Flexible Caudal Fin Research Articles

Numerical Study on the Hydrodynamic Performance of a Flexible Caudal Fin with Different Trailing-Edge Shapes.

This paper presents a three-dimensional fluid-structure-coupled simulation of a flexible caudal fin with different trailing-edge shapes. The influences of caudal-fin shape on hydrodynamic performance are investigated by comparing the results of a simplified model of a square caudal fin with forked and deeply forked caudal fins under a wider range of non-dimensional flapping frequency, 0.6 < f* < 1.5, where f* is the ratio of flapping frequency to the natural frequency of each caudal fin, i.e., f* = f/fn. The leading edge of each caudal fin is forced to oscillate vertically in a water tank with zero free-stream conditions. The numerical results show that the amount of forking in the geometry of the caudal fin has significant effects on its hydrodynamic performance. A comparison of thrust coefficients shows that the square caudal fin has a greater thrust coefficient in the non-dimensional frequency range of 0.6 < f* < 1.2, while the deeply forked caudal fin generates higher thrust when 1.2 < f* < 1.5. In terms of propulsive efficiency, the square caudal fin is more efficient when 0.6 < f* < 0.9, while the propulsive efficiency of a deeply forked caudal fin is significantly enhanced when 0.9 < f* < 1.5. Based on our results, the deeply forked caudal fin has greater thrust coefficients and a higher propulsive efficiency in a higher frequency range than the natural frequency of each caudal fin. The thrust characteristics and flow fields around each caudal fin are investigated in detail.

CMBUV: A Composite-Mechanism Bioinspired Underwater Vehicle Integrated With Elasticity and Shear Damping Possesses High-Performance Capability

Benefiting from the potential advantages of low noise, high efficiency and little disturbance, bionic propulsion has attracted wide attentions. Compared with the rigid structure, the performance of the elastic propulsion structure such as flexible caudal fin and passive compliant joint has been improved, yet the effective frequency range is limited due to the single mechanism. The optimal propulsion can only be produced in a certain frequency range. In this article, a biological passive peduncle joint integrated with the composite mechanism of elasticity and shear damping is proposed, solving the problem of the narrow frequency range of effective propulsive capacity. Through the optimal regulation of the elastic function at a certain frequency range and characterization of the damping function which increases with frequency, the response features of the passive joint are optimized over a wide range of frequencies, thereby improving the propulsive performance of the composite-mechanism bioinspired underwater vehicle (CMBUV). A dynamic model is built and the deformation analysis of the compliant caudal fin is carried out. The propulsive efficiency is characterized, and the results indicate that the compliant caudal fin modulates the power transmission for enhancing thrust production. Extensive simulations and experiments reveal that the CMBUV achieves both high swimming speed with 4.42 body length per second and low cost of transport with 90.33 J kg <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$^{-1}$</tex-math></inline-formula> m <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$^{-1}$</tex-math></inline-formula> . Bioinspired propulsion from this study takes advantage of undulating propulsion of natural fish, offering valuable insights into performing marine tasks in ocean environments.

Underwater dynamic hysteresis modeling and feedforward control of flexible caudal fin actuated by macro fiber composites

Underwater bionic robotics and vehicles that use flexible structures as power sources have attracted considerable attention. Thus, the underwater dynamic behaviors of the flexible structure of a variable cross-section actuated by smart actuators must be further investigated. In this study, underwater dynamic hysteresis modeling and feedforward compensation of a flexible caudal fin driven by macro fiber composites (MFC) at different frequencies were investigated. The MFC-actuated flexible caudal fin is considered a Euler–Bernoulli beam. A revised hydrodynamic function governed by the thickness of the viscous layer and the gap-to-width ratio of the cross-section was developed. Then, a characteristic-frequency-dependent extended transform function model is proposed for the hydrodynamic response of a non-uniform beam. An asymmetric hysteresis model is presented to characterize the rate-independent hysteresis behavior of the MFC actuators. Further, the underwater dynamic equation of the MFC-actuated caudal fin with hysteresis is obtained by connecting the two established models in series. Experiments demonstrate the dynamic behavior between the underwater responses of the caudal fin and the input voltages have an ellipse-like shape and vary in shape and size with oscillating frequency. The ellipse-like dynamic hysteresis loop first grows, reaching its maximum at the resonant frequency, and then decreases, because of the frequency-dependent dynamic behavior. Meanwhile, a phase shift of approximately 90°between the input voltage and underwater dynamic response was observed at the resonant state. Furthermore, the experimental results demonstrate that the proposed model can describe the nonlinear underwater dynamic hysteresis behavior of the proposed caudal fin at different frequencies. The trajectory tracking performances are remarkably improved over a broad frequency range with the proposed compensator. Consequently, the effectiveness of the proposed dynamic model and compensation method was demonstrated. These results are helpful for robotic fish or autonomous underwater vehicles propelled by oscillating foils actuated by smart actuators, including MFC.

Hydrodynamic effect and Fluid-Structure coupled vibration of underwater flexible caudal fin actuated by Macro fiber composites

Underwater bionic robotics or vehicles using oscillating flexible structures as power sources are attracting considerable attention. In this study, the hydrodynamic effect and fluid–structure coupled vibration of a flexible caudal fin actuated by macro fiber composites(MFC) are investigated. A fluid–structure coupled dynamic equation of the MFC-actuated caudal fin with a variable cross-section is established, and both the internal moment generated by the MFC and the complex-valued hydrodynamic forces are considered. Distributions and evolutions of the flow velocity and pressure in the vicinity of the oscillating caudal fin with different parameters are visualized through comprehensive parametric CFD simulations. Simulation results show that the presence of the gap introduces significant flow reshaping effects to the flow distribution and hydrodynamics. Distributions of the flow velocities and concentrated pressure regions depend highly on the gap width of the forked caudal fin. Then, a revised hydrodynamic function depending on three nondimensional governing parameters is developed, this is, the characteristic oscillating frequency, the width ratio, and the gap-to-width ratio. Formulas for the real and -imaginary parts of the complex-valued hydrodynamic function are developed respectively through the comprehensive CFD framework. Theoretical and experimental results show that the revised hydrodynamic function and developed model are capable of estimating the hydrodynamic effect and underwater dynamic response of the MFC-actuated caudal fin. Compared with the classical hydrodynamic function for the rectangular beam, the expression for the beam overestimates the added mass effect exerted on the caudal fin, and underestimates the hydrodynamic damping effect, thus leading to a smaller estimated resonant frequency and bandwidth, but a higher predicted response peak. These findings are useful for the robotic fish or autonomous underwater vehicles which are propelled by oscillating foils actuated by smart actuators.

Maximizing the thrust performance of flexible caudal fin panels via experimental optimization

This paper discusses the experimental optimization of an artificial caudal fin to maximize thrust production. A combination of direct experimental measurement and Gaussian Process modeling was applied to optimize the time-averaged net thrust force produced by the fin panel. Specifically, this paper investigates the effect of the fin panel’s stiffness and flapping frequency on the thrust force. The Gaussian Process regression is primarily used to model the relationship between the flapping frequency and thrust force, with variations in the fin panel’s stiffness. Results show that the optimum flapping frequency that yields maximum force tends to decrease as the stiffness decreases. Furthermore, increasing the lateral amplitude displacement of the fin base leads to a higher time-averaged net thrust force. Further investigation shows that the phase difference between the trailing and leading edge of the oscillating fin should be about 90°to yield optimum time-averaged net thrust force.

Modeling and Dynamics Analysis on Pseudo-Rigid-Body for the Swing Vibrator of the Caudal-Fin-Like Valve-Less Pump

A bio-inspired swing vibrator applied in fluid driving has the characteristics of a large deformation and rigid-lexible structure. Currently, there is a shortage of influential theories and methods to analyze its vibration. This research established a dynamic model for studying the bionic rigid-flexible swing vibrator based on pseudo-rigid-body theory. The weak coupling relationship between vibration arm DOF and flexible caudal-fin DOF was proposed by comparing the diagonal elements with the characteristic matrix's anti-diagonal elements. Analysis results showed that the presence of a flexible caudal-fin had minimal impact on the vibration modes of the vibration arm. The flexible caudal-fin vibration could be treated as a dynamic response that uses the vibration arm's end as a foundation. Experimental studies were conducted, and a laser Doppler vibrometer was used to measure the vibrator's vibration modes. The experimental results indicated that whether the vibrator works in water or in air, the presence of a flexible caudal-fin had little impact on the resonance frequency of the vibration arm. Finally, experimental results were discussed based on theoretical analysis and conclusions. This paper provides an academic tool for modeling, optimization, and a working mechanism analysis on the rigid-flexible swing vibrator.

The effects of caudal fin's bending stiffness on a self-propelled carangiform swimmer

The hydrodynamic performance of a self-propelled carangiform swimmer with a flexible caudal fin in the absence of a free stream is numerically investigated, where the fin's dimensionless bending stiffness varies from 10−3 to 150. It reveals that large flexibility of the caudal fin has a negative impact on the propulsion and moderate rigidity is found to increase the hydrodynamic performance. Two different vortex configurations are observed at low and high bending stiffnesses: (i) reverse Bénard–von Kármán (rBvK) vortex configuration and (ii) deflected reverse Bénard–von Kármán wake with the secondary vortex street, respectively. With the increase in bending stiffness, the thrust-producing part switches from the swimmer body to the caudal fin corresponding to the switch of the vortex configuration. Furthermore, the thrust and drag productions are examined. As the bending stiffness increases, the “active portion” of the caudal fin provides more kinetic energy to the wake flow. It is found that the deflected rBvK is induced by the vortical strength imbalance of two adjacent vortices, and the secondary vortex street is formed by the large strain between the primary vortex and the secondary vortex street. Meanwhile, the dynamic mode decomposition analysis indicates that the dominant mode of the dynamic flow field is the excited frequency resonant mode and the inherent frequency of the secondary vortex street is the same as the undulatory frequency. These results shed new light onto the role of the flexible caudal fin in self-propelled biological systems and may provide some inspirations to autonomous underwater vehicle design.

Hydrodynamics study of dolphin's self-yaw motion realized by spanwise flexibility of caudal fin

The hydrodynamic performance of the virtual underwater vehicle under self-yaw is investigated numerically in this paper, we aim to explore the fluid laws behind this plane motion achieved by the bionic flexibility, especially the spanwise flexibility of the caudal fin. The kinematics of the chordwise flexible body and the spanwise flexible caudal fin are explored through dynamic mesh technology and user-defined functions (UDF). The 3-D Navier-Stokes equations are applied to simulate the viscid fluid surrounding the bionic dolphin. The study focuses on quantitative problems about the fluid dynamics behind the specific motion law, including speed of movement, energy loss and working efficiency. The current results show that the self-yaw can be composed of two motions, autonomous propulsion and active steering. In addition, the degree of the flexible caudal fin can produce different yaw effects. The chordwise phase difference Ф is dominant in the propulsion function, while the spanwise phase difference δ has a more noticeable effect on the steering function. The pressure distribution on the surface of the dolphin and the wake vortex generated in the flow field reasonably reveal the evolution of self-yaw. It properly turns out that the dolphin can combine the spanwise flexible caudal fin and the chordwise flexible body to achieve self-yaw motion.

Using spanwise flexibility of caudal fin to improve swimming performance for small fishlike robots

This paper examines the beneficial effects of the spanwise flexibility of the caudal fin for the improvement of the swimming performance for small fishlike robots. A virtual swimmer is adopted for controlled numerical experiments by varying the spanwise flexible trajectories and the spanwise flexible size of the caudal fin while keeping the body kinematics fixed. 3-D Navier-Stokes equations are used to compute the viscous flow over the robot. Elliptical, parabolic and hyperbola trajectories are chosen to describe the spanwise flexible profile of the caudal fin. According to the sign (positive or negative) of the phase difference of the swinging motion, the spanwise flexibility can be divided into the fin surface of “bow” and the fin surface of “scoop”. It is observed that for both the fin surface of “bow” and the fin surface of “scoop”, the spanwise elliptical trajectory has the optimal swimming velocity, thrust, lateral force, and efficiency. With comparisons, using the flexible caudal fin with the fin surface of “bow”, the lateral force and the power consumption can be reduced effectively and the swimming stability can be increased while reducing little the swimming velocity and thrust. Meanwhile, using the flexible caudal fin with the fin surface of “scoop” can greatly improve the swimming velocity, thrust, and efficiency while increasing part of the lateral force and the power consumption. Three-dimensional flow structures clearly indicate the evolution process around the swimming robot. It is suggested that the fish, the dolphin, and other aquatic animals may benefit their hydrodynamic performance by the spanwise flexibility of the caudal fin.

Mechatronic Design and Manufacturing of the Intelligent Robotic Fish for Bio-Inspired Swimming Modes

This paper presents mechatronic design and manufacturing of a biomimetic Carangiform-type autonomous robotic fish prototype (i-RoF) with two-link propulsive tail mechanism. For the design procedure, a multi-link biomimetic approach, which uses the physical characteristics of a real carp fish as its size and structure, is adapted. Appropriate body rate is determined according to swimming modes and tail oscillations of the carp. The prototype is composed of three main parts: an anterior rigid body, two-link propulsive tail mechanism, and flexible caudal fin. Prototype parts are produced with 3D-printing technology. In order to mimic fish-like robust swimming gaits, a biomimetic locomotion control structure based on Central Pattern Generator (CPG) is proposed. The designed unidirectional chained CPG network is inspired by the neural spinal cord of Lamprey, and it generates stable rhythmic oscillatory patterns. Also, a Center of Gravity (CoG) control mechanism is designed and located in the anterior rigid body to ensure three-dimensional swimming ability. With the help of this design, the characteristics of the robotic fish are performed with forward, turning, up-down and autonomous swimming motions in the experimental pool. Maximum forward speed of the robotic fish can reach 0.8516 BLs-1 and excellent three-dimensional swimming performance is obtained.

Locomotion of neutrally buoyant fish with flexible caudal fin

Historically, burst-and-coast locomotion strategies have been given two very different explanations. The first one was based on the assumption that the drag of an actively swimming fish is greater than the drag of the same fish in motionless glide. Fish reduce the cost of locomotion by swimming actively during a part of the swimming interval, and gliding through the remaining part. The second one was based on the assumption that muscles perform efficiently only if their contraction rate exceeds a certain threshold. Fish reduce the cost of locomotion by using an efficient contraction rate during a part of the swimming interval, and gliding through the remaining part. In this paper, we suggest yet a third explanation. It is based on the assumption that propulsion efficiency of a swimmer can increase with thrust. Fish reduce the cost of locomotion by alternating high thrust, and hence more efficient, bursts with passive glides. The paper presents a formal analysis of the respective burst-and-coast strategy, shows that the locomotion efficiency can be practically as high as the propulsion efficiency during burst, and shows that the other two explanations can be considered particular cases of the present one.

Research and Simulation of a flexible robotic fish tail fin propulsion system

This article uses a flexible crescent caudal fin tuna as the research object, sets up the robot fish physical model ,researches the propulsion and advancing speed of the model, discusses forward speed, sliding and swing amplitude, frequency and phase to the flexible tail fin propulsive performance, and uses MATLAB to simulate, motion simulation is consistent with the way to achieve the real movement of the fish.

Evolutionary multiobjective design of a flexible caudal fin for robotic fish

Robotic fish accomplish swimming by deforming their bodies or other fin-like appendages. As an emerging class of embedded computing system, robotic fish are anticipated to play an important role in environmental monitoring, inspection of underwater structures, tracking of hazardous wastes and oil spills, and the study of live fish behaviors. While integration of flexible materials (into the fins and/or body) holds the promise of improved swimming performance (in terms of both speed and maneuverability) for these robots, such components also introduce significant design challenges due to the complex material mechanics and hydrodynamic interactions. The problem is further exacerbated by the need for the robots to meet multiple objectives (e.g., both speed and energy efficiency). In this paper, we propose an evolutionary multiobjective optimization approach to the design and control of a robotic fish with a flexible caudal fin. Specifically, we use the NSGA-II algorithm to investigate morphological and control parameter values that optimize swimming speed and power usage. Several evolved fin designs are validated experimentally with a small robotic fish, where fins of different stiffness values and sizes are printed with a multi-material 3D printer. Experimental results confirm the effectiveness of the proposed design approach in balancing the two competing objectives.

Numerical simulation and experimental research of a flexible caudal fin by piezoelectric fiber composite

A flexible caudal fin made of the macro fiber composites and the carbon fiber orthotropic composite was investigated by the numerical simulations and the experiments. First, a three-dimensional numerical simulation procedure was adopted to research the torsion propulsion mode of the caudal fin and the impact of the water for the structural torsion frequency of the caudal fin. Then, a two-dimensional unsteady fluid computational method was used to analyze the hydrodynamic performance with the periodic swing of the caudal fin on the torsion mode. Based on the simulation results, the flow field was demonstrated and discussed. The interaction between the caudal fin and the water was explained. Finally, the laser vibrometer system was built to verify the torsion propulsion mode. Meanwhile, the application of the caudal fin was realized on the torsion propulsion, and the measured system was established to demonstrate the performance of the caudal fin. The established simulation procedures and experimental methods in this study may provide guidance to the fins made of the composite materials during the structural design and the investigation of the flow field characteristics with the movement of the fins.

Dynamic Modeling of a Robotic Fish Propelled by a Compliant Tail

In this paper, a dynamic model for a robotic fish propelled by a tail with a flexible fin is presented. The robotic fish is composed of two links connected by an actuated joint; the frontal link is rigid and acts as the robotic fish body, while the rear link serves as the tail. The latter comprises a rigid element connected to a flexible caudal fin, whose underwater vibration is responsible for propulsion. The dynamics of the frontal link are described using Kirchhoff's equations of motion for rigid bodies in quiescent fluids. The tail vibration is modeled using Euler-Bernoulli beam theory and the effect of the encompassing fluid is described using the Morison equation. The thrust production is assessed from static thrust data in terms of the fin-tip displacement; other salient model parameters are estimated through a nonlinear least squares technique. The model is validated against experimental data on circular and S-shaped trajectories. The model can be used for simulation, prediction, design optimization, and control, as it allows for the description of the robot's motion as a function of the unique input of the system, that is, the servomotor angle. Within the latter application, a heading control algorithm, in which the controller is tuned on the basis of the dynamic model, is presented.

Influence from Length of Flexible Caudal-fin for Caudal-fin-type Piezoelectric Pump

In order to overcome existing common faults of the traditional volumetric type valve-less pump,such as fluctuation,backflow and lack ability of pumping,a valve-less pump which imitates the swing of the caudal-fin is proposed.The researches on the variable-cross-section oscillating vibrator with flexible caudal-fin are carried out.Based on the study carried on the swing of the tuna which has high cruise speed,a variable cross-section vibrator with flexible caudle-fin is designed.The harmonic analysis of vibrator immerged in water is conducted with the ANSYS software.The tip amplitude of vibrator,which has different flexible caudal-fin length,is extracted when the vibrator operates in the second order bending mode.The analysis results suggest that the tip amplitude has great influence on the theoretical flow rate.Thirdly,the tip amplitude is measured utilizing a charge coupled device(CCD) laser displacement sensor.When the length of the flexible caudal-fin is 5 mm,the tip amplitude of second bending mode reaches 0.4 mm.Meanwhile,the trend of the tip amplitude,which varies with the length of the flexible caudal-fin,coincides with the result of simulation.Finally,the performance of the pump is tested experimentally:Driven by 60 V AC signals,the pressure head reaches 78 mm when the length of the flexible caudal-fin is 5 mm.This research reveals that when the other structure parameters are fixed,the length of the flexible caudal-fin determined the performance of the pump.

Parametric study of the swimming performance of a fish robot propelled by a flexible caudal fin

In this paper, we aim to study the swimming performance of fish robots by using a statistical approach. A fish robot employing a carangiform swimming mode had been used as an experimental platform for the performance study. The experiments conducted aim to investigate the effect of various design parameters on the thrust capability of the fish robot with a flexible caudal fin. The controllable parameters associated with the fin include frequency, amplitude of oscillation, aspect ratio and the rigidity of the caudal fin. The significance of these parameters was determined in the first set of experiments by using a statistical approach. A more detailed parametric experimental study was then conducted with only those significant parameters. As a result, the parametric study could be completed with a reduced number of experiments and time spent. With the obtained experimental result, we were able to understand the relationship between various parameters and a possible adjustment of parameters to obtain a higher thrust. The proposed statistical method for experimentation provides an objective and thorough analysis of the effects of individual or combinations of parameters on the swimming performance. Such an efficient experimental design helps to optimize the process and determine factors that influence variability.

Experimental evaluation of open-loop swimming control for a robotic fish using electrostatic film motors

SUMMARYWe have developed an underwater robotic fish using a unique three-layer electrostatic film motor. In the robotic fish, the unique motor actuates a flexible caudal fin to propel the robot via an elaborate power transmission system. In the present study, we describe the major disadvantages of the previous prototype of the robotic fish and improvements of the prototype. In addition, we present experimental evaluations related to the control parameters and locomotion performance of the robotic fish. These control parameters include the frequency and initial phase of AC voltage, and the amplitude and period of frequency sweeping. A simple theoretical model concerning the power transmission system of the robotic fish is also analyzed to provide a possible explanation for the unique swimming control. By appropriately adjusting these control parameters, we achieve cruising, emerging, submerging, and turning of the robotic fish even though only the caudal fin is active. Finally, we show smooth human-operated turn-around motion similar to that seen in real fish. Based on these experimental results, we further clarify the relationships between the open-loop motor pattern and motion parameters.

Electrostatically Actuated Robotic Fish: Design and Control for High-Mobility Open-Loop Swimming

This paper presents a project that aims at fabricating a biologically inspired robotic fish. The robotic fish is designed to be capable of propelling itself through oscillations of a flexible caudal fin, like a real underwater fish. In this paper, we describe the design features that underlie the operation of the robotic fish. These features include a unique actuator referred to as electrostatic film motor and a light and flexible power transmission system. The electrostatic film motor is made of two pieces of flexible printed circuit film and can be utilized as a new-type artificial muscle. The power transmission system permits reciprocating power to be converted to periodic oscillations and distributed to the caudal fin. Based on several design considerations inspired by biological concepts, we propose several open-loop swimming control strategies for the constructed robotic fish to accomplish fish-like motion (i.e., cruising, turning, and diving). Experiments of Seidengyo I, the first prototype of our electrostatic fish family, are carried out to confirm the validity of the original design and control. We further design Seidengyo II to improve on Seidengyo I and show the results of the experiments.

Propulsion Performance of an Aquatic Mobile Robot Using Traveling-Wave Motion of a Flexible Fin. Relationship between Propulsion Efficiency and Flow Pattern.

This paper discusses an experimental study of the propulsion performance of an aquatic mobile robot using waving motion of a flexible plate modeled on the flexible caudal fin of fish. In the experiment, the propulsion force and side force generated by the waving motion of the flexible plate are examined in stationary water in a channel. And the propulsion speed and efficiency are examined with varing the length and flexiblility of the plate. As a result, it is found that the propulsion performance of the robot becomes high when the traveling-wave motion occurs in the flexible plate. And high propulsion performance of efficiency of 62% is obtained by using the traveling-wave motion of the flexible plate.