Mechanical Engineering

# Mechanics Corner

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A Journal of Applied Mechanics and Mathematics by DrD

## Torsional Stiffness of a Shaft - Part III -- #24

Mechanics Corner     A Journal of Applied Mechanics and Mathematics by DrD, # 24     © Machinery Dynamics Research, 2016 Torsional Stiffness of a Shaft -- Part III         Introduction     The discussion in previous parts of this series has focused on stiffness (or compliance) estimates for various shaft geometries. There has been nothing said yet about joining parts together, although most readers will readily agree that integral (single piece) shaft assemblies are very rare

## Torsional Stiffness of a Shaft - Part II -- #23

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; n

## Torsional Stiffness of a Shaft -- Part I -- #22

Mechanics Corner  A Journal of Applied Mechanics and Mathematics by DrD, # 22 (c)  Machinery Dynamics Research, 2016 Torsional Stiffness of a Shaft -- Part I          Introduction          A shaft is a common machine element, used to transmit rotational motion and torque from one component to the next. It is clear that the length of the shaft must be sufficient to span the distance from the first component to the second, but what should the diameter be? The answer to this quest

## Professional Responsibility — Do The Right Thing

Professional Responsibility — Do The Right Thing In Western culture, three professions are recognized. They are medicine, the law, and theology. The practitioners of these professions have long been accorded a special status in society in recognition of their special knowledge. The physician is expected to use his knowledge of healing only for good, and never to murder or maim a person. The lawyer is expected to give correct legal advice to his clients, to keep them free from legal entangle

## #21 -- Rigid Body Rotordynamic Instability, Part I

Mechanics Corner     A Journal of Applied Mechanics and Mathematics by DrD, #21     © Machinery Dynamics Research, 2015 Rigid Body Rotordynamic Instability, Part I      Introduction     The rotating elements of machinery are usually balanced to avoid vibration which results in noise and fatigue damage. That said, perfect balance is not possible, and there are practical and economic limits to the effort that can be expended to balance machine components. Consequently,

## #20 -- A Question of Stability (Revised)

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 un

## Value Engineering

A toothpaste factory had a problem.  They sometimes shipped empty boxes, boxes without the tube inside. This challenged their perceived quality with the buyers and distributors. Understanding how important the relationship with them was, the CEO of the company assembled his top people. They decided to hire an external engineering company to solve their empty boxes problem. The project followed the usual process: budget and project sponsor allocated, RFP, and third-parties selected.  Six months (

## Flying Fun

The URL below will take you to some amazing pictures and a story about the SR-71 aircraft. In my own opinion, this aircraft is some of the most stunning engineering ever done on earth. Enjoy the pictures and the story! DrD http://www.tickld.com/x/jaw/military-pilot-shares-the-most-amazing-story-ever

## How to Ask for Help

How to Ask for Help Throughout life, we all find ourselves needing to ask for help at times. Even the most rugged individualist will, at time, need help. You may need to ask a teacher for help, you may need to ask a fellow employee for help, or you may need to ask the boss for help. There are a few good ways to ask for help, and there are endless poor ways to ask. Make your request well, and there is a much better you will get the help you seek. Since I began writing for ME Forums, I have receiv

## Where Will I Find A Job??

Where Will I Find A Job?? As I read over the questions that readers post here on ME Forum and elsewhere, I sense a common theme in many of them. There seems to be a wide, dare I say almost universal, concern about where those currently in college will find employment after graduation. To a degree this is entirely understandable; we all wonder what is in our future. Even so, the level of anxiety that I sense in many of your postings strikes me as extraordinarily high. Let us consider this a bit.

## The VEProject --- Shifted Levers --- A Critical Assessment

The VEProject --- Shifted Levers A Critical Assessment      Introduction     The subject of this article is the VEProject Shifted Lever video, as found at the following URL:   https://www.youtube.com/watch?v=8TniRMwL2Vg     The video shows a "Shifted Lever" mechanism, a device that appears to be perpetually off balance. It is presented as a perpetual motion mechanism, that is, a machine that will run forever without any energy input other than, perhaps, an initial push. This presentation comes

## Twenty One Rules for Tech Writing

Twenty One Rules for Tech Writing Introduction One of the things that has surprised me about the readers of ME Forum is the number of folk who want to publish technical papers. When I was an undergraduate (a very, very long time ago), publishing papers was the farthest thing from my mind. I knew that publishing was a concern for some of the faculty, but it was certainly no concern of mine! To my even greater amazement, most of those desiring to write want to write in English, even though this is

## Problems With A Blog -- Differences Between SI and CI Engines

As most of us know, the Internet is a fantastic resource for information. You can find information on almost any topic you can imagine by doing an Internet search on the appropriate keywords. The flip side of this capability is that you can also find mis-information on almost any topic because there is no one to monitor the Internet for correctness. Wikipedia is a classic case in point. Many of the Wikipedia articles are highly informative and very valuable. Some, however, are highly biased and

## What/Where to Study -- Another Opinion Piece

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 a

## Help!! -- I'm Looking For A Book -- Update!

For quite some time now, I have been looking for a book that just does not seem to exist anymore. The title and author are -- Title:          Secondary Resonance and Subharmonics in Torsional Vibrations Author:      Per Draminsky It was published in Denmark, around 1961, or so I am told. It seems that it was probably a monograph, a single extended article that filled an entire volume of a journal. If anyone know where this can be found, I would much appreciate help with it. If I can borrow it fr

## #19 -- Vibrations - Part VI / Machinery Torsional Vibrations

Mechanics Corner     A Journal of Applied Mechanics and Mathematics by DrD, # 19     © Machinery Dynamics Research, 2015 Vibrations -- Part VI Machinery Torsional Vibrations      Introduction     The preceding five parts of this series on vibrations have dealt with relatively simple system, even though those systems are representative of many real situations encountered in engineering practice. For this section, a very specific class of machinery vibration problems, the torsional vibration of e

## #18 -- Free-Free MDOF Vibrations / Part V

Mechanics Corner     A Journal of Applied Mechanics and Mathematics by DrD, # 18     © Machinery Dynamics Research, 2015 Vibrations -- Part V Free-Free Systems Introduction     In the first three parts of this series on vibrations, only single degree of freedom systems were considered. In Part IV of the series, the idea of multiple degrees of freedom vibrations was introduced particularly in the context of two degree of freedom systems. In this, the penultimate part of this series, another aspe

## Something Light -- A few jokes

1. Team building is very popular in industry these days, so here is a team building joke. A group of mathematicians are attending a weekend seminar on team building. During the night, a fire breaks out in the room of one of the mathematicians. He quickly tears pages out of his notes and lights them on fire, one by one. He then runs down the hall, shoving burning sheets of paper under the doors of all the other mathematicians. In the morning, after the building is burnt to the ground, the fire ma

## A Community Built On False Values -- An Opinion Piece

A Community Built on False Values This may well prove to be the least popular thing I ever post on this blog because what I have to say may offend many. I do not say it with the intent to offend, but because I am compelled to give a warning. One of the most interesting things that has developed from my blog, Mechanics Corner, here on the ME Forum has been the opportunity to correspond directly with a modest number of readers. This has included both young men and young women scattered across Indi

## #17 -- MDOF Vibrations / Part IV

Mechanics Corner     A Journal of Applied Mechanics and Mathematics by DrD, # 17     © Machinery Dynamics Research, 2015   Vibrations -- Part IV Multiple Degrees of Freedom Introduction     The first three parts of this series have involved only a single mass moving in a single direction. Such a system constitutes a single degree of freedom. In this part, a second mass is added which changes the required approach considerably. The new system is shown in Figure 1.            Fig. 1  Two Degree o

## #16 -- Vibration Part III/Effects of Damping

Mechanics Corner     A Journal of Applied Mechanics and Mathematics by DrD, # 16     © Machinery Dynamics Research, 2015 Vibrations -- Part III Effects of Damping Introduction     In the previous discussions of the simple, displacement driven mechanical oscillator, damping has been explicitly omitted. In this part, viscous damping is taken into account. Viscous damping is the effect of forces that (1) always oppose existing relative motion, and (2) are proportional to the relative velocity bet

## #15 -- SDOF Near & At Resonance, Part II

Mechanics Corner     A Journal of Applied Mechanics and Mathematics by DrD, # 15     © Machinery Dynamics Research, 2015 Introduction & Review     In Part I of this discussion, the single degree of freedom oscillator was introduced with displacement excitation. The system is shown in Figure 1.            The impressed support motion is s(t) and the response of the mass is measured by x(t). As shown in the upper figure, s(0)=0, x(0)=0, and there is no strain in the spring. The elongation (or

## #14 -- SDOF Vibrations Part I

Mechanics Corner     A Journal of Applied Mechanics and Mathematics by DrD, # 14     © Machinery Dynamics Research, LLC, 2015      SDOF Vibrations -- Part I Undamped System With Non-Resonant Conditions      Introduction     The undamped single degree of freedom oscillator is a suitable model for countless physical systems. It might represent a wheel on a vehicle (without shock absorbers), a machine on an elastic foundation, a sensitive instrument mounted on a shaky support, or any number of othe

## #13 -- Numerical Methods/Roots & Solutions of Equations

Mechanics Corner     A Journal of Applied Mechanics and Mathematics by DrD, #13     © Machinery Dynamics Research, LLC, 2015     Numerical Methods Roots & Solutions of Equations   Introduction       When we write a mathematical expression of the form y=f(x), a value of x for which y=0 is called a root of the equation. The root is a value of x at which the ordinate is zero and the curve passes through the x-axis.     Further, we are often called upon to consider two equations of the form y=f₁

## #12 -- Numerical Solution of Ordinary Differential Equations

Mechanics Corner A Journal of Applied Mechanics and Mathematics by DrD, #12 © Machinery Dynamics Research, LLC, 2015     Numerical Solution of Ordinary Differential Equations   Introduction   When we take the mathematics course titled Differential Equations, we learn a bag of tricks for the solution of many different types of differential equations. We also learn that every different type seems to require a completely new approach. There is no general approach to differential equations as a whol

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