ContentsArticlesDynamic Vibration Absorber Entertainment engineering Mechanical engineering Vibration AFGROW Agitator (device) Air handler Air preheater Airshaft American Machinists' Handbook Applied mechanics Atmosphere (unit) Automaton clock Backdrive Ball detent Beale number Bearing surface Bellcrank Bimetallic strip Block and bleed manifold Blood viscoelasticity Bolted joint Brake shoe Break-in (mechanical run-in) Brinelling Built-up gun Bullwheel Burmester's theory Burnishing (metal) Bushing (isolator) Calibrated orifice Cam Cam follower Cam plastometer 1 1 5 15 27 29 30 34 38 38 40 43 45 46 46 47 48 49 50 52 53 59 64 65 67 68 71 72 74 77 79 79 81 83

Campbell diagram Central Mechanical Engineering Research Institute Centrifugal-type supercharger Century tower clocks Chilled water Chiller CILAS Circle grid analysis Coefficient of performance Collapse action Combined cycle Compliant mechanism Compound lever Compression (physical) Constant air volume Constrained-layer damping Contact mechanics Frictional contact mechanics Cooling tower Coupling Crank (mechanism) Critical speed Cryogenic engineering d'AlembertEuler condition D-value (transport) Damper (flow) Damping matrix Demister (vapor) Design and manufacturing of gears Design for manufacturability for CNC machining Dexel Disc coupling Docking sleeve Drive by wire Duality (mechanical engineering) Dunkerley's method Duty cycle Dynamometer

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Edmund Key Embedment Engineering design process Engineering Equation Solver Engineering fit Envelope (motion) ERF damper EulerBernoulli beam equation Fan coil unit Feedwater heater Fillet (mechanics) Flange Float (liquid level) Flow stress Fluid power Formability Fretting Wear Friction loss Galling Gear Gudgeon pin Heat transfer Heisler Chart Mechanical Engineering Heritage (Japan) User:Hg82/Larry Howell Hinge Hydraulics Hydrogen pinch Hydrogen turboexpander-generator Ideal machine Idler Idler-wheel Index of mechanical engineering articles Indexing (motion) Injector Interference fit ITA Iscar Tool Advisor Jaw coupling

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JIC fitting Kinematic coupling Kinematic determinacy Kinematic diagram Laboratory for Energy Conversion Lamina emergent mechanisms (LEMs) Larry Howell Light Aid Detachment Limits and fits List of gear nomenclature Machine (mechanical) Machinery's Handbook Maintenance engineering Maintenance, repair, and operations Marks' Standard Handbook for Mechanical Engineers Mass transfer Mating connection McKinley Climatic Laboratory Mechanical advantage device Mechanical efficiency Mechanical engineering technology Mechanical singularity Mechanical system Metallurgical failure analysis Microelectromechanical systems User:Mkoronowski/turbomachinery Modal analysis Motion ratio Multi-function structure Multiphase heat transfer Non-synchronous transmission Nutation Orifice plate Ortman Key Oscillating reciprocation Overspeed (engine) Parallel motion Particle damping

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Photoelasticity Pinch analysis Piping Piston motion equations Power engineering Precision engineering Pressure exchanger Proactive maintenance Process integration Pulverizer Radiation properties Railworthiness Range of motion Reciprocating compressor Reciprocating motion Recuperator Reel Relief valve Residual stress Reynolds transport theorem Roadworthiness Roark's Formulas for Stress and Strain Rotary feeder Rotor Run-around coil Sacrificial part Screw theory Self-exciting oscillation Shear pin Shear strength Sieving coefficient Sight glass Simple machine Slip joint Slip line field Society of Tribologists and Lubrication Engineers South-pointing chariot Split pin

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Standard conditions for temperature and pressure Steam rupture Stick-slip phenomenon Strain hardening exponent Streamlines, streaklines, and pathlines Structural load Surface integrity Surface roughness Swivel Systematic Hierarchical Approach for Resilient Process Screening (SHARPS) Tail lift Thermal efficiency Thermal engineering Thermal science Thermo-mechanical fatigue Thermomechanical generator Timken OK Load Tip clearance Tolerance analysis Tooth Interior Fatigue Fracture Torque density Total indicator reading Transmission (mechanics) Treadle Tribology Trunnion Tuned mass damper Turboexpander Turbomachinery Undercut (manufacturing) Units conversion by factor-label Variable air volume Vibration isolation Vibratory stress relief Victaulic Virtual work VOICED Water cascade analysis

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Water chiller Water pinch analysis Wells turbine West number Work (physics) Zero seek

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ReferencesArticle Sources and Contributors Image Sources, Licenses and Contributors 594 605

Article LicensesLicense 615

Dynamic Vibration Absorber

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Dynamic Vibration AbsorberIn vibration analysis, a dynamic vibration absorber, or vibration neutralizer, is a tuned spring-mass system which reduces or eliminates the vibration of a harmonically excited system. Rotating machines such as engines, motors, and pumps often incite vibration due to rotational imbalances. A dynamic absorber can be affixed to the rotating machine and tuned to oscillate in such a way that exactly counteracts the force from the rotating imbalance. This reduces the possibility that a resonance condition will occur, which can cause rapid catastrophic failure.[1] Properly implemented, a dynamic absorber will neutralize the undesirable vibration, which would otherwise reduce service life or cause mechanical damage. Dynamic absorbers differ from tuned mass dampers in that dynamic absorbers do not require any damping to function satisfactorily. Damping can, however, be introduced to increase the range of frequencies for which the dynamic absorber is effective.

References[1] "The Dynamic Vibration Absorber" (http:/ / paws. kettering. edu/ ~drussell/ Demos/ absorber/ DynamicAbsorber. html). Acoustics and Vibrations Animations. Retrieved: Dec 12, 2010.

Rao, S. (2003), Mechanical Vibrations, Upper Saddle River, N.J.: Prentice Hall, ISBN0130489875.

External links (http://www.diracdelta.co.uk/science/source/d/y/dynamic vibration absorber/source.html) - Dynamic Vibration Absorber

Entertainment engineeringEntertainment engineering is an engineering discipline that involves the application of traditional engineering programs such as mechanical engineering, electrical engineering and structural engineering to create the highly technical designs that the entertainment industry has come to demand. It involves the use of equipment from many industries to create highly specialized devices for the entertainment industry.

EducationCurrently, the only university offering a degree specifically in Entertainment Engineering and Design (EED) is the University of Nevada, Las Vegas (UNLV). Because UNLV's program is in its infancy, current entertainment engineers come from a wide variety of educational backgrounds, the most prevalent of which are theater and mechanical engineering. Several other institutions of higher education offer similar programs for entertainment related ventures.

LicenseEngineers may seek license by a state, provincial, or national government. The purpose of this process is to ensure that engineers possess the necessary technical knowledge, real-world experience, and knowledge of the local legal system to practice engineering at a professional level. Once certified, the engineer is given the title of Professional Engineer (in the United States, Canada, Japan, South Korea, Bangladesh and South Africa), Chartered Engineer (in the UK, Ireland, India and Zimbabwe), Chartered Professional Engineer (in Australia and New Zealand) or European Engineer (much of the European Union). Not all mechanical engineers choose to become licensed; those

Entertainment engineering that do can be distinguished as Chartered or Professional Engineers by the post-nominal title P.E., P. Eng., or C.Eng., as in: John Doe, P.Eng. In the U.S., to become a licensed Professional Engineer, an engineer must pass the comprehensive FE (Fundamentals of Engineering) exam, work a given number of years as an Engineering Intern (EI) or Engineer-in-Training (EIT), and finally pass the "Principles and Practice" or PE (Practicing Engineer or Professional Engineer) exams. In the United States, the requirements and steps of this process are set forth by the National Council of Examiners for Engineering and Surveying (NCEES), a national non-profit representing all states. In the UK, current graduates require a BEng plus an appropriate masters degree or an integrated MEng degree plus a minimum of 4 years post graduate on the job competency development in order to become chartered through the Institution of Mechanical Engineers. In most modern countries, certain engineering tasks, such as the design of bridges, electric power plants, and chemical plants, must be approved by a Professional Engineer or a Chartered Engineer. "Only a licensed engineer, for instance, may prepare, sign, seal and submit engineering plans and drawings to a public authority for approval, or to seal engineering work for public and private clients."[1] This requirement can be written into state and provincial legislation, such as Quebec's Engineer Act.[2] In other countries, such as Australia, no such legislation exists; however, practically all certifying bodies maintain a code of ethics independent of legislation that they expect all members to abide by or risk expulsion.[3] Further information: FE Exam,Professional Engineer,Chartered Engineer,Incorporated Engineer,andWashington Accord

2

Modern toolsMany mechanical engineering companies, especially those in industrialized nations, have begun to incorporate computer-aided engineering (CAE) programs into their existing design and analysis processes, including 2D and 3D solid modeling computer-aided design (CAD). This method has many benefits, including easier and more exhaustive visualization of products, the ability to create virtual assemblies of parts, and the ease of use in designing mating interfaces and tolerances. Other CAE programs commonly used by mechanical engineers include product lifecycle management (PLM) tools and analysis tools used to perform complex simulations. Analysis tools may be used to predict product response to expected loads, including fatigue life and manufacturability. These tools include finite element analysis (FEA), computational fluid dynamics (CFD), and computer-aided manufacturing (CAM). Using CAE programs, a mechanical design team can quickly and cheaply iterate the design process to develop a product that better meets cost, performance, and other constraints. No physical prototype need be created until the design nears completion, allowing hundreds or thousands of designs to be evaluated, instead of a relative few. In addition, CAE analysis programs can model complicated physical phenomena which cannot be solved by hand, such as viscoelasticity, complex contact between mating parts, or non-Newtonian flows As mechanical engineering begins to merge with other disciplines, as seen in mechatronics, multidisciplinary design optimization (MDO) is being used with other CAE programs to automate and improve the iterative design process. MDO tools wrap around existing CAE processes, allowing product evaluation to continue even after the analyst goes home for the day. They also utilize sophisticated optimization algorithms to more intelligently explore possible designs, often finding better, innovative solutions to difficult multidisciplinary design problems.

Entertainment engineering

3

MechanicsMechanics is, in the most general sense, the study of forces and their effect upon matter. Typically, engineering mechanics is used to analyze and predict the acceleration and deformation (both elastic and plastic) of objects under known forces (also called loads) or stresses. Subdisciplines of mechanics include Statics, the study of non-moving bodies under known loads Dynamics (or kinetics), the study of how forces affect moving bodies Mechanics of materials, the study of how different materials deform under various types of stress Fluid mechanics, the study of how fluids react to forces[4]Mohr's circle, a common tool to study stresses in a mechanical element

Continuum mechanics, a method of applying mechanics that assumes that objects are continuous (rather than discrete) Mechanical engineers typically use mechanics in the design or analysis phases of engineering. If the engineering project were the design of a vehicle, statics might be employed to design the frame of the vehicle, in order to evaluate where the stresses will be most intense. Dynamics might be used when designing the car's engine, to evaluate the forces in the pistons and cams as the engine cycles. Mechanics of materials might be used to choose appropriate materials for the frame and engine. Fluid mechanics might be used to design a ventilation system for the vehicle (see HVAC), or to design the intake system for the engine.

KinematicsKinematics is the study of the motion of bodies (objects) and systems (groups of objects), while ignoring the forces that cause the motion. The movement of a crane and the oscillations of a piston in an engine are both simple kinematic systems. The crane is a type of open kinematic chain, while the piston is part of a closed four-bar linkage. Mechanical engineers typically use kinematics in the design and analysis of mechanisms. Kinematics can be used to find the possible range of motion for a given mechanism, or, working in reverse, can be used to design a mechanism that has a desired range of motion.

Mechatronics and roboticsMechatronics is an interdisciplinary branch of mechanical engineering, electrical engineering and software engineering that is concerned with integrating electrical and mechanical engineering to create hybrid systems. In this way, machines can be automated through the use of electric motors, servo-mechanisms, and other electrical systems in conjunction with special software. A common example of a mechatronics system is a CD-ROM drive. Mechanical systems open and close the drive, spin the CD and move the laser, while an optical system reads the data on the CD and converts it to bits. Integrated software controls the process and communicates the contents of the CD to the computer.

Training FMS with learning robot SCORBOT-ER 4u, workbench CNC Mill and CNC Lathe

Robotics is the application of mechatronics to create robots, which are often used in industry to perform tasks that are dangerous, unpleasant, or repetitive. These robots may be of any shape and size, but all are preprogrammed and

Entertainment engineering interact physically with the world. To create a robot, an engineer typically employs kinematics (to determine the robot's range of motion) and mechanics (to determine the stresses within the robot). Robots are used extensively in industrial engineering. They allow businesses to save money on labor, perform tasks that are either too dangerous or too precise for humans to perform them economically, and to insure better quality. Many companies employ assembly lines of robots, and some factories are so robotized that they can run by themselves. Outside the factory, robots have been employed in bomb disposal, space exploration, and many other fields. Robots are also sold for various residential applications.

4

Structural analysisStructural analysis is the branch of mechanical engineering (and also civil engineering) devoted to examining why and how objects fail. Structural failures occur in two general modes: static failure, and fatigue failure. Static structural failure occurs when, upon being loaded (having a force applied) the object being analyzed either breaks or is deformed plastically, depending on the criterion for failure. Fatigue failure occurs when an object fails after a number of repeated loading and unloading cycles. Fatigue failure occurs because of imperfections in the object: a microscopic crack on the surface of the object, for instance, will grow slightly with each cycle (propagation) until the crack is large enough to cause ultimate failure. Failure is not simply defined as when a part breaks, however; it is defined as when a part does not operate as intended. Some systems, such as the perforated top sections of some plastic bags, are designed to break. If these systems do not break, failure analysis might be employed to determine the cause. Structural analysis is often used by mechanical engineers after a failure has occurred, or when designing to prevent failure. Engineers often use online documents and books such as those published by ASM[5] to aid them in determining the type of failure and possible causes. Structural analysis may be used in the office when designing parts, in the field to analyze failed parts, or in laboratories where parts might undergo controlled failure tests.

Related fieldsLike manufacturing engineering and aerospace engineering, entertainment engineering and design are typically grouped with mechanical engineering. A bachelor's degree in these areas will typically have a difference of only a few specialized classes.

References[1] "Why Get Licensed?" (http:/ / www. nspe. org/ Licensure/ WhyGetLicensed/ index. html). National Society of Professional Engineers. . Retrieved May 6, 2008. [2] "Engineers Act" (http:/ / www. canlii. org/ qc/ laws/ sta/ i-9/ 20050616/ whole. html). Quebec Statutes and Regulations (CanLII). . Retrieved July 24, 2005. [3] "Codes of Ethics and Conduct" (http:/ / web. archive. org/ web/ 20050619081942/ http:/ / onlineethics. org/ codes/ ). Online Ethics Center. Archived from the original (http:/ / onlineethics. org/ codes/ ) on June 19, 2005. . Retrieved July 24, 2005. [4] Note: fluid mechanics can be further split into fluid statics and fluid dynamics, and is itself a subdiscipline of continuum mechanics. The application of fluid mechanics in engineering is called hydraulics and pneumatics. [5] [[ASM International (society)|ASM International (http:/ / asmcommunity. asminternational. org/ portal/ site/ asm/ )]'s site containing more than 20,000 searchable documents, including articles from the ASM Handbook series and Advanced Materials & Processes]

Entertainment engineering

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External linkshttp://www.entertainmentengineering.com

Mechanical engineeringMechanical engineering is a discipline of engineering that applies the principles of physics and materials science for analysis, design, manufacturing, and maintenance of mechanical systems. It is the branch of engineering that involves the production and usage of heat and mechanical power for the design, production, and operation of machines and tools.[1] It is one of the oldest and broadest engineering disciplines. The engineering field requires an understanding of core concepts including mechanics, kinematics, thermodynamics, materials science, and structural analysis. Mechanical engineers use these core principles along with tools like computer-aided engineering and product lifecycle management to design and analyze manufacturing plants, industrial equipment and machinery, heating and cooling systems, transport systems, aircraft, watercraft, robotics, medical devices and more.

Mechanical engineers design and build engines and power plants...

Mechanical engineering emerged as a field during the industrial revolution in Europe in the 18th century; however, ...structures and vehicles of all sizes. its development can be traced back several thousand years around the world. Mechanical engineering science emerged in the 19th century as a result of developments in the field of physics. The field has continually evolved to incorporate advancements in technology, and mechanical engineers today are pursuing developments in such fields as composites, mechatronics, and nanotechnology. Mechanical engineering overlaps with aerospace engineering, building services engineering, civil engineering, electrical engineering, petroleum engineering, and chemical engineering to varying amounts.

DevelopmentApplications of mechanical engineering are found in the records of many ancient and medieval societies throughout the globe. In ancient Greece, the works of Archimedes (287 BC212 BC) deeply influenced mechanics in the Western tradition and Heron of Alexandria (c. 1070 AD) created the first steam engine.[2] In China, Zhang Heng (78139 AD) improved a water clock and invented a seismometer, and Ma Jun (200265 AD) invented a chariot with differential gears. The medieval Chinese horologist and engineer Su Song (10201101 AD) incorporated an escapement mechanism into his astronomical clock tower two centuries before any escapement can be found in clocks of medieval Europe, as well as the world's first known endless power-transmitting chain drive.[3] During the years from 7th to 15th century, the era called the Islamic Golden Age, there were remarkable contributions from Muslim inventors in the field of mechanical technology. Al-Jazari, who was one of them, wrote his famous Book of Knowledge of Ingenious Mechanical Devices in 1206, and presented many mechanical designs. He is also considered to be the inventor of such mechanical devices which now form the very basic of mechanisms,

Mechanical engineering such as the crankshaft and camshaft.[4] Important breakthroughs in the foundations of mechanical engineering occurred in England during the 17th century when Sir Isaac Newton both formulated the three Newton's Laws of Motion and developed Calculus. Newton was reluctant to publish his methods and laws for years, but he was finally persuaded to do so by his colleagues, such as Sir Edmund Halley, much to the benefit of all mankind. During the early 19th century in England, Germany and Scotland, the development of machine tools led mechanical engineering to develop as a separate field within engineering, providing manufacturing machines and the engines to power them.[5] The first British professional society of mechanical engineers was formed in 1847 Institution of Mechanical Engineers, thirty years after the civil engineers formed the first such professional society Institution of Civil Engineers.[6] On the European continent, Johann Von Zimmermann (18201901) founded the first factory for grinding machines in Chemnitz (Germany) in 1848. In the United States, the American Society of Mechanical Engineers (ASME) was formed in 1880, becoming the third such professional engineering society, after the American Society of Civil Engineers (1852) and the American Institute of Mining Engineers (1871).[7] The first schools in the United States to offer an engineering education were the United States Military Academy in 1817, an institution now known as Norwich University in 1819, and Rensselaer Polytechnic Institute in 1825. Education in mechanical engineering has historically been based on a strong foundation in mathematics and science.[8]

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EducationDegrees in mechanical engineering are offered at universities worldwide. In Brazil, Ireland, Philippines, China, Greece, Turkey, North America, South Asia, India and the United Kingdom, mechanical engineering programs typically take four to five years of study and result in a Bachelor of Science (B.Sc), Bachelor of Science Engineering (B.ScEng), Bachelor of Engineering (B.Eng), Bachelor of Technology (B.Tech), or Bachelor of Applied Science (B.A.Sc) degree, in or with emphasis in mechanical engineering. In Spain, Portugal and most of South America, where neither BSc nor BTech programs have been adopted, the formal name for the degree is "Mechanical Engineer", and the course work is based on five or six years of training. In Italy the course work is based on five years of training, but in order to qualify as an Engineer you have to pass a state exam at the end of the course. In Australia, mechanical engineering degrees are awarded as Bachelor of Engineering (Mechanical) or similar nomenclature[9] although there are an increasing number of specialisations. The degree takes four years of full time study to achieve. To ensure quality in engineering degrees, Engineers Australia accredits engineering degrees awarded by Australian universities in accordance with the global Washington Accord. Before the degree can be awarded, the student must complete at least 3 months of on the job work experience in an engineering firm. Similar systems are also present in South Africa and are overseen by the Engineering Council of South Africa (ECSA). In the United States, most undergraduate mechanical engineering programs are accredited by the Accreditation Board for Engineering and Technology (ABET) to ensure similar course requirements and standards among universities. The ABET web site lists 276 accredited mechanical engineering programs as of June 19, 2006.[10] Mechanical engineering programs in Canada are accredited by the Canadian Engineering Accreditation Board (CEAB),[11] and most other countries offering engineering degrees have similar accreditation societies. Some mechanical engineers go on to pursue a postgraduate degree such as a Master of Engineering, Master of Technology, Master of Science, Master of Engineering Management (MEng.Mgt or MEM), a Doctor of Philosophy in engineering (EngD, PhD) or an engineer's degree. The master's and engineer's degrees may or may not include research. The Doctor of Philosophy includes a significant research component and is often viewed as the entry point to academia.[12] The Engineer's degree exists at a few institutions at an intermediate level between the master's degree and the doctorate.

Mechanical engineering

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CourseworkStandards set by each country's accreditation society are intended to provide uniformity in fundamental subject material, promote competence among graduating engineers, and to maintain confidence in the engineering profession as a whole. Engineering programs in the U.S., for example, are required by ABET to show that their students can "work professionally in both thermal and mechanical systems areas."[13] The specific courses required to graduate, however, may differ from program to program. Universities and Institutes of technology will often combine multiple subjects into a single class or split a subject into multiple classes, depending on the faculty available and the university's major area(s) of research. The fundamental subjects of mechanical engineering usually include: Statics and dynamics Strength of materials and solid mechanics Instrumentation and measurement Electrotechnology Electronics Thermodynamics, heat transfer, energy conversion, and HVAC Combustion, automotive engines, fuels Fluid mechanics and fluid dynamics Mechanism design (including kinematics and dynamics) Manufacturing engineering, technology, or processes Hydraulics and pneumatics Mathematics - in particular, calculus, differential equations, and linear algebra. Engineering design Product design Mechatronics and control theory Material Engineering Design engineering, Drafting, computer-aided design (CAD) (including solid modeling), and computer-aided manufacturing (CAM)[14] [15]

Mechanical engineers are also expected to understand and be able to apply basic concepts from chemistry, physics, chemical engineering, civil engineering, and electrical engineering. Most mechanical engineering programs include multiple semesters of calculus, as well as advanced mathematical concepts including differential equations, partial differential equations, linear algebra, abstract algebra, and differential geometry, among others. In addition to the core mechanical engineering curriculum, many mechanical engineering programs offer more specialized programs and classes, such as robotics, transport and logistics, cryogenics, fuel technology, automotive engineering, biomechanics, vibration, optics and others, if a separate department does not exist for these subjects.[16] Most mechanical engineering programs also require varying amounts of research or community projects to gain practical problem-solving experience. In the United States it is common for mechanical engineering students to complete one or more internships while studying, though this is not typically mandated by the university. Cooperative education is another option.

LicenseEngineers may seek license by a state, provincial, or national government. The purpose of this process is to ensure that engineers possess the necessary technical knowledge, real-world experience, and knowledge of the local legal system to practice engineering at a professional level. Once certified, the engineer is given the title of Professional Engineer (in the United States, Canada, Japan, South Korea, Bangladesh and South Africa), Chartered Engineer (in the United Kingdom, Ireland, India and Zimbabwe), Chartered Professional Engineer (in Australia and New Zealand) or European Engineer (much of the European Union). Not all mechanical engineers choose to become

Mechanical engineering licensed; those that do can be distinguished as Chartered or Professional Engineers by the post-nominal title P.E., P.Eng., or C.Eng., as in: Mike Thompson, P.Eng. In the U.S., to become a licensed Professional Engineer, an engineer must pass the comprehensive FE (Fundamentals of Engineering) exam, work a given number of years as an Engineering Intern (EI) or Engineer-in-Training (EIT), and finally pass the "Principles and Practice" or PE (Practicing Engineer or Professional Engineer) exams. In the United States, the requirements and steps of this process are set forth by the National Council of Examiners for Engineering and Surveying (NCEES), a national non-profit representing all states. In the UK, current graduates require a BEng plus an appropriate masters degree or an integrated MEng degree, a minimum of 4 years post graduate on the job competency development, and a peer reviewed project report in the candidates specialty area in order to become chartered through the Institution of Mechanical Engineers. In most modern countries, certain engineering tasks, such as the design of bridges, electric power plants, and chemical plants, must be approved by a Professional Engineer or a Chartered Engineer. "Only a licensed engineer, for instance, may prepare, sign, seal and submit engineering plans and drawings to a public authority for approval, or to seal engineering work for public and private clients."[17] This requirement can be written into state and provincial legislation, such as in the Canadian provinces, for example the Ontario or Quebec's Engineer Act.[18] In other countries, such as Australia, no such legislation exists; however, practically all certifying bodies maintain a code of ethics independent of legislation that they expect all members to abide by or risk expulsion.[19] Further information: FE Exam,Professional Engineer,Incorporated Engineer,andWashington Accord

8

Salaries and workforce statisticsThe total number of engineers employed in the U.S. in 2009 was roughly 1.6 million. Of these, 239,000 were mechanical engineers (14.9%), the second largest discipline by size behind civil (278,000). The total number of mechanical engineering jobs in 2009 was projected to grow 6% over the next decade, with average starting salaries being $58,800 with a bachelor's degree.[20] The median annual income of mechanical engineers in the U.S. workforce was roughly $74,900. This number was highest when working for the government ($86,250), and lowest in education ($63,050).[21] In 2007, Canadian engineers made an average of CAD$29.83 per hour with 4% unemployed. The average for all occupations was $18.07 per hour with 7% unemployed. Twelve percent of these engineers were self-employed, and since 1997 the proportion of female engineers had risen to 6%.[22]

Mechanical engineering

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Modern toolsMany mechanical engineering companies, especially those in industrialized nations, have begun to incorporate computer-aided engineering (CAE) programs into their existing design and analysis processes, including 2D and 3D solid modeling computer-aided design (CAD). This method has many benefits, including easier and more exhaustive visualization of products, the ability to create virtual assemblies of parts, and the ease of use in designing mating interfaces and tolerances. Other CAE programs commonly used by mechanical engineers include product lifecycle management (PLM) tools and analysis tools used to perform complex simulations. Analysis tools may be used to predict An oblique view of a four-cylinder inline crankshaft with pistons product response to expected loads, including fatigue life and manufacturability. These tools include finite element analysis (FEA), computational fluid dynamics (CFD), and computer-aided manufacturing (CAM). Using CAE programs, a mechanical design team can quickly and cheaply iterate the design process to develop a product that better meets cost, performance, and other constraints. No physical prototype need be created until the design nears completion, allowing hundreds or thousands of designs to be evaluated, instead of a relative few. In addition, CAE analysis programs can model complicated physical phenomena which cannot be solved by hand, such as viscoelasticity, complex contact between mating parts, or non-Newtonian flows. As mechanical engineering begins to merge with other disciplines, as seen in mechatronics, multidisciplinary design optimization (MDO) is being used with other CAE programs to automate and improve the iterative design process. MDO tools wrap around existing CAE processes, allowing product evaluation to continue even after the analyst goes home for the day. They also utilize sophisticated optimization algorithms to more intelligently explore possible designs, often finding better, innovative solutions to difficult multidisciplinary design problems.

SubdisciplinesThe field of mechanical engineering can be thought of as a collection of many mechanical engineering science disciplines. Several of these subdisciplines which are typically taught at the undergraduate level are listed below, with a brief explanation and the most common application of each. Some of these subdisciplines are unique to mechanical engineering, while others are a combination of mechanical engineering and one or more other disciplines. Most work that a mechanical engineer does uses skills and techniques from several of these subdisciplines, as well as specialized subdisciplines. Specialized subdisciplines, as used in this article, are more likely to be the subject of graduate studies or on-the-job training than undergraduate research. Several specialized subdisciplines are discussed in this section.

Mechanical engineering

10

MechanicsMechanics is, in the most general sense, the study of forces and their effect upon matter. Typically, engineering mechanics is used to analyze and predict the acceleration and deformation (both elastic and plastic) of objects under known forces (also called loads) or stresses. Subdisciplines of mechanics include Statics, the study of non-moving bodies under known loads, how forces affect static bodies Dynamics (or kinetics), the study of how forces affect moving bodies Mechanics of materials, the study of how different materials deform under various types of stress Fluid mechanics, the study of how fluids react to forces[23]Mohr's circle, a common tool to study stresses in a mechanical element

Kinematics, the study of the motion of bodies (objects) and systems (groups of objects), while ignoring the forces that cause the motion. Kinematics is often used in the design and analysis of mechanisms. Continuum mechanics, a method of applying mechanics that assumes that objects are continuous (rather than discrete) Mechanical engineers typically use mechanics in the design or analysis phases of engineering. If the engineering project were the design of a vehicle, statics might be employed to design the frame of the vehicle, in order to evaluate where the stresses will be most intense. Dynamics might be used when designing the car's engine, to evaluate the forces in the pistons and cams as the engine cycles. Mechanics of materials might be used to choose appropriate materials for the frame and engine. Fluid mechanics might be used to design a ventilation system for the vehicle (see HVAC), or to design the intake system for the engine.

Mechatronics and roboticsMechatronics is an interdisciplinary branch of mechanical engineering, electrical engineering and software engineering that is concerned with integrating electrical and mechanical engineering to create hybrid systems. In this way, machines can be automated through the use of electric motors, servo-mechanisms, and other electrical systems in conjunction with special software. A common example of a mechatronics system is a CD-ROM drive. Mechanical systems open and close the drive, spin the CD and move the laser, while an optical system reads the data on the CD and converts it to bits. Integrated software controls the process and communicates the contents of the CD to the computer.

Training FMS with learning robot SCORBOT-ER 4u, workbench CNC Mill and CNC Lathe

Robotics is the application of mechatronics to create robots, which are often used in industry to perform tasks that are dangerous, unpleasant, or repetitive. These robots may be of any shape and size, but all are preprogrammed and

Mechanical engineering interact physically with the world. To create a robot, an engineer typically employs kinematics (to determine the robot's range of motion) and mechanics (to determine the stresses within the robot). Robots are used extensively in industrial engineering. They allow businesses to save money on labor, perform tasks that are either too dangerous or too precise for humans to perform them economically, and to ensure better quality. Many companies employ assembly lines of robots,especially in Automotive Industries and some factories are so robotized that they can run by themselves. Outside the factory, robots have been employed in bomb disposal, space exploration, and many other fields. Robots are also sold for various residential applications.

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Structural analysisStructural analysis is the branch of mechanical engineering (and also civil engineering) devoted to examining why and how objects fail and to fix the objects and their performance. Structural failures occur in two general modes: static failure, and fatigue failure. Static structural failure occurs when, upon being loaded (having a force applied) the object being analyzed either breaks or is deformed plastically, depending on the criterion for failure. Fatigue failure occurs when an object fails after a number of repeated loading and unloading cycles. Fatigue failure occurs because of imperfections in the object: a microscopic crack on the surface of the object, for instance, will grow slightly with each cycle (propagation) until the crack is large enough to cause ultimate failure. Failure is not simply defined as when a part breaks, however; it is defined as when a part does not operate as intended. Some systems, such as the perforated top sections of some plastic bags, are designed to break. If these systems do not break, failure analysis might be employed to determine the cause. Structural analysis is often used by mechanical engineers after a failure has occurred, or when designing to prevent failure. Engineers often use online documents and books such as those published by ASM[24] to aid them in determining the type of failure and possible causes. Structural analysis may be used in the office when designing parts, in the field to analyze failed parts, or in laboratories where parts might undergo controlled failure tests.

Thermodynamics and thermo-scienceThermodynamics is an applied science used in several branches of engineering, including mechanical and chemical engineering. At its simplest, thermodynamics is the study of energy, its use and transformation through a system. Typically, engineering thermodynamics is concerned with changing energy from one form to another. As an example, automotive engines convert chemical energy (enthalpy) from the fuel into heat, and then into mechanical work that eventually turns the wheels. Thermodynamics principles are used by mechanical engineers in the fields of heat transfer, thermofluids, and energy conversion. Mechanical engineers use thermo-science to design engines and power plants, heating, ventilation, and air-conditioning (HVAC) systems, heat exchangers, heat sinks, radiators, refrigeration, insulation, and others.

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Design and DraftingDrafting or technical drawing is the means by which mechanical engineers design products and create instructions for manufacturing parts. A technical drawing can be a computer model or hand-drawn schematic showing all the dimensions necessary to manufacture a part, as well as assembly notes, a list of required materials, and other pertinent information. A U.S. mechanical engineer or skilled worker who creates technical drawings may be referred to as a drafter or draftsman. Drafting has historically been a two-dimensional process, but computer-aided design (CAD) programs now allow the designer to create in three dimensions. Instructions for manufacturing a part must be fed to the necessary machinery, either manually, through programmed instructions, or through the use of a computer-aided manufacturing (CAM) or combined CAD/CAM program. Optionally, an engineer may also manually manufacture a part using the technical drawings, but this is becoming an increasing rarity, with the advent of computer numerically controlled (CNC) manufacturing. Engineers primarily manually manufacture parts in the areas of applied spray coatings, finishes, and other processes that cannot economically or practically be done by a machine. Drafting is used in nearly every subdiscipline of mechanical engineering, and by many other branches of engineering and architecture. Three-dimensional models created using CAD software are also commonly used in finite element analysis (FEA) and computational fluid dynamics (CFD).A CAD model of a mechanical double seal

Frontiers of researchMechanical engineers are constantly pushing the boundaries of what is physically possible in order to produce safer, cheaper, and more efficient machines and mechanical systems. Some technologies at the cutting edge of mechanical engineering are listed below (see also exploratory engineering).

Micro electro-mechanical systems (MEMS)Micron-scale mechanical components such as springs, gears, fluidic and heat transfer devices are fabricated from a variety of substrate materials such as silicon, glass and polymers like SU8. Examples of MEMS components are the accelerometers that are used as car airbag sensors, modern cell phones, gyroscopes for precise positioning and microfluidic devices used in biomedical applications.

Friction stir welding (FSW)Friction stir welding, a new type of welding, was discovered in 1991 by The Welding Institute (TWI). This innovative steady state (non-fusion) welding technique joins materials previously un-weldable, including several aluminum alloys. It may play an important role in the future construction of airplanes, potentially replacing rivets. Current uses of this technology to date include welding the seams of the aluminum main Space Shuttle external tank, Orion Crew Vehicle test article, Boeing Delta II and Delta IV Expendable Launch Vehicles and the SpaceX Falcon 1 rocket, armor plating for amphibious assault ships, and welding the wings and fuselage panels of the new Eclipse 500 aircraft from Eclipse Aviation among an increasingly growing pool of uses.[25] [26] [27]

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CompositesComposites or composite materials are a combination of materials which provide different physical characteristics than either material separately. Composite material research within mechanical engineering typically focuses on designing (and, subsequently, finding applications for) stronger or more rigid materials while attempting to reduce weight, susceptibility to corrosion, and other undesirable factors. Carbon fiber reinforced composites, for instance, have been used in such diverse applications as spacecraft and fishing rods.

Mechatronics

Composite cloth consisting of woven carbon fiber.

Mechatronics is the synergistic combination of mechanical engineering, Electronic Engineering, and software engineering. The purpose of this interdisciplinary engineering field is the study of automation from an engineering perspective and serves the purposes of controlling advanced hybrid systems.

NanotechnologyAt the smallest scales, mechanical engineering becomes nanotechnology one speculative goal of which is to create a molecular assembler to build molecules and materials via mechanosynthesis. For now that goal remains within exploratory engineering.

Finite element analysisThis field is not new, as the basis of Finite Element Analysis (FEA) or Finite Element Method (FEM) dates back to 1941. But evolution of computers has made FEM a viable option for analysis of structural problems. Many commercial codes such as ANSYS, Nastran and ABAQUS are widely used in industry for research and design of components. Other techniques such as finite difference method (FDM) and finite-volume method (FVM) are employed to solve problems relating heat and mass transfer, fluid flows, fluid surface interaction etc.

BiomechanicsBiomechanics is the application of mechanical principles to biological systems, such as humans, animals, plants, organs, and cells.[28] Biomechanics is closely related to engineering, because it often uses traditional engineering sciences to analyse biological systems. Some simple applications of Newtonian mechanics and/or materials sciences can supply correct approximations to the mechanics of many biological systems.

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Related fieldsManufacturing engineering and Aerospace Engineering are sometimes grouped with mechanical engineering. A bachelor's degree in these areas will typically have a difference of a few specialized classes.

Notes and references[1] engineering "mechanical engineering. (n.d.)" (http:/ / dictionary. reference. com/ browse/ mechanical). The American Heritage Dictionary of the English Language, Fourth Edition. Retrieved: May 08, 2010. [2] "Heron of Alexandria" (http:/ / www. britannica. com/ EBchecked/ topic/ 263417/ Heron-of-Alexandria). Encyclopdia Britannica 2010 Encyclopdia Britannica Online. Accessed: 09 May 2010. [3] Needham, Joseph (1986). Science and Civilization in China: Volume 4. Taipei: Caves Books, Ltd. [4] Al-Jazar. The Book of Knowledge of Ingenious Mechanical Devices: Kitb f ma'rifat al-hiyal al-handasiyya. Springer, 1973. ISBN 9027703299. [5] Engineering (http:/ / www. britannica. com/ eb/ article-9105842/ engineering) - Encyclopedia Brittanica, accessed 06 May 2008 [6] R. A. Buchanan. The Economic History Review, New Series, Vol. 38, No. 1 (Feb., 1985), pp. 4260. [7] ASME history (http:/ / anniversary. asme. org/ history. shtml), accessed 06 May 2008. [8] The Columbia Encyclopedia, Sixth Edition. 2001-07, engineering (http:/ / www. bartleby. com/ 65/ en/ engineer. html), accessed 06 May 2008 [9] "Mechanical Engineering" (http:/ / www. flinders. edu. au/ science_engineering/ csem/ disciplines/ mecheng/ ). . Retrieved 8 December 2011. [10] ABET searchable database of accredited engineering programs (http:/ / www. abet. org/ accrediteac. asp), Accessed June 19, 2006. [11] Accredited engineering programs in Canada by the Canadian Council of Professional Engineers (http:/ / www. engineerscanada. ca/ e/ acc_programs_1. cfm), Accessed April 18, 2007. [12] Types of post-graduate degrees offered at MIT (http:/ / www-me. mit. edu/ GradProgram/ GradDegrees. htm) - Accessed 19 June 2006. [13] 2008-2009 ABET Criteria (http:/ / www. abet. org/ Linked Documents-UPDATE/ Criteria and PP/ E001 08-09 EAC Criteria 11-30-07. pdf), p. 15. [14] University of Tulsa Required ME Courses - Undergraduate Majors and Minors (http:/ / www. me. utulsa. edu/ Undergraduate. html). Department of Mechanical Engineering, University of Tulsa, 2010. Accessed: 17 December 2010. [15] Harvard Mechanical Engineering Page (http:/ / www. deas. harvard. edu/ undergradstudy/ engineeringsciences/ mechanical/ index. html). Harvard.edu. Accessed: 19 June 2006. [16] Mechanical Engineering courses (http:/ / student. mit. edu/ catalog/ m2a. html), MIT. Accessed 14 June 2008. [17] "Why Get Licensed?" (http:/ / www. nspe. org/ Licensure/ WhyGetLicensed/ index. html). National Society of Professional Engineers. . Retrieved May 6, 2008. [18] "Engineers Act" (http:/ / www. canlii. org/ qc/ laws/ sta/ i-9/ 20050616/ whole. html). Quebec Statutes and Regulations (CanLII). . Retrieved July 24, 2005. [19] "Codes of Ethics and Conduct" (http:/ / web. archive. org/ web/ 20050619081942/ http:/ / onlineethics. org/ codes/ ). Online Ethics Center. Archived from the original (http:/ / onlineethics. org/ codes/ ) on June 19, 2005. . Retrieved July 24, 2005. [20] 2010-11 Edition, Engineers (http:/ / www. bls. gov/ oco/ ocos027. htm#earnings) - Bureau of Labor Statistics, U.S. Department of Labor, Occupational Outlook Handbook, Accessed: 9 May 2010. [21] Document National Sector NAICS Industry-Specific estimates (xls) (http:/ / www. bls. gov/ oes/ oes_dl. htm) Accessed: 9 May 2010. [22] Mechanical Engineers (http:/ / www. jobfutures. ca/ noc/ 2132p4. shtml) - Jobfutures.ca, Accessed: June 30, 2007. [23] Note: fluid mechanics can be further split into fluid statics and fluid dynamics, and is itself a subdiscipline of continuum mechanics. The application of fluid mechanics in engineering is called hydraulics and pneumatics. [24] [[ASM International (society)|ASM International (http:/ / asmcommunity. asminternational. org/ portal/ site/ asm/ )]'s site containing more than 20,000 searchable documents, including articles from the ASM Handbook series and Advanced Materials & Processes] [25] Advances in Friction Stir Welding for Aerospace Applications (http:/ / www. niar. wichita. edu/ media/ pdf/ nationalpublication/ Nov2-06. pdf) [26] PROPOSAL NUMBER: 08-1 A1.02-9322 (http:/ / sbir. nasa. gov/ SBIR/ abstracts/ 08/ sbir/ phase1/ SBIR-08-1-A1. 02-9322. html?solicitationId=SBIR_08_P1) - NASA 2008 SBIR [27] Nova-Tech LLC (http:/ / www. ntefsw. com/ military_applications. htm) [28] R. McNeill Alexander (2005) Mechanics of animal movement (http:/ / www. sciencedirect. com/ science?_ob=ArticleURL& _udi=B6VRT-4GXV66S-6& _user=10& _coverDate=08/ 23/ 2005& _rdoc=6& _fmt=high& _orig=browse& _srch=doc-info(#toc#6243#2005#999849983#604671#FLA#display#Volume)& _cdi=6243& _sort=d& _docanchor=& view=c& _ct=27& _acct=C000050221& _version=1& _urlVersion=0& _userid=10& md5=a2e1364289e07dd87feb65f9dc4086c0), Current Biology Volume 15, Issue 16, 23 August 2005, Pages R616-R619

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Further reading Burstall, Aubrey F. (1965). A History of Mechanical Engineering. The MIT Press. ISBN0-262-52001-X.

External links Kinematic Models for Design Digital Library (KMODDL) (http://kmoddl.library.cornell.edu/index.php) Movies and photos of hundreds of working mechanical-systems models at Cornell University. Also includes an e-book library (http://kmoddl.library.cornell.edu/e-books.php) of classic texts on mechanical design and engineering. Mechanical Engineering (http://mechanicalengineerings.com) Global community and platform connecting all mechanical engineers. Engineering Motion (http://www.engineeringmotion.com) Mechanical engineering videos.

VibrationVibration refers to mechanical oscillations about an equilibrium point. The oscillations may be periodic such as the motion of a pendulum or random such as the movement of a tire on a gravel road. Vibration is occasionally "desirable". For example the motion of a tuning fork, the reed in a woodwind instrument or harmonica, or the cone of a loudspeaker is desirable vibration, necessary for the correct functioning of the various devices. More often, vibration is undesirable, wasting energy and creating unwanted sound noise. For example, the vibrational motions of engines, electric motors, or any mechanical device in operation are typically unwanted. Such vibrations can be caused by imbalances in the rotating parts, uneven friction, the meshing of gear teeth, etc. Careful designs usually minimize unwanted vibrations. The study of sound and vibration are closely related. Sound, or "pressure waves", are generated by vibrating structures (e.g. vocal cords); these pressure waves can also induce the vibration of structures (e.g. ear drum). Hence, when trying to reduce noise it is often a problem in trying to reduce vibration.

Types of vibrationFree vibration occurs when a mechanical system is set off with an initial input and then allowed to vibrate freely. Examples of this type of vibration are pulling a child back on a swing and then letting go or hitting a tuning fork and letting it ring. The mechanical system will then vibrate at one or more of its "natural frequency" and damp down to zero.

One of the possible modes of vibration of a circular drum (see other modes).

Forced vibration is when an alternating force or motion is applied to a mechanical system. Examples of this type of vibration include a shaking washing machine due to an imbalance, transportation vibration (caused by truck engine, springs, road, etc.), or the vibration of a building during an earthquake. In forced vibration the frequency of the vibration is the frequency

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of the force or motion applied, with order of magnitude being dependent on the actual mechanical system.

Vibration testingVibration testing is accomplished by introducing a forcing function into a structure, usually with some type of shaker. Alternately, a DUT (device under test) is attached to the "table" of a shaker. For relatively low frequency forcing, servohydraulic (electrohydraulic) One of the possible modes of vibration of a cantilevered I-beam. shakers are used. For higher frequencies, electrodynamic shakers are used. Generally, one or more "input" or "control" points located on the DUT-side of a fixture is kept at a specified acceleration.[1] Other "response" points experience maximum vibration level (resonance) or minimum vibration level (anti-resonance). Two typical types of vibration tests performed are random- and sine test. Sine (one-frequency-at-a-time) tests are performed to survey the structural response of the device under test (DUT). A random (all frequencies at once) test is generally considered to more closely replicate a real world environment, such as road inputs to a moving automobile. Most vibration testing is conducted in a single DUT axis at a time, even though most real-world vibration occurs in various axes simultaneously. MIL-STD-810G, released in late 2008, Test Method 527, calls for multiple exciter testing.

Vibration analysisThe fundamentals of vibration analysis can be understood by studying the simple massspringdamper model. Indeed, even a complex structure such as an automobile body can be modeled as a "summation" of simple massspringdamper models. The massspringdamper model is an example of a simple harmonic oscillator. The mathematics used to describe its behavior is identical to other simple harmonic oscillators such as the RLC circuit. Note: In this article the step by step mathematical derivations will not be included, but will focus on the major equations and concepts in vibration analysis. Please refer to the references at the end of the article for detailed derivations.

Free vibration without dampingTo start the investigation of the massspringdamper we will assume the damping is negligible and that there is no external force applied to the mass (i.e. free vibration). The force applied to the mass by the spring is proportional to the amount the spring is stretched "x" (we will assume the spring is already compressed due to the weight of the mass). The proportionality constant, k, is the stiffness of the spring and has units of force/distance (e.g. lbf/in or N/m). The negative sign indicates that the force is always opposing the motion of the mass attached to it.

The force generated by the mass is proportional to the acceleration of the mass as given by Newtons second law of motion.

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The sum of the forces on the mass then generates this ordinary differential equation:

If we assume that we start the system to vibrate by stretching the spring by the distance of A and letting go, the solution to the above equation that describes the motion of mass is:

Simple harmonic motion of the massspring system

This solution says that it will oscillate with simple harmonic motion that has an amplitude of A and a frequency of The number is one of the most important quantities in vibration analysis and is called the undamped natural frequency. For the simple massspring system, is defined as:

Note: Angular frequency

(

) with the units of radians per second is often used in equations because it

simplifies the equations, but is normally converted to standard frequency (units of Hz or equivalently cycles per second) when stating the frequency of a system. If you know the mass and stiffness of the system you can determine the frequency at which the system will vibrate once it is set in motion by an initial disturbance using the above stated formula. Every vibrating system has one or more natural frequencies that it will vibrate at once it is disturbed. This simple relation can be used to understand in general what will happen to a more complex system once we add mass or stiffness. For example, the above formula explains why when a car or truck is fully loaded the suspension will feel softer than unloaded because the mass has increased and therefore reduced the natural frequency of the system.

Vibration What causes the system to vibrate: from conservation of energy point of view Vibrational motion could be understood in terms of conservation of energy. In the above example we have extended the spring by a value of and therefore have stored some potential energy ( ) in the spring. Once we let go of the spring, the spring tries to return to its un-stretched state (which is the minimum potential energy state) and in the process accelerates the mass. At the point where the spring has reached its un-stretched state all the potential energy that we supplied by stretching it has been transformed into kinetic energy ( ). The mass then begins to decelerate because it is now compressing the spring and in the process transferring the kinetic energy back to its potential. Thus oscillation of the spring amounts to the transferring back and forth of the kinetic energy into potential energy. In our simple model the mass will continue to oscillate forever at the same magnitude, but in a real system there is always something called damping that dissipates the energy, eventually bringing it to rest.

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Free vibration with dampingWe now add a "viscous" damper to the model that outputs a force that is proportional to the velocity of the mass. The damping is called viscous because it models the effects of an object within a fluid. The proportionality constant c is called the damping coefficient and has units of Force over velocity (lbf s/ in or N s/m).

Mass Spring Damper Model

By summing the forces on the mass we get the following ordinary differential equation:

The solution to this equation depends on the amount of damping. If the damping is small enough the system will still vibrate, but eventually, over time, will stop vibrating. This case is called underdamping this case is of most interest in vibration analysis. If we increase the damping just to the point where the system no longer oscillates we reach the point of critical damping (if the damping is increased past critical damping the system is called overdamped). The value that the damping coefficient needs to reach for critical damping in the mass spring damper model is:

To characterize the amount of damping in a system a ratio called the damping ratio (also known as damping factor and % critical damping) is used. This damping ratio is just a ratio of the actual damping over the amount of damping required to reach critical damping. The formula for the damping ratio ( ) of the mass spring damper model is:

For example, metal structures (e.g. airplane fuselage, engine crankshaft) will have damping factors less than 0.05 while automotive suspensions in the range of 0.20.3. The solution to the underdamped system for the mass spring damper model is the following:

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19 the

The value of X, the initial magnitude, and

phase shift, are determined by the amount the spring is stretched. The formulas for these values can be found in the references. Damped and undamped natural frequencies The major points to note from the solution are the exponential term and the cosine function. The exponential term defines how quickly the system damps down the larger the damping ratio, the quicker it damps to zero. The cosine function is the oscillating portion of the solution, but the frequency of the oscillations is different from the undamped case. The frequency in this case is called the "damped natural frequency", and is related to the undamped natural frequency by the following formula:

The damped natural frequency is less than the undamped natural frequency, but for many practical cases the damping ratio is relatively small and hence the difference is negligible. Therefore the damped and undamped description are often dropped when stating the natural frequency (e.g. with 0.1 damping ratio, the damped natural frequency is only 1% less than the undamped). The plots to the side present how 0.1 and 0.3 damping ratios effect how the system will ring down over time. What is often done in practice is to experimentally measure the free vibration after an impact (for example by a hammer) and then determine the natural frequency of the system by measuring the rate of oscillation as well as the damping ratio by measuring the rate of decay. The natural frequency and damping ratio are not only important in free vibration, but also characterize how a system will behave under forced vibration.

Forced vibration with dampingIn this section we will see the behavior of the spring mass damper model when we add a harmonic force in the form below. A force of this type could, for example, be generated by a rotating imbalance.

If we again sum the forces on the mass we get the following ordinary differential equation:

The steady state solution of this problem can be written as:

The result states that the mass will oscillate at the same frequency, f, of the applied force, but with a phase shift

Vibration The amplitude of the vibration X is defined by the following formula.

20

Where r is defined as the ratio of the harmonic force frequency over the undamped natural frequency of the massspringdamper model.

The phase shift ,

is defined by the following formula.

The plot of these functions, called "the frequency response of the system", presents one of the most important features in forced vibration. In a lightly damped system when the forcing frequency nears the natural frequency ( ) the amplitude of the vibration can get extremely high. This phenomenon is called resonance (subsequently the natural frequency of a system is often referred to as the resonant frequency). In rotor bearing systems any rotational speed that excites a resonant frequency is referred to as a critical speed. If resonance occurs in a mechanical system it can be very harmful leading to eventual failure of the system. Consequently, one of the major reasons for vibration analysis is to predict when this type of resonance may occur and then to determine what steps to take to prevent it from occurring. As the amplitude plot shows, adding damping can significantly reduce the magnitude of the vibration. Also, the magnitude can be reduced if the natural frequency can be shifted away from the forcing frequency by changing the stiffness or mass of the system. If the system cannot be changed, perhaps the forcing frequency can be shifted (for example, changing the speed of the machine generating the force). The following are some other points in regards to the forced vibration shown in the frequency response plots. At a given frequency ratio, the amplitude of the vibration, X, is directly proportional to the amplitude of the force (e.g. if you double the force, the vibration doubles) With little or no damping, the vibration is in phase with the forcing frequency when the frequency ratio r1 When r1 the amplitude is just the deflection of the spring under the static force This deflection is called the static deflection Hence, when r1 the effects of the damper and the mass are minimal. When r1 the amplitude of the vibration is actually less than the static deflection In this region the force generated by the mass (F=ma) is dominating because the acceleration seen by the mass increases with the frequency. Since the deflection seen in the spring, X, is reduced in this region, the force transmitted by the spring (F=kx) to the base is reduced. Therefore the massspringdamper system is isolating the harmonic force from the mounting base referred to as vibration isolation. Interestingly, more damping actually reduces the effects of

Vibration vibration isolation when r1 because the damping force (F=cv) is also transmitted to the base. What causes resonance? Resonance is simple to understand if you view the spring and mass as energy storage elements with the mass storing kinetic energy and the spring storing potential energy. As discussed earlier, when the mass and spring have no external force acting on them they transfer energy back and forth at a rate equal to the natural frequency. In other words, if energy is to be efficiently pumped into both the mass and spring the energy source needs to feed the energy in at a rate equal to the natural frequency. Applying a force to the mass and spring is similar to pushing a child on swing, you need to push at the correct moment if you want the swing to get higher and higher. As in the case of the swing, the force applied does not necessarily have to be high to get large motions; the pushes just need to keep adding energy into the system. The damper, instead of storing energy, dissipates energy. Since the damping force is proportional to the velocity, the more the motion, the more the damper dissipates the energy. Therefore a point will come when the energy dissipated by the damper will equal the energy being fed in by the force. At this point, the system has reached its maximum amplitude and will continue to vibrate at this level as long as the force applied stays the same. If no damping exists, there is nothing to dissipate the energy and therefore theoretically the motion will continue to grow on into infinity. Applying "complex" forces to the massspringdamper model In a previous section only a simple harmonic force was applied to the model, but this can be extended considerably using two powerful mathematical tools. The first is the Fourier transform that takes a signal as a function of time (time domain) and breaks it down into its harmonic components as a function of frequency (frequency domain). For example, let us apply a force to the massspringdamper model that repeats the following cycle a force equal to 1 newton for 0.5 second and then no force for 0.5 second. This type of force has the shape of a 1Hz square wave. The Fourier transform of the square wave generates a frequency spectrum that presents the magnitude of the harmonics that make up the square wave (the phase is also generated, but is typically of less concern and therefore is often not plotted). The Fourier transform can also be used to analyze non-periodic functions such as transients (e.g. impulses) and random functions. With the advent of the modern computer the Fourier transform is almost always computed using the Fast Fourier Transform (FFT) computer algorithm in combination with a window function. In the case of our square wave force, the first component is actually a constant force of 0.5 newton and is represented by a value at "0" Hz in the frequency spectrum. The next component is a 1Hz sine wave with an amplitude of 0.64. This is shown by the line at 1Hz. The remaining components are at

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How a 1 Hz square wave can be represented as a summation of sine waves(harmonics) and the corresponding frequency spectrum. Click and go to full resolution for an animation

Vibration odd frequencies and it takes an infinite amount of sine waves to generate the perfect square wave. Hence, the Fourier transform allows you to interpret the force as a sum of sinusoidal forces being applied instead of a more "complex" force (e.g. a square wave). In the previous section, the vibration solution was given for a single harmonic force, but the Fourier transform will in general give multiple harmonic forces. The second mathematical tool, "the principle of superposition", allows you to sum the solutions from multiple forces if the system is linear. In the case of the springmassdamper model, the system is linear if the spring force is proportional to the displacement and the damping is proportional to the velocity over the range of motion of interest. Hence, the solution to the problem with a square wave is summing the predicted vibration from each one of the harmonic forces found in the frequency spectrum of the square wave. Frequency response model We can view the solution of a vibration problem as an input/output relation where the force is the input and the output is the vibration. If we represent the force and vibration in the frequency domain (magnitude and phase) we can write the following relation:

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is called the frequency response function (also referred to as the transfer function, but not technically as accurate) and has both a magnitude and phase component (if represented as a complex number, a real and imaginary component). The magnitude of the frequency response function (FRF) was presented earlier for the massspringdamper system. where The phase of the FRF was also presented earlier as:

For example, let us calculate the FRF for a massspringdamper system with a mass of 1kg, spring stiffness of 1.93 N/mm and a damping ratio of 0.1. The values of the spring and mass give a natural frequency of 7Hz for this specific system. If we apply the 1Hz square wave from earlier we can calculate the predicted vibration of the mass. The figure illustrates the resulting vibration. It happens in this example that the fourth harmonic of the square wave falls at 7Hz. The frequency response of the massspringdamper therefore outputs a high 7Hz vibration even though the input force had a relatively low 7Hz harmonic. This example highlights that the resulting vibration is dependent on both the forcing function and the system that the force is applied to. The figure also shows the time domain representation of the resulting vibration. This is done by performing an inverse Fourier Transform that converts frequency domain data to time domain. In practice, this is rarely done because the frequency spectrum provides all the necessary information. The frequency response function (FRF) does not necessarily have to be calculated from the knowledge of theFrequency response model

Vibration mass, damping, and stiffness of the system, but can be measured experimentally. For example, if you apply a known force and sweep the frequency and then measure the resulting vibration you can calculate the frequency response function and then characterize the system. This technique is used in the field of experimental modal analysis to determine the vibration characteristics of a structure.

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Multiple degrees of freedom systems and mode shapesThe simple massspring damper model is the foundation of vibration analysis, but what about more complex systems? The massspringdamper model described above is called a single degree of freedom (SDOF) model since we have assumed the mass only moves up and down. In the case of more complex systems we need to discretize the system into more masses and allow them to move in more than one direction adding degrees of freedom. The major concepts of multiple degrees of freedom (MDOF) can be understood by looking at just a 2 degree of freedom model as shown in the figure. The equations of motion of the 2DOF system are found to be:

2 degree of freedom model

We can rewrite this in matrix format:

A more compact form of this matrix equation can be written as:

where

and

are symmetric matrices referred respectively as the mass, damping, and stiffness

matrices. The matrices are NxN square matrices where N is the number of degrees of freedom of the system. In the following analysis we will consider the case where there is no damping and no applied forces (i.e. free vibration). The solution of a viscously damped system is somewhat more complicated.[2]

This differential equation can be solved by assuming the following type of solution:

Note: Using the exponential solution of

is a mathematical trick used to solve linear differential equations.

If we use Euler's formula and take only the real part of the solution it is the same cosine solution for the 1 DOF system. The exponential solution is only used because it easier to manipulate mathematically. The equation then becomes:

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Since

cannot equal zero the equation reduces to the following.

Eigenvalue problemThis is referred to an eigenvalue problem in mathematics and can be put in the standard format by pre-multiplying the equation by

and if we let

and

The solution to the problem results in N eigenvalues (i.e.

), where N corresponds to the number of

degrees of freedom. The eigenvalues provide the natural frequencies of the system. When these eigenvalues are substituted back into the original set of equations, the values of that correspond to each eigenvalue are called the eigenvectors. These eigenvectors represent the mode shapes of the system. The solution of an eigenvalue problem can be quite cumbersome (especially for problems with many degrees of freedom), but fortunately most math analysis programs have eigenvalue routines. The eigenvalues and eigenvectors are often written in the following matrix format and describe the modal model of the system:

and A simple example using our 2 DOF model can help illustrate the concepts. Let both masses have a mass of 1kg and the stiffness of all three springs equal 1000 N/m. The mass and stiffness matrix for this problem are then: and Then The eigenvalues for this problem given by an eigenvalue routine will be:

The natural frequencies in the units of hertz are then (remembering The two mode shapes for the respective natural frequencies are given as:

)

and

.

Since the system is a 2 DOF system, there are two modes with their respective natural frequencies and shapes. The mode shape vectors are not the absolute motion, but just describe relative motion of the degrees of freedom. In our case the first mode shape vector is saying that the masses are moving together in phase since they have the same value and sign. In the case of the second mode shape vector, each mass is moving in opposite direction at the same rate.

Vibration

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Illustration of a multiple DOF problemWhen there are many degrees of freedom, the best method of visualizing the mode shapes is by animating them. An example of animated mode shapes is shown in the figure below for a cantilevered I-beam. In this case, a finite element model was used to generate the mass and stiffness matrices and solve the eigenvalue problem. Even this relatively simple model has over 100 degrees of freedom and hence as many natural frequencies and mode shapes. In general only the first few modes are important.In this table the first and second (top and bottom respectively) horizontal bending (left), torsional (middle), and vertical bending (right) vibrational modes of an

I-beam have been visualized. There also exist other kinds of vibrational modes in which the beam gets compressed/stretched out in the height, width and lengthdirections respectively. The mode shapes of a cantilevered I-beam

Multiple DOF problem converted to a single DOF problemThe eigenvectors have very important properties called orthogonality properties. These properties can be used to greatly simplify the solution of multi-degree of freedom models. It can be shown that the eigenvectors have the following properties:

and

are diagonal matrices that contain the modal mass and stiffness values for each one of the

modes. (Note: Since the eigenvectors (mode shapes) can be arbitrarily scaled, the orthogonality properties are often used to scale the eigenvectors so the modal mass value for each mode is equal to 1. The modal mass matrix is therefore an identity matrix) These properties can be used to greatly simplify the solution of multi-degree of freedom models by making the following coordinate transformation.

If we use this coordinate transformation in our original free vibration differential equation we get the following equation.

Vibration

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We can take advantage of the orthogonality properties by premultiplying this equation by

The orthogonality properties then simplify this equation to:

This equation is the foundation of vibration analysis for multiple degree of freedom systems. A similar type of result can be derived for damped systems.[2] The key is that the modal and stiffness matrices are diagonal matrices and therefore we have "decoupled" the equations. In other words, we have transformed our problem from a large unwieldy multiple degree of freedom problem into many single degree of freedom problems that can be solved using the same methods outlined above. Instead of solving for x we are instead solving for q, referred to as the modal coordinates or modal participation factors. It may be clearer to understand if we write as:

Written in this form we can see that the vibration at each of the degrees of freedom is just a linear sum of the mode shapes. Furthermore, how much each mode "participates" in the final vibration is defined by q, its modal participation factor.

References[1] Tustin, Wayne. Where to place the control accelerometer: one of the most critical decisions in developing random vibration tests also is the most neglected (http:/ / findarticles. com/ p/ articles/ mi_hb4797/ is_10_45/ ai_n29299213/ ), EE-Evaluation Engineering, 2006 [2] Maia, Silva. Theoretical And Experimental Modal Analysis, Research Studies Press Ltd., 1997, ISBN 0471970670

Further reading Tongue, Benson, Principles of Vibration, Oxford University Press, 2001, ISBN 0-195-142462 Inman, Daniel J., Engineering Vibration, Prentice Hall, 2001, ISBN 013726142X Rao, Singiresu, Mechanical Vibrations, Addison Wesley, 1990, ISBN 0-201-50156-2 Thompson, W.T., Theory of Vibrations, Nelson Thornes Ltd, 1996, ISBN 0-412-783908 Hartog, Den, Mechanical Vibrations, Dover Publications, 1985, ISBN 0-486-647854

External links Hyperphysics Educational Website, Concepts (http://hyperphysics.phy-astr.gsu.edu/hbase/permot. html#permot''Oscillation/Vibration) Nelson Publishing, Evaluation Engineering Magazine (http://www.evaulationengineering.com/) Structural Dynamics and Vibration Laboratory of McGill University (http://structdynviblab.mcgill.ca) Normal vibration modes of a circular membrane (http://web.mat.bham.ac.uk/C.J.Sangwin/Teaching/ CircWaves/waves.html) Free Excel sheets to estimate modal parameters (http://www.noisestructure.com/products/MPE_SDOF.php)

AFGROW

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AFGROWAFGROW is the Air Force Growth (AFGROW) crack life prediction software tool that allows users to analyze crack initiation, fatigue crack growth, fracture, and assess the life of metallic structures. AFGROW is one of the fastest, most efficient, and user-friendly crack life prediction tools available today. AFGROW is mainly used for aerospace applications; however it can be applied to any type of metallic structure that experiences fatigue cracking.

Software architectureThe stress intensity factor library provides models for over 30 different crack geometries (including tension, bending and bearing loading for many cases). In addition, an advanced, multiple crack capability allows AFGROW to analyze two independent cracks in a plate (including hole effects), non-symmetric corner cracked. Finite Element (FE) based solutions are available for two, non-symmetric through cracks at holes as well as cracks growing toward holes. This capability allows AFGROW to handle cases with more than one crack growing from a row of fastener holes. AFGROW implements five different material models (Forman Equation, Walker Equation, Tabular lookup, Harter-T Method and NASGRO Equation) to determine crack growth per applied cyclic loading. Other AFGROW user options include five load interaction (retardation) models (Closure, FASTRAN, Hsu, Wheeler, and Generalized Willenborg), a strain-life based fatigue crack initiation model, and the ability to perform a crack growth analysis with the effect of the bonded repair. AFGROW also includes useful tools such as: user-defined stress intensity solutions, user-defined beta modification factors (ability to estimate stress intensity factors for cases, which may not be an exact match for one of the stress intensity solutions in the AFGROW library), a residual stress analysis capability, cycle counting, and the ability to automatically transfer output data to Microsoft Excel. AFGROW provides COM (Component Object Model) Automation interfaces that allow users to build scripts in other Windows applications to perform repetitive tasks or control AFGROW from their applications. AFGROW also has new plug-in crack geometry interface that allows AFGROW to interface with any structural analysis program capable of calculating stress intensity factors (K) in the Windows environment. Users may create their own stress intensity solutions by writing and compiling dynamic link libraries (DLLs) using relatively simple codes. This includes the ability to animate the crack growth as is done in all other native AFGROW solutions. This interface also makes it possible for FE analysis software (for example, StressCheck) to feed AFGROW three-dimensional based stress intensity information throughout the crack life prediction process, allowing for a tremendous amount of analytical flexibility.

HistoryAFGROW's history traces back to a crack growth life prediction program (ASDGRO) which was written in BASIC for IBM-PCs by Mr. Ed Davidson at ASD/ENSF in the early-mid-1980s. In 1985, ASDGRO was used as the basis for crack growth analysis for the Sikorsky H-53 Helicopter under contract to Warner-Robins ALC. The program was modified to utilize very large load spectra, approximate stress intensity solutions for cracks in arbitrary stress fields, and use a tabular crack growth rate relationship based on the Walker equation on a point-by-point basis (Harter T-Method). The point loaded crack solution from the Tada, Paris, and Irwin Stress Intensity Factor Handbook was originally used to determine K (for arbitrary stress fields) by integration over the crack length using the unflawed stress distribution independently for each crack dimension. After discussions with Dr. Jack Lincoln (ASD/ENSF), a new method was developed by Mr. Frank Grimsley (AFWAL/FIBEC) to determine stress intensity, which used a 2-D Gaussian integration scheme with Richardson Extrapolation which was optimized by Dr. George Sendeckyj (AFWAL/FIBEC). The resulting program was named MODGRO since it was a modified version of ASDGRO.

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Early yearsMany upgrades were made during the late 1980s and early 1990s. The primary improvement was modifying the coding language from BASIC to Turbo Pascal and C. Numerous small changes/repairs were made based on errors that were discovered. During this time period, NASA/Dryden implemented MODGRO in the analysis for the flight test program for the X-29.

Recent timesIn 1993, the Navy was interested in using MODGRO to assist in a program to assess the effect of certain (classified) environments on the damage tolerance of aircraft. Work began at that time to convert the MODGRO, Version 3.X to the C language for UNIX to provide performance and portability to several UNIX Workstations. In 1994, the results of the Navy project were presented to the Navy sponsor and MODGRO was renamed AFGROW, Version 3.X. Since 1996, the Windows based version of AFGROW has replaced the UNIX version since the demand for the UNIX version did not justify the cost to maintain it. There was also an experiment to port AFGROW to the Mac OS. The Mac version had the same problem (lack of demand) as the UNIX version. An automated capability was added to AFGROW in the form of a Microsoft Component Object Model (COM) interface. The AFGROW COM interface allows users to use AFGROW as the crack growth analysis engine for any Windows based software.

Present DayAn advanced model feature has been added to allow users to select cases with two, independent cracks (with and without holes). This feature continues to be improved and expanded to cover more combinations of corner and through-the-thickness cracks. A user-defined plug-in stress intensity model capability has also been added to AFGROW. This allows users to create their own stress intensity solutions in the form of a Windows DLL (dynamic link library). Drawing tools have been included in AFGROW to allow the user-defined solution to be animated during the analysis. Interactive stress intensity solutions have been demonstrated using AFGROW to perform life predictions while sending geometric data to an external FEM code, which returns updated stress intensity solutions back to AFGROW. Verification testing is a continuing process to improve AFGROW and expand the available database. There are plans to continue to add new technology and improvements to AFGROW. A Consortium has been started with users in Government and Industry to combine the best fracture mechanics methods available.

External links Homepage [1] Version Information [2]

References[1] http:/ / www. afgrow. net/ [2] http:/ / www. afgrow. net/ about/ currentver. aspx

Agitator (device)

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Agitator (device)An agitator is a device or mechanism to put something into motion by shaking or stirring.

Manual agitator Manual dishwashers A rock can be a device used to agitate dirt and other solids from fabric in washing A stirring rod

agitating vessel

Washing machine agitatorIn a top load washing machine the agitator projects from the bottom of the wash basket and creates the wash action by rotating back and forth, rolling garments from the top of the load, down to the bottom, then back up again and due to that it seems so. There are several types of agitators with the most common being the "straight-vane" and "dual-action." The "straight-vane" is a one-part agitator with bottom and side fins that usually turns back and forth. The Dual-action is a two-part agitator that has bottom washer fins that moves back and forth and a spiral top that rotates clockwise to help guide the clothes to the bottom washer fins.

Agitator for a laundromat washing machine.

The modern agitator, which is the dual action, was first made in Kenmore washing machines in the 1980s to present. These agitators are known by Kenmore as dual-rollover and triple-rollover action agitators.

Magnetic agitatorThis is a device formed by a little metallic bar (called the agitation bar) which is normally covered by a plastic layer, and by a sheet that has underneath it a rotatory magnet or a series of electromagnets arranged in a circular form to create a magnetic rotatory field. It is very common that the sheet