Introduction to Modeling I: Overview

Finally! This is the first ‘core’ material post for Design Impact. One of the most fundamental concepts in engineering design is that of an engineering model, that is, something that approximates the real behavior of a product or system without actually having to build it. This post is the first of a series that will introduce you to what engineering models are and how they are used in design. Have a look at this earlier post to read a basic definition of engineering design. I will use a simple example (a basic pendulum) in this series to illustrate some modeling concepts. I will assume that readers can follow a little algebra related to the example model, but I will try to keep most explanations graphical and conceptual. If anything is not clear please speak up! You can give your feedback by commenting on this post or by sending me an email.

When engineers design something, they start out by making a list of things that their product or system needs to do, and limitations their design must abide by. This list of requirements might specify things like cost limitations, size, weight, or a host of possible performance metrics. Engineers hope to find a design that meets these product requirements the best way possible. Sometimes it is a real challenge just to find any design that meets all the requirements simultaneously. Design is an iterative process where new designs are proposed, evaluated, and then modified. This process repeats until an acceptable design is found. Here is a (simplified) depiction of the engineering design process:

Engineers have a few options for testing out how well proposed designs do at meeting product requirements. The most obvious is to build a physical prototype of a proposed design and test it out. Depending on the product, this can get very expensive (and time consuming). In some cases, it may impossible to build a physical prototype, or if you can build one, the tests you need to do are impractical while still in the design stage. Engineers need to be able to make predictions about how a design will perform without having to actually build and test it. This is where modeling comes in. An engineering model approximates the behavior of a real system, but is less expensive or time consuming to create and use. Notice the word approximation: there is always some error between how a model behaves and the real system. More sophisticated models reduce this error, but are more difficult to create and use. Engineers must manage the tradeoff between model accuracy and expense: they need to choose a model that is accurate enough for their needs. On the other hand, models that are substantially more sophisticated than the design project requires could end up costing more in terms of development time, design and computing resources, and other expenses.

One option for an engineering model is to build a smaller or simplified physical prototype. This does save some time and expense over a full-scale prototype, but can still be costly. Another class of models are ‘virtual’; engineers can build virtual prototypes that can be tested on a computer, which is typically much faster than testing physical prototypes. Recall that design is an iterative process where many designs must be tested before determining the final design of a product. Consider the impact of virtual prototyping on the design process. If a computer model takes seconds to evaluate, while physical prototypes require days, weeks, or even longer to construct, what happens when engineers start using virtual prototypes? Design development time collapses. Even if the last few design iterations involve physical prototyping, the overall process is shortened dramatically. There are many other benefits to using appropriate computational models throughout the design process that we will explore in later posts. Unless I specify otherwise, when I use the term ‘model’ from here on out I am referring to a computational engineering model, that is, a virtual prototype.

I am going to use a simple model of a basic pendulum to introduce some modeling concepts in subsequent posts. Here I am just going to describe the physical system. A pendulum may not be the most exciting example to start off with, but it works very well for introducing important ideas using a single example. (So for now just pretend that the pendulum is a small part of a much cooler example). In the drawing below we have a metal rod that is hanging from a pivot that lets the rod move back and forth in one direction. The rod has a cylindrical cross-section with diameter d, and is supporting a heavy object below. This object has a mass m [1]. When the pendulum is swinging back and forth the object has a velocity v [2], and when the rod is not straight up and down we can measure how far it has moved to the side with the angle theta θ.

What do think about the idea of using ‘virtual prototypes’ in engineering design? Can you think of any cases where physical prototypes might be impractical or impossible to use?

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Notes:
[1] The mass of an object is different from it’s weight. The mass refers to how much stuff there is an object, and weight specifically means how much force gravity is pulling down on an object. In some calculations we need to use the mass of an object and not its weight. The mass and weight of an object are related to each other by the acceleration of gravity g, which depends on where an object is. At the surface of the earth g is 32.2 feet per second per second (ft/sec²), or using metric units (which make calculations easier in most cases), g is 9.81 meters per second per second (m/s²). An objects weight is its mass times the acceleration of gravity. So if we are on earth, and an object has a mass of 10 kilograms, then gravity pulls down in it with a force of 98.1 Newtons (N). The metric unit of measurement for force is the Newton. In other words, the object weighs 98.1 N (or about 22 pounds). If we were on the moon, where g=1.62 m/s², then the object would then only weight 16.2 N (about 3.6 pounds), but it would still have the same mass of 10 kg. You can read more details here.

[2] The velocity of something is both its speed, and the direction in which it is headed. In the second diagram of the pendulum the velocity of the mass is described graphically by the arrow labeled by v. The object’s speed is proportional to the length of the arrow, and the direction it is moving is decribed by the direction the arrow is pointing. In this pendulum, the velocity of the mass at the bottom of the pendulum is always in a direction perpendicular to the rod. For more details about velocity, click here.

Posted: May 10th, 2009 | Filed under: Design, Modeling |

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