Informal Models

https://www.youtube.com/watch?v=eGkvZNRC8E0

When a typical design concept is developed, it is first conceived in informal terms. Customer needs lists use informal (English) descriptions. A function structure uses English terms with graphical structure. Morphological charts use rough pictorial sketches. Even quantities that eventually become precise start informally. Requirements that a design must satisfy, for example, are usually first described in a natural language, complete with personal connotations.

Definition. An informal model is a designer's interpretation of a description of the customers' needs, engineering requirements, manufacturing requirements, and any other product requirement, along with the designer's interpretation of the conceived solutions.

Example

Let's consider a fingernail clipper product. We have a number of concepts for the product, as depicted in Figure 13.4. An interpretation of these concepts is our informal model of each. We have a list of criteria for evaluating the concepts (Table 13.5). Our interpretation of what these criteria mean is our informal model of the objectives.

Formal Models

http://www.youtube.com/watch?v=i_Ey4rx7I_A

What is Formal?

W e are seeking to construct a computable (or analytical) model of the design problem. The fundamental characteristics assumed to define a formal model are twofold. The first characteristic is that we can elucidate the alternatives to choose among them; the alternatives are assumed to have the structure of a set.

The second characteristic of defining a formal model is that when shown two different objects in the set, we can determine whether or not they are distinct. We can, with enough analysis, distinguish between the different alternatives.

V. Constructing product models: basic method

Early stages of product development provide us with the necessary informal description of what we need to model a design problem. Model preparation and selection (Section II) establishes the first link of this informal description to a quantified metric. Having a complete functional model and architectural layout provides us with additional structure to construct a formal model.

A Basic Modeling Approach

To transform informal models into formal ones, we can consider a structured approach to modeling:

1. Identify a flow for the informal effect.

2. Identify a balance relationship for the flow.

3. Identify a boundary for the balance relationship.

4. Formulate an equation (or set of simultaneous equations) for the balance relationship in the system.

5. Use the resulting model to explore design configuration options.

STEP 1: Identify a Flow

We first identify a material, energy, or information flow associated with each effect of the product concept. This identification is a direct choice from the functional model of the product and overlaps with the preparation phase of product modeling.

Example: Let's examine our customer-needs-to-flow diagram used to construct the function structure for a fingernail clipper product, as shown in Table 13.6.

Now let's choose a customer need (informal objective) to model, say "Easy to squeeze = Low finger force." The energy flow is "finger force," based on the function chain for the clipper, and the metric is "low finger force" as identified from benchmarking. Tracing finger force through the clipper, we have the representation shown in Figure 13.5. This representation helps us to develop a new fingernail clipper concept, understand its physics, and choose appropriate design parameter values to satisfy the customer needs.

The cutting motion acts like a scissors across the fingernail. A valid force flow is the force from the fingers, through the clipper, through the fingernail.

STEP 2: Identify a Balance Relationship

H aving identified a material, energy, or information flow, we now must identify a balance relationship for the flow. Example: In the fingernail clipper, the forces above the cutting teeth must equal the forces below. The moments about the fulcrum must also sum to zero (assuming quasi-static analysis). The concept balance relationship is shown in Figure 13.6.

STEP 3: Identify the Boundaries

This step entails the recognition of the boundary conditions of the

product concept. How is it loaded, and how does it interact as a system with its environment (including the human interface)? What are the inputs and outputs across the boundaries, and what are the limits or ranges of these inputs and outputs?

E xample: In the fingernail clipper, it is profitable to model the forces by starting with the finger forces acting across the system boundary (Figure 13.7).

For this model, we could include the finger forces that are internal to the system and create a model of the forces through the finger, hand, and thumb. Such an approach is not necessary. We could zoom in on the cutting blades and not model the finger forces. Then we only have forces acting on the blades, which are not directly related to the forces required of the fingers. This approach is insufficient, since it does not capture the chosen product metric of finger force.

This example hopefully makes it clear how to select a proper level of abstraction for a model. The issue is pervasive to all engineering problems. The effect-to-flow-to-balance-to-system method is a reasonable approach-and generalizes. For example, fluid dynamics, heat transfer, solid mechanics (material stress and strain), and manufacturing process modeling typically use a control volume, and flows in and out are balanced.

STEP 4: Derive an Equation (or Set of Simultaneous Equations)

The next step involves converting the balance relationship to a mathematical form. This step is one of assigning geometric variables, material property constants, and others to formulate an equation (or set of simultaneous equations) that can be solved. The engineer's toolbox of applied mathematics and science is required here. In addition, a number of assumptions and simplifications will be required to develop a suitable model.

Example: Assigning dimension variables in the first control volume, the labeled fingernail clipper concept is shown in Figure 13.8. Summing moments about the fulcrum, the finger force required to actuate the clipper is:

The distances from the fulcrum to the force applications are design parameters (components of the D). The force F from the nail is unknown, however. We need to repeat the modeling process for the fingernail force, where we have a system of forces within a system of forces. To derive the force F, we model the fingernail being clipped. Figure 13.9 illustrates the fingernail force system.

We may model the nail force as the shear stress over the nail cross-sectional area. Therefore:

Now, how do we represent dW? Another system and model is needed. We can visualize that dW depends on the angle of the blade, as shown in Figure 13.10.

A balance relationship for the orthogonal coordinate system is the summation of individual feature distances along the fingernail clipper that must be added to a value that is less than a target value for the dimension. Considering this metric, a model of the clipper along the length (x) direction is given by Figure 13.8. Figure 13.11 provides additional geometry for modeling the height and width of the fingernail clipper.