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Analysis of Mechanical Vibration in 
spring mass damper model and 
Machining Processes 
for the partial fulfillment to the...
INTRODUCTION
• Vibration is a mechanical phenomenon 
whereby oscillations occur about an 
equilibrium point. 
• The oscillations may be...
Types of Vibrations 
• FREE VIBRATION occurs when a mechanical system is set 
off with an initial input and then allowed t...
DAMPING 
• Damping is an influence within or upon an oscillatory system that 
has the effect of reducing, restricting or p...
SCOPE AND DESCRIPTION OF WORK
• In this study we analyzed very basic form of vibrations 
such as free, forced vibration with and without damping. 
• We ...
LITERATURE REVIEW
• Vibration can be regarded as a branch of dynamics that deals with periodic 
and oscillatory motion. Common example of vi...
•Jiao Chunwang, Liu Jie, Guo Dameng and Wang Qianqian [10] studied that 
It is of paramount importance to acquire the resp...
NUMERICAL FORMULATION
Natural frequency for free vibration without damping 
k 
m 
1 
2 
푑2푥 
푑푡2
Natural frequency for free vibration with damping 
c 
2 
m 
Time response:
FORCED VIBRATION WITHOUT DAMPING
Forced Vibration with damping
Two Degrees of Freedom: Vibration 
Equations of Motion: 
Using matrix notation:
Definition of matrices: 
Mass Matrix (M): 
Stiffness Matrix (k): 
General Equation: 
General Solution:
Two Degree of Freedom: Vibration 
with damping 
Equations of motion: 
This can be rewritten in matrix format:
More compact form: 
This differential equation can be solved by assuming the following type of 
solution: 
Now equation be...
MODELLING
Simscape Model
Simulink Model
MATLAB : Time Response For 
Different Types of Vibration
Displacement-Time Response of Free Vibration : Undamped
Velocity-Time Responce of Free Vibration: Undamped
Displacement-Time Responce of damped Free Vibration: Critically Damped
Velocity-Time Responce of damped Free Vibration: Critically Damped
Displacement-Time Responce of damped Free Vibration: Under Damped
Velocity-Time Response of damped Free Vibration: Under Damped
Displacement-Time Response of damped Free Vibration: Over Damped
Velocity-Time Response of damped Free Vibration: Over Damped
Displacement-Time Response of Forced Vibration: Undamped
Velocity-Time Response Of Forced Vibration: Undamped
Displacement-Time Response of damped Forced Vibration: Critically Damped
Velocity-Time Response of damped Forced Vibration: Critically Damped
Displacement-Time Response of damped Forced Vibration: Under Damped
Velocity -Time Response of damped Forced Vibration: Under Damped
Displacement-Time Response of damped Forced Vibration: Over Damped
Velocity -Time Response of damped Forced Vibration: Over Damped
VIBRATION ANALYSIS
• The frequency analysis involves a frequency spectrum which 
provides us with the detailed information of the signal sour...
• The overall level will reflect the increase just as well as the 
spectrum. 
• Monitoring of a gearbox: Damaged or worn g...
VIBXPERT 
• VIBXPERT is a device that helps in vibrations analysis. It provides us 
with many key functions. 
• Route base...
Refrences
Bibliography 
[1]. Tobias, S.A. Machine Tool Vibration. Spain : UMRO, 1961. 
[2]. Chatter in machining process: A review. ...
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Mechanical Vibration

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I made this ppt for my minor project submission. The subject of this ppt is "Analysis of mechanical vibration in machining process."

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Mechanical Vibration

  1. 1. Analysis of Mechanical Vibration in spring mass damper model and Machining Processes for the partial fulfillment to the degree of Bachelor of Technology in Mechanical Engineering by Ankur Shukla (2K12/ME/044) Ankur Gupta (2K12/ME/043) Aman Handa (2K12/ME/028) Under the supervision of Dr. R.C. Singh Shri Rooplal Mechanical Engineering Department Delhi Technological University,Delhi-110042
  2. 2. INTRODUCTION
  3. 3. • Vibration is a mechanical phenomenon whereby oscillations occur 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 undesirable, wasting energy and creating unwanted sound – noise.
  4. 4. Types of Vibrations • FREE VIBRATION occurs when a mechanical system is set off with an initial input and then allowed to vibrate freely. • FORCED VIBRATION is when a time-varying disturbance (load, displacement or velocity) is applied to a mechanical system. The disturbance can be a periodic, steady-state input, a transient input, or a random input.
  5. 5. DAMPING • Damping is an influence within or upon an oscillatory system that has the effect of reducing, restricting or preventing its oscillations. • OVERDAMPED: The system returns (exponentially decays) to equilibrium without oscillating. • CRITICALLY DAMPED: The system returns to equilibrium as quickly as possible without oscillating. • UNDERDAMPED: The system oscillates (at reduced frequency compared to the undamped case) with the amplitude gradually decreasing to zero. • UNDAMPED: The system oscillates at its natural resonant frequency (ωo).
  6. 6. SCOPE AND DESCRIPTION OF WORK
  7. 7. • In this study we analyzed very basic form of vibrations such as free, forced vibration with and without damping. • We have included our experimentation results and these results are compared with results obtained via MATLAB, to plot the model natural frequency curve. • In this study we have represented a vibration analyser, which is able to analyse the chatter vibration in machining processes and machine parts and represent it in an easy and understandable form. • The objective to conduct this study is to analyse the different type of vibration in machining processes by presented vibration analyser.
  8. 8. LITERATURE REVIEW
  9. 9. • Vibration can be regarded as a branch of dynamics that deals with periodic and oscillatory motion. Common example of vibration problems are the response of civil engineering structures to dynamic loading, ambient condition and earthquakes, vibration of the unbalanced rotating machines and vibration of power line due to wind excitations, and aircraft wings [11]. • Vibrations are produced in machine having unbalanced masses. These vibrations will be transmitted to the foundation upon which the machine is installed. This is usually undesirable. To diminish the transmitted vibration, machines are usually mounted on spring or dampers, or on some other vibration isolating material [12]. • Phani Srikantha A., Woodhouse J. [9] studied parametric identification of viscous damping models in the context of linear vibration theory. Frequency domain identification methods based on measured frequency response functions (FRFs) are considered.
  10. 10. •Jiao Chunwang, Liu Jie, Guo Dameng and Wang Qianqian [10] studied that It is of paramount importance to acquire the response of many nonlinear forced vibration system. They developed a new method to explore the approximate analytical solution of forced vibration system which is named harmonic iteration method (HIM). •Hao Jiang, Xinhua Long, and Guang Meng [13] said Cutting vibration is unavoidable during a machining process and has great impact on the machined surface. With the increase of the demand on the highquality of surface finish, the effects of cutting vibrationon surface generationattract a lot of attentions. •A great deal of research has been carried out on the chatter problem since the late 1950s, when Tobias and Fishwick [3], Tlusty and Polacek [6] and Merrit [7] presented the first research results focused on this phenomenon. Lots of significant advances have been made over the years. Advances in computers, sensors and actuators have increased understanding of the phenomena, and developed and improved strategies to solve the problem [2].
  11. 11. NUMERICAL FORMULATION
  12. 12. Natural frequency for free vibration without damping k m 1 2 푑2푥 푑푡2
  13. 13. Natural frequency for free vibration with damping c 2 m Time response:
  14. 14. FORCED VIBRATION WITHOUT DAMPING
  15. 15. Forced Vibration with damping
  16. 16. Two Degrees of Freedom: Vibration Equations of Motion: Using matrix notation:
  17. 17. Definition of matrices: Mass Matrix (M): Stiffness Matrix (k): General Equation: General Solution:
  18. 18. Two Degree of Freedom: Vibration with damping Equations of motion: This can be rewritten in matrix format:
  19. 19. More compact form: This differential equation can be solved by assuming the following type of solution: Now equation becomes an eigen value problem The solution to the problem results in N eigenvalues (i.e. ), where N corresponds to the number of degrees of freedom. Note: This method can applied for multiple degree of vibration.
  20. 20. MODELLING
  21. 21. Simscape Model
  22. 22. Simulink Model
  23. 23. MATLAB : Time Response For Different Types of Vibration
  24. 24. Displacement-Time Response of Free Vibration : Undamped
  25. 25. Velocity-Time Responce of Free Vibration: Undamped
  26. 26. Displacement-Time Responce of damped Free Vibration: Critically Damped
  27. 27. Velocity-Time Responce of damped Free Vibration: Critically Damped
  28. 28. Displacement-Time Responce of damped Free Vibration: Under Damped
  29. 29. Velocity-Time Response of damped Free Vibration: Under Damped
  30. 30. Displacement-Time Response of damped Free Vibration: Over Damped
  31. 31. Velocity-Time Response of damped Free Vibration: Over Damped
  32. 32. Displacement-Time Response of Forced Vibration: Undamped
  33. 33. Velocity-Time Response Of Forced Vibration: Undamped
  34. 34. Displacement-Time Response of damped Forced Vibration: Critically Damped
  35. 35. Velocity-Time Response of damped Forced Vibration: Critically Damped
  36. 36. Displacement-Time Response of damped Forced Vibration: Under Damped
  37. 37. Velocity -Time Response of damped Forced Vibration: Under Damped
  38. 38. Displacement-Time Response of damped Forced Vibration: Over Damped
  39. 39. Velocity -Time Response of damped Forced Vibration: Over Damped
  40. 40. VIBRATION ANALYSIS
  41. 41. • The frequency analysis involves a frequency spectrum which provides us with the detailed information of the signal sources not able to be obtained from the time signal. • It provides information on the vibrations caused due to rotating parts and tooth meshing. • Process involves sending a signal through a filter and at the same time sweeping the filter over the frequency range of filters, it gives us the frequency spectrum. • Monitoring of a fan: The most likely fault to occur is unbalance, This will normally also be the highest level in the spectrum. To see if unbalance is developing, it is therefore sufficient to measure the overall level at regular intervals
  42. 42. • The overall level will reflect the increase just as well as the spectrum. • Monitoring of a gearbox: Damaged or worn gears will show up as an increase in the vibration level at the tooth meshing frequencies (shaft RPM number of teeth) and their harmonics. • The levels at these frequencies are normally much lower than the highest level in the frequency spectrum, so it is necessary to use a full spectrum comparison to reveal a developing fault. • Presenting the data: The data is presented in the form of linear scales with ranges dictated by the range of data but it does not allow to see some important data ,Hence logarithmic scales are used.
  43. 43. VIBXPERT • VIBXPERT is a device that helps in vibrations analysis. It provides us with many key functions. • Route based data collection ,Vibration diagnosis ,Field balancing , Multimeter ,Data logging ,Visual inspection ,Print reports on USB stick ,Time waveform ,Amplitude spectrum , Static shaft position (for balancing) ,Long term recording ,Printing of measurement reports are the functions it performs
  44. 44. Refrences
  45. 45. Bibliography [1]. Tobias, S.A. Machine Tool Vibration. Spain : UMRO, 1961. [2]. Chatter in machining process: A review. Guillem Quintana, Joquim Ciurana. 2011, International Journal of Machine tools and Manufacture, pp. 363-376. [3]. S.A. Tobais, W. Fishwick. Theory of regenerative machine tool chatter. s.l. : The Engineer, 1958. [4]. A review of chatter vibration research in turning. M. Siddhpura, R. Paurobally. 1, s.l. : ELSEVIER, 2012, International Journal of machine tools and manufacture, Vol. 61, pp. 27-47. [5]. On the art of cutting metals. F.Taylor. 1907, Transactions of ASME , Vol. 28. [6]. The stability of machine tools against self-excited vibrations in machining. J. Tlusty, M. Polacek. 1963, International Research in Production Engineering, pp. 465–474. [7]. Theory of self-excited machine-tool chatter-contribution to machine tool chatter research—1. Merrit, H.E. 1965, ASME Journal of Engineering for Industry, pp. 447-454. [8]. Robust Analysis of Stability in Internal Turning. Giovanni Totis, Marco Sortino. Udine, Italy : ELSEVIER, 2014. 24th DAAAM International Symposium on Intelligent Manufacturing and Automation. Vol. 69, pp. 1306-1315. [9]. Viscous damping identification in linear vibration. S. Adhikari, J. Woodhouse. 2007, Journal of Sound and Vibration , Vol. 303, pp. 475-500. [10]. Jiao Chunwang, Liu Jie, Guo Dameng and Wang Qianqian. A New Method for Solving Nonlinear Forced Vibration System Response. 2010. [11]. Wahab, M. A. Dynamics and Vibration: An Introduction. s.l. : John Wiley & Sons Ltd., 2008. [12]. Rattan, S.S. Theory of Machines. 3. New Delhi : McGraw Hill Education (India) Private Ltd., 2009. [13]. Study of the correlation between surface generation and cutting vibrations in peripheral milling. Hao Jiang, Xinhua Long, Guang Meng. Shanghai, China : s.n., 2008, journal of materials processing technology, Vol. 208, pp. 229-238.

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