Development of Fish type Robot based on the Analysis of Swimming Motion of Bluefin Tuna Comparison between Tuna-type Fin and Rectangular Fin -

Transcription

1 Development of Fish type Robot based on the Analysis of Swimming Motion of Bluefin Tuna Comparison between Tuna-type Fin and Rectangular Fin - Katsuya KUGAI* Abstract The swimming motion of Tuna type fishes has excellent ability for its speed and efficiency. And some studies have been reported about the most efficient swimming motion by using numerical analysis on two dimensional oscillated wing theory. And several fish type robots are developed based on these studies, but almost all robots have spring held tail fin. Because the tail of tuna type fishes is very smart, and very difficult to implement the tail fin angle actuate mechanism. So, these fish type robots cannot confirm theoretical result by experimental way. So we designed and developed smart caudal fin angle actuating mechanism and made up fish type swimming robot. By using this robot, we made some experiments about the relationship between the swimming motion scheme and the swimming speed. As the result, a theoretical proposal about the most effective motion of caudal fin is confirmed as the fastest swimming speed of the fish type robot. But in these studies, the caudal fin has rectangular shape because of enabling theoretical examination. This situation is the same in many other former studies. We assume that the shape of tuna caudal fin has excellent feature to generate propulsive force because of long time evolution. So, this paper will report about the difference of the propulsive efficiency between tuna type caudal fin and rectangular type caudal fin by experimental and numerical way. Keyword Fin, Lift, Drag, Robot, Swim, Propulsive force 1. Introduction Swimming with the fin has some excellent features toward the screw, that is the fin doesn t get entangled the weeds like the screw which sometimes stop the submarine, and also the fin will make little cloud of settled dust which disturb the visibility. But the propulsive with the fin seems to be less effective than the screw in the meaning of speed and energy efficiency. So we focused on the excellent swimming ability of blue-fin tuna. The maximum speed of the blue-fin tuna is estimated as 80km/h, and it swims over 3000km so as to make a round trip of the Pacific Ocean (Kato.N. et al., 2010). The Calangiform style propulsion of Tuna or Dolphin is modeled with 2-joint bending mechanism by Azuma (1992). Light hill applied the 2-dimensional linearized wing theory toward the 2-joint bending mechanism so as to get accurate analysis of tuna swimming ability. Nakashima and Ono (1996a) (1996b) described the combination of the analytical method in which the slender body theory and the linearized wing theory, and made a suggestion of most effective swimming motion as feathering parameter θ=0.8. However, in this study the motion of fin angle is limited in sinusoidal waveform. According to our study of motion analysis with actual blue-fin tuna, the motion of fin angle seems like arctangent waveform (Kugai and Gomyouta, 2009). So we suggest θf/θw=0.85 motion to get most effective propulsive force through the theoretical and experimental study. Where θf is caudal fin angle and θw is water input angle toward caudal fin (Kugai and Hamaguchi, (2010). To perform this experiment, we developed a tuna type robot which can control tail oscillation and caudal fin angle independently. This robot can reproduce any motion of caudal fin toward tail oscillation with software (Kugai and Horiuchi, (2012). By using this robot, we made an experiment to compare the swimming speed with several controlling way of caudal fin. As the result, we found the θf/θw=0.85 motion produces the fastest speed (Kugai and Ogata, (2014). By using this motion, this paper shows the comparison between tuna type caudal fin and rectangular caudal fin in the meaning of swimming speed. *Kindai University Technical College, Department of Total System Engineering, Mechanical System Engineering Course. 2. Tuna type robot We developed a tuna type robot shown in fig.1. To oscillate the tail, scotch-yoke mechanism is employed so as to converse the rotation of motor to oscillation of tail. This

2 Caudal Fin Angle Controlling Motor Parallel Block Caudal Fin Clearance Scotch-yoke Mechanism The Fulcrum of Tail Oscillation Oscillation Motor Fig.1 Mechanism of tuna type robot The detection of swimming velocity Vx (The detection of pulse width) Water flow sensor PC for program CPU development board The oscillation velocity signal (Analog voltage) Velocity Oscillation control circuit motor Scotch yoke mechanism Motion angle signal θf of the caudal fin (Analog voltage ) The detection of Oscillation velocity Vy Angle control Caudal fin circuit controlling Motor Fig.2 Control system of tuna type robot Encoder Caudal Fin Tuna type robot Controller Float Tape Measure Fig.3 Fish type boat robot mechanism can make accurate sinusoidal waveform. The amplitude of the oscillation is fixed, but frequency can be changed by motor speed. To change the angle of caudal fin, parallel block mechanism is employed. By controlling the clearance between parallel block and caudal fin block, the caudal fin will tilt till the clearance is closed by the water force during tail oscillation. This mechanism provides high rigidity to keep caudal fin angle and smart shape around the caudal fin. This mechanism is controlled by a single board computer with several sensors. Swimming speed is detected by a water flow sensor, and tail oscillation speed is detected by a rotary encoder which is put on the fulcrum of tail oscillation. These

3 signals are transferred to the I/O of single board computer, and the water input angle θw is calculated. From this value, the caudal fin tilt angle θf is decided and the caudal fin controlling motor will actuated so as to realize that angle. This flow is shown in Fig.2. The water proof system of this tuna type robot does not finished yet, so we set up this robot on the ship shaped float and aligned only the caudal fin to sink into the water. This Ship type robot is shown in fig.3. Swimming speed of this ship is measured by taking movie which catches the ship motion and tape measure at the same time. 3. Caudal fin motion scheme When tuna type robot swims, we assumed that the caudal fin moves to forward at constant speed with oscillation. This trajectory can be described as sinusoidal waveform. The tilt angle of this sinusoidal waveform toward swimming direction becomes the water input angle toward caudal fin. Thai is θw. So as to create propulsive force by utilizing lift force of caudal fin, the motion angle θf of caudal fin must be smaller than water input angle θw. So we proposed the caudal fin motion scheme as θf/θw=constant (<1). How to create propulsive force Fx by utilizing lift force L is shown in Fig.4. below. The kinematic relationship between each parameters are as (1) (2) (3) (4) (5) (6) (7) Where and are obtained by experimental result shown in Fig.5. By changing the parameter θf/θw, we calculate the Equations (1) to (7) by using Fig.5 data, we have gotten the mean of propulsive force Fx and the mean of driving force Fy as shown in Fig.6. We can find the case θf/θw=0.85 is most effective. We also made an experiment by using the Fish type boat robot so as to compare swimming speed toward θf/θw changes. By applying the control software to change θf/θw value, we measured the swimming speed of the Fish type boat robot. This experiment is not quantitative because of the drag force of ship is not equal to tuna body. But qualitative comparison will have the meaning of propulsive force. The result is shown in Fig.7. We also made a comparison with feathering parameter θ=0.8 (Nakashima and Ono, 1996a). Then we can find the caudal fin motion θf/θw=0.85 is most effective in the meaning of numerical and experimental examination. Swimming Direction Fx Fy Fig.4 L θa D θf θw:input Angle of Flow θw θf:motion Angle of Caudal Fin θa:attacking Angle L:Lift Force D:Drag Force Fx:Propulsive Force Fy:Driving Force Caudal fin angle toward water flow to generate propulsive force

4 Fig.5 Lift and Drag coefficient of tuna type caudal fin Fig.6 Propulsive efficiency toward θf/θw Fig.7 The speed of Fish type boat robot toward θf/θw value 4. Tuna type caudal fin and rectangular caudal fin By using the result of upper examination. We planned to evaluate the efficiency of caudal fin of Bluefin tuna. So, we prepared the 1/1 scale caudal fin model of actual Bluefin tuna and rectangular caudal fin which has same wing area and span. These caudal fins are made by wood and they can be considered to have rigid characteristic. So these fins do not reproduce the elasticity of actual caudal fin of Bluefin tuna. We think the effect of elasticity must be considered in future study. These caudal fin models are shown in Fig.8 and Fig.9. We put the both caudal fin on the Fish type boat robot, and made a swimming experiment by using θf/θw=0.85 caudal fin motion scheme. The speed difference between tuna type caudal fin and rectangular caudal fin is shown in Fig.10. The horizontal axis of Fig.10 is the frequency of tail oscillation, and the vertical axis is swimming speed of fish type boat robot. According to the increasing of frequency, swimming speed will become high. But we found the rectangular caudal fin provides higher speed than tuna type caudal fin. This result is just the opposite of our surmise because we suppose that the tuna caudal fin must have most effective shape to generate the propulsive force. So, we decided to clarify the reason of this result of the experiment. At first, we checked the lift and drag coefficient of both caudal fin. As we surmised, both caudal fins have almost same characteristics as shown in Fig.11. Needless to say, this data cannot explain Fig.10 result that is rectangular caudal fin is faster than tuna type caudal fin. Therefore we assume that the combination of caudal fin shape and caudal fin motion scheme must have some effect to the efficiency of propulsive force generation. So as to think about this, it needs some contrivance to treat the shape of tuna type fin into theoretical examination. So we suggest the conversion of the swept back angle of tuna type caudal fin to the swept back distance. This image is shown in Fig.12. As the combination with this caudal fin modeling, we prepared the three types of caudal fin motion scheme. The first is θf/θw=0.85 motion, and the second is feathering parameter θ=0.8 motion (Nakashima and Ono, 1996a). And the last is spring held caudal fin motion. The motion of tail oscillation is settled as 2Hz cosine waveform and its amplitude is 0.08m. These are shown in Fig.13.

5 700mm 700mm 140mm 70mm Fig.8 1/1 Scale model of Bluefin tuna caudal fin Fig.9 Rectangular caudal fin (same area and span) Fig.10 Swimming Velocity by using Both Fin Fig.11 Lift and Drag coefficient of both caudal fin Fig.12 Replacing of sweptback angle to sweptback distance As the result of simulation, we got the waveform shown in Fig.14 to Fig.16. The water input angle toward caudal fin and attack angle of caudal fin with the caudal fin motion θf/θw=0.85 is shown in Fig.14. When swept back distance is zero, we can find the attacking angle θa is kept to generate the lift force. But the swept back angle is 50mm case, actual water input angle at the leading edge of caudal fin changes with the angle motion. Because of caudal fin angle is controlled with the water input angle of the position that the swept back angle is zero. So, the attacking angle becomes near 90 degrees around the both end of tail oscillation. This must decrease the efficiency of generating propulsive force. In the case of feathering parameter θ=0.8, as shown in Fig.15, the situation is almost same with Fig.14. When the swept back distance is zero, the attacking angle θa is kept to generate the lift force. But the swept back angle is 50mm case, the attacking angle becomes near 90 degrees around the both end of tail oscillation. In the case of spring held caudal fin, as shown in Fig.16, when swept back distance is zero, the attacking angle becomes near 90 degrees around the both end of tail oscillation. Against that, when swept back distance is 50mm, the attacking angle is reduced around the both end of tail fin oscillation. This suggests some swept back distance contributes the increasing of efficiency of generating propulsive force.

6 Fig.13 Tail Oscillation and Caudal Fin Motion Angle (a) Swept back distance = 0mm Fig.14 (b) Swept back distance = 50mm The relationship between water input angle and attack angle with caudal fin motion scheme θf/θw=0.85 (a) Swept back distance = 0mm Fig.15 (b) Swept back distance = 50mm The relationship between water input angle and attack angle with caudal fin motion scheme θ=0.8

7 (a) Swept back distance = 0mm Fig.16 The relationship between water input angle and attack angle with spring held caudal fin The summery of this numerical experiments is shown in Fig.17. Under the caudal fin motion scheme θf/θw=0.85 and θ=0.8, the propulsive efficiency decreases in accordance with the increasing of sweepback distance. This means, under these caudal fin motion, the propulsive efficiency of rectangular caudal fin becomes greater than tuna type caudal fin. On the other hand, with respect to spring held caudal fin, the propulsive efficiency show the peak value at the sweepback distance is 0.05m. This means, under the spring held caudal fin motion, the propulsive efficiency of tuna type caudal fin might be greater than rectangular caudal fin. At this time, we have to look back Fig.13. The notable feature of the caudal fin motion when it is held by spring, the phase of motion delays about 35 degrees toward tail oscillation. So, we simulated the effect of phase delay on the motion scheme θf/θw=0.85. This results is shown in Fig.18. We can find in the case of -30 degrees delay, at the sweepback distance is 0.05m, propulsive efficiency shows the peak value. This result gives us the thinking that is some motion delay of caudal fin brings the propulsive effectiveness of tuna type caudal fin. But, in this simulation, a question is still remaining. That is the most effective case is no sweepback distance and no delay of caudal fin motion. So, from now we have to study more about the combination of caudal fin motion and caudal fin shape. Furthermore, we may have to consider about the elasticity of actual caudal fin of blue fin tuna. Fig.17 Propulsive and Driving Forces toward Sweptback Distance

8 Fig.18 Propulsive and Driving Force toward Caudal fin Motion Delay 5. Conclusion From experiments by using Fish type boat robot, we found the rectangular caudal fin generates bigger propulsive force than tuna type caudal fin, under the caudal fin motion θf/θw=0.85. So we searched for effective caudal fin motion for tuna type caudal fin. Through the numerical calculation, spring held caudal fin motion leads good propulsive efficiency for tuna type caudal fin. In this case, the motion of caudal fin has some delay toward tail oscillation. Therefore we tried to add some phase delay toward the caudal fin motion θf/θw=0.85. As the result, we found even if the caudal fin motion is θf/θw=0.85, some phase delay leads good propulsive efficiency for tuna type caudal fin. However, the most effective case is no delay of caudal fin motion with rectangular caudal fin. Therefore, from now, we have to study more about the combination of caudal fin motion and caudal fin shape. In the advance of our study, we assume that we may have to consider about the elasticity of caudal fin like actual blue fin tuna. References Azuma.A, The Bio kinetics of Flying and Swimming, Springer-Verlag Tokyo (1992) Okano.S, Study on swimming behavior of cultured Pacific bluefin tuna using biotelemetry, Kindai University Faculty of Agriculture Bulletin, No.39 (2006), p.78~82 Kato.N. et al., Aero Aqua Bio-Mechanics, Study Group of Aero Aqua Bio-Mechanisms (2010) Kugai.K and Katayama.Y, Analysis of Swimming Motion of Blue Fin Tuna and Application to the Robot(2nd report), The Japan Society of Mechanical Engineers 2008Annual Conference, Vol.6, p93-94 Kugai.K and Gomyouta.Y, Analysis of Swimming Ability of Blue Fin Tuna, Research Bulletin of KINDAI University Technical College, No.3 (2009) Kugai.K and Hamaguchi.R, Development of Fish type Robot based on the Analysis of Swimming Motion of Blue Fin Tuna, Research Bulletin of KINDAI University Technical College, No.4 (2010) Kugai.K and Horiuchi.M, Development of Fish type Robot based on the Analysis of Swimming Motion of Blue Fin Tuna, Research Bulletin of KINDAI University Technical College, No.6 (2012) Kugai.K and Ogata.K, Development of Fish type Robot based on the Analysis of Swimming Motion of Blue Fin Tuna, Research Bulletin of KINDAI University Technical College, No.8 (2014) Hirata.K, Propulsion Performance of the Experimental Fish Robot, Japan Society for Design Engineering, Research Presentation Lecture of 2000 Fall Nakashima.M and Ono.K, Dynamics of Two-Joint Dolphinlike Propulsion Mechanism (1st Report, Analytical Model and Analysis Method), Journal of The Japan Society of Mechanical Engineers (B Edition), Volume62, Issue600 (1996a) Nakashima.M and Ono.K, Dynamics of Two-Joint Dolphinlike Propulsion Mechanism (2nd Report, Optimum Motion for Primary Body Form), Journal of The Japan Society of Mechanical Engineers (B Edition), Volume62, Issue602 (1996b) Nakashima.M and Ono.K, Dynamics of a Two-Joint Dolphinlike Propulsion Mechanism (5th Report, Analysis of a model of Spring Support for Second Joint), Journal of The Japan Society of Mechanical Engineers (B Edition), Volume66, Issue643 (2000) Nakashima.M, Fun of swimming movement of fish and dolphins, Journal of Society of Biomechanisms Japan, Vol.28, No1 (2004)