VI. Constructing product models: advanced method

http://www.youtube.com/watch?v=mmcK7oZ51ko

The previous section presents a basic model construction process as containing five fundamental steps. The focus of this process is to transform an informal description of product desires, obtained from earlier analysis, to a formal quantified model. Model preparation begins the process by establishing links of the informal description with product metrics. A functional model of the product concept, as well as the established architectural layout, provides additional links.

Functional models of a product concept relate material, energy, and information flows from the environment to the outputs produced by the product. These relationships, while informal, provide a basic structure for representing the underlying physics of the product's performance. This structure provides a solid foundation for incrementally building a formal analytical model. The chosen product metrics, in fact, are simply measures of the flows exiting functions in the product.

Approach

To build on the functional model foundation, transforming the informal models to formal ones, a systematic development approach is considered. Figure 13.22 shows an advanced modeling approach for product metrics, after Ashby (1992; 1987) and Beaumont (1998) and the previous discussion. It begins by considering the important effects (customer needs and associated engineering specifications), advances the model through physical mechanisms and interrogation, and ends with implementation of the model to explore alternative product configurations. Let's briefly examine the steps involved in this modeling approach.

Method

STEP 1: Identify the Effect (Customer Need/Engineering Specification)

We first contemplate what the model is for. Customer needs mapped to the main function carriers and then mapped to engineering specifications (metrics) is the essence of this step.

STEP 2: Identify a "Flow"

We next identify a material, energy, or signal flow associated with each customer need/metric of the product concept. This identification corresponds to the flows in the product's functional model. It may be used to understand the input-output transformation of the product in the sense of control volume analysis.

STEP 3: Identify the Physical Mechanisms

But how is the identified flow converted to a desired state by the product? How will the environment affect this transformation? We begin to answer these questions in this step. Physical principles must be listed that govern the product functions.

STEP 4: Target the Precision

With the metrics, flows, and physical mechanisms identified, the required precision of the model must be established. The precision must be chosen so that the model will produce effective results to make design decisions. Usually a percentage of the target values for the product metrics is used to set the precision of the product model.

STEP 5: Construct the Boundary and Balance Relationship

This step entails the establishment of system boundaries and the derivation of balance relationships that represent governing physical mechanisms. Basic mechanics from a variety of fields may be called on to create these balance relationships, equations, and boundary representations. It is also expected that the targeted precision is continuously referenced so that simplifications and assumptions may be made and justified (or not). This step concludes with an integration of all balance relationships and boundary conditions as a set of simultaneous equations or equivalent representation.

STEP 6: Apply Similitude/Dimensional Analysis

It is always a good idea to manipulate analytical product models into appropriate groups of dimensionless parameters whenever possible. Dimensionless parameters provide "scale lengths" for understanding the models and obtaining physical insights and trends. They also minimize problems encountered with unit conversions.

STEP 7: Embody the Model Computationally

The model should be converted to a computational form. This form may entail detailed finite element or difference models or other simulations. Alternatively, it may entail the simple coding of formulas in a spreadsheet or symbolic analysis. In either case, a computational form will provide a useful model for interrogation and design application.

STEP 8: Interrogate the Model

Once a model is constructed and integrated, it must be simplified, verified, and tested for its limits. Physical tests and known first-order solutions (such as beam theory) provide a sound basis for model interrogation. A subset of physical data (more than one point) must be collected to calibrate and validate the model. Unknown constants and model order must be adjusted during the calibration to improve the predictive capability of the model.

STEP 9: Display and Use the Model

Following interrogation, calibration, and validation, the model is ready for use. The design parameters must be clearly identified and bounded (if not already done so). The range of possible design configurations is then explored, followed by focused experiments/physical models to verify design choices and to uncover physical phenomena not included in the model.

This nine-step process augments and supplements the basic method of modeling product metrics. It adds keys steps such as interrogation and calibration of a model. The next section develops examples using this methodology.