Mechanical Vibration 2 Marks questions with answer

1.                  What is meant by vibrations? 
Vibration 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. 

2.                   Define Force vibration. 
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 machining due to an imbalance, transportation vibration (caused by truck engine, springs, road, etc), or the vibration of a building an earthquake. 
In forced vibration the frequency of the vibration is dependent on the frequency content of the force or motion applied, but the magnitude of the vibration is strongly dependent on the behaviour of the mechanical system. 

3.                  What is meant by logarithmic decrement? 
Logarithmic decrement method is used to measure damping in time domain. In this method, the free vibration displacement amplitude history of a system to an impulse is measured and recorded. Logarithmic decrement is the natural logarithmic value of the ratio of two adjacent peak values of displacement in free decay vibration. 

4.                  Define transmissibility. 
Transmissibility is a term that is a term that is used to describe the response of a vibration isolation system. Literally, transmissibility is the ratio of displacement of an isolated system to the input displacement. It is used to describe the effectiveness of a vibration isolation system. Transmissibility varies with frequency. 

5.                  What is dry friction damper? 
The dry-friction damper consists of a shock-absorbing mass with a flexible link with the frame, dry friction shoes coupled to the mass, and an expansion spring to provide the necessary amount of dry friction. The damper is designed to reduce normal pressure on the contact surfaces when there is a change in direction of the absorbing mass by incorporating an inertia mass which has a flexible link with the shoes. During oscillation in a system, inertia mass undergoes various accelerations and the greater the acceleration on the inertia mass the smaller is the effort with which shoes are pressed against the friction surfaces. With a sufficiently rigid link the acceleration of the inertia mass is virtually equal to the acceleration of the absorbing mass which means that with maximum acceleration of the absorbing mass the dry friction force will be the least. 

6.                  Mention the uses of vibration. 
In the branch of engineering vibration is useful in the analysis, design, construction, operation and maintenance of complex structures. 

7.                   What is Rayleigh’s method, write its applications. 
It is a method used for calculating approximate natural frequencies for a vibrating system assuming a deflected shape and balancing kinetic and strain energies. 

8.                  What is the critical speed of shaft? 
The angular speed at which a rotating shaft becomes dynamically unstable with large lateral amplitudes, due to resonance with the natural frequencies of lateral vibration of the shaft is called as the critical speed of shaft. 

9.                  Define continuous beam.

A beam having more than two supports is called as continuous beam. 

10.              What is meant by natural vibration? 
Natural vibration 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. 

11.               Define Resonance. 
Resonance is the tendency of a system to oscillate at maximum amplitude at a certain frequency. This frequency is known as the system’s natural frequency of vibration, resonant frequency, or eigenfrequency. 

12.              Mention important types of free vibrations. 
Type of free vibration are, pulling a child back on a swing and then letting go or hitting a tuning fork and letting it ring. 

13.              What is meant by viscous damping. 
A method of converting mechanical vibrational energy of a body into heat energy, in which a piston is attached to a support is called viscous damping. 

14.              Define vibration isolation. 
Vibration isolation, in structures, of those vibrations or motions that are classified as mechanical vibration; involves the control of the supporting structure, the placement and arrangement of isolators, and control of the internal construction of the equipment to be protected. 

15.              What is an accelerometer and what is its use? 
 An accelerometer is a device for measuring acceleration. An accelerometer inherently measures its own motion (locomotion), in contrast to a device based on remote sensing. One application for accelerometer is specifically configured for use in gravimetry. 

16.              Define influence coefficients. 
It is defined as action required for or due to unit acceleration. It is used for deriving the equations of motion for a vibrating system. There are two types of influence coefficient; stiffness influence coefficient and the flexibility influence coefficient. 

17.              What is continuous system? 
A continuous system has infinite degree of freedom hence infinite number of natural frequencies. These systems have their inertia and stiffness properties distributed in a continuous way. 

18.              What are three elementary part of a vibrating system?

1.      Mass of the body

2.      Elasticity of available spring.

3.      Dash – pot which is for domping

19.               What is logarithmic decrement? 
Logarithmic decrement is the “logarithmic ratio of any two consecutive amplitudes on the same side of the main position” it is a measure of decay of amplitude of the vibrating system it is denoted by  

20.              Define the term magnification factor.
Magnification factor or magnifier is defined as the ratio of amplitude of vibration to the amplitude of zero frequency deflection. 

21.              How can we make a system to vibrate in one of its natural made? 

The motion where every point the system executes harmonic motion with one of is natural frequencies of the system, is called the principal mode of vibration, the amplitude for one of the masses is taken as unity the principal mode is said to be normal mode of vibration.

22.              What is basic assumption is deriving Dunkerlay’s formula? 

1.      Dunkerlay’s formula is applicable to a uniform diameter shaft carrying several loads.

2.      This method can also account for f\self weight of the shift.

23.              How does a continuous system differ from a discrete system in the nature of its equation of motion? 
Continuous system is equivalent to an infinite elements of masses concentrated at different points. The equation of the continuous systems are derived on the assumption that the bodies are homogeneous & isotropic & that they obey Hooke’s law within the elastic limit. 

24.              What ate various methods available for vibration control? 

1.      Removing the Causes of vibration.

2.      Putting the screen if noise is the objection

3.      Placing the machinery on proper type of isolators

4.      Shock absorbers

5.      Dynamic vibration absorbers.

25.              What are vibrometer? 

A vibrometer is an instrument to measure the displacement of a vibrating machine part generally; the instrument natural frequency is designed twice as slow as the slowest vibration recorded.

26.              What are common type of damping? 
1)      Viscous damping            2)      dry friction damping
3)      structural damping      4)      slip or interfacial damping

27.              Define spring stiffness and damping constant. 
Spring stiffness (K) : It is the force required to produce unit displacement in the direction of applied force it is expressed in N/m.

K =      F = N/m
                        S
Damping coefficient (C) : It is the damping force or resistance force developed per unit velocity of viscouse fluid it is expressed in N-sec/m
C =    F  = N/m/sec
          v

28.              Why is it important to find the natural frequency of a vibrating system? 
When the frequency of externally excited system equal to natural frequency of vibration system it get failure due to resonance. So to avoid the resonance at vibrating system natural frequency must be known. 

29.              What happens to the response of an undamped system at resonance? 

In undamped vibrating system; the system get vibrate till it’s frequency reaches to the natural frequency. So it likely cause to failure of body. So if system is having undamped vibration it leads’s to failure of body or system. 

30.              What are Principal coordinates? 
Principal coordinates: The three directions in space i.e. x, y, z direction are known as the basic or principle co-ordinates these are very important in designing of robots as it decide the degree of freedom for every action. 

31.              Define the flexibility and stiffness influence coefficients. 
Flexibility: It is defines as the design that can adapt any change when any external change occurs.
Stiffness influence coefficients:  It is defined as when the system is unconstrained the stiffness matrix is positive semi definite hence a constant is used to show the stiffness of system is knows as stiffness influence coefficient denoted as ‘K’. 

32.              What is Rayleigh’s Principle? 
Rayleigh principle: It is stated that the distribution of the potential and kinetic energies of conservation, elastic system in the fundamental mode of vibration is such that the frequency is minimum. 

33.              How many natural frequencies does a continuous system have? 

A continuous system which is under a vibration have only one natural frequency which create the resonance if the frequency of system matches with natural frequency. 

34.              What is the difference between a vibration absorber and a vibration isolator? 

Difference between a vibration absorber and a vibration isolator:
A vibration absorber is a device that can absorb the vibration and make it’s intensity low while an isolator is device that can keep apart the vibration between two surface or system in contact in which one is vibrate continuously.

35.              What is an Accelerometer? 
A accelerometer is device or a transducer that sense the acceleration of system and convert in into a useful signal are known as accelerometer. 

36.              What are the causes of vibration?

Unbalanced centrifugal forces in the system

Elastic nature of the system

External excitation applied on the system

Winds may cause vibrations of certain systems such as electricity lines, telephones lines etc.

37.              Give two examples each of the bad and good effects of vibration

Bad effects

1.      Proper readings of the instrument cannot be taken

2.      Many building , structures and bridges may fall

Good effects:

1.      Useful for the propagation of sound

2.      Vibratory conveyors

3.      Musical instruments

38.              Define degree of freedom of a vibrating system

The minimum number of independent coordinates required to specify the motion of a system at any instant is known as degrees of freedom of the system

39.              In vibration analysis, can we always disregard damping?

No

40.              Can we identify a nonlinear vibration problem by looking at its governing differential equation?

Yes

41.              What is the difference between deterministic and random vibration? In deterministic the magnitude of excitation force is know but in random magnitude of excitation is not known

42.              What methods are available foe solving the governing equations of a vibration problem?

Rayleigh method, energy method, equilibrium method

43.              How do you connect several springs to increase the overall stiffness?

By connect springs in parallel.

44.              What is the difference between harmonic motion and periodic motion?

The motion which repeat itself after an equal interval of time while harmonic motion is one form of the periodic motion. All the harmonic motions are periodic in nature while the vice-versa is not always true.

45.              Define the terms: cycle, amplitude, phase angle, frequency, period and natural frequency.

EXTRUSION

Machine Design -II Assignment No - I

Date of issue: 20^th Jan, 2012                                             Last date of Submission: 27^th Jan, 2012

1.     Design a suitable flywheel for a 12 BHP, 2clyinder vertical 4 stroke diesel engine coupled to a 7.5 kW A.C. generator. The normal speed of the engine is 900 rpm.

2.      An Otto cycle engine develops 50KW at 150 rpm with 75 explosions per minute. The change of speed from the commencement to the end of power stroke must not exceed 0.5% of mean on the either side. Design a suitable rim section having width four times the deoth so that the hoop stress does not exceed 4 MPa. Assume that the flywheel stores 16/15 times the energy stored by the rim and that the work done during power stroke is 1.40 times the work done during the cycle. Density of rim material is 7200 kg/m³.

3.      A spring is to be designed which is subjected to a load varying from 0.4 kN to 1 kN.  Assume suitable data.

4.      A punching machine is required to produce 30 holes per minute of 20 mm diameter in a steel plate of 15 mm thickness having ultimate shearing strength of 340 MPa. The actual punching operation last for a period of 36° rotation of punching machine crankshaft. Mechanical efficiency of punching machine is 80%. It rotates at 240 rpm. Design s suitable flywheel for the punching machine.

5.      A semi-elliptical laminated spring 900 mm long and 55 mm wide is held together at the centre by a band 50 mm wide. If the thickness of each leaf is 5 mm, find the number of leaves required to carry a load of 4500 N. Assume a maximum working stress of 490 MPa. If the two of these leaves extend the full length of the spring, find the deflection of the spring. The Young’s modulus for the spring material may be taken as 210 kN/mm².

High Velocity Forming

The concept of high velocity forming of metal is one of the newest technological advantages in manufacturing. These processes have proved to be very useful in solving many fabrication processes where conventional processes are find more difficult and more costly. Increase in size of the work piece highly heat resistant materials, deep recessing, shallow recessing and bulging operations are the examples which led to the development of high velocity forming methods. A major advantage of high velocity forming is the ability to form one piece complex part shapes in single operation, where as conventional methods require several operations and result in a welded structure.

The variety of energy sources and techniques for applying the energy to accomplish deformation of work piece makes the scope of high velocity forming as broad  as the field of metal working operation like draw forming, cupping, bulging, swaying, flanging joining. The other application is die forming cutting, welding and surface hardening. The variety of materials that have been fabricated with velocity methods includes magnesium, aluminum, beryllium, titanium, zirconium, carbon and stainless steel, superalloy and the refractory metals and alloys.      

The process is based on the principle of deformation of metal by using very high velocities, provided on the movements of rams and dies. Since the kinetic energy is proportional to the square of the velocity, high energy is delivered to the metal with relatively small weight (ram or die). It reduces the cost and size of the machine. Since accelerations are high, high velocities are obtained by using short stroked of the ram. This increases the rate of production.

It is important to mention here the difference between high energy rate forming (HERE) and high velocity forming (HVF) processes. In the former the energy is stored in some medium is used directly to deform the metal. In HVF, high velocities are used for the forming the process

The behavior of a metal is important and the following points need to be considered before carrying out high velocity forming operations

1.      Effect of velocity on the ductility and strength of materials. The process is applicable on ductile material only.

2.      Effects of relative velocity on the blank.

3.      Effect of friction

4.      Geometrical stability of the components

5.      Wave effect: whenever a shock is transmitted through a medium denser than the blank part, it is partly transmitted and partly reflected back as compressive shock waves. This causes the metal deform towards the die.

There are several advantages of using these forming processes, like die costs are low, easy maintenance of tolerances, possibility of forming most metals, and material does not show spring-back effect. The production cost of components by such processes is low. The limitation of these processes is the need for skilled personnel.

         

 There are three main high energy rate forming processes:

1.      Explosive forming,

2.      Magnetic forming,

3.    Electro hydraulic forming.

Explosive Forming

Explosive forming, is distinguished from conventional forming in that the punch or diaphragm is replaced by an explosive charge. The explosives used are generally high – explosive chemicals, gaseous mixtures, or propellants. There are two techniques of high – explosive forming: stand – off technique and the contact technique.

Standoff Technique . The sheet metal work piece blank is clamped over a die and the assembly is lowered into a tank filled with water. The air in the die is pumped out. The explosive charge is placed at some predetermined distance from the work piece, see Fig 9.1. On detonation of the explosive, a pressure pulse of very high intensity is produced. A gas bubble is also produced which expands spherically and then collapses. When the pressure pulse impinges against the work piece, the metal is deformed into the die with as high velocity as 120 m/s.

Fig 9.1 Sequeuce of underwater explosive forming operations.(i) explosive charge is set in position (ii) pressure pulse and gas bubble are formed as the detonation of charge occurs, (iii) workpiece is deformed, and (iv) gas bubbles vent at the surface of water.

The use of water as the energy transfer medium ensures a uniform transmission of energy and muffles the sound of the explosive blast. The process is versatile – a large variety of shapes can be formed, there is virtually no limit to the size of the work piece, and it is suitable for low – quantity production as well.

The process has been successfully used to form steel plates 25 mm thick x 4 m diameter and to bulge steel tubes as thick as 25 mm.

Contact Technique. The explosive charge in the form of cartridge is held in direct contact with the work piece while the detonation is initiated. The detonation builds up extremely high pressures (upto 30,000MPa) on the surface of the work piece resulting in metal deformation, and possible fracture. The process is used often for bulging tubes, as shown in Fig 9.2.

Fig 9.2 Schematic illustration of contact technique of explosive forming. 
The process is generally used for bulging of tubes.

Applications. Explosive forming is mainly used in the aerospace industries but has also found successful applications in the production of automotive related components. The process has the greatest potential in limited – production prototype forming and for forming large size components for which conventional tooling costs are prohibitively high.

Electro Magnetic Forming

The process is also called magnetic pulse forming and is mainly used for swaging type operations, such as fastening fittings on the ends of tubes and crimping terminal ends of cables. Other applications are blanking, forming, embossing, and drawing. The work coils needed for different applications vary although the same power source may be used.

To illustrate the principle of electromagnetic forming, consider a tubular work piece. This work piece is placed in or near a coil, Fig 9.3. A high charging voltage is supplied for a short time to a bank of capacitors connected in parallel. (The amount of electrical energy stored in the bank can be increased either by adding capacitors to the bank or by increasing the voltage). When the charging is complete, which takes very little time, a high voltage switch triggers the stored electrical energy through the coil. A high – intensity magnetic field is established which induces eddy currents into the conductive work piece, resulting in the establishment of another magnetic field. The forces produced by the two magnetic fields oppose each other with the consequence that there is a repelling force between the coil and the tubular work piece that causes permanent deformation of the work piece.

Fig 9.3 Various applications of magnetic forming process. (i) Swaging, (ii) Expanding, and (iii) Embossing or blanking.

Either permanent or expandable coils may be used. Since the repelling force acts on the coil as well the work, the coil itself and the insulation on it must be capable of withstanding the force, or else they will be destroyed. The expandable coils are less costly and are also preferred when high energy level is needed.

Magnetic forming can be accomplished in any of the following three ways, depending upon the requirements.

·         Coil surrounding work piece. When a tube – like part x is to fit over another part y (shown as insert in Fig 9.3(i)), coil is designed to surround x so that when energized, would force the material of x tightly around y to obtain necessary fit.

·         Coil inside work piece. Consider fixing of a collar on a tube – like part, as shown in Fig 9.3(ii). The magnetic coil is placed inside the tube – like part, so that when energized would expand the material of the part into the collar.

·         Coil on flat surface. Flat coil having spiral shaped winding can also be designed to be placed either above or below a flat work piece, see Fig 9.3(iii).These coils are used in conjunction with a die to form, emboss, blank, or dimple the work piece.

In electromagnetic forming, the initial gap between the work piece and the die surface, called the fly distance , must be sufficient to permit the material to deform plastically. From energy considerations, the ideal pressure pulse should be of just enough magnitude that accelerates the part material to some maximum velocity and then let the part come to zero velocity by the time it covers the full fly distance. All forming coils fail, expendable coils fail sooner than durable coils, and because extremely high voltages and currents are involved, it is essential that proper safety precautions are observed by the production and maintenance personnel.

Applications

Electromagnetic forming process is capable of a wide variety of forming and assembly operations. It has found extensive applications in the fabrication of hollow, non – circular, or asymmetrical shapes from tubular stock. The compression applications involve swaging to produce compression, tensile, and torque joints or sealed pressure joints, and swaging to apply compression bands or shrink rings for fastening components together. Flat coils have been used on flat sheets to produce stretch (internal) and shrink (external) flanges on ring and disc – shaped work pieces.

Electromagnetic forming has also been used to perform shearing, piercing, and rivettting.

Electro Hydraulic Forming

Electro hydraulic forming (EHF), also known as electro spark forming, is a process in which electrical energy is converted into mechanical energy for the forming of metallic parts. A bank of capacitors is first charged to a high voltage and then discharged across a gap between two electrodes, causing explosions inside the hollow work piece, which is filled with some suitable medium, generally water. These explosions produce shock waves that travel radially in all directions at high velocity until they meet some obstruction. If the discharge energy is sufficiently high, the hollow work piece is deformed. The deformation can be controlled by applying external restraints in the form of die or by varying the amount of energy released, Fig 9.4.

Fig 9.4 Unrestrained and restrained electro-hydraulic forming process.

Advantages

1.      EHF can form hollow shapes with much ease and at less cost compared to other forming techniques.

2.      EHF is more adaptable to automatic production compared to other high energy rate forming techniques.

3.      EHF can produce small – to intermediate sized parts that don't have excessive energy requirements.

Accuracy of parts produced

Accuracy of electro hydraulically formed parts depends on the control of both the magnitude and location of energy discharges and on the dimensional accuracy of the dies used. With the modern equipment, it is now possible to precisely control the energy within specified limits, therefore the primary factor is the dimensional accuracy of the die. External dimensions on tubular parts are possible to achieve within ± 0.05 mm with the current state of technology.

Materials formed

Materials having low ductility or having critical impact velocity less than 30 m/s are generally not considered to be good candidate for EHF. All materials that can be formed by conventional forming processes can be formed by EHF also. These materials are aluminum alloys, nickel alloys, stainless steels, titanium, and Inconel 718.