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A Journal of Applied Mechanics and Mathematics by DrD

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DrD

Mechanics Corner

A Journal of Applied Mechanics and Mathematics by DrD, #36

 

Base Acceleration Problem

Introduction

In a recent post (#35) I mentioned that I often participate in another forum called Physics Forums (PF). The problem that I want to discuss here is an elaboration on a problem that recently appeared at PF. I'm going to add a little bit of complexity to the problem (the problme as stated at PF was extremely simple) in order to make a particular point.

123.png

The system of interest is shown in Figure 1, a body with a single wing attached to one side. You might consider this to be one side of an airplane, or perhaps a stirring paddle used to mix paint. The mass of the wing is M, and the center of mass for the wing is at the point marked CM, a known distance u from the main body. We are told that the main body has an acceleration a sub z in the z-direction, and that the whole system is immersed in a viscous liquid such that the drag force is proportional to the square of the velocity in the z-direction. Our concern is with the connection between the wing and the main body. We need to determine the shear and bending moment on that connection due to z-direction motion.

 

BaseAccelerationProblem-36.pdf

DrD

    Mechanics Corner
    A Journal of Applied Mechanics and Mathematics by DrD, #20
    © Machinery Dynamics Research, 2015


A Question of Stability

Introduction

    The word stability in its several forms is widely used in nontechnical communication. A person whose life it highly consistent from day to day is said to have a stable life. When the political situation in a particular area appears to be unlikely to change, it is said to be stable. A person who is well balanced and unlikely to be easily provoked to anger is said to be a stable person. When the medical condition of a sick or injured person ceases to get worse, the person is said to be stabilized. A company on the verge of bankruptcy is said to be an unstable company. But what does the word stability mean in a technical context? Each of the foregoing examples hints at the technical meaning without really being explicit about it.

img1.png.919eb4ab059d77ce74a31be552405df

 

A factor g = accel of gravity was missing in the potential energy expression. That is now corrected.
    
 
 

 

Stability.pdf

DrD

    Mechanics Corner
    A Journal of Applied Mechanics and Mathematics by DrD, # 35
      Machinery Dynamics Research, 2017


Good News --- Bad News
Rolling Disk in a Rolling Ring

    

Introduction

    Well, it looks like Mechanics Corner is back, at least in terms of an occasional post. It will probably be less frequent than previously, but there are just too many interesting things to talk about to remain entirely silent! The title for this post may leave you wondering what is the Good News, and what is the Bad News? Why is there both? Well, let me tell you about it ...

GoodNews-BadNews-DiskInRing.pdf

rolling.png

DrD

   

Mechanics Corner
    A Journal of Applied Mechanics and Mathematics by DrD
    © Machinery Dynamics Research, 2016


Becoming An Expert -- Part 2

    

Introduction

    In the previous article on How To Become An Expert, I covered a lot of points in generalities with some short anecdotes from my own experience. In this article and the next, I will describe in considerably more detail a critical period in my own formation, an time of considerable professional embarrassment which was a real spur to learning.
    In the summer of 1974, I took a position as the head of the engineering analysis section with a large diesel engine distributor in Houston, TX. This company purchased diesel engines, mostly from General Motors (GM) and packaged them on a skid with some driven machine such as a generator, a pump, air compressor, or other driven machine, along with the required controls. For me, it was a fascinating place to be as I had always been intrigued by diesel engines. I soon found out how little I actually knew about the whole matter.
    The analysis section consisted of three other engineers (two men from India and a lady from Turkey) and myself. The men were there before I came, and I hired the lady. They were all good workers, but they were best at following directions. They did not ask "Why?" very often. If this is the way it had been done previously and nobody objected, they would repeat that same pattern over and over without wondering why we do it that way. More about that aspect later.
    This was a time of great activity in terms of nuclear power plant construction in the USA, and the company was building a lot of very large engine-generator sets to serve as standby power in nuclear power plants. In a nuke plant, pumps continuously supply cooling water to the core to take away the heat and as a means to move heat to the steam generators. If those pumps fail for any reason, the core can over heat and meltdown, a major catastrophe. The great fear was that the pumps would lose power from their regular supply, in which case the standby generators would need to start up and provide power to the pumps. The proposed cause of loss of power was an earthquake, and that meant that the standby generator set must survive the earthquake and be able to start and run.

BecomingAnExpert--Part2.pdf

DrD
   
Mechanics Corner
    A Journal of Applied Mechanics and Mathematics by DrD
    © Machinery Dynamics Research, 2016

How To Become An Expert
    
Introduction
    This is going to be another of those personal experience/opinion pieces, so if these bore you, be warned! This may be the time to click on something else.
    A reader recently wrote to me asking how to become an expert. I have to tell you, I don't spend much time thinking about being an expert, but I suppose on some reflection, the shoe probably fits. (Most of the time, I see myself as simply a tired old man, still enjoying the things I have done almost all my working life.) In the discussion below, I will describe a few events and observations that seem to relate to the question at hand.
Find Your Place
    Nobody can hope to be an expert on everything, there is simply too much to know. You have to find the area that excites you, the area that really makes you want to dig in more. If you do not really enjoy it, you will never be an expert!
    I was very fortunate in this regard. When I was in High School, I was rather good in Mathematics, and my school advisers all told me, "You should become an engineer." Sadly, I really had no idea what that meant, and neither did they. The town where I grew up had rather little industry, and no one in my family knew an engineer of any sort. I did a little bit of research on engineering (this was thousands of years before the Internet), and it sounded interesting in a very vague way; there seemed to be little specific information available to me. But I went off to college, intending to study mechanical engineering, whatever that was.
    In my first semester of college, I took a Physics course in classical mechanics, and I really enjoyed it. This was exactly what I wanted to do, I just did not know the right name for it. I thought Newton's Second Law was the greatest thing ever discovered, and when implemented with Calculus, it was really fun. I was astounded at the power of it all, the questions that could be answered. If I could just get a job doing mechanics problems, I was sure I would be happy.
HowToBecomeAnExpert.pdf
DrD
    Mechanics Corner
    A Journal of Applied Mechanics and Mathematics by DrD
    © Machinery Dynamics Research, 2017

Last Post
Time to Hang It Up
   
This will be the final post of Mechanics Corner here on Mechanical Engineering Forums. It has run almost exactly two years, and there have been ups and downs along the way. In this final post, I want to reflect a bit on my original goals for the blog, and also on what has actually happened.
When our host first proposed to me that I might write a blog for ME Forums, I was excited about it. About half of my career had been spent in engineering education, and I always loved working with students. It seemed like a way to get back to something that I had long enjoyed, and so I accepted his suggestion.
A long time ago, back when I was about 14 or 15 years old, in Junior High School, my shop teacher mentioned, in an off-hand way in class, that various curves could be described mathematically. I’d never heard that before, but I thought immediately, “This has interesting possibilities.” Moving ahead a few years, I discovered that I wanted to study and build my career around was the area known as Applied Mechanics, although it was a time before I first heard that term. In my freshman physics class, I discovered the laws of motion, and thought to myself, “This is great stuff! I can use math to describe how things move!” All of that happened back in the 1950s, and I’m still doing the same thing today (some might say I am in a rut!).
As a teacher, I taught mostly undergraduate engineering courses, although I taught my share of graduate courses as well. It was the undergraduate courses that I liked most, because I firmly believe that the economy of a nation is strongly dependent on the quality of the baccalaureate level engineers produced in that nation. Engineers with graduate degrees are valuable as well, but the vast majority of the national engineering workload falls to BS level engineers.    Thus, I envisioned Mechanics Corner as a sort of continuation of the several undergraduate courses I most enjoyed teaching — kinematics, dynamics of machines, vibrations, and mechanics of materials. For the most part, I have stuck to the plan, so that most of the technical posts I have made have dealt with problems that I considered suitable for undergraduate engineering students, say perhaps, junior level. I have posted a few topics from my industrial experience, but those have been situations that baccalaureate level engineers would be expected to handle.
Now I knew it would not be exactly like continuing to teach my classes. In particular, you would not have any homework or tests, and I would not have any grading to do – a win-win, or so I thought. I did hope, that even with no assigned homework, readers would take an interest in the problems discussed, even to the point of working through the details for themselves (I was terribly naive, apparently!). I knew from my own experience that the only way I ever really learned a new idea was to get in and work with it, work some problems, make some numbers, plot some curves, until I really understood what it was all about. I’ll venture to say that nobody ever learned any technical material simply by reading only.
In actual fact, in the early days, I had one or two folks say that they would in fact work through the problems, so I was encouraged. What I was not prepared for, however, was the fact that the vast majority never seemed to even read very carefully, much less work through the problems! The questions that have come, and there have been a few, have largely been about matters totally unrelated to the posts. The most common question has been, “Suggest a topic for my final project,” which relates to not a single post. Needless to say, that aspect of my vision was totally unfulfilled.
But there is another side. I ventured to write a few “philosophical” articles, items dealing with academic integrity and cheating, with how to ask for help, with how to write a report or a paper, and various other matters. I really thought all of this would be considered obvious and trivial, so I was completely unprepared for the excitement that some of these articles generated. There were, in some cases, many, many comments, and people seemed to really be interested. I’m left to wonder: why? Are these ideas foreign to the culture of India and SE Asia? Are these things not all taught at home and in the public schools? I don’t know, but there was a lot of interest in these matters.
But Mechanics Corner was intended to be primarily a technical blog, and there, it just did not excite the interest of the readership. As time passed, there was less and less interest. First, the comments dropped off to just about zero, and later, there were fewer and fewer who even bothered to “like” the articles. Finally, the number of reads has dropped to almost nothing (there may be no one left to read this final note). Well, there could hardly be any more clear indication that it is time to stop.
I asked for opinions about this from some of the administrators, and was told that the blog was just over the heads of the readership. That makes me sad; that was never the intent. If it is true, I do not see how engineering has a very bright future among this readership. Even so, I wish all of you the best for your careers. I hope that you are able to find rewarding and beneficial work in which you will be happy and make a real contribution to your societies.
To use an old cowboy metaphor perhaps familiar to many of you from Bollywood, “It is time to hang up the bridle and saddle, and say, ‘Adios’ (Adios is literally, “to God”).
 
DrD
Mechanics Corner
A Journal of Applied Mechanics and Mathematics by DrD, # 7
© Machinery Dynamics Research, LLC, 2015
Degrees of Freedom &  Constraints
Introduction

 
The term "Degrees of Freedom" (often abbreviated as DOF) has been carefully avoided for the most part in these presentations up to this point, although it has crept in unavoidably a time or two. In this article, we attempted to face the matter squarely and deal with it fully. It is an important concept, one that is very widely confused, and is critical to correct understanding of countless mechanics problems. There are several other concepts that must be discussed along with degrees of freedom including the idea of a particle or point mass and the idea of various types of constraints.
This article is different from those that went before in that there is (almost) no calculation involved. It is almost entirely focused on matters of philosophy, a perspective or point of view, that has proven useful for countless generations of workers in the field of mechanics.
DOF-Constraints.pdf
DrD
Mechanics Corner
A Journal of Applied Mechanics & Mathematics by DrD, #6
© Machinery Dynamics Research, LLC, 2015
AC Power in Real Variables Only
 

Most mechanical engineers get a pretty good understanding of DC circuits, and this carries over fairly well into single phase AC circuits. The difficulties come when we get into industry and discover that almost everything is powered by three phase AC circuits. This is where it starts getting sticky!
In the discussion of three phase AC electrical power, it is almost universal to use complex notation, otherwise known as phasor notation. For most purposes, the results might just as well be simply pulled out of the blue for all the understanding that complex mathematics gives, because everyone knows that the quantities involved -- voltage and current -- are fundamentally real, physical variables. These real quantities are not described by complex numbers, but rather by real numbers. The customary mantra says, "... we are considering the real part ...," but that really does not explain things very well because all of the mathematics being done is using complex algebra which considerably obscures the picture. Complex variables are, to use a colloquial term, "unreal." What is needed is a simple, straight--forward presentation of the problem in terms of real variables. We will give that a shot here.
ACPowerInRealVariables.pdf
DrD
Mechanics Corner
A Journal of Applied Mechanics and Mathematics by DrD, # 4
© Machinery Dynamics Research, LLC, 2015
 
 
Vector Loop Kinematics -- Part II
Velocity Analysis
 
Introduction

In the previous article in this series, titled "Vector Loop Kinematics - Part I/Position Analysis" the idea of using closed vector loops for the position analysis of mechanisms and machines was introduced. This is an extremely powerful method; I have never found a kinematics problem that was beyond its scope (now watch someone challenge me with such a problem!). As we left it at the end of that article, the technique of finding out all of the position information was at hand, but we had done nothing at all about discussing velocities or accelerations. This article will introduce the extension of this method to velocity analysis, but accelerations are differed until a later article.
This article is built upon the previous article, even to the extent of using some of the same example problems. If you have forgotten the content of the previous article, you might want to review it before getting to far into the present article.
Kinematics-II.pdf
DrD
 
Position Analysis
Introduction

Many years ago, when I first began to study mechanics, the "conventional wisdom," expressed by both teachers and fellow students, was this: "Statics is easy, Dynamics is hard, and Kinematics -- who bothers to actually study kinematics? Kinematic relations, when needed, simply drop from the sky like rain, but nobody seriously studies kinematics." I eventually found the truth to be a bit more subtle: Statics of structures is generally easy, while the statics of mechanisms and machines may, or may not, be easy, depending a lot on the kinematics. Further, I found that the key to most dynamics problems is having a good tool to deal with the necessary kinematics.
The purpose for this article is to present the most powerful tool I have ever found for dealing with mechanism and machine kinematics, the vector loop method. This will be demonstrated in the context of two simple problems.
Kinematics-I.pdf
DrD
Welcome to the first installment of Mechanics Corner, a feature that we hope will become a regular blog item on Mechanical Engineering Forum. The intent is that every week we will have a new article on some aspect of Applied Mechanics and Mathematics, things of broad interest to mechanical engineers. Some of these articles will be fairly elementary, while others will be considerably more advanced, but the idea is to have something for everyone. We will hope to amuse, entertain, and most importantly, to inform you with each article. We may even have a little bit of engineering humour from time to time!
 

Most of these articles will involve the use of pictures, diagrams, and mathematics, all things that are fairly difficult to accomplish in a blog post. For this reason, and beginning today, the bulk of the post will be in an attached PDF file. It turns out that there are fairly simple ways to have all the necessary tools available in a PDF file even though they are not available directly on the Internet. Thus I hope that each of you will click on over to the attached PDF file to read the rest of today's article.
 
Mechanics Corner is written by DrD, which of course raises the question, "Who is DrD?" Well, that’s me, but that doesnt tell you very much, does it? My intention is to say very little about myself in most of the articles, but since today is the day for introductions, for the blog, for myself, and a few other matters, it seems appropriate to tell you a little bit more about who I am.
 
I am an elderly man, a semiretired engineer and Mechanical Engineering Professor, living in Texas, USA. All of my engineering degrees are from The University of Texas at Austin, and I have professional engineering registrations in both Texas and Wisconsin (in the USA, engineers are licensed by the several states to prevent incompetents from holding themselves out as engineers and thus endangering the public safety and welfare). As I mentioned, I am old, many would say "older than dirt." I have had a long and very interesting career as an engineer working in a number of different industries, as an engineering faculty member, and as a consulting engineer (I continue to do some consulting yet today). In my engineering career, I have worked in the automotive, aerospace, naval, offshore, gas compression, steel, and electric power generation industries. I have worked on diesel and natural gas engines, steam turbines, gas turbines, large electric motors, generators and host of other machine types. If it moves, it is likely that I have worked on it; if I have not, I sure would like to work on it!
 
Being as old as I am, I have seen a lot of changes in my life, a few of which I wanted to touch on here. One of the most profound changes has been the shift of manufacturing industry away from the USA to India, China, Mexico, Brazil, and Southeast Asia. When I was young, the USA was arguably the greatest manufacturing power in the world, but that is no longer true today. We talk about being an "information society" (although Im not sure what that is) but we have very little to do with machinery and similar things today. But here I am, and this is one of the reasons why I feel a need to talk with many of you in the developing countries.
 
In October, 1957, Russia put the Sputnik satellite in orbit. It was a tiny thing, about the size of a soccer ball, but it shook the world. At that time I was in my last year in high school, preparing to go off to study engineering in college. Sputnik caused a great shake-up in American engineering education, with many warning cries that we were "behind" and had to "catch up." This meant many changes in education, but one in particular: now everything had to be done in vector notation, something that had not been done much before. In my freshman year in college, I took the introductory Mechanics course in physics, and fell in love with the subject matter. As a result, I have been studying mechanics, in one form or another, for well over half a century. Interestingly, although I initially learned everything in vector notation, I have come to the conclusion that I prefer to use scalars wherever possible. In particular this means the use of energy methods whenever they are suitable.
 
We all go off to college to study mechanical engineering; this is how we enter the profession. We are constantly told that we must never stop learning, but how many really believe that? Do you still hit the books every night? Are you still doing homework problems? I want to tell you a story about learning after school has ended.
 
About 12 years after I completed a Ph.D., I was on the faculty at Texas A&M University, one of the great engineering schools of America. I was assigned to teach Theory of Machines, and I figured that I could handle it, even though I had never had such a course in my own education. I selected a textbook that was somewhat unorthodox but I thought it looked attractive. It was a very good textbook, and it proved to be one of the greatest learning experiences in my whole life (there is nothing like trying to teach a course to be sure that you learn the course). I struggled to stay a few days ahead of the students, but that book brought me many new and powerful ideas that I had never seen previously. At the end of the semester, I asked the students what they thought of the book. They hated it! Their complaints really came down to two things: (1) the book was too big, too long, nearly 700 pages, and (2) the author had some really awkward notations. A few years later, when I set out to write my own textbook on Theory of Machines, I kept these two objections in mind and was able to produce what I think was a much better text. The point of the story is this: here I was, supposedly educated and having industrial experience, and yet I had the greatest learning experience of my life. It profoundly changed the way I work all kinds of problems to this day. The moral of the story is that we are never too old to learn, unless we think we are.
 
One of the great changes that I have seen, and you have seen it also, is the profound impact of the Internet. Thirty years ago there is no way that I would have been writing for you, and no possibility that you would have been reading the words of an old man in Texas. But all of that has changed now. Sadly, there is much trash on the Internet. On the good side, there is also much of a value. Among those good things, I would like to direct you to the site of a friend who has done some most excellent work in mechanism animations. When you see his animations you simply cannot help but have a better feel for how these machines work.
 
The URL is: http://www.mekanizmalar.com/ By all means take a look at them and see for yourself! I hope to see all of you and many more next week when we will go on to things of a more technical nature. Please check back here at Mechanical Engineering Forum for the next article.
 
Article1.pdf
DrD
   
Mechanics Corner
    A Journal of Applied Mechanics and Mathematics by DrD, # 32
    © Machinery Dynamics Research, LLC, 2015

Braced Cantilever
Introduction
    Anyone who has actually gotten into machine design is familiar with this difficulty. Consider the situation where a project is well advanced, many plans have been made, and it is all based on the assumption of the adequacy of one particular part. When you finally get to the detailed analysis of that part, the calculations show that it is not adequate. What can you do?
    To make the problem much more concrete, consider the cantilever beam shown in Figure 1. It supports a weight W at the free end, and when someone finally makes the calculation, the tip deflection, δ, is unacceptably large. The whole system design has been developed on the assumed adequacy of that cantilever, and there is no room to put in a beam with a larger section to give more stiffness. What can be done?
    Any of countless machine design texts, mechanics of materials texts, etc., give the formula for the end deflection,
δ=(WL³)/(3EI)
    where
    E= Young's modulus for the beam material
    I= area moment of inertia for the beam cross section
    L= length of the beam
    W= tip load value
    While we can argue that someone should have checked this earlier, finger-pointing does not fix the problem.
 
BracedCantilever.pdf
DrD
   
Mechanics Corner
    A Journal of Applied Mechanics and Mathematics by DrD, # 31
      Machinery Dynamics Research, 2016

ODE Solution --- Fail!!
    
Introduction
    Digital computation has become a major tool for engineers, and it is a great benefit. It can also lead to many pitfalls for the unwary. This note is about the latter, a potential pitfall that many engineers risk on a daily basis, most of them with little awareness of the danger.
    Early in the development of digital computation, every problem required that the user write a program specific to the problem at hand. If speed was a very important issue, the programs were written in machine language, so that they would execute as fast as possible. If speed was a little less critical, programs were written in so-called "high level languages." This included FORTRAN, BASIC, ALGOL, C, C++, and a host of other such names. But even with a high level language, there was the problem of generating a program for the solution of the specific problem at hand.
    As things have continued to evolve, it was soon evident that a lot of the work in writing each program was the same from one problem to the next. The major mathematical operations, such things as numerical integration, matrix operations and the solution of systems of linear equations, plotting, and many other steps were re-usable from one problem to the next. It was natural that this would eventually lead to the development of general purpose programs, able to solve broad classes of problems. This group includes programs like Mathematica, Maple, MatLab, SciLab, Maxima, TKSolver, and numerous others. Most of those just mentioned have built-in capability to solve ordinary differential equations, in some cases by analytical means, and in practically all cases, by numerical means. This has taken the sting out of working with differential equations
from many engineering problems, and we must all be grateful for that.
    At the same time, we must also be somewhat skeptical about any general purpose solver when applied to a particular problem. How do we know that the solution generated is correct? How do we even know if it is reasonable? Most of the time, when engineers resort to numerical solutions, it is because there is no readily available analytical solution. Thus, when faced with a problem that cannot be solved in closed form, how can we know when to trust the numerical solution? This is a very serious question, one that all must consider. It you blindly trust a numerical solution, the old excuse, "The computer said it was OK" will not get you very far. The computer cannot be fined, fired, or (in extreme cases) possibly sent to prison, but all of these things can happen to an engineer!
    So, what can the engineer do when the differential equation has no known solution? Well, there are several options.
    (1) He can resort to any physical principles that apply to the situation. For example, if the system is such that energy should be conserved, then he can add code to calculate the total system energy at every instant. Just verifying that energy is conserved does not "prove" that the solution is correct, but if energy is not conserved when it should be, you can be sure there is an error in the solution.
    (2) He can try various approximations that may apply to see if they are in reasonable agreement with the computed solution.
    (3) He can verify the solution code by applying it to a similar problem for which there is a known solution. It is this last approach that I want to talk about in this post.
ODE_Soln_Fail.pdf
DrD
    Mechanics Corner
    A Journal of Applied Mechanics and Mathematics by DrD
    © Machinery Dynamics Research, 2016

Becoming An Expert -- Part 3
    
Introduction
    In the previous article on Becoming An Expert--Part 2, I mentioned that there were two big issues for the engineering analysis section at my Houston position, the first being the matter of seismic survivability and the second being torsional vibration. The first item was dealt with in Part 2, and in this article we will take up the second item of concern.
    When I joined the engine distributor in Houston in the mid-1970s, the company was about 65 years old, and the torsional vibration problem was not new. This was a problem that they had been dealing with, in one way or another, for many years. There were lots of old torsional vibration analysis reports available to study. I was not at all familiar with torsional vibration of machine trains; I had not studied anything quite like that in school and it had not come up in my previous industrial experience. So I eagerly began reading the old reports, and that is when the problem became acute for me: They did not seem to make any sense. I could not, with any integrity, continue to write reports like that when I thought they were complete nonsense, but I did not know how to analyze the problem correctly. I was in a jam!
    There were three major difficulties:
    1. The entire crank assembly rotates endlessly, so the stiffness matrix for the system is singular. This results in a zero eigenvalue, something that did not take too long to figure out.
    2. It is obvious that the system does more than just go round-and-around; it goes up and down as well. I was baffled for a long time about how to deal with the kinematics and their impact on the dynamics.
    3. It is apparent that there is a torque acting on the crank, but it is not directly applied to the crank by the combustion process. There is the slider-crank mechanism between the two, and I was at a loss as to how to transfer the cylinder pressure into a crank torque. This is again directly related to the kinematic problem mentioned just above.
BecomingAnExpert--Part3.pdf
DrD
What/Where to Study
Introduction
I do not have the definite statistics available, but it appears to me that the majority of the readership of ME Forums is made up of students, with a much smaller number of readers at other points in their careers. By far the greatest part of these students appear to be in India, with a number in Southeast Asia and the Middle East; there are of course a few folks scattered all over the globe. It has been very interesting to me to learn about all of you, to gain an insight into your interests and concerns. I have been very surprised by a few of the things I've learned. There are two themes that stand out in my mind:

(1) there is much uncertainty about what to study, that is, what to choose for a major,
and
(2) where to study.

I want to offer a few comments on both of those topics in this post. Please understand that these are simply opinions, not necessarily facts. They are based upon what I think I see in the readership and in the way the world is going at large.
What to Study
Most of you are here because you have some interest in mechanical engineering. But quite a few express uncertainty about that interest. There are questions such as, "Should I switch to EE?" or "Would it be better to major in computer science?" These questions are often connected with questions and concerns about the future job market for whatever area one does choose to major in. So what can we say about such things?
It appears to me that the world economy is shifting considerably in favor of China and India. I do not think that the United States will disappear in the world economy by any means, but I do think these other two are going to become major rivals. If that is correct, the expanding economies of China and India will have a huge need for engineers and other technical people of all sorts in the years to come. It appears to me that the economies of both China and India are rapidly developing industrial economies, economies based on industrial production of goods. This would be much like the economy of the United States during the period from 1900 to about 1975. Sadly, the United States has entered a post-industrial era, also called a service economy. This does not mean that there is no industry in the US today, but it does mean that the bigger part of the economy is now based on paper shuffling, such things as banking, insurance, litigation, and fast food. The best automobiles produced in the United States today are those produced by Japanese companies such as Toyota and Honda. The machine tool industry, which was once a thriving business sector, is almost completely dead today in the US, because it has gone overseas. Almost all electronics production has moved to Southeast Asia. The production of textiles left the United States almost 100 years ago. The United States continues to have a very large agricultural industry, but that industry employs fewer people every year to produce even greater food yields. The point I hope to make here is simply that, many of you are right where you need to be to ride the crest of the rising wave of a developing industrial economy.
Many people looking at the future think very much in terms of electronic devices doing essentially everything. But I doubt that the day will ever come when we will do such things as plant crops entirely by electronics. We may use computer programs to anticipate when to plant a crop, perhaps to determine the most economically advantageous mix of crops, to help us choose fertilizers and pesticides to maximize the yield, but putting the seed in the ground and harvesting the crop will always be mechanical functions. This is simply one example but I think there are many others similar to it. There is a great future in electronics, but there is still a great future in mechanical devices as well. A growing industrial economy needs both of these and many other things as well.
Many of you seem to be concerned about the job market in the future. Will I be able to find a job as a mechanical engineer? Should I switch to computer engineering because there will be more jobs for computer engineers than there will be for mechanical engineers? These are questions that no one can really answer with full knowledge, but I can tell you a little bit. If you are really good at what you do, whether it be mechanical engineering, electrical engineering, chemical engineering, architectural engineering, etc., you will always be able to find employment. Many people look at salary surveys and say to themselves, "oh my, this year such and such a group of engineers are receiving higher salary offers that any of the others." Well, so what? When you pause to think about it, some group must always receive the highest offers, and some other group must always receive the lowest offers. That much is a mathematical certainty, but it doesn't really tell us very much.
I should add right here that if your intention is to acquire great wealth, then you should probably get out of engineering and go into business, law, or banking. That's where the big money is. Stay in engineering only if your interest is in doing something useful and meaningful with your life while earning a comfortable living. You're not likely to get rich, but I have never seen a starving engineer.
The other side of the job market concern is about the availability of jobs. We read various publications that say that X number of engineers were hired recently by Y Corporation. Depending on whether X is a large number or a small number, we think that the job market is good or that it is bad. But I would remind everyone of you that you only need, indeed can only handle, one job at a time. As long as you have a good job, one that provide satisfaction and a reasonable standard of living, there is little more you can ask for. Whether there are job advertisements for 1000 engineers or only for a few really makes no difference at all if you have a good job.
So how do you decide what to study? The answer is really rather simple. Within broad limits, you study whatever interests you. If civil engineering is really what interests you, then by all means you should study civil engineering. There will always be jobs for civil engineers. If those imaginary little things called electrons fascinate you, then you should most certainly study electrical engineering (I always enjoy teasing EEs about working with things that are not really there. I ask them how many electrons they have actually seen. I can show them a gear, a shaft, or a cam, but can they show me an electron?) There is a great future for electrical engineers. If you enjoy seeing how things move, how work gets done, how machines can make life easier for all mankind, then you should certainly become a mechanical engineer. We will always need mechanical engineers.
But there's more to this matter of "study what interests you" than simply amusing yourself. To be assured of a job, a good job, you have to be really good at your profession. There is one way, and only one way, to become really good. That is work, work, work, and then when you think you're through, work some more. During your student days, it is important that you learn everything you possibly can. You cannot possibly put in the required level of effort for the long haul if you are not studying the topic that interests you most. If you don’t know what that topic is, then you should drop out of school and only return when you have the necessary sense of direction.
Do not ask, "why do I have to learn this?" If it is presented to you as necessary course work, your response should be to dig in and learn every bit of it as thoroughly as you possibly can. You may have no idea why you need to know about this particular subject matter, but you can be pretty well assured that it would not be in the curriculum if your faculty did not think it was important. To be sure, there are a few topics that you will study and not see again for many years, but at this point in your life there is absolutely no way to predict which of those topics fall into that category. In my own case, I really did not particularly enjoy learning crystallography in the study of materials. As things have turned out, I have never needed any of that information about crystallography. But I had no way to know that when it was presented in my materials class, and in your case, crystallography may prove to be very important. During our days as students, we simply are in no position to make informed judgments about what we will need to know and what we will not need to know. For that reason, you should strive to learn everything you possibly can, in order to be the best, most versatile, most complete engineer you possibly can when you graduate. So I say again, "study what interests you" and look forward to a great future.
Where to Study
It has come as a considerable surprise to me to see the number of students who want to leave their home country to study. Many express a desire to come to the USA, or to Europe, for study. Let me deal with undergraduate and graduate study separately.
For undergraduate study, I would strongly advise everyone to stay pretty close to home. It will usually cost less money, and it will be easier in the sense that the language, customs, and overall environment will be much more familiar. To travel to a foreign land as an undergraduate can be a pretty daunting experience, one that in too many cases results in isolation, difficulty fitting into the new environment, and educational failure. None of these are good outcomes, and most can be avoided by staying pretty close to home.
In terms of quality of education, it appears to me that the Indian Institutes of Technology (IITs) are all pretty good. I have never visited one of their campuses, but I have looked at a number of videos made by IIT faculty on various engineering topics. The material covered seems to be about typical of what I would expect to see in the US. I have three principal criticisms of the IIT engineering education:
(1) The material presented seems to me to be a bit dated, that is, old-fashioned. There is continued emphasis on graphical methods of solution, to the detriment of computer numerical solution techniques. This is unfortunate.
(2) The faculty leave me with the impression that most of them are simply scholars, but very few seem to be real, practicing engineers. This comes across in the choice of example problems, in their approach to problems, and their emphasis.
(3) The faculty are, quite naturally, almost entirely native Indian nationals. This is what we would expect. But since they are teaching in English (at least all the ones I have seen), their own limited ability in English is transferred to the students. The students really need better models, so that they hear and learn from their teachers more correct English. I will say more about this in another post.
Now there may be many of you who will be quick to disagree with me, and I cannot really argue with you. I certainly have a very small sample of Indian education, but I can only tell you what I think I see.
If you were to come to the US for undergraduate study, you might be surprised to find your situation not a whole lot better. In the US, many if not most of the undergraduate courses are taught, not by regular faculty, but by Teaching Assistants (TA s). These TA s are graduate students, many from India, the Middle East, Africa, China, and Japan. The choice of material and solution methods may be a bit more up to date, but none of these TA s is a practicing engineer, and they all have linguistic limitations as well.
In short then, I urge everyone to stay relatively close to home for undergraduate study. It just make sense, I think.
For graduate study, it is a different situation. By the time you are ready for graduate school, you should be (1) considerably more mature personally, (2) more confident in your own abilities, and (3) much more ready to deal with a new cultural environment. Some problems will remain, and may be major. If you go to Germany for example, but do not know German, there will be a major language difficulty (I could not study in Germany; I know only a few, very limited, phrases in German.) If you were to come to the USA, the language would be English which you already know to some extent, but it would probably be somewhat new even so. American English is different from British English in some subtle ways, and the spoken language may be difficult for you even though you can read it well.
Sadly, in most American universities, you will find a huge emphasis on modern research ideas, and relatively little emphasis on actual engineering practice. The faculty are judged and rewarded for their research and the money that their research brings in, so naturally, that is what they tend to emphasize to their students. The world does not need countless “research engineers.” It does need a large number of highly skilled, well educated practicing engineers. But this is not where the money is for the schools, so this is not what they do.
In American universities, essentially all graduate courses are taught by regular faculty, so you would encounter the best faculty the school has to offer. You could expect to hear proper American English in the classroom all the time. You would still encounter only a relative few faculty that are actual practicing engineers (this conflicts with “research” which is where the money is).
It appears to me that a great many students come to the US to study, particularly with the hope that a student visa can be turned into a permanent visa and perhaps even eventual citizenship. Do not do this! Plan to make your home, in the long term, in your native country. The US does not need more foreign born engineers; it has plenty of native born engineers. Conversely, most of your countries have a great need for excellent engineers, people who can contribute to the economic and social development of your country. The very best people to do that are the ones born there. You can do that far better than I could. If I were to go to India, for example, I might be able to help some, but not nearly as much as you can. I would not know the customs and the culture, the languages, or the history like you do. Whether you do graduate school at home or abroad, plan to return home for the long term. That is where you can do the most good for mankind.
Conclusion
To sum up then, I recommend undergraduate work near your home. Graduate work may continue there, or abroad, but your goal should be to return to your home to make your career there. Be sure to study the topic that really interests you, and pay little or no attention to employment or salary surveys. You only want one job, and it will be there for you if you are really well prepared.
DrD
The following is a verbal description of a Doonesbury cartoon of unknown date by Garry Trudeau. Doonesbury has long been one of America’s major cartoon strips, with a very dry wit and a decidedly left-of-center outlook. I found this today in going through some old files.

SCENE: A college classroom, the teacher lecturing in a rather absent minded fashion, the students silently bent over, taking notes and keeping their heads down.

TEACHER: Of course, in his deliberations on American capitalism, Hamilton could not have foreseen the awesome private fortunes that would be amassed at the expense of the common good.

TEACHER: Take the modern example of the inventor of the radar detector. In less than ten years, he made $175 million selling a device whose sole purpose is to help millions of people break the law.

TEACHER: In other words ...

STUDENT (suddenly sitting up and interjecting): Maybe the fuzz buster is a form of Libertarian civil disobedience, man. You know, like a blow for individual freedom.

TEACHER: I ... I don’t believe it!

STUDENT: Believe what, man?

TEACHER (smiling in happy elation!): A Response! I finally got a thinking response from one of you. And I thought you were all stenographers! I have a student! A student LIVES!

TEACHER (kneeling down, hand extended like one might approach a shy animal): Who are you lad? Where did you come from? Don’t be frightened ...

STUDENT: (looking around himself): What’s the deal here? Am I in trouble?

The above all appeared in print many years ago, but it is an apt description of Mechanics Corner.
DrD
    Mechanics Corner
    A Journal of Applied Mechanics and Mathematics by DrD, # 34
    © Machinery Dynamics Research, 2015

A Problem in Statics & Dynamics
    
    
Introduction
        A problem was recently posted on this Forum, requesting help, that has led me to consider a somewhat more general problem for this post. The scope of this post will include the original problem, although not by the method required there, but will also go beyond to a more general geometry. We begin here by stating the present problem; interested readers are invited to search back for the original problem posted 19 December, 2016, by iivii.
    

Assembly Drawing, with Dimensions
 
StatDynProb.pdf
DrD
Mechanics Corner
A Journal of Applied Mechanics and Mathematics by DrD, # 5
© Machinery Dynamics Research, LLC, 2015
 
 
Vector Loop Kinematics -- Part III
Acceleration Analysis
Introduction

In the first article in this series, titled "Vector Loop Kinematics - Part I/Position Analysis" the idea of using closed vector loops for the position analysis of mechanisms and machines was introduced. A second article, "Vector Loop Kinematics - Part II/Velocity Analysis" extended the process to include mechanism velocity analysis. In this, the third article in the series, the process is extended further to cover the analysis of acclerations.

For each mechanism considered, we have first identified a single variable as the input, a variable to be assigned at will over some range representing the full motion of the system. (In so doing, we are limiting the discussion to Single Degree of Freedom systems, although this term has not yet been defined in this series.) It happens that in both examples used, the primary variable has been called θ, but there is no real significance to this naming. The position loop equations have then been written in terms of this primary variable and such other secondary variables as might be needed (secondary variables have been denoted as A, B, and x in the examples). The first step is always completion of the position solution, determining values for the secondary variables for any values of the primary varible of interest.
Kinematics-III.pdf
DrD
 
The use of desktop, laptop, tablet, and other computers has become routine these days for engineering work. Along with this, there has been an ever-increasing number of software options for engineering calculations. It would be interesting to know just what software the readership here uses in their daily work and/or study.

DrD
Mechanics Corner
A Journal of Applied Mechanics and Mathematics by DrD, No. 2
© Machinery Dynamics Research, LLC, 2015
It is a common practice for manufacturers to ship their products in packing crates that are strapped down on pallets for handling. There is often concern about the stability of this package as it is handled in transit to the purchaser. For this problem, we understand that the manufacturer wants to perform a simple test on each package shipped to assure that it will not tip over in transit. The test will consist of tipping the package slightly to the left and placing a block under the right edge of the pallet. The block is then quickly pulled out and the question is whether or not the package will fall over to the right. The answer depends upon the amount of the initial tip to the left and the location of the center of mass of the combined packing crate and pallet.

It is clear that the falling box impacts the floor, causing an impulsive distributed load to act on the bottom of the package. This will apply both an impulsive upward force and an impulsive moment to act on the box. Since the actual distribution of the force is unknown (and unknowable), an impulse--momentum approach to this problem is not likely to get very far. There is, however, a much simpler energy analysis available. Go on over to the attached PDF for more details.
BoxTipping.pdf
DrD
    Mechanics Corner
    A Journal of Applied Mechanics & Mathematics by DrD, #33
    © Machinery Dynamics Research, 2016

Advanced Polynomial Curve Fitting

    The use of polynomials to fit engineering data is a common engineering practice. In school, we learn that "A data set consisting of n data points ((x_{i},y_{i}), i=1,2,3,…n) can be exactly fitted with a polynomial of degree n-1. Thus three data points can be fitted exactly with a quadratic expression, four data points can be fitted exactly with a cubic expression, and so on. If this approach is pursued much further, something ugly appears: while a polynomial of degree n-1 will pass exactly through n data points, for large values of n, it will oscillate wildly in between the data points. Since one of the most common reason for using a polynomial fit in the first place is for interpolation -- to be able to estimate a function value at locations between the known data points -- this wild oscillation is devastating. It is at this point that least squares fitting is usually introduced to give an approximate fit using a much lower order polynomial. A different approach is employed here.
AdvancedPolynomialCurveFitting.pdf
DrD
Many of you have asked me various questions, so now it is my turn. Let me lay a bit of background first, and then the questions.
 
I have had some conversations recently with JAG (one of the other writers here at ME Forums) regarding the choice of software for 3D modeling and analysis. JAG has made some excellent suggestions, specifically a cloud based program called Onshape. Unfortunately, for reasons that are unclear, my computer cannot run Onshape; I have worked with their help people for several hours, all to no avail. JAG recommends this in part because there is a "free version for the hobbyist" and a relatively inexpensive "full version for the professional." That is pretty attractive, but since I can't run it, I'm stuck.
 
I gather that virtually all engineering colleges these days are teaching some sort of 3D modeling and analysis software, but that raises a few questions in my mind.
1. If your college teaches brandX 3D software, what will you do when you go to work for a small company that cannot afford anything more than 2D drafting (simple CAD), with no analysis capability at all? How will you do your job then? You probably have your own pocket calculator, but will you have your own copy of ANSYS or Pro-E?
2. What software does your school teach (every students should have an answer to this question, so I expect lots of replies on this one!)?
3. If you have used software extensively for analysis of engineering problems (beam deflections, stress analysis, fluid flow, heat transfer, etc), are you confident  that you will be able to work all of those problems if there is no such software available to you on the job?
 
I might add, as sort of a postscript, most of you know that I am older than dirt (I just had another birthday, so the situation is even worse!), so I tend to look at things from an elderly perspective. One of my great fears as a working engineer was "What will happen when I'm ask to do something that I don't know how to do?" It happened more than once, and it usually resulted in a flurry of intense research to come up to speed on whatever topic was involved. I could usually do that because I have a pretty good library, and I knew how to use a university library as well. But in terms of software, I was always concerned that I had no FEA program, so how could I do problems that others were doing by FEA? I have come up with some interesting work-arounds, including writing my own FEA for some problems, but I never wanted to be dependent on software that I could not afford to own. So, back to my questions about: How are you going to buy your own copy of ANSYS?
DrD
DrD
Does anyone recognize where this video is shot? Is it a group of students at a school (what school?), or is it an industrial site (what company)? I am anxious for someone to locate this for me, please.
DrD
 
Saurabh Jain, our host, has identified this location for me, and that is much appreciated.
When I watched the video, I was aghast at all those nearly bare feet in a machine shop! I can appreciate that in Indian culture, the simple sandals are socially quite acceptable, but from a safety perspective, this is an absolute horror. Think of all the opportunities for something to drop on a foot, a tool, a machine part, sparks, etc.
 
Some years ago (quite a few years ago), I worked in a steel mill. We were required to wear hard hats and steel toed shoes at all times in the mill. And these were not just any old steel toed shoes. These shoes came up ankle high, and had massive steel toes and an additional steel plate, called a metatarsal plate, that came up over the top of the foot almost to the ankle. Each shoe weighed 4 lb, and it was very tiring simply to walk around wearing them. But, .... and this is the key part .... they added much to our safety. Even today, in my advanced old age, I have a pair of steel toed boots (but not metatarsal plates) for when I go into an industrial environment.
 
What is shown in this video is actually a cautionary tale, a warning of just about everything not to do from a safety perspective. Take heed! Be warned, or you could easily loose all your toes on one foot of the other.
 
DrD
 
DrD
   
Mechanics Corner
    A Journal of Applied Mechanics and Mathematics by DrD, # 23
    © Machinery Dynamics Research, 2016

Torsional Stiffness of a Shaft -- Part II
    
    Introduction
    
    In the previous post of this series, a variety of shaft forms involving both solid and hollow sections were considered. A general approach was developed, applicable to various sorts of non-uniform shafts, but always subject to the provision that the variation in section was gradual; no sudden changes in section were permitted among the forms considered. This leads directly to the question that is the focus of this post: "How are sudden changes in diameter taken into account?" Steps, also called "shoulders" are a common feature of many shaft designs, used to locate rotating elements (fans, flywheels, pulleys, etc) on the shaft. They are also used in connection with bearings and seals. It is important that the means be established to account for shoulders in the shaft stiffness calculations.
    
Compliance of a Stepped Shaft
    At typical shaft section involving a step or shoulder is shown in Fig. 1. As usual, it is assumed that all of the dimensional data is known. The difficulty is the rather abrupt step from diameter D1  up to D2 . For the development below, it is always understood that D1 < D2. By the methods previously established in Part I, the compliance of each shaft segment can easily be computed,
    

ShaftStiff-Pt2.pdf