Unit 4 Dynamics of Machines formula
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The document presents 6 key formulae relating to forced vibration. Formula 1 gives the magnification factor or amplitude relation for forced vibration as a function of excitation frequency and damping ratio. Formula 2 gives the phase lag between displacement and force vectors. Formula 3 gives the non-dimensional amplitude relation for vibration due to unbalance as a function of excitation frequency and damping ratio. Formula 4 gives the non-dimensional displacement transmission relation for forced vibrations due to base excitation. Formula 5 gives the relation for force or displacement transmissibility. Formula 6 gives the relation for phase lag between motion of the mass and motion of the support or between applied and transmitted force.
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![Important Formulae - UNIT IV - Forced Vibration
1. Whatis the relationfor magnificationfactororamplituderelationin the case of a forced
vibration?
𝑴.𝑭.=
𝑨
𝑿 𝟎
=
𝟏
√[ 𝟏− (
𝝎
𝝎 𝒏
)
𝟐
]
𝟐
+ [𝟐𝝃 (
𝝎
𝝎 𝒏
)]
𝟐
… …(𝟏)
2. Whatis the relationfor phase lagbetween displacementandforce vector?
𝑷𝒉𝒂𝒔𝒆 𝒍𝒂𝒈, 𝝓 = 𝐭𝐚𝐧−𝟏 {
𝟐𝝃(
𝝎
𝝎 𝒏
)
[ 𝟏− (
𝝎
𝝎 𝒏
)
𝟐
]
} … …(𝟐)
3. Whatis the non-dimensional relationforamplitudeofvibrationdueto rotating/reciprocating
unbalance?
𝑨
(
𝒎 𝟎
𝒎
𝒆)
=
(
𝝎
𝝎 𝒏
)
𝟐
√[ 𝟏− (
𝝎
𝝎 𝒏
)
𝟐
]
𝟐
+ [𝟐𝝃 (
𝝎
𝝎 𝒏
)]
𝟐
… …(𝟑)
4. Whatis the non-dimensional relationforamplitudeofforcedvibrationsdueto base
excitation?
𝑫𝒊𝒔𝒑𝒍𝒂𝒄𝒆𝒎𝒆𝒏𝒕 𝒕𝒓𝒂𝒏𝒔𝒎𝒊𝒔𝒔𝒊𝒐𝒏,
𝑨
𝒀
=
√ 𝟏 + [𝟐𝝃 (
𝝎
𝝎 𝒏
)]
𝟐
√[ 𝟏 − (
𝝎
𝝎 𝒏
)
𝟐
]
𝟐
+ [𝟐𝝃 (
𝝎
𝝎 𝒏
)]
𝟐
…… (𝟒)
5. Whatis the relationfor force transmissibilityordisplacementtransmissibility?
𝑻𝒓𝒂𝒏𝒔𝒎𝒊𝒔𝒔𝒊𝒃𝒊𝒍𝒊𝒕𝒚 𝒓𝒂𝒕𝒊𝒐, 𝜺 =
𝑭 𝑻
𝑭 𝟎
=
√ 𝟏 + [𝟐𝝃 (
𝝎
𝝎 𝒏
)]
𝟐
√[ 𝟏 − (
𝝎
𝝎 𝒏
)
𝟐
]
𝟐
+ [𝟐𝝃 (
𝝎
𝝎 𝒏
)]
𝟐
…… (𝟓)
6. Whatis the relationfor phase lagbetween motionofmass (A) and motionofsupport (Y) (or)
FT and F0?
𝑷𝒉𝒂𝒔𝒆 𝒍𝒂𝒈, 𝝋 = 𝝓 − 𝜶 = 𝐭𝐚𝐧−𝟏 {
𝟐𝝃(
𝝎
𝝎 𝒏
)
[ 𝟏− (
𝝎
𝝎 𝒏
)
𝟐
]
} − 𝐭𝐚𝐧−𝟏 𝟐𝝃 (
𝝎
𝝎 𝒏
) …… (𝟔)](https://image.slidesharecdn.com/unit-4domformula-150816080211-lva1-app6892/85/Unit-4-Dynamics-of-Machines-formula-1-320.jpg)
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Unit5 lectbyvrk dynofmachinery
- The document discusses mechanisms for control of machinery like flywheels, governors, and gyroscopes. It provides details on different types of governors like centrifugal governors and inertia governors.
- It describes key concepts related to governors like range of speed, mean speed, sensitiveness, stable and unstable governors. It also discusses the functions of governors and factors like friction that affect governors.
- The document covers gyroscopes and key concepts like gyroscopic couple, plane of spinning, axis of precession. It explains gyroscopic effects on ships during rolling, pitching, and steering movements.
Unit1 lectbyvrk dynofmachinery
The document discusses static and dynamic force analysis of mechanisms. It defines key terms like static equilibrium, inertia force, inertia torque, and D'Alembert's principle. It explains the conditions for a body to be in equilibrium under different force configurations. Dynamic force analysis considers inertia forces to determine input torque required. Equivalent masses and Klein's construction diagram are discussed for dynamic analysis of reciprocating engines. Correction couple and torque are also summarized.
Gas dynamics and jet propulsion – presentationof problemsanswers
Air enters a combustion chamber with a mach number of 0.15. Sufficient heat is added to raise the stagnation temperature ratio to 3 and the final mach number is 0.8. To determine:
1) The entry mach number is 0.15
2) Due to heating, the static pressure decreases along the flow. The percentage loss in static pressure needs to be determined.
3) The properties of air (γ, Cp) are given to solve the problem.
Me2351 gas dynamics and jet propulsion-qb
The document contains questions related to gas dynamics and jet propulsion. It covers topics such as compressible and incompressible fluids, stagnation pressure and temperature, Mach number, zones of action and silence, open and closed systems, intensive and extensive properties, shock waves, normal and oblique shocks, jet and rocket propulsion, rocket engine classifications, specific impulse, specific consumption, thrust coefficient, propulsive efficiency, Fanno and Rayleigh flows, and one-dimensional isentropic flow through nozzles, ducts, and diffusers. The questions range from definitions and differentiations to derivations and multi-step calculations involving isentropic flow equations.
Unit2 lectbyvrk dynofmachinery
Balancing is the process of designing or modifying machinery to reduce or eliminate unbalanced forces caused by rotating and reciprocating masses. Unbalanced forces produce vibrations and noise. There are different types of balancing for rotating masses, such as static balancing of a single mass or dynamic balancing of multiple masses in different planes. Reciprocating masses are more difficult to fully balance due to the hammer blow effect from vertical forces. Multicylinder engines require consideration of primary and secondary forces as well as tractive force, swaying couple, and hammer blow to reduce vibrations over the operating cycle.
Dom lab manual new
This document describes an experiment on the dynamics of machines lab at Ideal Institute of Technology. It provides instructions on how to perform experiments on slider crank mechanisms and cams. The objectives, apparatus, theory, procedures, observations tables, calculations, graphs, results and discussions are outlined for experiments 1 and 2 on the slider crank mechanism and cams respectively. Precautions and potential sources of error are also noted.
ME 313 Mechanical Measurements and Instrumentation Lecture 01
ME 313 Mechanical Measurements and Instrumentation Lecture 01Dr. Bilal Siddiqui, C.Eng., MIMechE, FRAeS
This document provides an overview of a course on measurements and instrumentation. The course will cover topics such as measurement systems, calibration, accuracy, precision, and instruments for measuring length, force, torque, strain, pressure, flow, and temperature. The objectives are to understand instrumentation principles and learn basic measurement methods. The primary textbook will be Theory and Design for Mechanical Measurements by Figliola and Beasley, along with class notes.Dynamics of Machines: Question bank unitwise from vtu old question papers
Dynamics of Machines: Question bank unitwise from vtu old question papersHareesha N Gowda, Dayananda Sagar College of Engg, Bangalore
This document contains, Dynamics of Machines: Question bank unitwise from vtu old question papers, Prepared by Hareesha N G, DSCE, BengaluruMETROLOGY LAB MANUAL 26 12-16
This document provides instructions for experiments to be conducted in a metrology lab. It includes 10 experiments involving calibration of measurement tools like micrometers and dial gauges using slip gauges, measurement of angles using a bevel protractor and sine bar, measurement of gear features, surface roughness, and more. The document was prepared by B.Sudarshan, Assistant Professor of Mechanical Engineering, for students to record their experiment details, objectives, theories, procedures, observations and results.
Unit 5 Fluid Mechanics
The document discusses fluid dynamics and Bernoulli's equation. It provides:
1) Objectives of understanding measurements of fluids in motion and applying Bernoulli's equation to calculate energy in pipes, venturi meters, and orifices.
2) An explanation of Bernoulli's equation and its components of potential, pressure, and kinetic energy.
3) Examples of applying the equation to calculate discharge in a horizontal venturi meter using measurements of pressure and height differences.
Types of fluid flow
This document discusses the different types of fluid flows. It describes 6 main types of fluid flows: 1) steady and unsteady, 2) uniform and non-uniform, 3) laminar and turbulent, 4) compressible and incompressible, 5) rotational and irrotational, and 6) one-, two-, and three-dimensional flows. For each type of flow, it provides a brief definition and examples to explain the differences between the types.
Chapter four fluid mechanics
1) The document discusses fluid kinematics, which deals with the motion of fluids without considering the forces that create motion. It covers topics like velocity fields, acceleration fields, control volumes, and flow visualization techniques.
2) There are two main descriptions of fluid motion - Lagrangian, which follows individual particles, and Eulerian, which observes the flow at fixed points in space. Most practical analysis uses the Eulerian description.
3) The Reynolds Transport Theorem allows equations written for a fluid system to be applied to a fixed control volume, which is useful for analyzing forces on objects in a flow. It relates the time rate of change of an extensive property within the control volume to surface fluxes and the property accumulation.
Dynamics lab manual
This document provides information about an experiment to determine the torsional vibration characteristics of single and double rotor systems. It includes the objectives, equipment description, procedures, sample calculations and observations. The experiment aims to determine the period and frequency of torsional vibration experimentally and compare to theoretical values. Key steps involve twisting and releasing rotors to measure oscillation times and calculating moments of inertia, torsional stiffness and natural frequencies.
Types of fluid flow
Report on Types of fluid flow
fluid dynamics
Introduction
In physics, fluid flow has all kinds of aspects: steady or unsteady, compressible or incompressible, viscous or non-viscous, and rotational or irrotational to name a few. Some of these characteristics reflect properties of the liquid itself, and others focus on how the fluid is moving. Note that fluid flow can get very complex when it becomes turbulent. Physicists haven’t developed any elegant equations to describe turbulence because how turbulence works depends on the individual system whether you have water cascading through a pipe or air streaming out of a jet engine. Usually, you have to resort to computers to handle problems that involve fluid turbulence. Types of fluid flow:
Aerodynamic force
Cavitation
Compressible flow
Couette flow
Free molecular flow
Incompressible flow
Theory of Machine and Mechanisms (Gears)
This document discusses different types of gears used in mechanical systems to transmit rotational motion between parallel or intersecting shafts. It describes spur gears, helical gears, bevel gears, and worm gears. Key terminology for gears like pitch circle, diametral pitch, module, addendum, dedendum, and contact ratio are defined. The fundamental law of gearing relating the rotational speeds of meshing gears is explained. Involute tooth profiles and pressure angles are also covered.
Theory of machines
The document discusses the analysis and synthesis of mechanisms and machines. It provides definitions and explanations of key concepts related to kinematics and dynamics of machines including links, kinematic pairs, degrees of freedom, mechanisms, and machines. The summary discusses the analysis of existing mechanisms to study their motions and forces, while synthesis involves designing the parts of a mechanism. Key types of links, kinematic pairs, and methods for determining degrees of freedom of mechanisms are also summarized.
Mechanical Vibration- An introduction
This presentation gives an introduction to mechanical vibration or Theory of Vibration for BE courses. Presentation is prepared as per the syllabus of VTU.For any suggestions and criticisms please mail to: hareeshang@gmail.com or visit:ww.hareeshang.wikifoundry.com.
Thanks for watching this presentation.
Hareesha N G
Gas turbine and Jet Propulsion
Gas turbines operate by compressing air, adding fuel and igniting it to generate high-temperature gas, and expanding this gas through a turbine to power the compressor and provide output shaft work. There are various types including turbojets used in aircraft, turboprops which drive propellers via reduction gears, and turbofans which have a large fan at the front and achieve higher efficiency. Ramjets have no moving parts and rely solely on forward speed for compression, making them unable to produce static thrust.
Gas dynamics and_jet_propulsion- questions & answes
1. The document discusses compressible and incompressible fluid flow, defining key terms like Mach number and stagnation state. It also provides equations for adiabatic energy, stagnation pressure and temperature, and Prandtl-Meyer relation.
2. Various regions of compressible flow are defined based on the Mach number, including incompressible, subsonic, transonic, supersonic, and hypersonic. Normal and oblique shock waves are also discussed.
3. Examples of where Fanno flow occurs are given as gas ducts in aircraft engines and air conditioning ducts. Fanno flow is steady, one-dimensional flow with friction but no heat transfer.
Solution shigley's
This document provides equations and calculations for determining the mean cycles to failure (x-bar) and standard deviation of cycles to failure (s_x) for a sample of fatigue test data. The sample data consists of the number of cycles to failure (x) and applied force (f) for 10 tests. The mean x-bar is calculated as the sum of the product of f and x divided by the sum of f, which equals 122.9 kcycles. The standard deviation s_x is calculated using the variance formula, which equals 30.3 kcycles.
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Unit 4 Dynamics of Machines formula
- 1. Important Formulae - UNIT IV - Forced Vibration 1. Whatis the relationfor magnificationfactororamplituderelationin the case of a forced vibration? 𝑴.𝑭.= 𝑨 𝑿 𝟎 = 𝟏 √[ 𝟏− ( 𝝎 𝝎 𝒏 ) 𝟐 ] 𝟐 + [𝟐𝝃 ( 𝝎 𝝎 𝒏 )] 𝟐 … …(𝟏) 2. Whatis the relationfor phase lagbetween displacementandforce vector? 𝑷𝒉𝒂𝒔𝒆 𝒍𝒂𝒈, 𝝓 = 𝐭𝐚𝐧−𝟏 { 𝟐𝝃( 𝝎 𝝎 𝒏 ) [ 𝟏− ( 𝝎 𝝎 𝒏 ) 𝟐 ] } … …(𝟐) 3. Whatis the non-dimensional relationforamplitudeofvibrationdueto rotating/reciprocating unbalance? 𝑨 ( 𝒎 𝟎 𝒎 𝒆) = ( 𝝎 𝝎 𝒏 ) 𝟐 √[ 𝟏− ( 𝝎 𝝎 𝒏 ) 𝟐 ] 𝟐 + [𝟐𝝃 ( 𝝎 𝝎 𝒏 )] 𝟐 … …(𝟑) 4. Whatis the non-dimensional relationforamplitudeofforcedvibrationsdueto base excitation? 𝑫𝒊𝒔𝒑𝒍𝒂𝒄𝒆𝒎𝒆𝒏𝒕 𝒕𝒓𝒂𝒏𝒔𝒎𝒊𝒔𝒔𝒊𝒐𝒏, 𝑨 𝒀 = √ 𝟏 + [𝟐𝝃 ( 𝝎 𝝎 𝒏 )] 𝟐 √[ 𝟏 − ( 𝝎 𝝎 𝒏 ) 𝟐 ] 𝟐 + [𝟐𝝃 ( 𝝎 𝝎 𝒏 )] 𝟐 …… (𝟒) 5. Whatis the relationfor force transmissibilityordisplacementtransmissibility? 𝑻𝒓𝒂𝒏𝒔𝒎𝒊𝒔𝒔𝒊𝒃𝒊𝒍𝒊𝒕𝒚 𝒓𝒂𝒕𝒊𝒐, 𝜺 = 𝑭 𝑻 𝑭 𝟎 = √ 𝟏 + [𝟐𝝃 ( 𝝎 𝝎 𝒏 )] 𝟐 √[ 𝟏 − ( 𝝎 𝝎 𝒏 ) 𝟐 ] 𝟐 + [𝟐𝝃 ( 𝝎 𝝎 𝒏 )] 𝟐 …… (𝟓) 6. Whatis the relationfor phase lagbetween motionofmass (A) and motionofsupport (Y) (or) FT and F0? 𝑷𝒉𝒂𝒔𝒆 𝒍𝒂𝒈, 𝝋 = 𝝓 − 𝜶 = 𝐭𝐚𝐧−𝟏 { 𝟐𝝃( 𝝎 𝝎 𝒏 ) [ 𝟏− ( 𝝎 𝝎 𝒏 ) 𝟐 ] } − 𝐭𝐚𝐧−𝟏 𝟐𝝃 ( 𝝎 𝝎 𝒏 ) …… (𝟔)