Appunti Optimization and innovation of production processes (parte 2)

In most of the case the transfer function is not linear: I want to increase robustness of the

system.

Robust design:

I reduce the sti?ness of the system, and I obtain a smaller variation of the output (but a higher

value, visible in the output)

Identify factors: the parameters design factors can be of various types:

- Levelling

- Scaling

- Which only a?ect σ

- Which a?ect neither σ nor μ.

Is important to define if a factor has a influence or not. In design I have to find the best

compromise between di?erence responses. The best is the one that minimize the noise

factor, that is the variability.

Leveling factors that only influence μ (the mean):

a) Scaling factors only influence μ and σ proportionally

b) Non-proportional influence on μ and σ

Control factors, factors that do not influence either μ or σ.

If there is a leveling or scaling factor, all other factors are optimized in order to minimize

variability, then the chosen factor is used to tune the response on the target (double

optimization). If these factors do not exist, we try to maximize the overall performance of the

process (indicated by Taguchi as the S/N ratio).

Two steps approach: the first is reduce the variability. The reduction of variability is

mandatory, I have to use any solutions I can apply to reduce variability, it is the main aim.

Usually, I reduce variability using scaling factors. The second step is to use levelling factors to

center the variability.

The parameter design usually doesn’t a?ect the cost.

Tolerance design: tolerance design is an approach that usually a?ect the manufacturing

cost, it’s the last solution, we use this only if it’s necessary. The tolerance values for control

factors are determined as cost/quality trade-o? (tightening tolerances increases quality but

also costs). Only to be used when the necessary results have not been achieved with the

previous phase.

Axiomatic design

This approach aims to rationalize the work of designers in order to make the product

development process more e?ective.

The key concept, when talking about Axiomatic Design (AD), is Concurrent Engineering: the

various design aspects – functionality and manufacturability – are analyzed and optimized

simultaneously.

At the core of the AD approach is the creation of four design domains:

- Customer Domain: what the customer wants (feelings of the customers)

- Functional Domain: transforms customer requirements into functional requirements.

- Physical Domain: manufacturing processes.

- Process Domain.

These domains contain the respective information, and the flow of information between them

leads to the development of an optimized product.

This information is exchanged through a matrix representation of the product (design

matrices) that link one domain to the next.

The axiomatic design approach is based on the idea that, to improve a given product, it is

necessary to analyze and refine the design matrix. The analysis of these matrices focused

mainly on the study of functional coupling between the elements of one domain and those of

the next. Coupling can be measured using the first axiom, which defines three possible levels

of coupling within a matrix. Technical solutions that reduce coupling also guarantee overall

improvements in product performance, cost, and manufacturing e?iciency.

The second axiom, called the Information Axiom, is used to choose which of the low-coupling

solutions is preferable by measuring how well the proposed solution meets the

specifications. Naturally, the product must be development to ensure an ever-increasing

information content. The main di?erence between the first and second axioms is that the first

applies at an early stage of product development, to assess which general technical solutions

can be used.

The main di?erence between the first and second axioms is that first applies at an early stage

of product development, to assess which general technical solutions can be used. The

second, which requires statistical characterization of system behavior, is applied only once

the detailed design is complete.

The axioms and design theorems have a dual purpose. First, they are used to determine

specific modifications to be made to the product in order to improve its performance with

respect to the specifications. Second, they are used to determine specific modifications to be

made to the product in order to improve its performance with respect to the specifications.

The axioms, in fact, provide guidelines for product improvement. The axiom, in fact, provide

guidelines for product improvement. Every human creation – whether physical or intellectual

– is driven by a design process.

These domains contain the respective information, and the flow of information between them

leads to the development of an optimized product.

Axiomatic design proposes adapting its domains to all types of projects. In this context, it is

crucial for the designer to clearly understand the di?erences among the various domains. As

will be seen later, developing a project consists of moving from one domain to the next

through a procedure called Mapping.

To clearly explain what axiomatic Design is, it is necessary to precisely define the parameters

introduced earlier:

- Costumer Needs (CNs).

- Functional Requirements (FRs): minimum set of independent requirements to

characterize functional output of the product (or software, organization, system, etc.)

within the functional domain. By definition, the FRs must be chosen so that they are

independent from one another.

- Design Parameters (DPs): the design parameters are the key physical variables within

the physical domain that satisfy the FRs and characterize a design. In the case of a

mechanical project, the DPs may correspond to components or specific

characteristics of components.

- Constraints (Cs): There are two types of constraints: input constraints (imposed by

project specifications) and system constraints (imposed by the chosen technical

solutions). The constraints are the limitations that define an acceptable solution. Input

constraints are imposed together with the design specifications (e.g., cost, size,

weight, etc.), while system constraints arise from the choices of certain DPs and FRs –

that is, from the system being created, in which the solution must operate properly. It is

important to note that first-level FRs must be considered together with the input

constraints.

- Process variables (PVs): the process variables are the key variables of the process

domain and define the process capable of generating the specified DPs. For a

mechanical project, the PVs represent the parameters that characterize the

manufacturing process of the product.

Design axioms

Two axioms define the structure of axiomatic design:

- Axiom 1: The Independence Axiom

This axiom requires that the Functional Requirements (FRs) be satisfied independently

of one another. For an optimal design, the Design Parameters (DPs) and the FRs must

be related in such a way that changing the value of any DP only its corresponding FR,

without a?ecting the others.

- Axiom 2: The Information Axiom

For a better design, we must seek to maximize the probability that all FRs are satisfied

– in practice, this means minimizing the information content of the design. The

information content represent the error or deviation that occurs when the

specifications are not fully met.

Design matrix: chosen a set of DPs able to satisfy the FRs, we have a matrix defined by the

following equation.

Independence axiom: requires that the FRs of the system are satisfied independently (does

not imply independence of the physical parts).

Functional coupling

Example

If I want to achieve a certain flow and temperature, I need to have a trial and error approach,

to find the desired flow and temperature combination.

With this I reduce coupling, we decoupled the system. The variability of the flow and the

temperature is lower because it’s depending only on one variable.

This is the proof of reducing the coupling of the system reduce the variability and the

complexity of the system itself.

Information axiom

Information axiom: states that the best project is the one most likely to meet specifications.

Information content measures the probability that FRs will meet the specification.

Decomposition and zigzagging

Let us now examine how a project is developed using Axiomatic Design (AD). One of the

features that makes this method widely used is its ability to represent a design through

hierarchically ordered objectives. The process begins with the main goal of the projects – the

highest-level functional requirements (FRs) – which are then decomposed into sub-goals. The

same is done for the Design Parameters (DPs).

Usually, the highest-level FRs and DPs are called top FRs and top DPs to emphasize their

importance, as they define the overall specifications of the project. The lower levels, which

cannot be decomposed further, are called leaves, to highlight that the project structure takes

the form of a tree. There are, in fact, two trees – one for the FRs and one for the DPs – and the

decomposition proceeds level by level, from the top to the leaves, following a specific rule.

This rule states that before decomposing a level of FRs into a lower level, one must first find

the DPs that satisfy that level. Only once the corresponding DPs have been identified can the

lower-level FRs be defined. This is because lower-level FRs always depend on the design

choices made at the higher level. In other words, the two trees must not be decomposed

separately; instead, one must continuously move from on to the other – a process called

zigzagging. since the FR tree belongs to the functional domain and the DP tree to the physical

domain, moving between domains in this alternating manner gives rise to the term zigzagging.

Thus, the transition between domains is not unidirectional, but rather iterative, moving back

and forth. In practice, the first step is to define first-level FRs from the project specifications,

then to identify the DPs that satisfy them, and then to move on to define the second-level FRs.

From there, the cycle repeats at next level: the second-level DPs are determined, followed by

the next of FRs, and so on – until only leaves remain. An FR or a DP becomes a leaf when it can

no longer be decomposed further.

This process allows the designer to focus each time on a limited number of FRs, specifically

those at a single level, with the goal of identifying the components (DPs) that satisfy them.

Otherwise, an inexperienced designer might find themselves facing a large number of FRs

across multiple levels, making problem-solving much more complex and delaying project

development. Naturally, throughout the decomposition process, one must always consider

the input constraints, which must never be violated by design choices. Furthermore,