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Introduction This is MAE3501, Machine Design I Lesson Plans I will e-mail the lesson plans to you and post them on my website. Print them out and bring them to class or have them available electronically, and take supplemental notes. Please do not use this as an excuse to miss class. Tests There will be three tests. A cue sheet will be permitted. Homework Homework is very important. It is the primary manner by which you learn the material, including calculation techniques and methods of checking your work. In addition, there are many homework problems that are too long for tests, but that you must learn to solve. Homework must be worked on real engineering paper, one side only, multiple sheets stapled together, unfolded. Neatly print your name at the top of the first page. All homework assignments will be due at the beginning of the following class period. In calculating your homework total, I will discard the lowest grade. Answers must be clearly indicated; Many problems in this class will require one or more drawings. Make these neat, approximately to scale, including angles, and use a straightedge for every line, including forces and dimensions. Engineering paper is required because it assists you in preparing neat work. Equations and calculations should follow the lines on the paper. Use three significant figures for all results, other than integer values. Grading I use a grading scale which appears in the on-line gradebook. Three tests, 100 points each; about twenty homework assignments, 10 points each; final examination, 200 points. MAE3501 - 1 - 1 Success in this Course Pay attention and ask questions when there is something you do not understand. If there is something you do not understand, there are probably lots of other people who also do not understand. Please give me the opportunity to help all of you at once. Begin your homework as soon as possible, so you can obtain assistance if needed. Fundamentals I believe that, if I can teach you the fundamental principles behind the material we cover in this course, you will be able to successfully address problems that are similar to, but different from, any specific problems we addressed in this course. Rather than attempt to address as many specific problems as possible, and end up racing through all of them, we will address fewer problems, and try to understand every step in every analysis. It is your job to help me do this. Do not let me “get by” with anything; insist that you understand what I just did before you let me proceed. MAE3501 - 1 - 2 Chapter One Chapter one presents primarily introductory material. I asked you to rapidly skim this material, but not get bogged down in details. Following are the sections of this chapter I want to emphasize. Section 1 – 3, Phases and Interactions of the Design Process Two, long, drawn-out pages are spent stating the following. Design is not a linear process; it is an iterative process. We are even presented with a figure that attempts to explain this concept graphically. Unfortunately, this figure appears to indicate that the design process is an almost neverending series of feedback loops. This is not the case. Design is an art, not a science. Some design processes proceed almost linearly, with little feedback, while others continuously “discover” information that requires a previous conclusion to be revised. In addition, this figure and the text in this section omit what I consider to be a very important aspect of good design: the minimization of what is referred to as “feature creep.” It is extremely easy to continue to add additional features that are justified because they “make the product a lot better” and “don’t cost very much.” Unfortunately, at the end of such a design process, the overall cost of the product can very easily make the product unmarketable. MAE3501 - 1 - 3 Section 1 – 7, Economics A few concepts are discussed that assist a designer in reducing the final cost of the product. The sub-section entitled “Standard Sizes” makes an important, non-obvious point. Some standard sizes are rarely used, and consequently are not readily available. For this reason, it is wise to determine availability before specifying size. It may be that a 9/16 inch diameter rod “should be” cheaper than a 5/8 inch diameter rod, but not if it requires a special order from a supplier. Table A – 17 lists preferred sizes, in both engineering and SI units. The same is true of materials. It may be that SS-304 is superior to SS-301 for a particular application, but SS-301 will generally be cheaper and should be considered if its properties are acceptable. Section 1 – 9, Stress and Strength Two terms are defined, one differently than the manner in which it was defined in strength of materials. Stress refers to the force per unit area acting within a material. denotes a normal stress, perpendicular to a given plane. denotes a shear stress, parallel to a given plane. Subscripts are used to identify particular stresses, e.g., X to denote a normal stress parallel to the X –axis, or perpendicular to a plane of constant X. Strength refers to a property of a material and is denoted by S. Subscripts are used to denote various strengths, e.g., S Y to denote a yield strength and S U to denote an ultimate strength. Sections 1 – 10 and 1 - 11, Uncertainty, Design Factor, and Factor of Safety. The following fundamental relationship defines the design factor, denoted by n D . Note that Shigley uses lower-case d as the subscript while I use capital D because I believe it is easier to read. nD loss of function strength allowable stress MAE3501 - 1 - 4 (1.1) Example 1 – 2 A rod with a circular cross-section is subjected to an axial force of 2,000 lbf. The material strength is 24 ksi and the design factor is 3.0. Determine the smallest preferred diameter and the resultant factor of safety. n D 3.0 loss of function strength 24 ksi allowable stress ALLOW ALLOW 8 ksi 2 kip A (E.1) (E.2) d2 A 0.25 inch2 4 (E.3) d 0.564 inch (E.4) From Table A – 17, the next preferred size is 0.625 inch, resulting in a factor of safety, denoted by n, of 3.68. n loss of function strength 24 ksi stress 2 kip (0.625) 2 4 3.68 (E.5) Section 1 – 14, Units lbf s 2 lbf s 2 1 slug , but that 1 has no official name. Maybe ft inch not official, but it does have a name. Any guesses? Shigley tells us that 1 We are also presented with some non-sensical rules for writing numbers. Please ignore these. MAE3501 - 1 - 5 Chapter Two Chapter two discusses a number of aspects of different materials. I will attempt to summarize those that I consider valuable at this point. Section 2 – 1, Material Strength and Stiffness A uniaxial tensile test provides valuable stress-strain data. A test specimen similar to the following is used. P denotes the axial force. d 0 denotes the initial diameter of the specimen within the gauge length, denoted by L 0 . Note that I use capital L rather than lower-case l for length because I believe it is easier to read. A 0 denotes the cross-sectional area within the gauge length. d02 A0 4 (1.2) Normal stress along the axis of the specimen is defined. P A0 (1.3) Normal strain along the axis of the specimen is defined. L L0 L0 (1.4) The stress and strain defined in this manner are referred to as the engineering stress and strain. MAE3501 - 1 - 6 When the measured stress is plotted against the strain, diagrams such as the following are obtained Shigley tells us that the diagram on the left is typical for a ductile material, such as lowalloy steel, and the diagram on the right is typical for a brittle material, such as 400 series stainless steel. Sort of, except the diagram on the left is not remotely to scale. There is no plastic region, characterized by a more-or-less horizontal line, that should be much wider than the linear region. The “dome,”the region following the plastic region should be much wider than the first two regions combined. Consider the ductile-material stress-strain diagram. Point PL is referred to as the proportional limit, the point at which the diagram begins to deviate from a straight line. The slope of the straight-line portion of the diagram defines the modulus of elasticity of the material, denoted by E. This modulus is also referred to as Young’s modulus, and is frequently denoted by Y in physics texts. Not in engineering. Within the straight-line portion of the diagram, stress and strain satisfy the following relationship. E (1.5) Point EL is referred to as the elastic limit, the point at which an additional strain would cause plastic (permanent) deformation. The portion of the stress-strain diagram between point PL and point EL is not straight. However, the material could, in theory, be repeatedly cycled between these two points in a perfectly elastic manner, such that no heat is generated. There are no perfectly elastic materials. We will not need to concern ourselves with the distinction between these two points. MAE3501 - 1 - 7 Point Y is referred to as the yield point, at which the strain begins to increase with little or no increase in stress. In general, as in the above diagram, the location of point Y is not obvious. The following convention has been generally adopted by metallurgical engineers. The strain at point A is 0.002 or 0.2 %. A straight line is drawn from point A with a slope equal to E, the slope within the straight-line portion of the diagram. The intersection of that straight line with the stress-strain diagram determines point Y. The stress at point Y is a strength, a property of the material, and is denoted by S Y , rather than Y as was used in strength of materials. Section 2-3, Strength and Cold Work Consider the following stress-strain diagram for a ductile material. If the material were loaded, at a normal temperature, past the yield point, to point I, there would be permanent deformation. If the material were then unloaded, it would follow the rightmost curve back to a stress of zero. The material could then be repeatedly loaded and un-loaded up to a stress of I in an almost-linear manner. Note that the loading and unloading curves are not precisely the same, reflecting the non-elastic behavior of the material. The area between the two curves is the heat generated, per unit volume, in the material. This process, referred to as cold working, has effectively increased the value of S Y for the material. The material is said to be strain-hardened. MAE3501 - 1 - 8 Section 2 – 4, Hardness The Rockwell and Brinell hardness numbers are introduced and briefly discussed. The following relationship is then presented as valid for steels. S U (ksi) 0.5 H B (1.6) The only problem is that this is incorrect. Consider the following property table from the text used in Machine Design II. Equation (2.5) is seen to be an excellent approximation for cold-rolled and hot-rolled steels. However, it is not even close for steel that has been heat-treated and quenched. Equation (2.5) is an excellent approximation for low-alloy steels that have not been heat-treated. This relationship is a fair test question, for the following reason. A story from Ed McBride: “I was at Prudhoe Bay on the North Slope of Alaska. I had finished whatever I was doing that day, and was eating dinner when I heard this engineer at the next table going berserk. He had received two batches of pipe, identical except that one batch had a yield strength of 45 ksi and the other batch had a yield strength of 75 ksi. The paperwork had become mixed, and nobody knew which batch was the high-strength pipe. It was therefore necessary to send samples back to Anchorage for testing. That would delay installation by about four days, and the installation was going to save Arco $150 k per day. So I told him to calm down, found a hardened-steel center punch, a big hammer, and performed the McBride version of the Brinell Hardness test. I made a half dozen or so dents in each material, concluded without doubt which set of dents was smaller, and identified the high-strength steel.” MAE3501 - 1 - 9 Homework Read Section 3-2. Problem 1-12, work in fractions of inches. MAE3501 - 1 - 10