maximum Von Misses Stress.
* Observation: this value will be taken by the reference to
compare the results.
4.1.3) Maximum Damage
The max damage for the virtual durability
simulation is presented below:
Figure 5 – Maximum Damage with RBE2 element.
* Observation: this value will be taken by the reference to
compare the results.
For the first simulation, the element used to attach
the shock absorber and the spring in its base (RBE2), did
not represent the reality of the vehicle, because of the
rubber element that makes this linking and element RBE2,
is not the indicated one, therefore does not allow to the
load transference/displacements between the nodes.
4.2) Second model – Second simulation.
For the second simulation, the previous model
with applied similar forces in the same points and the same
elements type RBE2 will be used, however using the
element type RBE3 to attach spring and shock absorber in
the base.
100%
principal
stress
range
reference
value *
92%
of
principal
stress
range
reference
value
98,9%
of
maximum
Von Misses
stress
reference
value
100%
Maximum
damage
reference
value *
48,9%
of
maximum
damage
reference
value
100%
Maximum
Von
Misses
stress
reference
value *
8. 8
Two Rigids RBE3:
1) Coil Spring: one row nodes.
2) Shock Absorber and Jounce Bumper
on three row nodes.
RBE3: application forces in two rigids. One with
the coil springs forces and another with the
shock absorber and jounce bumper.
Figure 6 – Points of attachment of the spring and the shock
absorber.
RBE3 definition: define the reference movement in the
node with a factor of weight of the movements defined in
the other nodes, that is, all the forces and/or displacements
that will be applied in the nodes will be transmitted
partially for the posterior node, in function of the factor of
weight attributed to each one of them.
4.2.1) Principal Stress Range
The principal stress range for the virtual durability
simulation is presented below:
Figure 7 – Principal Stress Range.
* Observation: this value is 106% bigger than the RBE2
principal stress range reference value in the same region.
** Observation: this value is 182% bigger than the RBE2
principal stress range reference value in the same region.
4.2.2) Maximum Von Misses Stress
The maximum Von Misses stress for the virtual
durability simulation is presented below:
Figure 8 – Maximum Von Misses Stress.
* Observation: this value is 103% bigger than the RBE2
max Von Misses stress range reference value in the same
region.
** Observation: this value is 177% bigger than the RBE2
max Von Misses stress range reference value in the same
region.
4.2.3) Maximum Damage
The maximum damage for the virtual durability
simulation is presented below:
Figure 9 – Maximum Damage
* Observation: this value is 107% bigger than the RBE2
maximum damage reference value in the same region.
** Observation: this value is 1008% bigger than the RBE2
maximum damage reference value in the same region.
For the second simulation, the use of RBE3
element is better to attach the shock absorber and spring in
its base, because of the better represented reality of the
vehicle and because of the rubber element simulates this
linking better allowing the load transference/displacements
between the nodes.
182%
bigger
than RBE2
principal
stress
range
reference
value**
106%
bigger than
RBE2
principal
stress range
reference
value*
177%
bigger
than
RBE2
maximum
Von
Misses
stress
reference
value**
103%
bigger
than RBE2
maximum
Von Misses
stress
reference
value*
1008%
bigger than
RBE2
pmaximum
damage
reference
value**
107%
bigger
than RBE2
maximum
damage
reference
value*
9. 9
Comparing the results of this application with the
requirements listed in Pugh Matrix [8], the RB3 elements
is according the most important design requirements:
maximize the reliability of the model, increase the
repeatability of the simulation and reduce the time of
simulation of the model.
Applying the TRIZ principle “local quality”,
based on the knowledge and experience of design team and
the CAE theory, it is possible to conclude that RBE3
elements do not to have distortion in the quality of the
elements and the risks can be assumed to increase the
quality of the results. Another principle to support the
decision is "to convert damage into benefit”, that is, the
time of confection of the mesh can be raised stops with this
also raising the reliability in the model.
5. CONCLUSIONS
The TRIZ method, used with the QFD, even so more
is applied in the initial phases of project also can assist in
the stages of detailed project, as the stages of simulation in
CAE.
According to the QFD House of Quality, the best
element to be used to fix the shock absorber and the spring
on the base are the RBE3 element.
The simulation with the models using RBE3 elements
shows better results instead of RBE2.
These conclusion is supported by the proposed
methodology, as well reflected the opinion of seniors
engineers.
This methodology can be applied in new projects
where the design team must determine the best strategy for
solving problem to reduce the simulation cost and time, as
well to increase the results reliability.
The Matrix of Contradiction of TRIZ was originally
developed considering products in general, not a specific
domain of knowledge as injection molded component
design. To be used appropriately in the development of
specific domain, as CAE Simulation, can be necessary to
adapt TRIZ information (engineering parameters and
inventive principles). To adapt this information, the rules
and recommendations for simulation engineers must be
used. Considering this aspects, a new design tool called
“Matrix to Define the Design Guidelines for Engineering
Simulation” can be developed. This Matrix is a base of
knowledge to simulate components and it considered the
rules, the specialists' knowledge, recommendations and
restrictions imposed by the different fields of knowledge
involved in this activity.
6. REFERENCES
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Web site: http://www-personal.umich.edu/
[5] iSix Sigma site:
http://www.isixsigma.com/dictionary/Pugh_Matrix-
384.htm
Statitical Design Institute site:
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(R1988).
[13] FORD MOTOR COMPANY (2002) - FTEP (Ford
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[14] INTRANET FORD MOTOR COMPANY.
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