Vibrations are produced during any machining process. For drilling operation, analysis of these vibrations plays an important role in order to predict phenomenon of ‘chatter’. This paper emphasizes the analysis of vibration during drilling operation. The output results of analysis are useful to find out amplitude of vibrations produced with respect to drill size and spindle speed for standard rate of recommended feed/min. Analysis is quantified and tabulated as per available machining parameters of ‘THAKUR PELTER DRILLING MACHINE’ which is present in the Workshop of Fr. Conceiceo Rodrigues Institute of Technology, Vashi, Navi Mumbai. The optimum values of spindle speed and feed for maximium amplitude of transverse vibrations with respect to drill size are highlighted in the table and brought to the notice of Workshop Superintendent. The table of formulated results is displayed near this drilling machine

Bhate, Vaibhav K.

Sagavkar, Gayatri S.

Wani, Amit S.

English

Gyandhara International Academic Publication (GIAP): Journals

International Journal of Students Research in Technology & Management  
Vol 1(2), April 2013, pg 163-175 
www.giapjournals.com Page 163 
 
VIBRATION ANALYSIS OF DRILLING OPERATION 
Amit S. Wani1, Gayatri S. Sagavkar2, Vaibhav K. Bhate3 
Department of Mechanical Engineering, 
Fr.Conceiceo Rodrigues Institute of Technology, Vashi, Navi Mumbai, Maharastra, India 
1amitwn08@gmail.com, 2gayatrisagavkar@yahoo.com, 3bhatev@gmail.com 
 
Abstract 
Vibrations are produced during any machining process. For drilling operation, analysis of these 
vibrations plays an important role in order to predict phenomenon of ‘chatter’. This paper 
emphasizes the analysis of vibration during drilling operation. The output results of analysis are 
useful to find out amplitude of vibrations produced with respect to drill size and spindle speed for 
standard rate of recommended feed/min. 
Analysis is quantified and tabulated as per available machining parameters of ‘THAKUR 
PELTER DRILLING MACHINE’ which is present in the Workshop of Fr. Conceiceo Rodrigues 
Institute of Technology, Vashi, Navi Mumbai. The optimum values of spindle speed and feed for 
maximium amplitude of transverse vibrations with respect to drill size are highlighted in the table 
and brought to the notice of Workshop Superintendent. The table of formulated results is displayed 
near this drilling machine. 
Keywords- Chatter, drilling operation 
I.  INTRODUCTION 
Drilling Process is widely used in various types of industries. During drilling many a times, a 
phenomenon of ‘chatter’ of drill bit is observed. The reason for this ‘chatter’ is the vibrations 
produced during the drilling operation. The vibrations if produced by external parameters can be 
controlled by the methods of vibration isolation and carrying out periodic preventive maintenance of 
the machine. But, vibrations produced because of drilling itself i.e. due to spindle speed and feed 
cannot be controlled completely. 
So, such internal vibrations need to be avoided. As these vibrations depend upon the various 
machining parameters, calculation of vibrations can be done under different machining parameters. 
The results can be summarized and the critical values of machining parameters for which excessive 
vibration is produced can be obtained for a specific machine. 
This paper deals with the mathematical analysis of the drilling operation where vibrations due to 
‘drilling’ are solely considered and values of critical machining parameters for ‘THAKUR PELTER 
DRILLING MACHINE’ are calculated.  
II. NEED OF VIBRATION ANALYSIS DURING DRILLING OPERATION 
• Phenomenon of ‘chatter’ is widely observed during drilling operation.  •  Vibration Analysis is the best soluti
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• Due to vibrations produced by drill dimensional accuracy of the hole gets affected. E.g. 
Transverse Vibration of 0.3 mm amplitude can result into enlarged hole of 0.6 mm 
excessive diameter. • Vibration during drilling operation affects the surface finish of the hole produced. • Assembly problems can be raised if the improper surface finished or enlarged holed 
workpiece is required to assemble with other.  • Operational Problems can be raised if such part is installed on site e.g. tube and shell heat 
exchanger if the size of holes on baffles is enlarged then loosening of it may happen when 
fluid is flowing above them. 
III. SOURCES OF VIBRATION DURING DRILLING OPERATION 
In Drilling Operation two types of vibrations are observed: 
A. External Vibrations 
In drilling operation spindle of drill may vibrate because of the vibration developed by machine due to 
malfunctioning. These vibrations can be categorized as vibrations due to external parameters. Sources 
of external vibrations are as follows:  
• Shaft Misalignment in spindle, motor, nut-bolts and transmitting elements viz., pulley or gear 
drives  
• Improper Foundation of machine 
• Loosen fasteners such as nut-bolts, clamps etc. 
B. Internal Vibrations 
Internal Vibrations in the drilling operation are produced due to ‘drilling process itself!. Internal 
vibrations are unavoidable as they occur because of internal characteristics of the system. Sources of 
Internal Vibrations are as follows: • Spindle Speed • Force exerted by workpiece in opposite direction to the drill motion • Resistive torque by induced by workpiece during material cutting • High feed rate • High Overhung of drill 
IV. TYPES OF VIBRATIONS PRODUCED DURING DRILLING OPERATION 
A. Vibrations in the drilling operation are produced in the two stages: 
1) When the drill is rotating and approaching towards workpiece 
 
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Fig 1 Drill has not entered into the work piece  
2) When the drill is rotating and drilling a hole into the workpiece 
 
Fig 2 Drill has entered into the work piece 
B. Following types of vibrations needs to be considered for drilling operation: 
1) Free Vibration: Free vibration of the system helps to determine natural frequency of the system 
(ωn). 
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2) Forced Vibration: Forced vibrations are produced because of rotation of spindle. These 
vibrations have frequency of external excitation (ω) which is nothing but spindle speed in rad/sec. 
In forced vibration we have to consider force applied by the machine on the tool in no loading 
(Stage 1) and resistive force applied by the workpiece during drilling operation (Stage 2). 
V. THEORY PART (MATHEMATICAL ANALYSIS) 
A. Assumptions 
1) Only the vibrations produced because of machining are considered. Effect of external 
vibrations is neglected as these vibrations can be controlled with various techniques. On the 
other hand internal vibrations which we are analysing can be controlled only by adopting safe 
machining parameters. 
2) During analysing of particular type of vibration, only that type is assumed to be taking place. 
Effect of the other types is neglected for that analysis 
3) We have considered cylindrical drill bit for the analysis as our scope is to find out the 
vibrations that are going to take place not the cutting operation which is being carried out.  
4) During our analysis our main focus is concentrated on the transverse vibrations. This is 
because of the fact that the transverse vibrations produced during drilling operation are the 
main cause of the enlargement of the diameter of hole being produced beyond tolerance limit. 
B. Actual Procedure 
1) For the drilling operation following three types are observed: • Transverse Vibrations • Longitudinal Vibrations • Torsional Vibrations 
 
Fig 3 Types of vibrations 
2) Following procedure essential for Vibration Analysis of the drilling operation: 
 
International Journal of Students Research in Technology & Management  
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o Identification of the type of vibrations produced during machining operation 
o Determination of the factors affecting these vibrations 
o Applying concepts of the equilibrium to solve the problem 
o Finding out the forces that are exerted on the tool under various conditions 
LIST OF SYMBOLS: 
    d = Diameter of drill 
    l = Length of drill 
   E = Young’s Modulus 
   σ = Tensile Strength 
   τ = Shear strength 
  ω = Frequency of vibration 
  ωn= Natural Frequency 
  ωt = Frequency with which spindle is rotating 
  V = Tangential velocity of drill 
   r  = Radius of drill 
   F = Force 
   ξ = Damping ratio 
   A = Amplitude of excitation 
   B = Amplitude of support • Longitudinal Vibrations 
1) Free Longitudinal Vibration Analysis: 
Free longitudinal vibrations exist in the drill which are produced due to self-weight of the drill. These 
vibrations can be analysed with the help of the following formula: 
ωn=ට௞ೝ೐೟ೌ೔೙೒ ೞ೛ೝ೔೙೒௠  rad/sec 
 
ωn= ଵଶగ ට௞ೝ೐೟ೌ೔೙೔೙೒ ೞ೛ೝ೔೙೒௠  Hz 
 
However these vibrations are not useful when we want to analyse the ‘chatter’ phenomenon of the 
drilling operation.  
Hence these vibrations are not considered during preparation of our table. 
2) Forced Longitudinal Vibrations Analysis: 
Cases: 
1) When the drill is rotating and approaching towards work piece 
Forced Longitudinal Vibrations do not exist when drill is approaching towards the work piece. It 
is because of the fact that as drill is approaching, no force acts on the drill in the upward direction.  
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Due to this, the vibrations of the drilling during approaching towards the workpiece can be 
neglected.  
2) When the drill is rotating and drilling a hole into the work piece. 
When drill touches the work piece and starts cutting the material to produce the hole, the upward 
resistive force acts on the drill because of the tensile stress of the work piece material.  
When the material breaks during drilling the hole, its failure in the longitudinal direction can be 
considered as the compressive failure. 
The force exerted in the upward longitudinal direction during the failure of the workpiece can be 
calculated using the following formula: 
 
F=ߪ௪௢௥௞௣௜௘௖௘ כ గସ כ ݀ଶ 
The amplitude of the forced longitudinal vibration can be computed using the formula given below[5]: 
 
׵ ܣܤ ൌ ටͳ ൅ ቀʹξ ωω౤ቁଶඨ൬ͳ െ ቀ ఠఠ೙ቁଶ൰ଶ ൅ ቀʹξ ωω౤ቁଶ 
For our drilling machine we have considered no damping condition (since we want to consider the 
worst possible case) 
i.e. ξ ൌ Ͳ ׵ ܣܤ ൌ ͳͳ െ ሺ߱ ߱௡ൗ ሻଶ 
 
However, these longitudinal vibrations can be restricted with the help of restricting spring or suitable 
damping mechanism.  These vibrations however, do not effect on the diameter of the hole produced.  
In Thakur Pelter Drilling Machine, which is used for very simple applications, these vibrations can be 
neglected since this machine is generally practiced to produce through holes only. • Torsional Vibrations 
1) Free Torsional Vibration Analysis: 
Free torsional vibrations exist in the drill which can be computed as follow: 
 
ωn=ට௞೟ூ  rad/sec 
but, 
kt=
ீ௃௟  
 
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I=mk2=
௠ௗమ଼  
 
ωn=ටீ௃௟ כ ௠଼ௗమ 
 
m=ρ*volume of drill 
 ׵m=ρ*గସ ݀ଶ*l 
 ׵ωn=ටீ௃ ௟మ  
 ׵ωn=ଵ௟ ට  ீ  rad/sec 
These vibrations are useful to determine torsional natural frequency of the system (ωnt) 
This frequency is useful to obtain the forced natural torsional frequency of the system.  
2) Forced Torsional Vibration Analysis: 
Cases: 
1) When the drill is rotating and approaching towards work piece. 
No resistive force exerts on the drill in torsional direction when drill is approaching towards the work 
piece and hence the vibrations produced can be neglected. 
2) When the drill is rotating and drilling a hole into the work piece. 
When drill enters into the work piece and starts cutting the material, torsional shear failure of the 
material takes place. 
Force exerted on the drill material during torsional failure of the work piece material can be 
computed as below: 
F=
గଵ଺ כ ݀ଷ כ ߬ௐ௢௥௞௣௜௘௖௘ 
Where, 
 
F=
Tୢଶൗ  
Torque exerted is related with power in the following manner: 
 
P=
ଶπ୒T଺଴  
Torsional Vibrations are created because of the rotary motion of drill. These vibrations create resistive 
twisting moment on the drill and higher values of these vibrations may break the drill.  
 
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Vol 1(2), April 2013, pg 163-175 
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Formula for finding amplitude of forced torsional vibration (ߠ) is given as: 
Considering value of damping to be negligible, ߠߙ௢ ൌ ݇௧݇௧ െ ܲ 
 
However as these vibrations do not affect in the transverse direction of motion which is responsible 
for the enlargement of the hole. Thus it is not considered in the calculation. • Transverse Vibrations 
1) Free Transverse Vibrations Analysis: 
 
 
Fig 4 Free transverse vibrations in any body[2] 
The Vibrations in the drill in free state i.e. w/o rotation can be assumed as free transverse vibrations 
(as in case of compound pendulum) 
The Natural Frequency of the free transverse vibration (ωn) can be computed by using following 
formula: 
ωn ൌ ඨ݄݉݃ܫ  
 
But, mass moment of inertia,     
 ܫ ൌ ݈݉ଶʹ ൅ ݈݉ଶͶ  
׵ ωn ൌ ඩg כ ሺ ୪ଶሻ୪మଶ ൅ ୪మସ  
International Journal of Students Research in Technology & Management  
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 ׵ ωn=ଷ.଼ଷହ√୪  
 
2) Forced Transverse Vibration Analysis
 
 
Cases: 
1) When the drill is rotating and approaching towards work piece 
When the drill approaches towards the work piece, the no external force on the drill except the force 
of vibration developed by the motor torque. 
And thus these vibrations can be neglected because there is no restricting force acting on the drill bit 
in the direction of the transverse vibration of the drill. 
2) When the drill is rotating and drilling a hole into the work piece. 
When drill enters into the workpiece, the force is exerted by the workpiece material on the drill bit in 
the direction of the transverse motion of the drill. i.e. perpendicular to the axis of the drill.  
The analysis of this force can be understood from the following diagram: 
 
 
Fig 5 Force analysis during transverse vibration 
The drill and work piece are considered to be attached with the help of the spring whose stiffness is 
‘k’. 
Under equilibrium conditions, 
k = σ*v 
 
This is because of the fact  when the drill transverses with the linear velocity ‘v’, the force is exerted 
on the drill in the direction of the transverse motion due to the stress induced in the material.  
Force is the resistive force applied by the work piece in the direction perpendicular to the axis of the 
drill. 
F=σ୛୭୰୩୮୧ୣୡୣ*πସ dଶ*(feed/sec) 
The forced frequency of transverse vibration can be computed with the help of following  procedure: 
International Journal of Students Research in Technology & Management  
Vol 1(2), April 2013, pg 163-175 
www.giapjournals.com Page 172 
 
N= rpm of the spindle 
ωt=ଶగே଺଴ ; 
 
Fig 6 Free transverse vibrations in any body 
The relation between angular velocity and linear velocity of the drill cross section in the transverse 
direction can be given in the following manner: 
v= 
ω౪כୢଶ  
Now consider, the length of the drill oscillating at forced transverse frequency of ′ω′ in the following 
manner: 
ω=௩௟  
Now the amplitude of the transverse forced vibration when the drill enters into the workpiece can be 
computed by using the following formula[3]: ܣ ൌ ி௞ඨ൬ͳ െ ቀ ఠఠ೙ቁଶ൰ଶ ൅ ቀʹξ ωω౤ቁଶ  
For our drilling machine we have considered no damping condition (since we want to consider the 
worst possible case) 
i.e. ξ ൌ Ͳ ׵ ܣ ൌ ͳͳ െ ሺ߱ ߱௡ൗ ሻଶ 
IV. PRACTICAL APPROACH 
SAMPLE CALCULATIONS (For N=92 rpm, feed = 4.6736 mm/min, drill diameter =3.175mm 
DATA: 
d=0.00317m 
l=0.150m 
E=4.461*109N/m2 
International Journal of Students Research in Technology & Management  
Vol 1(2), April 2013, pg 163-175 
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σ=420*106N/m2      [4] 
                 
TO FIND OUT: ω,ωn,K,F,A 
SOLUTION: 
For 92 rpm ωt= 2*Π*N/60 
= 2*Π*92/60 
=9.63rad/sec. 
 
Fig 7 Chart prepared for the workshop 
 
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ωn=3.835/√݈ 
          =3.835/√Ͳ.ͳͷͲ 
          =9.901rad/sec. 
       F=Π*d*(feed/sec)*σ 
      Feed/sec=((feed/rev)*N)/60 
[1]
  
           =(0.0508*0.001*92)/60 
                        =7.789e-5m/sec 
      F = Π*0.00317*7.789e-5*420e6 
         =329.84N/sec 
      v = ωt*r 
          =9.63*0.00317/2 
          =0.015m/s 
      K = σ*v 
          =420e6*0.015 
          =63e5N/m 
      ω = v/l 
          = 0.015/0.150 
          = 0.1rad/sec 
       ω/ωn =  0.1/9.901 
                =0.01 
       A = (F/K)/(1-(ω/ωn)2) 
           = (329.84/63e5)/(1-0.012) 
           = 0.051mm 
A=0.051 mm 
 
 
Fig 8 Photograph with Workshop Superintendent near the Thakur Pelter Drilling Machine 
along with the chart displayed  
International Journal of Students Research in Technology & Management  
Vol 1(2), April 2013, pg 163-175 
www.giapjournals.com Page 175 
 
V. CONCLUSIONS 
We used the straight and simplified approach in the analysis of the vibrations produced during drilling 
operation on “THAKUR PELTER DRILLING MAHCINE”. We arrived to the conclusion that the 
“chatter” phenomenon is produced due to the transverse vibrations of the drill, which adversely affect 
the assembly problem. Longitudinal vibration only changes the length of blunt hole and does not 
affect the though hole. Torsional vibration leads to the removal of the material from the workpiece 
with the help of chisel edge and flanks on drill, but does not affect the dimensions of the hole. This 
report is the best example to show that how the theory knowledge gained in the academic curriculum 
can be effectively applied to the practical scenario. 
ACKNOWLEDGMENT 
We are thankful to R.G.I.T., Andheri, for giving us this platform to think over our regular academic 
curriculum. During preparation of this paper, we got various guidelines from our professors in the 
college, particularly; we want to thank Prof. Girish Dalvi and Prof. Shamim Pathan for their technical 
support in our work. We are equally thankful to workshop superintendent Mr.Rajesh and workshop 
supervisor Mr.Moreshwar for their support in our practical work.   
REFERENCES 
[1] Erik Oberg and Franklin D Jones, “Machinery’s  Handbook”(28th Edition). 
[2] F. B. Sayyad, “Mechanical Vibration”,Tech-max Publications. 
[3] V. P. Singh,“Mechanical Vibration”,Dhanpat rai Publication. 
[4] S. K. Hajra choudhury, A. K. Hajra choudhury and Nirjhar Roy, “Elements Of Workshop 
Technology Volume -2 Machine Tools” 
[5] S. S. Rao, “Mechanical Vibrations ”,Pearson publication 
[6] Mr. Muhammad Munawar, “Optimization of Surface Finish by Considering the Effect of 
Vibration in Machining Operations” [online].  
 
 
 


VIBRATION ANALYSIS OF DRILLING OPERATION

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