Dynamics Of Machinery Essay

2304 words - 9 pages

ME 302 Dynamics of Machinery Lecture Notes
© 2011
This chapter studies the dynamics of a slider crank mechanisms in an analytical way. This is an example for the analytical approach of solution instead of the graphical accelerations and force analyses. The gas equations and models for combustion is not a concern of this chapter.
Fig: Indicator diagram showing the pressure versus crank rotation.
A 1
2 3
Pθ φ ω
l r
G3 G2
I2,m2 I3,m3
intake compression power exhaust
Crank angle
Pr es
su re

ME 302 Dynamics of Machinery Lecture Notes
© 2011
Fig:Slider crank mechanism
Loop closure equation can be:
φθ sinsin lr = (1) φθ coscos lrx += (2)
from trigonometric identities
⇒=+ 1cossin 22 φφ φφ 2cos1sin −= (3) from first equation
θφ sinsin l r
= (4)
Substitute this equation into 3 and then resulting equation into (2) 2
sin1cos  
  
 −+= θθ
l rlrx (5)
Dynamic analysis of reciprocating engines was done in late 1800's and by that time extensive
calculations had to be avoided. So there are many approximations in the analysis to simplify the arithmetic. In equation (5) square root term can be replaced by simplest expression. Taylor series expansion of square root term, first two term included is as follows:
θθ 22 22
sin 2
1sin1 l
l r
−= 
  
 − (6)
Squaring is also an arithmetically difficult process:
2 2cos1
sin 2 θθ −= (7)
Substituting equation 6 and 7 into 5
 
  
  
  
 − −+=
2 2cos1
2 1cos 2
2 θθ l
 
  
 ++−= t
l r
tr l
rlx ωω 2cos 4
cos 4

ME 302 Dynamics of Machinery Lecture Notes
© 2011
Equation (8) defines the displacement of the slider. Velocity and acceleration expressions are by successive differentiation of this equation with respect to time. If we assume that the angular velocity of the crank is constant then velocity and acceleration of the slider become:
 
  
 −−=

  
 −−= t
l r
trt l
r trx ωωωω
ω ωω 2sin
2 sin2sin
2 sin& (9)
 
  
 −−=

  
 −−= t
l r
trt l
r trx ωωωω
ω ωωω 2coscos2coscos 2&& (10)
In dynamic force analysis, we put inertia and external forces on top of existing mechanism and then solve statically. Under the action of external and inertia forces, too many forces exist on...

Find Another Essay On dynamics of machinery

The Book Review of "The End of Work" by Jeremy Rifkin

1231 words - 5 pages says that this is because of many human labor jobs is been replace by machinery for the mass production. In the 1980's corporations spent trillions of dollars on technology to improve their efficiency and this results large numbers of blue collar jobs disappears and robotics, telecommunications, technologies and computers will be the ones that is taking over. Millions of people will be unemployed or underemployed because of the technology

Characteristics of Non-coding RNA Essay

1262 words - 6 pages two genes Global transcriptome analysis of mammalian cells have shown that actually 60 – 70 % of all transcripts have antisense pairs which can change the expression of the sense gene. Instead of being “transcriptional noise”, lncRNAs are involved in chromosomal dynamics, telomere biology and subcellular structural organization (Mercer et al. 2009). Furthermore, they have been shown to regulate gene expression of neighboring genes

An Application of Malcolm Baldridge Quality Principles

1207 words - 5 pages organizational systems. As Dr. W. Edwards Deming (Neave, 1990) instructs, “Best efforts and hard work will not suffice, nor new machinery, computers, automation, gadgets. . . . There is no substitute for knowledge” (p. viii). To gain this prerequisite knowledge, the integrated framework of the Baldridge program uniquely builds on the “dynamic scientific process of acquiring knowledge” (Shewhart, 1939), commonly referred to as the Shewhart Cycle of

Financial Forecasting

1213 words - 5 pages Businesses develop budgets and business plans to ensure optimum financial performance. An important element of budgeting and planning is financial forecasting. Forecasting the finances of a business requires certain understanding of financial dynamics. This paper will examine the necessary steps for financial forecasting, important elements of projecting future growth, types and methods of financing capital requirements, the impact of changes in

Organizational Theory of Behavior of Frederick Taylor, Max Weber, and Henri Fayol

1025 words - 4 pages processes or rules. Unlike Weber and Taylor whose ideal organizations were impersonal with little human interaction, Fayol’s concept of an ideal organization included personal effort and group dynamics. In fact, Fayol thought it was imperative that employees be allowed some creativity and innovation (176). Fayol’s system used a top-down approach as its starting point was management. He believed that improving upper management would lead to an

Time Capsule

952 words - 4 pages time capsule containing early creations by Bach and Handel would be the find of the century. Since Baroque would be considered a form of jazz because the soloists would play their own versions of a basic melody with rhythm section improvises, based on a chord pattern. Baroque music sounds different from music of the Renaissance periods due to its lack of dynamic range. The composers at this time usually did not specify dynamics on their pieces

Define economic globalization and describe its consequences to developing countries in terms of trade and investment

865 words - 3 pages globalization, with the volume of trade and level of exchange between countries and the amount by which they have increased, furthermore, some more things.Main body:-Economic globalization expresses the economic activity in term of interdependence and integration between economies and economic activity; it can be defined as the process by which markets and production in different countries are becoming increasingly interdependent due to the dynamics of

Statement of Purpose

950 words - 4 pages machinery and thermodynamics laid in me the strong fundamentals and problem solving techniques. Moreover, subjects such as dynamics of machines, Design of Machine Elements, Foundry technology and CAD / CAM exposed me to new ideas which form the essence of today’s Engineering challenges. I have had a strong affinity towards design oriented software courses such as solid edge, Ansys and Pro-E as well as CNC lathe and milling programming; these subjects

Genetics: Model Organisms

725 words - 3 pages are well established. In the case of the bacteria, the most researched organism is Escherichia coli (it was used in pioneering recombinant DNA cloning). It has DNA and RNA fundamental characteristics in common with all other living organisms. In order to analyze phenomena in which occurs the metabolism of the eukaryotic cell dynamics and targeting of the membrane, the repair of the DNA and other important basic functions, there can be used

The Sound of Music in Piano and Voice

966 words - 4 pages played by the foot, to distort and smooth the sound. On average, the piano keyboard contains 88 keys. 52 of these keys are white and 36 are black (“Piano”). These 88 keys cover 7 octaves and a minor third. Interestingly enough, more than one note can sound instantaneously on the keyboard. This means that the left hand can play at the same time as the right, creating full, rich melodies. Singing, in and of itself, requires no machinery. All

Sociological Theory: Karl Marx: Major Features of Capitalist Mode of Production

4076 words - 16 pages Das Kapital is itself his 'definition' of the concept. However, from this and his other writings we can glean the meaning of a 'mode of production' as the following: that it is a specific combination of productive forces which include human labor-power, machinery and tools and technologies, materials, buildings and improved land; and social relations of production which include the property, power and control relations governing society's

Similar Essays

Loudness Wats Essay

1525 words - 6 pages a problem. If you were to look at a wavelength chart, one would see that there are some songs are that stay loud all the through and those lines are toward the top of the chat and if the song has dynamics, the waves will be toward the bottom the song gets softer and work its way to the top of the chart as the song builds (Lamere). The final two steps are dithering and creating the final product. Dithering is a process that adds random noise to

Biocatalysts Essay

1010 words - 5 pages for new enzymes . • Initial production for biocatalysts requires expensive and extensive machinery that requires high initial cost . • Constant regulation is required to maintain correct pH and temperature, causing specific chemical regulation and techniques to be met . The pulp and paper industry is one of the largest industries in the world producing over 200 million tonnes of paper in North America alone7. The negative environmental

Fuji Dynamics Ltd Marketing Strategy

6786 words - 27 pages Kong has suffered with a downturn economy, we need to fight with those big competitors in a long term medical product market, a healthy growth of business and profit by improving the efficiency of operational systems and maintenance a good product quality as the key for market share increase.2. Introduction2.1 Company Background InformationFuji Dynamics Ltd. was established in 1977 in Hong Kong with a Japanese capital. We are located in Hong

The Independence Class Littoral Combat Ship

2430 words - 10 pages separate companies competing for the permanent contract to build LCSs for the Navy. Lockheed at the Marinette Marine Shipyard in Wisconsin designed the Freedom LCS. These ships are odd numbered: LCS-1, LCS-3, and LCS-5. The design of the Independence class is by General Dynamics, which is in Mobile, Alabama (O’Rourke, 2013). The Independence class is identified by even numbers. LCS is not only valuable as a war machine but also an instrument for