I need better roller skates!

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engineers generally work in a team environment where they consult each other to solve com- plex problems. They divide up the task into smaller, manageable problems among themselves;

consequently, productive engineers must be good team players. Good interpersonal and com- munication skills are increasingly important now because of the global market. You need to make sure you clearly understand your portion of the problem and how it fits with the other problems. For example, various parts of a product could be made by different companies located in different states or countries. In order to ensure that all components fit and work well together, cooperation and coordination are essential, which demands good teamwork and strong com- munication skills. Make sure you understand the problem, and make sure that the problem is well defined before you move on to the next step.This point cannot be emphasized enough. Good problems solvers are those who first fully understand what the problem is.

Step 3: Research and Preparation

Once you fully understand the problem, as a next step you need to collect useful information.

Generally speaking, a good place to start is by searching to determine if a product already exists that closely meets the need of your client. Perhaps a product, or components of a product, already has been developed by your company that you could modify to meet the need. You do not want to “reinvent the wheel!” As mentioned earlier, depending on the scope, some projects require col- laboration with other companies, so you need to find out what is available through these other companies as well. Try to collect as much information as you can. This is where you spend lots of time not only with the client but also with other engineers and technicians. Internet search engines are becoming increasingly important tools to gather such information. Once you have collected all pertinent information, you must then review it and organize it in a suitable manner.

Step 4: Conceptualization

During this phase of design, you need to generate some ideas or concepts that could offer rea- sonable solutions to your problem. In other words, without performing any detailed analysis, you need to come up with some possible ways of solving the problem. You need to be creative and perhaps develop several alternative solutions. At this stage of design, you do not need to rule out any reasonable working concept. If the problem consists of a complex system, you need to identify the components of the system. You do not need to look at details of each possible solu- tion yet, but you need to perform enough analysis to see whether the concepts that you are proposing have merit. Simply stated, you need to ask yourself the following question: Would the concepts be likely to work if they were pursued further? Throughout the design process, you must also learn to budget your time. Good engineers have time-management skills that enable them to work productively and efficiently. You must learn to create a milestone chart detailing your time plan for completing the project. You need to show the time periods and the corre- sponding tasks that are to be performed during these time periods.

Step 5: Synthesis

Recall from our discussion in Chapter 1 that good engineers have a firm grasp of the funda- mental principles of engineering, which they can use to solve many different problems. Good engineers are analytical, detailed oriented, and creative. During this stage of design, you begin to consider details. You need to perform calculations, run computer models, narrow down the type of materials to be used, size the components of the system, and answer questions about how

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the product is going to be fabricated. You will consult pertinent codes and standards and make sure that your design will be in compliance with these codes and standards. We will discuss engi- neering codes and standards in Section 3.11.

Step 6: Evaluation

Analyze the problem in more detail. You may have to identify critical design parameters and con- sider their influence in your final design. At this stage, you need to make sure that all calcula- tions are performed correctly. If there are some uncertainties in your analysis, you must perform experimental investigation. When possible, working models must be created and tested. At this stage of the design procedure, the best solution must be identified from alternatives. Details of how the product is to be fabricated must be worked out fully.

Step 7: Optimization

Optimization means minimization or maximization. There are two broad types of design: a functional design and an optimized design. A functional design is one that meets all of the preestablished design requirements but allows for improvement to be made in certain areas.

To better understand the concept of a functional design, we will consider an example. Let us assume that we are to design a 3-meter-tall (10 ft) ladder to support a person who weighs 1335 newtons (300 pounds) with a certain factor of safety. We will come up with a design that consists of a steel ladder that is 3 meter tall (10 ft) and can safely support the load of 1335 N (300 lb) at each step. The ladder would cost a certain amount of money. This design would satisfy all of the requirements, including those of strength and size, and thus constitutes a Two engineers considering

details during the design process.

Source:Courtesy of DOE /NREL

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functional design. Before we can consider improving our design, we need to ask ourselves what criterion we should use to optimize the design. Design optimization is always based on some particular criterion, such as cost, strength, size, weight, reliability, noise, or performance.

If we use the weight as an optimization criterion, then the problem becomes one of minimiz- ing the weight of the ladder without jeopardizing its strength. For example, we may consider making the ladder from aluminum. We would also perform stress analysis on the new ladder to see if we could remove material from certain sections of the ladder without compromising the loading and safety requirements.

Another important fact to keep in mind is that optimizing individual components of an engineering system does not necessarily lead to an optimized system. For example, consider a thermal-fluid system such as a refrigerator. Optimizing the individual components indepen- dently —such as the compressor, the evaporator, or the condenser—with respect to some cri- terion does not lead to an optimized overall system (refrigerator).

Traditionally, improvements in a design come from the process of starting with an initial design, performing an analysis, looking at results, and deciding whether or not we can improve the initial design. This procedure is shown in Figure 3.1. In the past few decades, the optimization process has grown into a discipline that ranges from linear to nonlinear pro- gramming techniques. As is the case with any discipline, the optimization field has its own terminology. There are advanced classes that you can take to learn more about the design optimization process.

Evaluate results of analysis

Can the design be improved?

Perform analysis

Modify design

Initial design

Final design

No Yes

■

^{Figure 3.1}

An optimization procedure.

Presentation of a design includes both oral and written reports.

Source:Courtesy of DOE /NREL

Step 8: Presentation

Now that you have a final solution, you need to communicate your solution to the client, who may be your boss, another group within your company, or an outside customer. You may have to prepare not only an oral presentation but also a written report. As we said in Chapter 1, engineers are required to write reports. Depending on the size of the project, these reports might be lengthy, detailed technical reports containing graphs, charts, and engineering draw- ings, or they may take the form of a brief memorandum or executive summaries.

A reminder again that although we have listed the presentation as Step 8 of the design pro- cess, quite often engineers are required to give oral and written progress reports on a regular time basis to various groups. Consequently, presentation could well be an integral part of many other design steps. Because of the importance of communication, we have devoted an entire chapter to engineering communication (see Chapter 4).

Finally, recall from our discussion in Chapter 1 regarding the attributes of good engineers, we said that good engineers have written and oral communication skills that equip them to work well with their colleagues and to convey their expertise to a wide range of clients. More- over, engineers have good “people skills” that allow them to interact and communicate effec- tively with various people in their organization. For example, they are able to communicate equally well with the sales and marketing experts and with their own colleagues in engineering.

In Step 7 of the design process, we discussed optimization. Let us now use a simple example to introduce you to some of the fundamental concepts of optimization and its terminology.

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E xa m p l e 3.1 Assume that you have been asked to look into purchasing some storage tanks for your company, and for the purchase of these tanks, you are given a budget of $1680. After some research, you find two tank manufacturers that meet your requirements. From Manufacturer A, you can pur- chase 16-ft³-capacity tanks that cost $120 each. Moreover, the type of tank requires a floor space of 7.5 ft². Manufacturer B makes 24-ft³-capacity tanks that cost $240 each and that require a floor space of 10 ft². The tanks will be placed in a section of a lab that has 90 ft²of floor space available for storage. You are looking for the greatest storage capacity within the budgetary and floor-space limitations. How many of each tank must you purchase?

First, we need to define theobjective function, which is the function that we will attempt to minimize or maximize. In this example, we want to maximize storage capacity. We can rep- resent this requirement mathematically as

(3.1) subject to the following constraints:

(3.2) (3.3) (3.4) (3.5) In Equation (3.1),Zis the objective function, while the variablesx₁andx₂are calledde- sign variables, and represent the number of 16-ft³-capacity tanks and the number of 24-ft³- capacity tanks, respectively. The limitations imposed by the inequalities in Equations (3.2)–(3.5) are referred to as a set ofconstraints. Although there are specific techniques that deal with solv- ing linear programming problems (the objective function and constraints are linear), we will solve this problem graphically to illustrate some additional concepts.

Let us first review how you would plot the regions given by the inequalities. For example, to plot the region as given by the linear inequality 120x₁240x₂1680, we must first plot the line 120x₁240x₂1680 and then determine which side of the line represents the region. For example, after plotting the line 120x₁240x₂1680, we can test pointsx₁0 andx₂0 to see if they fall inside the inequality region; because substitution of these points into the inequal- ity satisfies the inequality, that is, (120)(0)(240)(0)1680, the shaded region represents the given inequality (see Figure 3.2(a)). Note that if we were to substitute a set of points outside the region, such asx₁15 andx₂0, into the inequality, we would find that the inequality is not satisfied. The inequalities in Equations (3.2)–(3.5) are plotted in Figure 3.2(b).

The shaded region shown in Figure 3.2(b) is called afeasible solution region. Every point within this region satisfies the constraints. However, our goal is to maximize the objective func- tion given by Equation (3.1). Therefore, we need to move the objective function over the fea- sible region and determine where its value is maximized. It can be shown that the maximum value of the objective function will occur at one of the corner points of the feasible region. By evaluating the objective function at the corner points of the feasible region, we see that the maximum value occurs atx₁8 andx₂3. This evaluation is shown in Table 3.1.

Thus, we should purchase eight of the 16-ft³-capacity tanks from Manufacturer A and three of the 24-ft³-capacity tanks from Manufacturer B to maximize the storage capacity within the given constraints.

x₂0 x₁0 7.5x₁10x₂90 120x₁240x₂1680 maximize Z16x₁24x₂

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x₂

x₂

x₁

x₁ 14

7

(a)

(14, 0) (12, 0) (0, 0)

(0, 0)

(0, 7) (0, 9)

(8, 3) Feasible

solution region

(b)

■

^{Figure 3.2}

(a) The region as given by the linear inequality 120x₁240x₂1680. (b) The feasible solution for Example 3.1.

TABLE 3.1 Values of the Objective Function at the Corner Points of the Feasible Region

Corner Points (x₁, x₂) Value of Zⴝ16x₁ⴙ24x₂

0, 0 0

0, 7 168

12, 0 192

8, 3 200 (max.)

It is worth noting here that most of you will take specific design classes during the next four years. In fact, most of you will work on a relatively comprehensive design project during your senior year. Therefore, you will learn more in depth about design process and its application specific to your discipline. For now our intent has been to introduce you to the design process, but keep in mind that more design is coming your way.