Axiomatic Design Framework

Axiom 1 : Independent Axiom

Axiom 2 : Information Axiom

Axiom 1 : Independence Axiom

Ex: Baverage Can Design

Consider an alumunium beverage can that contain carbonated drinks. How many FRs must the can satisfy? How many physical parts does it have? What are the DPs? How many DPs are there?

12 Plausible FR: 1. Contain axial & radial pressure, 2. Withstand a moderate impact

when the can dropped from a certain height,

3. Allow stacking on top of each other,

4. Provide easy access to the liquid in the can,

5. Minimize the use of alumunium,

6. Be printable on the surface, etc.

12 DPs (most of the DPs are associated with the geometry of the can) 1. The thickness of the can body, 2. The curvature at the bottom of

the can, 3. The smaller diameter of the can

at the top to reduce the material used to make the top lid

4. The corrugated geometry of the opening tab to increase the stiffness

5. The small extrusion on the lid to attach the tab, and so on

But, The can consist of only 3 pieces: Body, the Lid, and opener tab

Identifying Plausible DP

To conceive the design concept, database of all kinds and all available methods may be used:

Brainstorming

Morphological techniques

Analogy from another examples

Extrapolation & interpolation

Laws of nature

Order-of-magnitude analysis

Reverse engineering

Functional coupling should not be confused with physical coupling, which is often considerable as consequence of Axiom 2.

Integration of more than one function in a single part, as long as the functions remain independent, should reduce complexity.

An example that ilustrates the use of physical integration without compromising functional independence is the bottle/can opener design

Bottle/Can Opener Design

FR1: Open beverage bottles

FR2: Open beverage cans

If the requirement is not to perform these functions simultaneously, then this physical integrated device satisfies two independent FRs

Corollaries

Corollary 1: (Decoupling of Coupled Design). Corollary 2: (Minimization of FRs). Minimize the number of FRs and constrain

Corollary 3: (Integration of Physical Parts).

Corollary 4: Use of Standardization

Corollary 5: Use symmetry

Corollary 6: Largest Tolerance

Corollary 7: Uncoupled Design with Less Information

Ideal Design, Redundant Design, & Couple Design

Theorema 1: Coupling due to insufficient of DPs

Theorema 2: Decoupling of Coupled Design

Theorema 3: Redundant Design

Theorema 4: Ideal Design

Teorema 5: ...(next lesson)

Axiom 2 : Information Axiom

Axiom 2

12

Motivation for Axiom 2:

There may be more than one design that satisfies with Axiom 1. The problem is to

select one of them. Such a selection process demands criterion or criteria.

Is there any generic criterion or criteria?

Complexity of making or manufacturing designs.

What is complexity?

Uncertainty and vagueness of information that is presented in a design

specification for a system.

How can we measure complexity? difficulty to do

There are two aspects: (a) design or plan and (b) manufacturing and implementation, because difficulty to do depends on different techniques or tools used just the same as for a same problem, one human may feel difficult while another may feel not difficult.

Axiom 2

Example 1:

A design specification for a shaft is as follows: length of the shaft is 10 with a

tolerance being 0.10 mm.

Tool 1: measurement ability: 0.01 mm

Tool 2: measurement ability: 0.05 mm

Tool 3: measurement ability: 0.20 mm

Comment:

From the above, we can see that tool 1 can achieve the design specification with

the highest successful rate. Yet, tool 3 may never be able to make the shaft to

satisfy the requirement.

Need to define a quantity to represent the easy or difficult state to fulfill this task.

The result of detailed

design

It states that among those design that satisfy the independence axiom, The design that has the smallest information content is the best design.

When information content is grester than zero, information must be supplied to satisfy the FRs at all times

Because the information content is defined in terms of probability of success is the best design.

Design range is the range of values of the DP that will satisfy the FR;

System range is the range of values of the DP which can be made by a manufacturing system or system;

The common range is the intersection of the system range and the design range.

15

Axiom 2

Axiom 2

Information content, I, is defined by

The overall information content can be calculated by

16

Axiom 2: Information Content

Information content of designs should be minimized. Among designs that satisfy function requirements, the design with the minimum information content has the highest probability of success.

The information axiom provides a quantitative way to select the optimum from design solutions

17

Summary

1. Given n designs, which one is the best?

2. The best design should have the minimum information content

3. Information content is a measure of the complexity of a design in the context of means or systems that are available to make the design

4. In application, the key is to define design range and system range assuming that the probability density is uniform

18

N.P. Suh, The principle of design, Oxford University Press, 1990 Pages: beginning to 46-51; 147-153; 307-311.

Design Range, system range, common range& system PDF for FR

Example: Buying a House

A family is planning to buy a new house. They decided that the following are the four important functional requirements the house must satisfy: FR1= Commuting time must be in the range 15-30 minute FR2= The quality of local high school must be good (i.e.,

more than 65% of the high school graduates must go to reputable collage

FR3= The quality of air must be good over 340 days a year FR4= The price of the house must be reasonable (i.e., a

four-bedroom house with 3000 square feet of heated space must be less than $650.000

They look around town A,B,C & collected the following data:

Town FR1 = Commute time (min)

FR2 = Quality of Schools (%)

FR3= Quality of air (days)

FR4 = Price (1000 $)

A 20 to 40 50 to 70 300 to 320 450 to 550

B 20 to 30 50 to 75 340 to 350 450 to 650

C 20 to 45 50 to 80 350 and up 600 to 800

Which town meets the requirements of the familiy the best?

Solusi:

Town I1 (bits) I2 (bits) I3 (bits) I4 (bits)

A

B

C

Exercise

1. Analyze the design of Honda Accord (only operational feature) in term of the axiom, corollaries, and theorema.

2. Design a 35-mm camera that can automatically focus & set correct expossure

3. Design an educational system that provide lifelong learning (sometimes called continuing education) to practising engineers

4. Decouple the conventional Mobile Audio/ Radio