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13. Axiomatic Design

• Basically sets of rules are used to guide the design process.

13.1 Nam Suh’s Methodology
• Relates Design Parameters (DPs) to Functional Requirements (FRs) using matrices.

• Two basic axioms,

1. The Independence Axiom: sections of the design should be separable so that changes in one have no (or as little as possible) effect on the other.

2. The Information Axiom: the information inherent in a product design should be minimized.

• In a simple design FRs would be the requirements of a design. This will be a discrete list of independent items. If the FRs are not independent enough then complications will arise. An example would be for a parachute,

FR1: The parachute will slow down a descent to prevent injury

FR2: When not in use it will be easily carried by a user

FR3: Reliability will be greater than 1 failure in 20000 users

FR4: The user will be able to redirect the descent vector

• If we consider DPs, we want these to be independent also. These will express how we have decided to satisfy the FRs (Note: this technique is analytical). If we consider the parachute example,

DP1: Material chosen for chute- weight and strength

DP2: Length of cords between rider and chute

DP3: Number of cords between rider and chute

DP4: Area of chute

DP5: Vents in chute

DP6: Packing and release methodology

• It is possible to relate the FRs to the DPs using a sensitivity matrix,

• Obviously the relational matrix above is non-linear, so to allow simple analysis, we consider the matrix values near the operating point, and substitute in values of small (x) and large (X) effects. As a result the previous matrix might look like,

• Considering the independence axiom, we want a one-to-one relationship between FRs and DPs. Ideally we would want a square identity matrix. Practically we must compromise. The corollaries give direction to changes.

Corollary 1: Decoupling: We should attempt to decouple or separate different design elements. If done using the matrix method above this would result in an identity matrix (or equivalent).

Corollary 2: Minimize FRs: If we can reduce the number of FRs it will simplify the design.

Corollary 3: Integrate Parts: When possible, without significantly compromising the other principles, we want to reduce the number of parts.

Corollary 4: Standardization: Standardized parts tend to satisfy the design axioms, and should be used when possible to reduce the information content.

Corollary 5: Symmetry: When possible use symmetry to reduce the information content of the product.

Corollary 6: Large Tolerances: Reduce the information content by using the largest tolerances possible.

Corollary 7: Uncouple and Minimize Information: When possible the designer should strive to minimize information and interdependence between design components.

• Ideally there are a number of objectives to follow,

1. Strive for the same number of FRs and DPs, and have each independent.

2. Minimize the values in the relationship matrix by reducing the information in each part.

• If we consider the parachute example, we can see the problems that must be addressed.

1. First, FR3 has three major relationships. FR2 and FR4 have 2 major relationships. DP1 and DP4 have two major relationships. These are ideal candidates for redesign.

2. We might consider suitability of the DPs and FRs. If they are reasonable and don’t overlap, we might go farther. In this case FR3 and DP1, DP2, DP4 are prime candidates.

#### 13.1.1 The Information Axiom

• Information is a measure of complexity originally developed by Shannon []

• If we think about the information content (complexity) of some modern products, the implications are obvious,

very pure semiconductor materials increase yield and chip sizes.

the number of transistors per IC is also climbing

the tolerances for internal combustion engines have increased: and the idea of replacing an engine is now uncommon.

• For mechanical parts (with reasonable tolerances) the information content of a part might be rated by the formula,

• In another case we might have access to SPC data, and can calculate the Cpk for each feature we might measure information with,

• As common sense dictates we would want to generally increase our work dimensions (to a point) and increase our tolerances whenever possible.