1
Table 1-2
Problem Formulation and Calculation
1
Define the problem
2
State the givens
Definition stage
3
Make appropriate assumptions
4
Preliminary design decisions
Preliminary design stage
5
Design sketches
6
Mathematical models
7
Analysis of the design
Detailed design stage
8
Evaluation
9
Document results
Documentation stage
Detailed Design Stage
With a tentative design direction established we can create one or more engineering (mathematical) models of the element or system in order to analyze it. These models will usually include a loading model consisting of free-body diagrams which show all forces, moments, and torques on the element or system and the appropriate equations for their calculation. Models of the stress and deflection states expected at locations of anticipated failure are then defined with appropriate stress and deflection equations.
Analysis of the design is then done using these models and the safety or failure of the design determined. The results are evaluated in conjunction with the properties of the chosen engineering materials and a decision made whether to proceed with this design or iterate to a better solution by returning to an earlier step of the process.
Documentation Stage
Once sufficient iteration through this process provides satisfactory results, the documentation of the element’s or system’s design should be completed in the form of detailed engineering drawings, material and manufacturing specifications, etc. If properly approached, a great deal of the documentation task can be accomplished concurrent with the earlier stages simply by keeping accurate and neat records of all assumptions, computations, and design decisions made throughout the process.
1.4
THE ENGINEERING MODEL
The success of any design is highly dependent on the validity and appropriateness of the engineering models used to predict and analyze its behavior in advance of building any hardware. Creating a useful engineering model of a design is probably the most difficult and challenging part of the whole process. Its success depends a great deal on experience as well as skill. Most important is a thorough understanding of the first principles and fundamentals of engineering. The engineering model that we are describ-ing here is an amorphous thing which may consist of some sketches of the geometric configuration and some equations that describe its behavior. It is a mathematical model
10
MACHINE DESIGN -
An Integrated Approach
1
that describes the physical behavior of the system. This engineering model invariably requires the use of computers to exercise it. Using computer tools for analyzing engineering models is discussed in the next section. A physical model or prototype usually comes later in the process and is necessary to prove the validity of the engineering model through experiments.
Estimation and First-Order Analysis
The value of making even very simplistic engineering models of your preliminary designs cannot be overemphasized. Often, at the outset of a design, the problem is so loosely and poorly defined that it is difficult to develop a comprehensive and thorough model in the form of equations that fully describe the system. The engineering student is used to problems that are fully structured, of a form such as “Given A, B, and C, find D.” If one can identify the appropriate equations (model) to apply to such a problem, it is relatively easy to determine an answer (which might even match the one in the back of the book).
Real-life engineering design problems are not of this type. They are very unstructured and must be structured by you before they can be solved. Also, there is no “back of the book” to refer to for the answer.* This situation makes most students and beginning engineers very nervous. They face the “blank paper syndrome,” not knowing where to begin. A useful strategy is to recognize that
1 You must begin somewhere.
2 Wherever you begin, it will probably not be the “best” place to do so.
3 The magic of iteration will allow you to back up, improve your design, and eventually succeed.
With this strategy in mind, you can feel free to make some estimation of a design configuration at the outset, assume whatever limiting conditions you think appropriate, and do a “first-order analysis,” one that will be only an estimate of the system’s behavior.
These results will allow you to identify ways to improve the design. Remember that it is preferable to get a reasonably approximate but quick answer that tells you whether the design does or doesn’t work rather than to spend more time getting the same result to more decimal places. With each succeeding iteration, you will improve your understanding of the problem, the accuracy of your assumptions, the complexity of your model, and the quality of your design decisions. Eventually, you will be able to refine your model to include all relevant factors (or identify them as irrelevant) and obtain a higher-order, final analysis in which you have more confidence.
The Engineering Sketch
A sketch of the concept is often the starting point for a design. This may be a freehand sketch, but it should always be made reasonably to scale in order to show realistic geometric proportions. This sketch often serves the primary purpose of communicating the
* A student once commented
concept to other engineers and even to yourself. It is one thing to have a vague con-that “Life is an odd-numbered
cept in mind and quite another to define it in a sketch. This sketch should, at a mini-problem.” This (slow) author had
to ask for an explanation, which
mum, contain three or more orthographic views, aligned according to proper drafting was: “The answer is not in the
convention, and may also include an isometric or trimetric view. Figure 1-1 shows a back of the book. ”
freehand sketch of a simple design for one subassembly of a trailer hitch for a tractor.
Chapter 1