93- 112


Al-Khwarizmi Engineering Journal, Vol. 11, No. 1, P.P.  

 

The Effect of Soil Content, Drilling Parameters 
Diameter on the Vibration Assessment in the

Mauwafak Ali Tawfik*

*,**,*** Department

(Received  

Abstract 
 
This paper represents a study of the effect of the soil type, the drilling parameters and the drilling tool properties on 

the dynamic vibrational behavior of the drilling rig and its assessment in the drilling system. So first, an experimental 
drilling rig was designed and constructed to embrace the numer

The experimental work included implementation of the drill
according to the difference in the grains size, at different rotational spee
(Thrust force), in a way that allows establishing the charts that correlate the vibration acceleration, the rate of 
penetration (ROP), and the power consumption curves with the depth of drilling.

In addition to that the ANSYS Workbench
experimental results. And it was also used to model other numerical
 
Keywords: Soil, Vibration, and Drilling Rig
 

1. Literature Survey 
 

In 2000 Tucker and Wang were motivated by 
the need to understand the complex vibrational 
states experienced by the active components of a 

 

drilling assembly, in order to better control their 
potential [1]. In 2001 Ashley et al. dealt with the 
application of the multi-axis vibration chassis
(MVC) to measure vibrations in multiple axes and 
using the achieved data to provide the drilling 
team with the necessary means to cont
proper parameters to minimize specific vibration 
effects [2]. In 2002 Gui et al. studied the subject 
of instrumented borehole drilling and using the 
achieved data from the measured parameters as a 
tool in subsurface investigation [3]. 
et al. attempted to explain the complicated 
behavior of oil well drillstring motion when both 
torsional stick-slip and lateral whirl vibration are 
involved [4]. In 2004 Hendriks had focused on the 

 

Khwarizmi Engineering Journal, Vol. 11, No. 1, P.P. 93- 112 (2015)

 
The Effect of Soil Content, Drilling Parameters and 

on the Vibration Assessment in the Drilling Rig
 

Mauwafak Ali Tawfik*                Wafa Abd Soud*
Rami Safaa Alwan*** 

Department of Mechanical Engineering / University of Technology
E-mail: drmat19853@yahoo.com 
E-mail: wafaabd_92@yahoo.com 
E-mail: rami.safaa@yahoo.com

(Received 8 April 2014; accepted 15 December 2014)
 

This paper represents a study of the effect of the soil type, the drilling parameters and the drilling tool properties on 
the dynamic vibrational behavior of the drilling rig and its assessment in the drilling system. So first, an experimental 

and constructed to embrace the numerical work. 
he experimental work included implementation of the drill-string in different types of soil with different properties 

according to the difference in the grains size, at different rotational speeds (RPM), and different weights on bit (WOB) 
(Thrust force), in a way that allows establishing the charts that correlate the vibration acceleration, the rate of 
penetration (ROP), and the power consumption curves with the depth of drilling. 

that the ANSYS Workbench (the 14.0 release) software was used to simulate and verify the 
t was also used to model other numerical cases with different drill bit diameters.

il, Vibration, and Drilling Rig. 

Wang were motivated by 
the need to understand the complex vibrational 
states experienced by the active components of a  

better control their 
Ashley et al. dealt with the 

axis vibration chassis 
multiple axes and 

to provide the drilling 
with the necessary means to control the 

mize specific vibration 
Gui et al. studied the subject 

of instrumented borehole drilling and using the 
achieved data from the measured parameters as a 

 In 2002 Leine 
attempted to explain the complicated 

behavior of oil well drillstring motion when both 
slip and lateral whirl vibration are 

In 2004 Hendriks had focused on the 

analysis of torsional vibrations, lateral vib
and the interaction between those vibrations
specific experimental drill string set
2005 Mihajlovic had focused on the separate 
analysis of friction-induced vibration
mechanical systems and lateral vibratio
systems due to mass-unbalance 
Piovan and Sampio presented a continuous model 
to study, by means of finite element discretization, 
the coupling of extensional, flexural and torsion
vibration on a drill string 
al. modeled the drill string as a cantilever Euler
Bernoulli beam, and a tunable vibration absorber 
(TVA), as a semi active controller, was designed 
to suppress the forced bending (transverse) 
vibration during the drilling process 
Ritto analyzed nonlinear dynamics of the
string which included uncertaint
2011 Liao had studied the
through combined experimental

 

    
Al-Khwarizmi 
Engineering   

Journal 
(2015)

 Drilling Tool 
Drilling Rig  

Wafa Abd Soud** 

University of Technology 

This paper represents a study of the effect of the soil type, the drilling parameters and the drilling tool properties on 
the dynamic vibrational behavior of the drilling rig and its assessment in the drilling system. So first, an experimental 

string in different types of soil with different properties 
ds (RPM), and different weights on bit (WOB) 

(Thrust force), in a way that allows establishing the charts that correlate the vibration acceleration, the rate of 

software was used to simulate and verify the 
cases with different drill bit diameters. 

analysis of torsional vibrations, lateral vibrations 
and the interaction between those vibrations in  
specific experimental drill string set-up [5]. In 

Mihajlovic had focused on the separate 
induced vibrations in flexible 

mechanical systems and lateral vibrations in rotor 
unbalance [6]. In 2006 

Sampio presented a continuous model 
to study, by means of finite element discretization, 
the coupling of extensional, flexural and torsional 
vibration on a drill string [7]. In 2009 Moradi et 

led the drill string as a cantilever Euler-
Bernoulli beam, and a tunable vibration absorber 
(TVA), as a semi active controller, was designed 
to suppress the forced bending (transverse) 

ion during the drilling process [8]. In 2010 
near dynamics of the drill-

string which included uncertainty modeling [9]. In 
Liao had studied the drill-string dynamics 

combined experimental, modeling and 



Mauwafak A. Tawfik                       Al-Khwarizmi Engineering Journal, Vol. 11, No. 1, P.P.93- 112 (2015) 

94 
 

numerical effort [10]. In 2012 Rajnauth had 
focused on reducing the torsional vibration as a 
result of monitoring and implementing corrective 
actions [11]. In 2013 Richard Duff proposed an 
improved physical laboratory model to explore 
dynamic behaviors associated with vibration, 
where the model included contact with the 
borehole wall allowing a range of stabilization 
geometries while removing bit-formation 
interaction effects [12]. 

From the previously published works and 
papers it was observed that many drilling 
vibration associated problems were taken into 
consideration throughout the past years. These 
problems included the following: 
• Studying drill-string dynamics. 
• The effect of non-linearities. 
• The vibrational behavior states. 
• Utilizing measured drilling parameters data as 

an investigation tool. 
• Vibration analysis. 
• Vibration monitoring and control systems. 
• Bit and bearings design. 
• Finding new ways to model and analyze 

vibration. 
So this work can be considered as a first step 

towards the connecting link in the previously 
mentioned topics chain. 
 
 
2. Aims of the Work 
 
The main aims of this work were: 
1. Designing and constructing an experimental 

drilling rig. 
2. Studying the effect of different soil types on 

the drilling rig vibration assessment and the 
rate of penetration (ROP). 

3. Studying the effect of drilling parameters 
(rotational speed & WOB) on the vibration 
assessment and the (ROP). 

4. Studying the effect of the drill-bit size 
(diameter) on the drilling rig vibration 
assessment. 

 
 
3. The Experimental Drilling Rig 
 

For the sake of the experimental work an 
experimental drilling rig was designed and 
construct as shown in Figure (1), which also can 
be tuned easily to work as a field drilling rig 
thanks to its adjustable height due to its removable 
extension legs. 

 
 

Fig. 1. The experimental drilling rig. 
 
 

The drilling rig basically consists of three main 
parts: 
• The Drill-String (Drilling Core). 
• The Electrical Motor and the Inverter. 
• The Chassis (Frame). 
(Details of the experimental rig are shown in 
appendix (A)). 

The drill-string represents the mechanical part 
of the system, and in general its function is to 
receive and transmit the Weight on bit WOB 
(Thrust force) and the rotational movement to the 
drill bit, so that the downhole drilling action by 
the drill bit can take place. 

The electrical motor and the inverter can be 
characterized as the electronic part of the 
experimental drilling rig system, and it's the one 
responsible of generating the rotational motion 
and the torque (drilling energy) and controlling 
them. 

The chassis is made of angle iron welded to 
iron legs. the legs can be extended by adding the 
extension legs, where the rig is designed in a way 
that allows us to work on two levels, the first level 
is for field drilling which can be achieved by 
abandoning the extension legs, while the second 
level is for experimental drilling (i.e. drilling in a 
mold or a container) which can be achieved by 
adding the extension legs. 
 
 
4. Instruments 

 
Throughout the experimental work it was 

essential to measure and record the vibration 
acceleration, the power consumption, and the rate 
of penetration (ROP), and in order to achieve that 
piezoelectric charge accelerometers (B&K 4370) 
were used to measure vibration acceleration which 
was connected to a charge amplifier (B&K 2635) 
which was in turn connected to an oscilloscope 



Mauwafak A. Tawfik                       Al-Khwarizmi Engineering Journal, Vol. 11, No. 1, P.P.93- 112 (2015) 

95 
 

(ADS 1022C) to present the output signal. (See 
appendix D) 

Also an Inverter (Hyundai N100plus/015SF) 
was implemented to control the frequency of the 
electricity and in turn control the rotational speed 
of the motor. 

For measuring the rate of penetration (ROP) a 
simple mechanism was used which is illustrated in 
Fig. (2). It consists of a slide bush (part (a)) with 
an adjustable-length pin (part (b)), and as the drill-
string proceeds forehead during the drilling 
process the pin will be pushed downward with it 
by the upper slide bush (part (c)), the pin is in turn 
pointed to a ruler (part (d)) to measure the depth.  

 

 
 
Fig. 2. Rate of penetration (ROP) measuring 
mechanism. 
 
 
5. Soil Samples Analysis 
 

For the sake of the experimental work three 
different soil samples were selected, these 
samples were then taken to the soil laboratory to 
examine their texture by performing the following 
procedure: the first step was to dry each soil 
sample in the drying oven for (24 hours) to assure 
that the measured mass is of the soil only (i.e. 
purely soil without moisture), after that (500 
gram) were taken from each sample and washed 
with water on the No. 200 sieve (75 µm opening 
size) to primarily separate each sample into coarse 
grains portion and fine grained one. Later and 
after drying each portion for another (24 hours) 
and to be capable of finding out the grains size 
distribution of each sample a set of sieves was 
used for the coarse grained portion (grain size > 
75 µm), and for the fine grained portion (grain 
size < 75 µm) the hydrometer analysis was used. 
 

 
6. Theory of the Drill- String 
 

In general vibration whether it was free or 
forced vibration, whether harmonic, periodic or 
random, it is basically defined as the oscillatory 
movement of a body about its equilibrium 

position. Hereby in this work the vibration in the 
experimental drilling rig is resulting from the 
Borehole-Drill bit interaction. Where the non-
homogeneity of the soil results in variable drag 
forces on the drill-bit head, in addition to the 
contrastive friction forces between the conveyer 
and the borehole wall. 
 
 
6.1.  The Drill- String Model 
 

Let us consider the drill-string as an initially 
straight slender rotating beam with a circular 
cross-section (R) and length (L) in the un-
deformed state. The beam is referred to an inertial 
Cartesian system O:XYZ fixed to the undeformed 
beam. Another Cartesian reference system O:xyz 
measures the deformation and displacements of 
the beam. In Figure (3) it is possible to see that the 
system O:xyz is rotated with respect to the system 
O:XYZ by means of a typical sequence of rotation 
angles as usual in rotor-dynamics. 

 

 
    

Fig. 3. Reference systems and rotation angels. 
 
 
6.2. Kinetic and Strain Energies 
 

The kinetic energy can be expressed in the 
following form [19]: 

� = 0.5� ��		��
 � +	�
� +	�
 �� 	+ ����
 ′� +	�
 ′�� 	
�

� + 	����
�� + 	2����
��
 ′� ′�	�� 					… �1� 
The simplified expression of the strain energy 

(H), which will be (Hs), can be described in the 
following form [19]: 

�� = 0.5  !"	�#� + 	"�	��##� +	�##�� +�
�

	$����#�%	�� + 0.5  !$��	��##�# − 	�′�′′���# +�
�

	"		��#( +	�#�#� + 	�′�#��%	�� + 0.5  !"��	��#�## −�
�	�##�# +	��#�′���# + 	3"��#��##� +	�##��%	��	      …(2) 



Mauwafak A. Tawfik                       Al-Khwarizmi Engineering Journal, Vol. 11, No. 1, P.P.93- 112 (2015) 

96 
 

The beam is subjected to its own weight, and 
the external work done by a vertical force due to 
gravity field can be expressed as [20]: 

* =  ��+	��	���
� 																								                           …(3) 

 
 
6.3. The Numerical Analysis 
 

In order to complete the requirements of the 
numerical analysis which are the drill-string 
geometry, the boundary conditions including the 
supports stiffness values (foundation stiffness* 
(, -(⁄ )), and the loads, the following route was 
taken which starts with using the AutoCAD 2009 
software to achieve the geometry. 

Then to calculate the supports stiffness values, 
Beam Deflection formula was used, and the 
detailed calculations are as follows: 
1) the values of the supports reaction forces were 

calculated as shown in Figure (4) by adapting 
Beam Deflection formula: 

 

/0 = 1234	�5 + 2�
6"�05 					27�			/� = 8�3�

6"�5 �5� − �� − 3�� 
 

 
 

Fig. 4. The drill-string free-body-diagram. 
 
 

F = obstruction and friction forces to the bit 
      inserts and bit head surface respectively. (N) 
R = Supports reactions. (N) 
Y = Supports deflection. (m) 
E = Young’s modulus. (Pa) 
I = Area moment on inertia. (m4) 
 

Since the summation of deflection at the 
supports location is equal to zero, so the value of 
�8�� can be found (assuming rigid supports). 

Then by taking the summation of moment 
about (A), then the summation of forces, the 
values of �80�	27�	�8(� will be obtained 
respectively. 
2) The accelerometers were then attached to the 

location of the supports, each one at a time, so 
that the displacement of each support can be 
found and in turn its stiffness value (K). 
And finally comes the loads which were 

calculated as follow; at the beginning the power 

consumption curves for the experimental cases 
that have been achieved and for the free-run (idle 
run) (i.e. drilling with no contact between the 
drilling tool and the soil) were established, where 
the difference between the average values for the 
steady-state portion of them represents the drilling 
power consumption. And thus the loads were 
calculated as follows: 

9:�;<	�9� = =:<>�;	�=� ∗ 	7+�@2<	�;@:4AB/	�C�         
                                                                                …(4) 

9 = 9:�;<DEFFGHIJ − 9:�;<KIELJM	KELNNLJM 				      …(a) 

C = 2O�,� 60⁄ 				                                                   …(b) 

And according to the previous equations the 
only unknown value is that of �=� and by 
calculating it, the value of �1� for the 
experimental cases will be found as follows: 

 

∑= =	∑1	 ∗ 	<	QLRGSJ�FER�																                          …(c) 
 

Boundary conditions  
 

• At the supports position, radial deflection is 
constrained while axial translation about the 
drill string axis is permitted. 

• The drill-bit, the drill-string and the bearings 
are made of elastic homogeneous isotropic 
steel. 

• The soil stiffness is so small compared to the 
supports, and thus it was replaced by very low 
stiffness spring. 
Finally and after having all the analysis 

requirements (geometry, boundary conditions and 
loads) the simulation of the original drill bit model 
size was available to verify the experimental 
results, where Figure (5 and 6) shows the 
undeformed and deformed model of the drill-
string. 

 
 

 
 
 

Fig. 5. ANSYS undeformed model 
 
 

* Foundation Stiffness is the stiffness per the supports projected area 

The drill 
bit 

The 
supports 

(ball-

bearings) 

The 
drilling 
shaft 

The 
conveyer 



Mauwafak A. Tawfik                       Al-Khwarizmi Engineering Journal, Vol. 11, No. 1, P.P.93- 112 (2015) 

97 
 

 
 

Fig. 6. ANSYS deformed model. 
 
 

6.3.1. The Drill-String Natural Frequencies 
 

Since the drilling parameters, including the 
drill-string rotational speed, effect on the vibration 
assessment had been studied in this work, so the 
ANSYS Workbench were used to find the drill-
string natural frequencies, to make sure that the 
implemented operating rotational speeds that had 
been chosen in the experimental work are away 
from the natural frequencies, and in turn the 
achieved results are away from the effect of 
resonance. The results for the drill-string natural 
frequencies that were obtained from the ANSYS 
Workbench are as shown in Table (1) below: 
 
Table 1, 
The drill-string natural frequencies. 

Depth 
(cm) 

The Natural Frequencies (r.p.m.) 
1st 2nd 3rd 4th 

0 0.06 9 10 310 
2 0.07 9.04 10.63 310.61 
4 0.07 9.12 10.22 330.32 
6 9.03 10.75 313.25 ---- 
8 9.05 10.66 314.21 ---- 
10 9.07 10.67 311.42 ---- 
12 0.07 9.37 11.35 326.21 
14 0.06 9.48 11.84 333.21 
16 9.32 10.64 11.24 315.87 
18 9.47 10.85 13.45 329.47 
20 10.1 13.9 323.2 ---- 
22 0.05 9.37 10.35 318.18 
24 0.03 9.47 10.78 332.21 
26 9.64 10.78 13.25 331.77 
28 0.08 9.34 11.87 321.42 
30 9.26 10.81 319.47 ---- 
32 9.42 10.63 320.54 ---- 
34 0.05 9.21 13.98 310.25 
36 0.08 9.54 10.27 324.27 
38 9.32 10.88 314.87 ---- 
40 0.02 9.84 11.05 325.09 

 
 
 

6.3.2. The Drill-Bit Diameter Effect 
 

Additionally, the ANSYS Workbench software 
was used to model other numerical cases with 
different drill-bit size (diameter) which are 
�∓	25%� of the original drill bit model geometry 
size (diameter) to verify the effect of the drill bit 
size (diameter) on the vibration assessment and 
the results are as shown in Figure (7) below: 

 

 
 
Fig. 7. Acceleration curves for different diameters. 

 
 

It was observed that for the same conditions 
(soil type, rotational speed and weight on bit) the 
smaller the drill bit is, the higher the vibration 
acceleration levels will be, and this may be 
attributed either to difference in mass and in turn 
the difference in inertia, the fact that the larger 
model mass works on dissipating the transferred 
vibrations more than the smaller model does or 
other dynamical behaviors where this point needs 
more investigation (provided that the drill-string 
rotational speed is away from resonance zones). 
 
 
7. Results and Discussion 
 

For the sake of the experimental work the 
following parameters were chosen: three different 
samples of soil with different grain sizes, four 
different rotational speeds (50 – 100 – 150 – 200) 
rpm so that the rotational speed increases by folds 
and three weights on bit (WOB/Thrust force) with 
(50%) increment steps as follows (80 – 120 – 160) 
N. In addition to that and by using the ANSYS 
software it was available to simulate the original 
drill bit for the experimental cases that were 
accomplished for the purposes of verification, and 
further more the ANSYS software was used to 
model other theoretical cases with different drill 
bit model sizes (diameters) which are �±	25%� of 
the original drill bit model size (diameter). 
 

 
 



Mauwafak A. Tawfik                       Al-Khwarizmi Engineering Journal, Vol. 11, No. 1, P.P.93- 112 (2015) 

98 
 

7.1. Soil Samples Grains Size Distribution 
 

When it comes to vibration assessment and its 
severity, it turns out that they are clearly affected 
by the grains size distribution of the soil and the 
consistency of that distribution. Figure (8) below 
shows the grains size distribution curves of the 
soil samples, where x-axis represents the grains 
size, and y-axis represents the percentage of the 
grains. 

 

 
 

Fig. 8. Grains size distribution curves. 
 
 

7.2. The Experimental Results 
 

After finishing the soil samples analysis and 
the establishment of the grains size distribution 
curves, it was commenced with the experiments, 
and down hereby the obtained results, for each 
soil sample, are presented as follows: 
 
 

7.2.1. Silty-Clay 
 

For first soil sample (Silty-Clay), the average 
values of the vibration acceleration levels (m/s2) 
from Figure (9, 12, and 15) were as in table (1) in 
Appendix (B). 

Based on the revealed data, it can be said that 
vibration acceleration levels increase as the 
rotational speed increases. This can be attributed 
to the fact that external forces (that the soil exerts 
on the drill-bit whether they were obstruction 
forces to the rotation of the inserts or friction ones 
to the surface of the drill-bit head) which once 
were with little or no effect, now they do since 
�C� had increased. Which eventually means that 
the time stepping of the forces exertion is now 
became less, and that is make the drill string 
exposed to the effect of more forces, and by that 
the drill string will be displaced more distance 
than before. That brings up the conclusion that the 
second reason for that increment in vibration 
acceleration is when the external forces shake the 
drill string out of its rotation axis center an 

imbalance force due to imbalance mass will be 
generated. 

According to imbalance force law it appears 
that �C� is the factor of the biggest impact. So 
increasing �C� will greatly increase the centripetal 
forces and in turn the vibration levels as well 
(provided that the system is away from the critical 
rotational speeds). 

It can be noticed that vibration acceleration 
levels decrease as the (WOB) increases due to the 
fact that the higher the (WOB) is, the higher the 
friction between the drill bit and the soil. So in 
other words, there will be more power dissipation 
in overcoming friction rather than in vibration, 
and of course higher friction means more 
reduction in the rotational speed, which in turn 
means lower vibration acceleration (according to 
the relation that was first drawn between the 
vibration and the rotational speed). Not only that 
but also more importantly is that increasing the 
(WOB) will diminish the effect of the external 
forces on the drill bit since now they will have to 
shake larger mass than before. 

In general the vibration acceleration levels 
were neither too high nor too low. The most likely 
explanation for this behavior can be attributed to 
the following factors, which are the grains size 
distribution and the homogeneity of that 
distribution (i.e. the larger the grains size and the 
more non-homogeneity that the soil have, the 
higher the vibration acceleration levels that will 
be encountered in it). 

The vibration acceleration levels decrement 
increases as the (WOB) and the rotational speed 
increase. This observations can be attributed to the 
fact that forces that became effective in disturbing 
the drill string and shaking it out of its rotation 
center, as the rotational speed increased (i.e. the 
load stepping time was reduced), are more liable 
to dissipation due to increment in the (WOB). 

The average values of the rate of penetration 
(ROP) (cm/sec) from Figure (10, 13, and 16) were 
as in table (2) in Appendix (B). 

In reference to table (5), it can be stated that 
higher rotational speed results in higher rates of 
penetration (ROP), since more excavation of the 
soil will be done. 

The rate of penetration (ROP) is seemed to be 
affected by the (WOB) in the same way that it did 
by the rotational speed and the higher the (WOB) 
is, the higher the (ROP) will be, but that's not 
completely practical due to the fact that (ROP) 
will keep increasing with the (WOB) up to a 
certain point, namely the founder point. After that 
point increasing the (WOB) will have adverse 
effect on the (ROP), because the drill bit will have 



Mauwafak A. Tawfik                       Al-Khwarizmi Engineering Journal, Vol. 11, No. 1, P.P.93- 112 (2015) 

99 
 

more difficulty in overcoming increased friction, 
in addition to the fact that excessive (WOB) will 
force the inserts of the drill bit deeply in the 
formation in a way that they can't be moved 
properly. 

It is worthy to mention that the silty-clay soil 
has low rate of penetration. That's because the 
silty-clay soil grains were sticking to the drill bit 
inserts causing less efficient drilling and that if 
they don't even make the drill bit clog which 
agrees with what came in reference [3]. And again 
this can be attributed to the grains size, because of 
the fact that the soil grains are generally under the 
influence of two main kinds of forces which are 
the gravitational and the surface forces, and the 
factor that designate the dominant force is the 
ratio of the surface area to the volume, so that the 
dominant force for the fine-grained soil will be the 
surface force and vice versa. And that what makes 
the silty-clay soil grains sticky. 

The rate of penetration (ROP) increment 
increases as the (WOB) and the rotational speed 
increase. This observation is attributed to the fact 
that the (ROP) is in general the resultant of two 
factors, which are the rotational speed stirring 
action and the (WOB) piercing action. Based on 
that no (ROP) will be achieved, no matter how 
high is the rotational speed, without applying 
(WOB) and vice versa. And by relying on these 
facts it can be concluded that increment in one of 
these two factors will have a positive influence on 
the other factor's effect on the (ROP). 

Another point to be mentioned is that the rate 
of penetration (ROP), in general, decreases with 
depth. The rates of penetration (ROP) decrement 
percentage with depth from Figure (10, 13, and 
16) were as in table (3) in Appendix (B). And this 
decrement in (ROP) is the result of the decrement 
in rotational speed, as a consequence of higher 
drag forces due to accumulative increment in 
compaction. 

 

Finally, the average values of the power 
consumption (Watt) from Figure (11, 14, and 17) 
were as in table (4) in Appendix (B). 

For the power consumption it should be 
reminded here that it corresponds to the actual 
rotational speed not the preset one since constant 
torque was used in this thesis. By examining the 
power consumption curves it can be seen that the 
power consumption increases as the rotational 
speed increases, with a decrement in that 
increment which might be physically ascribed to 
having higher inertia. 
 
 

 
 

Fig. 9. Acceleration with depth. 
 

 

 
 

Fig. 10. Rate of penetration with depth. 
 
 

 
 

Fig. 11. Power with depth. 
 

 
 

Fig. 12. Acceleration with depth. 



Mauwafak A. Tawfik                       Al-Khwarizmi Engineering Journal, Vol. 11, No. 1, P.P.93- 112 (2015) 

100 
 

 
 

Fig. 13. Rate of penetration with depth. 
 
 

 
 

Fig. 14. Power with depth. 
 
 

 
 

Fig. 15. Acceleration with depth. 
 
 

 
 

Fig. 16. Rate of penetration with depth. 
 
 

 
 

Fig. 17. Power with depth. 
 
 
7.2.2. Sand 
 

For the second soil sample (Sand), the average 
values of the vibration acceleration levels (m/s2) 
from Figure (18, 21, and 24) were as in table (5) 
in Appendix (B). 

Based on the revealed data, it can be said that 
vibration acceleration levels increase as the 
rotational speed increases. It also can be noticed 
that the vibration acceleration levels decrease as 
the weight on bit (WOB) increases. In general the 
vibration acceleration levels were higher than 
those encountered in silty-clay soil by (16.58%). 
Vibration acceleration levels decrement increases 
as the (WOB) and the rotational speed increase. 
All of the above mentioned observations can be 
attributed to the same factors that were mentioned 
in the silty-clay soil. 

The average values of the rate of penetration 
(ROP) (cm/sec) from Figure (19, 22, and 25) were 
as in table (6) in Appendix (B). 

In reference to table (9), it can be stated that 
higher rotational speed means higher rates of 
penetration (ROP). The rate of penetration (ROP) 
is seemed to be affected by the (WOB) in the 
same way that it did by the rotational speed and 
the higher the (WOB) is, the higher the (ROP) 
will be, but that's not completely practical due to 
the fact that (ROP) will keep increasing with the 
(WOB) up to a certain point, namely the founder 
point. After that point increasing the (WOB) will 
has adverse effect on the (ROP). It is worthy to 
mention that the sand soil has the higher rate of 
penetration in comparison to the silty-clay soil by 
(97.88%). The rate of penetration (ROP) 
increment increases as the (WOB) and the 
rotational speed increase. Another point to be 
mentioned is that the rate of penetration (ROP), in 
general, decreases with depth. The rates of 
penetration (ROP) decrement percentage with 
depth from Figure (19, 22, and 25) were as in 
table (7) in Appendix (B). All of the above 
mentioned observations can be attributed to the 



Mauwafak A. Tawfik                       Al-Khwarizmi Engineering Journal, Vol. 11, No. 1, P.P.93- 112 (2015) 

101 
 

same factors that were mentioned in the silty-clay 
soil. 

Finally, the average values of the power 
consumption (Watt) from Figure (20, 23, and 26) 
were as in table (8) in Appendix (B). 

By examining the power consumption curves it 
can be seen that the power consumption increases 
as the rotational speed increases, with a decrement 
in that increment which might be physically 
ascribed to having higher inertia. 
 
 

 
 

Fig. 18. Acceleration with depth. 
 
 

 
 

Fig. 19. Rate of penetration with dept. 
 
 

 
 

Fig. 20. Power with depth. 
 
 

 
 

Fig. 21. Acceleration with depth. 
 
 

 
 

Fig. 22. Rate of penetration with depth. 
 
 

 
 

Fig. 23. Power with depth. 
 
 

 
 

Fig. 24. Acceleration with depth. 
 
 



Mauwafak A. Tawfik                       Al-Khwarizmi Engineering Journal, Vol. 11, No. 1, P.P.93- 112 (2015) 

102 
 

 
 

Fig. 25. Rate of penetration with dept. 
 
 

 
 

Fig. 26. Power with depth. 
 
 
7.2.3. River Sand 
 

For the final soil sample (River Sand), the 
average values of the vibration acceleration levels 
(m/s2) from Figure (27, 30, and 33) were as in 
table (9) in Appendix (B). 

Based on the revealed data, it can be said that 
vibration acceleration levels increase as the 
rotational speed increases. It also can be noticed 
that the vibration acceleration levels decrease as 
the weight on bit (WOB) increases. In general the 
vibration acceleration levels were lower than 
those in the sand and silty-clay soil by (25.53 % 
and 13.19 %) respectively. Vibration acceleration 
levels decrement increases as the (WOB) and the 
rotational speed increase. All of the above 
mentioned observations can be attributed to the 
same factors that were mentioned in the silty-clay 
soil. 

The average values of the rate of penetration 
(ROP) (cm/sec) from Figure (28, 31, and 34) were 
as in table (10) in Appendix (B). 

In reference to table (10), it can be stated that 
higher rotational speed means higher rates of 
penetration (ROP). The rate of penetration (ROP) 
is seemed to be affected by the (WOB) in the 
same way that it did by the rotational speed and 
the higher the (WOB) is, the higher the (ROP) 
will be, but that's not completely practical due to 
the fact that (ROP) will keep increasing with the 

(WOB) up to a certain point, namely the founder 
point. After that point increasing the (WOB) will 
has adverse effect on the (ROP). It is worthy to 
mention that the river sand soil has a higher rate 
of penetration than that of the silty-clay by (80.57 
%) and lower than that of the sand by (8.75 %). 
The rate of penetration (ROP) increment increases 
as the (WOB) and the rotational speed increase. 
Another point to be mentioned is that the rate of 
penetration (ROP), in general, decreases with 
depth. The rates of penetration (ROP) decrement 
percentage with depth from Figure (28, 31, and 
34) were as in table (11) in Appendix (B). All of 
the above mentioned observations can be 
attributed to the same factors that were mentioned 
in the silty-clay soil. 

Finally, the average values of the power 
consumption (Watt) from Figure (29, 32, and 35) 
were as in table (12) in Appendix (B). 

By examining the power consumption curves it 
can be seen that the power consumption increases 
as the rotational speed increases, with a decrement 
in that increment which might be physically 
ascribed to having higher inertia. 
 

 
 

Fig. 27. Acceleration with depth. 
 
 

 
 

Fig. 28. Rate of penetration with depth. 
 



Mauwafak A. Tawfik                       Al-Khwarizmi Engineering Journal, Vol. 11, No. 1, P.P.93- 112 (2015) 

103 
 

 
 

Fig. 29. Power with depth. 
 
 

 
 

Fig. 30. Acceleration with depth. 
 
 

 
 

Fig. 31. Rate of penetration with depth. 
 
 

 
 

Fig. 32. Power with depth. 
 
 

 
 

Fig. 33. Acceleration with depth. 
 
 

 
 

Fig. 34. Rate of penetration with depth. 
 
 

 
 

Fig. 35. Power with depth. 
 
 
7.2.4. Free-Run (Idle Run)  
 

In order to calculate the loads at the drill-bit 
inserts, establishing the power consumption 
curves for the free-run (idle run i.e. drilling with 
no contact between the drilling tool and the soil) 
was essential, so that the drilling power can be 
calculated by finding the difference between the 
steady state portion of the power consumption 
curves when drilling in the soil and outside the 
soil (i.e. the free-run). 

The average values of the power consumption 
(Watt) were as follows in table (2) below: 

 
 
 
 



Mauwafak A. Tawfik                       Al-Khwarizmi Engineering Journal, Vol. 11, No. 1, P.P.93- 112 (2015) 

104 
 

Table 2, 
Power Consumption (Watt). 

 Load (80 N) Load (120 N) Load (160 N) 

50 rpm 58.6 57.5 56.4 

100 rpm 78.8 78.2 77.4 

150 rpm 96 95.3 94.8 

200 rpm 108.7 108.5 108.3 
 
 
7.3. Results Verification 
 

As mentioned previously ANSYS Workbench 
software (the 14.0 release) was used to verify the 
experimental results, and that's was accomplished 
by reliance on power consumption curves to 
calculate the drag force, that encounter the bit 
inserts, at the intervals of two centimeters and by 
using the supports stiffness values that had 
already been calculated previously by adapting 
Beam Deflection formula, as the input to the 
ANSYS. Additionally, twenty AutoCAD 2009 
geometries due to the movement of the drill-string 
relative to the supports as the drilling operation 
proceeds forehead, which were also exported to 
the ANSYS. The deviation percentage was 
calculated by finding the average value of the 
trend lines of the numerical and actual 
acceleration curves, figure (1) – (12) in appendix 
(C), as follows in table (3) below: 

W;�A2BA:7	�%� = X	7�-;<A42@	244. −24B�2@	244.24B�2@	244. ∗ 100Y 
 
Table 3 
Results verification – Deviation percentage. 

Load - 8 N 

r.p.m 
Actual 
acc. 

Numerical 
acc. 

Deviation 
percentage (%) 

50 4 3.7 7.5 
100 10.5 9.5 9.52 
150 15.5 17 9.68 
200 22.5 21 6.67 
Load - 12 N 

r.p.m 
Actual 
acc. 

Theoritical 
acc. 

Deviation 
percentage (%) 

50 3 2.7 10 
100 7 7.5 7.14 
150 12 13 8.33 
200 16 17 6.25 
Load - 16 N 

r.p.m 
Actual 
acc. 

Theoritical 
acc. 

Deviation 
percentage (%) 

50 2.4 2.2 8.33 
100 5.1 5.6 9.8 
150 8.5 9 5.88 
200 14 15 7.14 

 

8. Conclusions 
 
When it comes to the conclusions and after 

observing the results illustrated by the charts that 
correlate the vibration acceleration, the rate of 
penetration and the power consumption curves 
with the depth of the borehole the following 
conclusions were pointed out. Part of them are 
special conclusions of the individual soil samples 
while the others are general conclusions, which 
are going to be mentioned later, and these 
conclusions are as follows: 

 

1- Sand has stands out to be in the first place 
when it comes to the highest vibration 
acceleration levels (with an average acc. value 
of (13.097 m/s2)), followed by silty-clay 
(11.234 m/s2) and river sand (9.753 m/s2) 
respectively. 

2- For the rates of penetration sand also seemed 
to be the one with the highest penetration rate 
(with an average ROP of (1.786 cm/sec)) 
followed with close difference by the river 
sand (1.629 cm/sec) meanwhile silty-clay 
comes with the lowest ROP average (which 
was (0.902 cm/sec). 

 

And now the general conclusions, which can be 
applied to all of the cases, are listed below: 
 

3- The vibration acceleration levels increase as 
the rotational speed increases (provided that 
the implemented operating speed is away from 
the resonance zones). 

4- The vibration acceleration levels decrease as 
the weight on bit (WOB) increases. 

5- The vibration acceleration levels decrement 
increases as the (WOB) and the rotational 
speed increase. 

6- Higher rotational speed means higher (ROP) 
since more excavation of the soil will be done. 

7- The (ROP) will keep increasing with the 
(WOB) up to a certain point, the founder point, 
and after that point increasing the (WOB) will 
have adverse effect on the (ROP). 

8- The rate of penetration (ROP) increment 
increases as the (WOB) and the rotational 
speed increase.    

9- In general the rate of penetration (ROP) 
decreases with depth. 

 

Finally, from the numerical analysis of 
the smaller and the larger drill bit models it was 
available to come up with the following: 
 

10- It was observed that for the same conditions 
(soil type, rotational speed, and WOB) 
smaller drill bit diameter means higher 
vibration acceleration levels. 



Mauwafak A. Tawfik                       Al-Khwarizmi Engineering Journal, Vol. 11, No. 1, P.P.93- 112 (2015) 

105 
 

Notation 
 

	      Area of the transversal section (m2) 
"      Young’s modulus (pa) 
$      Shear modulus (pa) 
+      Gravitational acceleration (m/s2) 
�	     Strain energy (N.m) 
��    Simplified strain energy (N.m) 
Z       Tensor of inertia (m4) 
�      Kinetic energy (N.m) 
�      Displacement in x-direction (m) 
�      Displacement in y-direction (m) 
�     Displacement in z-direction (m) 
 
Greek Letters 
 

�      Density (kg/m3) 
��    Rotation about x-axis (rad) 
�[    Rotation about y-axis (rad) 
�\    Rotation about z-axis (rad) 
 
 
9. References 
 
[1] R. W. Tucker and C. Wang, "An Integrated 

Model for Drill-String Dynamics", Article, 
2000. 

[2] D. K. Ashley, X. M. McNary, and J. C. 
Tomlinson, "Extending BHA Life with 
Multi-Axis Vibration Measurements", Paper 
(Society of Petroleum Engineers), 2001. 

[3] M. W. Gui, M.ASCE, K. Soga, M. D. Bolton, 
and J. P. Hamelin, "Instrumented Borehole 
Drilling for Subsurface Investigation", Paper 
(Journal of Geotechnical and 
Geoenvironmental Engineers), 2002. 

[4] R. I. Leine, D. H. van Campen, and W. J. G. 
Keultjes, "Stick-Slip Whirl Interaction in 
Drillstring Dynamics", Paper (Journal of 
Vibration and Acoustics), 2002. 

[5] M.P.M. Hendriks, "Analysis of Torsional and 
Lateral Vibrations in an Experimental Drill-
String Set-Up", Master thesis, 2004. 

[6] Nenad Mihajlovic, "Torsional and Lateral 
Vibrations in Flexible Rotor Systems with 
Friction", Ph.D. thesis, 2005. 

[7] Marcelo T. Piovan and Rubens Sampaio, 
"Non Linear Model for Coupled Vibrations 
of Drill-Strings", Paper, 2006. 

[8] Hamed Moradi, Mohammad Motamedi, and 
Firooz Bakhtiari-Nejad, "Suppression of 
Bending Vibration in Drilling Process via a 
Tunable Vibration Absorber", Paper (16th 
International Congress on Sound and 
Vibration ICSV), 2009. 

[9] Thiago Gamboa Ritto, "Numerical Analysis 
of the Nonlinear Dynamics of a Drill-String 
with Uncertainty Modeling", Ph.D. thesis, 
2010. 

[10] Chien-Min Liao, "Experimental and 
Numerical Studies of Drill-String 
Dynamics", Ph.D. thesis, 2011. 

[11] Jerome Rajnauth, PhD and Tennyson Jagai, 
PhD, "Reduce Torsional Vibration and 
Improve Drilling operations", Paper 
(International Journal of Applied Science 
and Technology), 2012. 

[12] Richard Duff, "An Experimental and 
Computational Investigation of Rotating 
Flexible Shaft System Dynamics in Rotary 
Drilling Assemblies for Down Hole 
Drilling Vibration Mitigation", Ph.D. thesis, 
2013. 

[13] M. Lalanne and G. Ferraris, John Wiley and 
Sons, Chichester, West Sussex, England, 
named "Rotor-dynamics Prediction in 
Engineering", 1990. 

[14] M.A. Trindade, C. Wolter, and R. Sampaio, 
"Karhunen-loeve Decomposition of 
Coupled Axial/Vending Vibrations of 
Beams Subject to Impacts", Journal of 
Sound and Vibration, 2005. 

 

 
 
 
 
 
 
 
 
 
 
 
 

 
 
 
 
 
 
 
 
 
 
 
 



Mauwafak A. Tawfik                       Al-Khwarizmi Engineering Journal, Vol. 11, No. 1, P.P.93- 112 (2015) 

106 
 

Appendix (A) 
 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

 
Fig. 1. the drill-string (drilling core) – upper parts. 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

Fig. 2. the drill-string (drilling core) – lower parts. 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

 
 

Fig. 3. the electrical motor and the inverter 
 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

 
Fig. 4. the chassis (frame) – side view. 

 
 
 
 
 

 

Drilling Shaft 

Adjustment 

Cylinder 

Slide Guide 

shaft Holding 

Bush 

Housing 

Cylinder 

Housing Cup 

Plate A 

Plate B 

Ruler sliding 

Holders 

Outer Slides 

Inner slides 

Sliding Guide 

Bush-1 

Loads 

Carrying 

Sliding Guide 

Bush-2 

Ruler 

Holders Shaft 

Adjustment 

guide/monito

ring pin 

Holders 

Shaft 

Slide Guide 

Shaft 

Driving Pulley 

Loads 

Loads 

Circular 

Rubber 

Drill-Bit 

Driving Bush 

Alignment 

Housing Cup 

the Motor 

Adjustment 

the Inverter the Inverter 

Input 220 V – 1 Ø Output 380 V – 3 Ø 

the Electrical 

Motor 

the Upper Plate 

the Motor 

the Lower Plate 

Rubber-Flange 

Fixed legs 

stage -1- 

Removable extension legs 

stage -2- 

the Chassis 

(Frame) 

Leveling 

Bushes 



Mauwafak A. Tawfik                       Al-Khwarizmi Engineering Journal, Vol. 11, No. 1, P.P.93- 112 (2015) 

107 
 

Appendix (B) 
 

1. Silty- Clay 
 
Table 1, 
Vibration Acceleration Levels (m/s2) & variation percentage. 
Vibration Acceleration Levels (m/s2) & variation percentage 

 Load (80 N)  Load (120 N)  Load (160 N) 
50 rpm 4.35 -28.3 % 3.12 -29.8 % 2.19 
 +154.7 %  +152.2 %  +161.6 % 
100 rpm 11.08 -29 % 7.87 -27.2 % 5.73 
 +79.4 %  +63.3 %  +83.8 % 
150 rpm 19.88 -35.4 % 12.85 -18.1 % 10.53 
 +18.2 %  +43.7 %  +44.7 % 
200 rpm 23.5 -21.4 % 18.47 -17.5 % 15.24 
 
Table 2, 
Rates of Penetration ROP (cm/sec) & variation percentage. 
Rates of Penetration ROP (cm/sec) & variation percentage 

 Load (80 N)  Load (120 N)  Load (160 N) 
50 rpm 0.225 +48 % 0.333 +42.9 % 0.476 
 +52 %  +110.8 %  +189.7 % 
100 rpm 0.342 +105.3 % 0.702 +96.4 % 1.379 
 +88.6 %  +23.9 %  +20.9 % 
150 rpm 0.645 +34.9 % 0.870 +91.6 % 1.667 
 +17.1 %  +24.3 %  +41.2 % 
200 rpm 0.755 +43.2 % 1.081 +117.7 % 2.353 
 
Table 3, 
Rates of Penetration (ROP) decrement percentage. 
Rates of Penetration (ROP) decrement percentage 
 Load (80 N) Load (120 N) Load (160 N) 
50 rpm 23.4 % 37.9 % 15 % 
100 rpm 26.3 % 31.4 % 33.1 % 
150 rpm 32.7 % 32.5 % 48.3 % 
200 rpm 32 % 45 % 70 % 
 
Table 4, 
Power Consumption (Watt). 
Power Consumption (Watt) 
 Load (80 N) Load (120 N) Load (160 N) 
50 rpm 51.67 50.02 47.55 
100 rpm 65.35 63.96 60.69 
150 rpm 77.14 76 71.73 
200 rpm 87.82 84.42 83.23 
 

2. Sand 
 
Table 5, 
Vibration Acceleration Levels (m/s2) & variation percentage. 
Vibration Acceleration Levels (m/s2) & variation percentage 
 Load (80 N)  Load (120 N)  Load (160 N) 
50 rpm 5.69 -17.9 % 4.67 -12.6 % 4.08 
 +145 %  +91.2 %  +104.7 % 
100 rpm 13.94 -35.9 % 8.93 -6.5 % 8.35 
 +44.5 %  +52 %  +66 % 
150 rpm 20.15 -32.7 % 13.57 +2.1 % 13.86 
 +31.5 %  +42.3 %  +30.7 % 
200 rpm 26.49 -27.1 % 19.31 -6.2 % 18.12 



Mauwafak A. Tawfik                       Al-Khwarizmi Engineering Journal, Vol. 11, No. 1, P.P.93- 112 (2015) 

108 
 

Table 6, 
Rates of Penetration ROP (cm/sec) & variation percentage. 
Rates of Penetration ROP (cm/sec) & variation percentage 
 Load (80 N)  Load (120 N)  Load (160 N) 
50 rpm 0.471 +18 % 0.556 +2.7 % 0.571 
 +123.6 %  +139.7 %  +191.9 % 
100 rpm 1.053 +26.6 % 1.333 +25.1 % 1.667 
 +51.9 %  +76.5 %  +50 % 
150 rpm 1.6 +47.1 % 2.353 +6.2 % 2.5 
 +47.1 %  +41.6 %  +45.4 % 
200 rpm 2.353 +41.6 % 3.333 +9.1 % 3.636 
 
Table 7, 
Rates of Penetration (ROP) decrement percentage. 
Rates of Penetration (ROP) decrement percentage 
 Load (80 N) Load (120 N) Load (160 N) 
50 rpm 15 % 14.4 % 10.8 % 
100 rpm 28.3 % 32 % 18.1 % 
150 rpm 32.5 % 32.5 % 35 % 
200 rpm 63.8 % 67.2 % 60 % 
 
Table 8, 
Power Consumption (Watt). 
Power Consumption (Watt) 
 Load (80 N) Load (120 N) Load (160 N) 
50 rpm 51.5 49.52 48.9 
100 rpm 67.49 64.5 61.83 
150 rpm 79.5 75.24 73.59 
200 rpm 89.14 84.17 83.48 
 
 
3. River sand 
 
Table 9, 
Vibration Acceleration Levels (m/s2) & variation percentage. 
Vibration Acceleration Levels (m/s2) & variation percentage 
 Load (80 N)  Load (120 N)  Load (160 N) 
50 rpm 4.64 26.9 % 3.39 5.3 % 3.21 
 153.9 %  77.3 %  87.2 % 
100 rpm 11.78 49 % 6.01 0 % 6.01 
 30.2 %  75.7 %  57.2 % 
150 rpm 15.34 31.2 % 10.56 10.5 % 9.45 
 27.4 %  25 %  47 % 
200 rpm 19.55 32.5 % 13.2 -5.2 % 13.89 
 
Table 10, 
Rates of Penetration ROP (cm/sec) & variation percentage. 
Rates of Penetration ROP (cm/sec) & variation percentage 
 Load (80 N)  Load (120 N)  Load (160 N) 
50 rpm 0.444 36.5 % 0.606 11.9 % 0.678 
 83.8 %  106.3 %  168.1 % 
100 rpm 0.816 53.2 % 1.25 45.4 % 1.818 
 53.2 %  39.1 %  29.4 % 
150 rpm 1.25 39.12 % 1.739 35.3 % 2.353 
 68.4 %  64.3 %  54.5 % 
200 rpm 2.105 35.7 % 2.857 27.3 % 3.636 
 
 
 
 



Mauwafak A. Tawfik                       Al-Khwarizmi Engineering Journal, Vol. 11, No. 1, P.P.93- 112 (2015) 

109 
 

Table 11, 
Rates of Penetration ROP (cm/sec) & variation percentage. 
Rates of Penetration (ROP) decrement percentage 
 Load (80 N) Load (120 N) Load (160 N) 
50 rpm 25.4 % 22.4 % 20 % 
100 rpm 26.3 % 28.3 % 27.1 % 
150 rpm 45 % 59.7 % 33.1 % 
200 rpm 48.8 % 65 % 55 % 
 
Table 12, 
Power Consumption (Watt). 
Power Consumption (Watt) 
 Load (80 N) Load (120 N) Load (160 N) 
50 rpm 51.57 50.52 48.48 
100 rpm 68.51 66.36 62.14 
150 rpm 79.33 76.95 73.68 
200 rpm 89.5 84.84 83.31 

 
 
Appendix (C) 

 

 
 

Fig. 1. Act. and Theo. Acc. With depth 
(80 N & 50 rpm) 
 

 
 
Fig. 2. Act. and Theo. Acc. With depth 
(80 N & 100 rpm) 
 

 
 

Fig. 3. Act. and Theo. Acc. With depth 
(80 N & 150 rpm) 

 

 
 

Fig. 4. Act. and Theo. Acc. With depth 
(80 N & 200 rpm) 
 

 
 
Fig. 5. Act. and Theo. Acc. With depth 
(120 N & 50 rpm) 
 

 
 

Fig. 6. Act. and Theo. Acc. With depth 
(120 N & 100 rpm) 



Mauwafak A. Tawfik                       Al-Khwarizmi Engineering Journal, Vol. 11, No. 1, P.P.93- 112 (2015) 

110 
 

 
 

Fig. 7. Act. and Theo. Acc. With depth 
(120 N & 150 rpm) 
 

 
 

Fig. 8. Act. and Theo. Acc. With depth 
(120 N & 200 rpm) 
 

 
 

Fig. 9. Act. and Theo. Acc. With depth 
(160 N & 50 rpm) 
 

 
 

Fig. 10. Act. and Theo. Acc. With depth 
(160 N & 100 rpm) 
 

 
 

Fig. 11. Act. and Theo. Acc. With depth 
(160 N & 150 rpm) 
 

 
 

Fig. 12. Act. and Theo. Acc. With depth 
(160 N & 200 rpm) 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 



Mauwafak A. Tawfik                        

Appendix (D) 

Instruments Connection 
 

The diagram below (Figure (1)) illustrates the 
position where the accelerometers were attached 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Fig. 

 

 
 
 
 
 

Y 

X 

Z 

  Al-Khwarizmi Engineering Journal, Vol. 11, No. 1, P.P.

111 
 

The diagram below (Figure (1)) illustrates the 
position where the accelerometers were attached 

to the drill-string for measuring the vibration 
acceleration and how the 
connected to each other. 

 
Fig. 1. Instruments connection diagram. 

Y 

X 

Two accelerometers 
were attached to the 
drill-string at the 
highlighted position. 

The accelerometers 
were in turn connected 
to the charge amplifier.

The charge amplifier transforms the charge, 
which comes from the accelerometers, into 
voltage and amplifies it to be displayed on the 
oscilloscope screen. 

The accelerometers 
are perpendicular to 
each other (one in the 
x-direction and one in 
the y

Khwarizmi Engineering Journal, Vol. 11, No. 1, P.P.93- 112 (2015)

string for measuring the vibration 
acceleration and how the instruments were 

The accelerometers 
were in turn connected 
to the charge amplifier. 

The charge amplifier transforms the charge, 
which comes from the accelerometers, into 

d amplifies it to be displayed on the 

The accelerometers 
are perpendicular to 
each other (one in the 

direction and one in 
the y-direction). 




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