The purpose of this work is to create a new remotely controlled mini submarine used in robotics or in toy industry. To prepare the numerical and mathematical models for identification of the most optimum ratio alfa1/alfa2 of raster discs, number of raster notches, and a required angle of one disc turn beta, for changing the flow direction and, simultaneously, the sailing direction of the mini submarin

M. Ragulskis

R. P. Bansevicius

R. Rimasauskiene

English

Rimasauskiene, R.

Bansevicius, R. P.

Ragulskis, M.

Journal of Mechanical Engineering, Automation and Control Systems

  VIBROMECHANIKA.  JOURNAL OF  VIBROENGINEERING.  JUNE   2008,   VOLUME  10,  ISSUE  2,  ISSN 1392-8716  176 355. Analysis of mini submarine control based on moiré interferometry   R. Rimasauskiene, R. P. Bansevicius Kaunas University of Technology Kestucio str. 27, LT-44312, Kaunas, Lithuania M. Ragulskis Kaunas University of Technology Studentu str. 50, LT-51368, Kaunas, Lithuania E-mail:  ruta.mitruleviciute@ktu.lt     ramutis.bansevicius@ktu.lt     minvydas.ragulskis@ktu.lt  (Received 2 April 2008; accepted 13 June 2008)          Abstract. The purpose of this work is to create a new remotely controlled mini submarine used in robotics or in toy industry. To prepare the numerical and mathematical models for identification of the most optimum ratio alfa1/alfa2 of raster discs, number of raster notches, and a required angle of one disc turn beta, for changing the flow direction and, simultaneously, the sailing direction of the mini submarine.  Keywords: Moiré interferometry, Mini submarine, Mini robot, Piezoelectric actuator.  Introduction   Mini submarines [1]  or robots [2] with piezoceramic actuators [3, 4] are widely described in scientific and engineering sources. Our goal was to develop a new type of mini submarine, operation of which is based on moiré interference pattern [5, 6]. This article describes the new patented mini submarine which is controlled due to the optical interference effect, based on the moiré interferometry. Mini submarine examined in this article is composed of housing and control unit with piezoceramic actuator. Ppropeller, which is connected to the motor, is embdded inside the cylinder body. Control device with piezoceramic actuator, comprised of two raster steel disks, fastened with fastening rings, is fixed on the other side of the body. Number of raster notches of one of the disks is n, and the same number for the other is (n+1) and it has the possibility to rotate in respect of the first disk. One fastening ring with raster steel disk is connected through the metal rods to the multilayer piezoceramic elements, which are interlinked with control unit and generato . Novelty of this mini submarine is that one of the parts of its control device, i.e. membrane, is comprised of two raster steel disks and the swimming direction of this mini robot is controlled by means of optical interferenc effect generated between them. Numerical and mathematical models of the effect of moiré interference occurring in the mini submarine w re investigated. The dependence of the membrane permeability on the turn angle beta of one of the raster steel disks is established and presented, as well as the dependence of the permeability on the ratio alfa1/alfa2. These relationships allow determining and designing of the best possible control strategies for the mini submarine.        Original patented construction and the impleentation of control strategies of the mini submarine is the object of analysis of this article.  Construction of the mini submarine  Mini submarine presented in this article has functional possibility to move in three-dimensional space (under water) Mini submarine is comprised of: cylinder body 1 with embedded propeller  2 that is connected to the motor 3; control device, fixed on the other side of the body 1, with piezoceramic actuator, composed of two raster el disks 4, 5, which are fastened with fastening rings 6, 7; number of raster notches of raster steel disk 4 is n; number of raster notches of raster steel disk 5 is (n+1) and it has the possibility to rotate in respect of the first disk; one fastening ring with raster steel disk is connected through the metal rods 8, 9 to the multilayer piezoceramic elements 10, 11, which are interlinked with control unit 12 and generator 13. The structural layout of the underwater mini submarine is shown on Figure 1. 355. ANALYSIS OF MINI SUBMARINE CONTROL BASED ON MOIRÉ INTERFEROMETRY.  R. RIMASAUSKIENE, R. P. BANSEVICIUS AND M. RAGULSKIS    VIBROMECHANIKA.  JOURNAL OF  VIBROENGINEERING.  JUNE   2008,   VOLUME  10,  ISSUE  2,  ISSN 1392-8716  177  Fig. 1. 1 – Cylinder body, 2 – propeller, 3 – motor, 4, 5 –raster disks, 6, 7 – fastening rings, 8, 9 – metal rods, 10, 11 – multilayer piezoceramic actuators, 12 – control unit, 13 – generator  After the motor 3 is started propeller 2 begins to rotate and to pump the water from the outside creating the water flow inside of the cylinder body 1. Then generator 13 is turned on remotely and passes the signal to the control unit 12, stimulates static and quasistatic shifts in the piezoceramic elements 10, 11, that transmit rotation motion through the metal rods 8, 9 to the raster stel disk 5, fastened in the fastening ring 7. Direction of the water flow through the membrane (composed of two raster steel disks 4 and 5) is controlled by changing the turn angle of raster disk 5 in respect of raster disk 4.   Construction of control membrane        New structural elements (ratio of the raster notches of steel disks n/n+1, ratio of angles of open and closed disk areas alfa1/alfa2) allow achieving increased mini submarine’s maneuverability in comparison with similar devices.       The control membrane is made of two steel disks with raster notches. The number of raster notches of one of these disks is n and number of notches for the other is n+1. Such ratio is necessary in order to obtain a single interference fringe.        By using ratio n/n+2 we’ll get two interference fringes (fig. 2). And by choosing ratio n/n+3 we’ll get the pattern presented in figure 3, with three interference fringes, and the required control of underwater mini robot we’ll not be feasible.      Fig. 2. Effect with two interference fringes Fig. 3. Effect with three          interference fringes When proper ratio of number of raster notches of the steel disks is chosen and only one interference fringe is obtained it is also necessary to choose proper ratio of angles of open and closed disk areas alfa1/alfa2 (fig. 4) and the flow would be allowed through only one side of the membrane and the other side would be fully closed.    Fig. 4. Ratio alfa1/alfa2 of open and closed areas of the disk raster  notches   After completing mathematical modeling relationship % (beta) was determined. This dependence demonstrates how the change of beta, the turn angle of one of the raster disks in respect to the other, influences the change in permeability at different membrane sides (left and right) (fig. 5). If maximum permeability is achieved through one side, on the other side permeability is minimal. In intermediate positions similar permeability on both sides can be obtained.  Permeability through the top and the bottom of membrane was not examined, but we could suppose that it should be similar to the results of performed modeling when the flow is allowed to pass through the sides of membrane. {x, y, z, φx ,φy, φz}  355. ANALYSIS OF MINI SUBMARINE CONTROL BASED ON MOIRÉ INTERFEROMETRY.  R. RIMASAUSKIENE, R. P. BANSEVICIUS AND M. RAGULSKIS    VIBROMECHANIKA.  JOURNAL OF  VIBROENGINEERING.  JUNE   2008,   VOLUME  10,  ISSUE  2,  ISSN 1392-8716  178 02040608010012000,030,060,090,120,150,180,210,240,27 0,30,330,360,390,420,450,48beta, radPermeability, %Permeability through the left side Permeability through the right side Total permeability Fig. 5. Relationship % (beta) When one raster steel disk is turned in respect to the other by 0 rad angle water flows through the right side of membrane and mini submarine turns to the left. When angle is changed to 0.05 rad – water flows through the left side only and the submarine turns to the right. As we see from the graph (fig. 5), cycles repeat if we furthe vary the angle. There are also possible transitional positions of swimming direction. For mathematical modeling ratio alfa1/alfa2 =0.3 was chosen because only in this case full closure at one side and sufficient total permeability can be obtained. This can be seen from figure 6 where dependence % (alfa1/alfa2) is plotted in the bar graph. 0204060801001200 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1alfa1/alfa2, radPermeability, %Permeability through the left side Permeability through the right side Total permeability Fig. 6. Dependence % (alfa1/alfa2)  As it was mentioned before, one of the raster disks  tightly fastened inside the housing of the robot, and another is fastened to the precise piezoceramic control device and has the possibility to rotate in respect to the first disk. While the control device does not receive any signal, the flow is passing just through the one side of the membrane (Fig. 7). When the signal is generated and the second disk turns at a required angle, the direction of membrane’s permeability, and the submarine swimming direction are changed (Fig. 8). It is also possible that the top or the bottom part of membrane will be opened by changing turn angle and the robot will swim upwards or downwards (Fig. 9, 10).  355. ANALYSIS OF MINI SUBMARINE CONTROL BASED ON MOIRÉ INTERFEROMETRY.  R. RIMASAUSKIENE, R. P. BANSEVICIUS AND M. RAGULSKIS    VIBROMECHANIKA.  JOURNAL OF  VIBROENGINEERING.  JUNE   2008,   VOLUME  10,  ISSUE  2,  ISSN 1392-8716  179                                                       Fig. 7. Flow through the right side   Fig. 8. Flow through the left side    Fig. 9. Flow through the bottom part  Fig. 10. Flow through the top part  Technology for the production of raster steel disk  Technology for the production of disks is quite complicated as the product is small (about 32 mm diameter), made from very thin 0.3 mm thickness steel sheet, and the laser is used for raster notches to cut ut. It is necessary to choose the best possible construction, because cutting width of the laser is constrained, also the sheet is heating and the deformation occurs during the manufacture.  For the construction of control device of this mini submarine considerable precision of raster steel disks s required in order to obtain proper interference effect. A proper ratio of angles of open and closed disk areas α1/α2 is particularly important and only when this ratio is equal to 0.3 we can achieve a proper permeability through one side of the membrane and to control swimming direction of mini submarine.  Conclusions  The design and control principles of the mini submarine based on moiré interferometry are described n this article. The mathematical and digital models of m iré interference between the fixed and the rotating disk are developed. These models allow identifying the disk control strategy for changing the swimming direction of themini submarine. Proper ratio alfa1/alfa2, which allows ensuring nearly full closure at one side of the membrane, was determined. Turning angles of one of the raster steel disks beta, which allows us to control the swimming direction f mini submarine by, also where determined.  References  [1] Madsen H. Ø., Christensen P. and Lauridsen K. Securing the operational reliability of an autonomous mini-submarine. Reliability Engineering & System Safety, Volume 68, Issue 1, April 2000, Pages 7-16. [2] Kim B., Lee M. G., Lee Y. P., Kim Y., Ho Lee G. An earthworm-like micro robot using shape memory alloy actuator. Sensors and Actuators A: Physical, Volume 125, Issue 2, 10 January 2006, Pages 429-437. [3] Lin Ch. and Yang S. Precise positioning of piezo-actuated stages using hysteresis-observer based control. Mechatronics, Volume 16, Issue 7, September 2006, Pages 417-426. [4] Tönshoff H.-K., Kruse U. and Mahner H.-J. Sensor Systems for Industrial Applications Under Water. CIRP Annals - Manufacturing Technology, Volume 48, Issue 1, 1999, Pages 445-448. [5] Wiederkehr R. S., Salvadori M. C., Brugger J., Degasperi F. T., Cattani M. The gas flow rate increase obtained by an oscillating piezoelectric actuator on a micronozzle.  Sensors and Actuators A: Physical, Volume 144, Issue 1, 28 May 2008, Pages 154-160 [6] Patorski K., Kujawinska M.  The Moire Fringe Technique. Elsvier science publisher, Netherlans, 1993. [7] Post D.,  Han B., Ifju P.  High Sensitivity Moire: Experimental Analysis for Mechanics and Materials. Springer-Verlag, January 1994.        

Analysis of mini submarine control based on moiré interferometry

Journal of Mechatronics and Artificial Intelligence in Engineering

JVE International

Journal of Vibroengineering

  VIBROMECHANIKA.  JOURNAL OF  VIBROENGINEERING.  JUNE   2008,   VOLUME  10,  ISSUE  2,  ISSN 1392-8716 
 
176 
355. Analysis of mini submarine control based on moiré interferometry 
 
 
R. Rimasauskiene, R. P. Bansevicius 
Kaunas University of Technology 
Kestucio str. 27, LT-44312, Kaunas, Lithuania 
M. Ragulskis 
Kaunas University of Technology 
Studentu str. 50, LT-51368, Kaunas, Lithuania 
E-mail: ruta.mitruleviciute@ktu.lt     ramutis.bansevicius@ktu.lt     minvydas.ragulskis@ktu.lt 
 
(Received 2 April 2008; accepted 13 June 2008) 
 
 
 
 
 
  
 
 
Abstract. The purpose of this work is to create a new remotely controlled mini submarine used in robotics or in toy 
industry. To prepare the numerical and mathematical models for identification of the most optimum ratio alfa1/alfa2 of 
raster discs, number of raster notches, and a required angle of one disc turn beta, for changing the flow direction and, 
simultaneously, the sailing direction of the mini submarine. 
 
Keywords: Moiré interferometry, Mini submarine, Mini robot, Piezoelectric actuator. 
 
Introduction  
 
Mini submarines [1]  or robots [2] with piezoceramic 
actuators [3, 4] are widely described in scientific and 
engineering sources. Our goal was to develop a new type 
of mini submarine, operation of which is based on moiré 
interference pattern [5, 6]. 
This article describes the new patented mini submarine 
which is controlled due to the optical interference effect, 
based on the moiré interferometry. 
Mini submarine examined in this article is composed of 
housing and control unit with piezoceramic actuator. 
Ppropeller, which is connected to the motor, is embedded 
inside the cylinder body. Control device with piezoceramic 
actuator, comprised of two raster steel disks, fastened with 
fastening rings, is fixed on the other side of the body. 
Number of raster notches of one of the disks is n, and the 
same number for the other is (n+1) and it has the 
possibility to rotate in respect of the first disk. One 
fastening ring with raster steel disk is connected through 
the metal rods to the multilayer piezoceramic elements, 
which are interlinked with control unit and generator. 
Novelty of this mini submarine is that one of the parts of 
its control device, i.e. membrane, is comprised of two 
raster steel disks and the swimming direction of this mini 
robot is controlled by means of optical interference effect 
generated between them. 
Numerical and mathematical models of the effect of 
moiré interference occurring in the mini submarine were 
investigated. The dependence of the membrane 
permeability on the turn angle beta of one of the raster 
steel disks is established and presented, as well as the 
dependence of the permeability on the ratio alfa1/alfa2. 
These relationships allow determining and designing of the 
best possible control strategies for the mini submarine. 
       Original patented construction and the implementation 
of control strategies of the mini submarine is the object of 
analysis of this article. 
 
Construction of the mini submarine 
 
Mini submarine presented in this article has functional 
possibility to move in three-dimensional space (under 
water) Mini submarine is comprised of: cylinder body 1 
with embedded propeller  2 that is connected to the motor 
3; control device, fixed on the other side of the body 1, 
with piezoceramic actuator, composed of two raster steel 
disks 4, 5, which are fastened with fastening rings 6, 7; 
number of raster notches of raster steel disk 4 is n; number 
of raster notches of raster steel disk 5 is (n+1) and it has 
the possibility to rotate in respect of the first disk; one 
fastening ring with raster steel disk is connected through 
the metal rods 8, 9 to the multilayer piezoceramic elements 
10, 11, which are interlinked with control unit 12 and 
generator 13. 
The structural layout of the underwater mini submarine 
is shown on Figure 1.
 355. ANALYSIS OF MINI SUBMARINE CONTROL BASED ON MOIRÉ INTERFEROMETRY.  R. RIMASAUSKIENE, R. P. BANSEVICIUS AND M. RAGULSKIS 
 
 
 VIBROMECHANIKA.  JOURNAL OF  VIBROENGINEERING.  JUNE   2008,   VOLUME  10,  ISSUE  2,  ISSN 1392-8716 
 
177 
 
Fig. 1. 1 – Cylinder body, 2 – propeller, 3 – motor, 4, 5 – raster disks, 6, 7 – fastening rings, 8, 9 – metal rods, 10, 11 – multilayer 
piezoceramic actuators, 12 – control unit, 13 – generator 
 
After the motor 3 is started propeller 2 begins to rotate 
and to pump the water from the outside creating the water 
flow inside of the cylinder body 1. Then generator 13 is 
turned on remotely and passes the signal to the control unit 
12, stimulates static and quasistatic shifts in the 
piezoceramic elements 10, 11, that transmit rotation 
motion through the metal rods 8, 9 to the raster steel disk 
5, fastened in the fastening ring 7. Direction of the water 
flow through the membrane (composed of two raster steel 
disks 4 and 5) is controlled by changing the turn angle of 
raster disk 5 in respect of raster disk 4.  
 
Construction of control membrane 
 
      New structural elements (ratio of the raster notches of 
steel disks n/n+1, ratio of angles of open and closed disk 
areas alfa1/alfa2) allow achieving increased mini 
submarine’s maneuverability in comparison with similar 
devices. 
      The control membrane is made of two steel disks with 
raster notches. The number of raster notches of one of 
these disks is n and number of notches for the other is n+1. 
Such ratio is necessary in order to obtain a single 
interference fringe.  
      By using ratio n/n+2 we’ll get two interference fringes 
(fig. 2). And by choosing ratio n/n+3 we’ll get the pattern 
presented in figure 3, with three interference fringes, and 
the required control of underwater mini robot we’ll not be 
feasible. 
 
 
 
 
 
Fig. 2. Effect with two 
interference fringes 
Fig. 3. Effect with three           
interference fringes 
When proper ratio of number of raster notches of the 
steel disks is chosen and only one interference fringe is 
obtained it is also necessary to choose proper ratio of 
angles of open and closed disk areas alfa1/alfa2 (fig. 4) 
and the flow would be allowed through only one side of the 
membrane and the other side would be fully closed. 
 
 
 
Fig. 4. Ratio alfa1/alfa2 of open and closed areas of the disk 
raster  notches 
 
 
After completing mathematical modeling relationship 
% (beta) was determined. This dependence demonstrates 
how the change of beta, the turn angle of one of the raster 
disks in respect to the other, influences the change in 
permeability at different membrane sides (left and right) 
(fig. 5). If maximum permeability is achieved through one 
side, on the other side permeability is minimal. In 
intermediate positions similar permeability on both sides 
can be obtained.  
Permeability through the top and the bottom of 
membrane was not examined, but we could suppose that it 
should be similar to the results of performed modeling 
when the flow is allowed to pass through the sides of 
membrane. 
{x, y, z, φx ,φy, φz} 
 355. ANALYSIS OF MINI SUBMARINE CONTROL BASED ON MOIRÉ INTERFEROMETRY.  R. RIMASAUSKIENE, R. P. BANSEVICIUS AND M. RAGULSKIS 
 
 
 VIBROMECHANIKA.  JOURNAL OF  VIBROENGINEERING.  JUNE   2008,   VOLUME  10,  ISSUE  2,  ISSN 1392-8716 
 
178 
0
20
40
60
80
100
120
0
0,0
3
0,0
6
0,0
9
0,1
2
0,1
5
0,1
8
0,2
1
0,2
4
0,2
7 0,3 0,3
3
0,3
6
0,3
9
0,4
2
0,4
5
0,4
8
beta, rad
Pe
rm
ea
bi
lit
y,
 
%
Permeability through the left side Permeability through the right side Total permeability
 
Fig. 5. Relationship % (beta)
 
When one raster steel disk is turned in respect to the 
other by 0 rad angle water flows through the right side of 
membrane and mini submarine turns to the left. When 
angle is changed to 0.05 rad – water flows through the left 
side only and the submarine turns to the right. As we see 
from the graph (fig. 5), cycles repeat if we further vary the 
angle. 
There are also possible transitional positions of 
swimming direction. 
For mathematical modeling ratio alfa1/alfa2 =0.3 was 
chosen because only in this case full closure at one side 
and sufficient total permeability can be obtained. This can 
be seen from figure 6 where dependence % (alfa1/alfa2) is 
plotted in the bar graph. 
0
20
40
60
80
100
120
0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1
alfa1/alfa2, rad
Pe
rm
ea
bi
lit
y,
 
%
Permeability through the left side Permeability through the right side Total permeability
 
Fig. 6. Dependence % (alfa1/alfa2)
 
 
As it was mentioned before, one of the raster disks is 
tightly fastened inside the housing of the robot, and 
another is fastened to the precise piezoceramic control 
device and has the possibility to rotate in respect to the first 
disk. 
While the control device does not receive any signal, 
the flow is passing just through the one side of the 
membrane (Fig. 7). When the signal is generated and the 
second disk turns at a required angle, the direction of 
membrane’s permeability, and the submarine swimming 
direction are changed (Fig. 8). It is also possible that the 
top or the bottom part of membrane will be opened by 
changing turn angle and the robot will swim upwards or 
downwards (Fig. 9, 10). 
 355. ANALYSIS OF MINI SUBMARINE CONTROL BASED ON MOIRÉ INTERFEROMETRY.  R. RIMASAUSKIENE, R. P. BANSEVICIUS AND M. RAGULSKIS 
 
 
 VIBROMECHANIKA.  JOURNAL OF  VIBROENGINEERING.  JUNE   2008,   VOLUME  10,  ISSUE  2,  ISSN 1392-8716 
 
179 
 
                                 
                   
 
Fig. 7. Flow through the right side 
 
 
Fig. 8. Flow through the left side 
  
 
Fig. 9. Flow through the bottom part 
 
Fig. 10. Flow through the top part 
 
Technology for the production of raster steel disk 
 
Technology for the production of disks is quite 
complicated as the product is small (about 32 mm 
diameter), made from very thin 0.3 mm thickness steel 
sheet, and the laser is used for raster notches to cut out. It 
is necessary to choose the best possible construction, 
because cutting width of the laser is constrained, also the 
sheet is heating and the deformation occurs during the 
manufacture.  
For the construction of control device of this mini 
submarine considerable precision of raster steel disks is 
required in order to obtain proper interference effect. A 
proper ratio of angles of open and closed disk areas α1/α2 is 
particularly important and only when this ratio is equal to 
0.3 we can achieve a proper permeability through one side 
of the membrane and to control swimming direction of 
mini submarine. 
 
Conclusions 
 
The design and control principles of the mini 
submarine based on moiré interferometry are described in 
this article. The mathematical and digital models of moiré 
interference between the fixed and the rotating disk are 
developed. These models allow identifying the disk control 
strategy for changing the swimming direction of the mini 
submarine. Proper ratio alfa1/alfa2, which allows ensuring 
nearly full closure at one side of the membrane, was 
determined. Turning angles of one of the raster steel disks 
beta, which allows us to control the swimming direction of 
mini submarine by, also where determined. 
 
References 
 
[1] Madsen H. Ø., Christensen P. and Lauridsen K. Securing 
the operational reliability of an autonomous mini-submarine. 
Reliability Engineering & System Safety, Volume 68, Issue 
1, April 2000, Pages 7-16. 
[2] Kim B., Lee M. G., Lee Y. P., Kim Y., Ho Lee G. An 
earthworm-like micro robot using shape memory alloy 
actuator. Sensors and Actuators A: Physical, Volume 125, 
Issue 2, 10 January 2006, Pages 429-437. 
[3] Lin Ch. and Yang S. Precise positioning of piezo-actuated 
stages using hysteresis-observer based control. 
Mechatronics, Volume 16, Issue 7, September 2006, Pages 
417-426. 
[4] Tönshoff H.-K., Kruse U. and Mahner H.-J. Sensor 
Systems for Industrial Applications Under Water. CIRP 
Annals - Manufacturing Technology, Volume 48, Issue 
1, 1999, Pages 445-448. 
[5] Wiederkehr R. S., Salvadori M. C., Brugger J., Degasperi 
F. T., Cattani M. The gas flow rate increase obtained by an 
oscillating piezoelectric actuator on a micronozzle.  
Sensors and Actuators A: Physical, Volume 144, Issue 1, 28 
May 2008, Pages 154-160 
[6] Patorski K., Kujawinska M. The Moire Fringe Technique. 
Elsvier science publisher, Netherlans, 1993. 
[7] Post D.,  Han B., Ifju P. High Sensitivity Moire: 
Experimental Analysis for Mechanics and Materials. 
Springer-Verlag, January 1994. 
 
 
 
 
 
 
 


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Analysis of mini submarine control based on moiré interferometry

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