Of a Biomimetic Tuna

Afzal Suleman and Curran Crawford

University of Victoria Canada

1. Introduction

Current unmanned undersea vehicles (UUVs) are almost exclusively propeller driven designs, which must inherently be optimized for a particular speed, sacrificing low speed manoeuvrability for cruising efficiency. Recently, biomimetic approaches to underwater vehicle propulsion have illuminated the exciting possibilities for performance improvements made possible by emulating fish motion. In particular, a number of test vehicles indicate that the carangiform swimming mode employed by highly developed species of fish, such as the Bluefin tuna, offers both a more efficient propulsion mechanism than propellers, in addition to the ability to perform quick manoeuvring. This book chapter presents studies on the propulsion efficiency of a biomimetic tuna at the University of Victoria. Two prototypes have been designed and implemented experimentally. The first prototype consists of a biomimetic tuna that employs shape memory alloy wires to affect shape induced propulsion. The second prototype propulsion model consists of four joints that are rotated using servomotors. Issues related to the mechanism, systems and energy are discussed. The performance and the lessons learned related to the two design philosophies are presented and discussed.

2. Background and motivation

Underwater vehicle design has in the past primarily focused on propeller driven designs. Research efforts have been directed towards optimizing propeller design for particular operating speeds, and also on improving manoeuvring performance through control surface, hull, and thruster configuration and design. Through computing power and mechanical system design improvements, unmanned undersea vehicles (UUVs) have been able to expand their operating envelope and carry out more ambitious, extended, and varied missions including oceanographic surveys, reconnaissance, cable laying, and mine hunting. Propeller driven designs inherently involve design tradeoffs; speed is traded for low speed manoeuvrability, and efficiency is balanced against operational speed range requirements. Natural biological evolution has also struggled with the same design considerations, and produced extremely efficient modes of propulsion over millions of years of natural selection. The emerging field of biomimetics seeks to exploit this natural design process by copying the refined forms of living creatures found in nature. In the area of hydrodynamic propulsion, highly evolved species such as the Bluefin tuna employing the carangiform swimming mode have been optimized for high speed cruising, while retaining excellent manoeuvring capabilities. Previous research, including the RoboTuna (Barret, 2000), RoboPike (Kumph, 2000), and VCUUV (Anderson & Kerrebrock, 2000), has proven the potential of emulating fish swimming in underwater vehicles, and suggest exciting possibilities for performance improvement over traditional UUV design in both efficiency and manoeuvrability. A study on the swimming modes for aquatic locomotion has been published by Stafiotakis et al (1999). Chiu et al. (2000, 2002) have analyzed and simulated the undulatory locomotion of a flexible slender body. Guo et al (2002) have proposed a method for coordinating body segments for controlling the motion of a biomimetic autonomous underwater vehicle. Barret et al (1996) used genetic algorithms to determine the optimal body motion of the RoboTuna. Harper et al (1998) and Blickhan and Chen (1994) have studied several methods for measuring the power of swimming fish. Due to the complexity of the fluid dynamics problem, analytic and computational analysis of the problem has not yet progressed to the point where proper simulation of the body and caudal fin is possible. Progress has been made though, starting with inviscid flow analysis in two dimensions (Lighthill, 1970), with current research efforts focusing on full CFD simulation of the entire fish with vorticity and turbulence.

Previous biomimetic fish designs have used conventional actuators, including cable drives, servomechanisms, and hydraulics. Development of multifunctional materials such as piezoelectrics, magnetostrictive materials, and shape memory alloys (SMAs) has presented an alternative actuation method. For this particular application, shape memory alloys are the most suitable of the multifunctional materials since they offer both the necessary strains and forces required for underwater propulsion.

Piezoelectrics may also find applications in such a vehicle for small shape changes in the fins or selective stiffening of the actuated structure. However, SMAs have a number of potential advantages, including simplicity, noiseless operation, and low driving voltages. They can be used as direct linear actuators, and do not require gearing systems, reducing system complexity and making them ideal for confined space applications. Since they are essentially solid-state electrical devices, they produce no acoustic signature, a valuable asset for some missions such as covert military operations and for sensitive acoustic measurements. The low driving voltages required are also suited to power supplies typically available on UUVs.

SMAs do have a number of drawbacks however, including low energy efficiency and performance degradation under repetitive operation beyond a couple of million cycles. The design of the SMA fish is such that new smart actuators could be easily integrated as they become available, in order to overcome some of these disadvantages. The "undulatory vehicle," has utilized SMAs for propulsion, however it was based on the hydrodynamically inefficient eel (Wardle & Reid, 1997). SMA actuators have also been successfully used for an actively controlled hydrofoil (Rediniotis, 1999).

The objective of this research is to develop a more efficient method of driving underwater vehicles using shape induced propulsion. The replacement of propellers with fish like locomotion is expected theoretically to offer 15-20% improvements in efficiency. Fish like propulsion should offer more stealthy designs of vehicles. The following strategies for shape induced propulsion have been considered: (i) in the first instance, prototype I using SMA wires to induce shape control of the tuna body was concetpualized, manufactured and tested. These SMA devices act like little muscles. When they are heated they contract and when cooled they expand. A fish was designed using SMA wires as muscles to produce the swimming action. This research resulted in some insightful observations based on the quantitative and qualitative results. The fish mechanism created measureable thrust while requiring large amounts of power for its operation. This finding suggested that a new approach was needed. The power requirement alone would mean that the fish would require a large battery source; (ii) next, the prototype II ServoTuna design was introduced to overcome these problems. This prototype was controlled by a single chip microcontroller which executed swimming motions using its four servomotors by autonomous control. The "travelling wave" type motion that is peculiar to fish was programmed into the single chip computer and it executed the correct wave pattern. The results obtained using the second generation prototype were more promising.

3. The shape memory alloy induced propulsion: prototype I 3.1 Design considerations

The design constraints initially placed on the vehicle included a 1m total length with 50% actuated length, typical of the biological carangiform swimming mode and previous biomimetic projects. In addition, some form of actuated surface for pitch and roll control was included, and provision for mounting a mast for tow tank testing was included. In order to preserve the biomimetic approach to the design of the SMA fish and in the absence of detailed results from computational hull form optimisation, the profile of a real Bluefin tuna was used for the side profile. The Bluefin tuna was selected for its highly evolved cruising speed efficiency, and its carangiform swimming mode that in nature involves actuating approximately 50% of the fish's length. Two physical features of the tuna are though to contribute to its efficiency in addition to the swimming mode: the "necking" of the profile at the caudal peduncle, and the high aspect ratio caudal fin. The top profile followed extremely closely the shape of modern low drag airfoils, and consequently a NACA 63-015A airfoil section was chosen for this profile. The cross section of the entire hull is elliptical, again emulating nature. This cross section was chosen to reduce the bending stiffness of the hull in the posterior actuated segment, and also to provide the optimum hydrodynamic shape for the actuated segment while still retaining internal volume in the pressure hull. Patching a circular cross section forward to an aft elliptical cross section may be an option for future deep-diving designs, but would almost certainly compromise efficiency.

Examination of the biological tuna reveals that all of the fins except for the caudal fin fold into the body at cruising speed. For this reason, all of the fins except for the caudal and pectoral fins were excluded. The pectoral fins are essentially canards as they are located forward of the centre of mass, and will be used for both roll and pitch control, with modulation of the tail motion to be used for yaw control. For propulsion efficiency studies, these were not considered. Figure 1 illustrates the general layout of the SMA fish Prototype I.

Since the forward 50% of the body is non-actuated, it was constructed as a rigid shell and contains controllers, sensors, and a power source. For design simplicity, the nose cone is designed as a pressure hull in order to easily include on-board power and control later in the development cycle. The nose cone was constructed as a moulded fibreglass shell, with an aluminium bulkhead at the aft end, which mates to another bulkhead to which the actuated segment is attached. The two bulkheads were sealed together by means of an O-ring, allowing for easy access to the interior of the nose cone. The nose cone was reinforced by aluminium ribs that would also include a hard point for mounting to the towing tank mast. In addition, the sealed pivots for the canards were located in the nose cone and attached to the ribs, along with the servos to control them. Any control electronics, internal ballast, and eventually batteries would also be attached to the ribs. This design has been successfully used in all of the other fish projects reported in the literature.

Caudal Fin

Fiberglass Nose

Biomimetic Tuna

Fig. 1. The shape memory alloy based design 3.2 The actuated tail section

This section of the hull occupies the aft portion of the hull, and accounts for the other 50% of the hull, including the caudal fin. The caudal fin contributes the bulk of the propulsive force in the carangiform swimming mode that is being emulated, however the travelling wave that is present in the tail is also an important factor to the overall efficiency of the design, and therefore the tail was designed to be flexible. In order to achieve this, a "skeletal" structure was developed over which "skin" is stretched. The basic element of the skeleton is a spline element running from the bulkhead aft to the tail peduncle. This spline provides a smooth curving shape to the tail along its length. Ribs (again with elliptical cross section) were then attached to the spline to provide the 3-D form of tail. The entire tail section was flooded in order to avoid the complicated problem of sealing it, especially for deep diving missions. Flooding of the tail will also drastically increase the cycle frequency possible with the SMAs due to the increased heat convection off of the wires during cooling in water however at a higher energy cost.

A number of rib designs have been used in the past. Most are a variation on complete cross sections built out of aluminium (RoboTuna), plastic (undulatory vehicle), or foam (Draper Tuna), bolted to the spline. An interesting approach to the rib design problem was used on the RoboPike project; the ribs were formed out of fibreglass as a continuous helical spring, bolted along its length to the spline. In order to simplify the rib production and assembly process, the SMA fish uses "half-ribs" formed out of fibreglass. Since the ribs are formed in two halves, a single half mold was used to form the ribs for both sides of the fish. Mounting of the ribs on the spline was also simplified, since the ribs were simply bolted together through the spline without the need for bonding mounting blocks to the ribs or other complicated schemes. The ribs were placed approximately every 2.54 cm, and have a width of approximately 1 cm.

The skin material for the tail must allow the tail to flex while at the same time avoid deflections in the unsupported regions between ribs. The skin must also be impermeable so that fluid is forced to move along with the surface of the tail and thereby provide some of the thrust. Previous designs have all used Lycra as the skin material over a layer of reticulated foam or steel mesh avoid the problem of bulging between the ribs. The Lycra is by its nature impervious to water (there are also some surface treatments of the fabric available to reduce the permeability further) and has a very low elastic modulus. The layer of foam essentially forms a composite plate structure by increasing the bending stiffness of the fabric while not adversely increasing the tensile modulus that must be low to allow bending of the overall tail. Neoprene (wetsuit material) combines these functions, since it is actually comprised of a core of foam covered on both sides by Lycra fabric. It is available in thicknesses down to 1.5 mm, the same thickness used on modern high performance full body swimsuits that allow for a free range of motion of the swimmer. By aligning the fibres of the Lycra at 45° to the lateral axis of the fish the tensile modulus of the skin is minimized while retaining the bending stiffness of the fabric. The skin was hemmed at the forward end and the elasticity of the material holds it in a groove in the nose cone. At the tail end, the material wraps around the end of the caudal fin with a Velcro strip to hold it in place. There are two possible approaches to actuating the tail section using SMAs. In the robotic based design, it seeks to adapt SMA actuators to the designs that have been used in past projects that construct the tail as a robotic linkage. In these designs, the actuators effect rotation of the links, and the motion of the tail links is transmitted in some manner to the spline. In the RoboTuna, the tail has 6 actively controlled degrees of freedom, while in the VCUUV there are four. In these designs, as the links rotate with respect to one and other, the spline must extend. This is accomplished in the RoboTuna by means of a segmented spline, while in the case of the VCUUV follower rods mechanisms are used to transfer the motion of the links to the spline. Adapting this approach to the SMA fish, the concept shown in Figure 2 was developed with four wires per side of the joint. There are four controlled joints in this design, all with SMAs mounted in the "lever" configuration. This design allows the actuating wire to strain the wire on the opposing side, in order to set-up for the next cycle. In this way, the one-way shape memory effect can be used with no need for an external force to re-strain the wires after each cycle. The SMAs are secured to the links by Plexiglas clamp blocks at one end, and individually clamped with a bolt and washers at the other end to allow for adjust of tension in the each wire, as illustrated in Figure 2.

Initially, the links themselves were made of aluminium, with two ball bearings at each pivot point. The axles for the ball bearings also served as the shafts about which the spline blocks pivot, and were secured in the links with setscrews. Two e-clips along each pivot shaft retained the bearing and locate each spline block assembly. These blocks allowed the spline to extend during operation, and must themselves pivot about the same axes as the links to ensure smooth curvature of the spline. They were made of Delrin with stainless steel for the slider rods. One end of each of the slider rods has an e-clip positioned so that the extension of the spline is limited to avoid excessive local curvature of the spline segment. The opposite end of the rod is screwed into the other block. The spline is simply bolted to the spline blocks, and located in the groove in the blocks. The tail linkage and root spline segments are all bolted to the aft bulkhead. It was found that this approach was suited to conventional actuation methods such as cables and hydraulics, but somewhat defeats the purpose of utilizing SMAs to reduce the complexity of the vehicle.

Fig. 2. The actuated tail section design

In an effort to adopt a more adaptive structures approach to the SMA fish, a new tail section was designed to take advantage of the SMA characteristics. In this design, the spline itself is actuated, much like the undulatory vehicle. The skeletal links are retained in this design, but their function changes to preventing torsion of the caudal fin about the lateral axis of the fish. In the absence of tail linkages, differential shedding of vortices off of the two tips of the fin would lead to a torsional moment on the spline, causing a change in the angle of attack of fin. This would lead to uncontrollable coupled pitching and yawing. It may be possible in future design to eliminate the need for tail linkages by using the torsional strength of the skin (note that the 45° orientation of the Lycra fibres increases the effective torsional stiffness of the tail) in conjunction with actuators at 45° to the lateral axis on the spline itself to control the torsion of the spline.

For the present prototype, the inclusion of the tail linkages greatly simplifies initial testing by eliminating torsional deformation from unbalanced forces on the tail, while not contributing undue complexity to the design. The links must contract in order for the spline to freely flex. This is accomplished in much the same manner as the spline sliders in the robotic design, using slider rods with the extent of travel limited by e-clips. The larger block is made of Delrin through which the rods will slide, while the other spine blocks are of aluminum. The rods thread into these blocks, and bearings are also located in the blocks, two per pivot axis. The aft spine linkage assembly is somewhat more complicated, since at the forward end it must be able to contract, and at the aft end be rigid for the set of SMAs controlling the caudal peduncle pivot. Note that this design again allows for three regions of the spline to be controlled, as well as the peduncle for a total of 4 DOF. The caudal fin was made in same manner as the canards with epoxy covered wood, laminated on a Plexiglas block at the peduncle pivot.

The spline is again attached to the links at the same pivot points as the links themselves by means of Delrin blocks that themselves pivot about the same axes as the links. The same blocks provide mounting points for the SMAs, clamped at the aft end between aluminium spacers and at the forward end by bolts and washers. The aluminium spacers are contained within grooves in the Delrin blocks and clamped with two bolts visible at the end of each spline block. The mounting of the SMAs for the caudal peduncle section is the same as outlined earlier. The cutouts in the spline serve to reduce its bending stiffness while preserving the structural integrity for supporting the ribs. The spline was made of 0.8 mm Delrin sheet. The completed tail section prototype is shown in Figure 3.

Fig. 3. The tail section prototype 4. SMA actuators

The shape memory effect is exhibited by a number of alloys, however the most common one is an alloy of Ni-Ti, referred to as Nitinol. The one-way shape memory effect occurs after an external force strains the material in its cold state. Upon heating, the material will return to the initial "remembered" shape, and if the material is constrained can produce a considerable force on the constraints. This effect is explained from a crystal structure approach by the following; the low temperature phase is martensite and possesses a low yield strength, which is easily plastically deformed by and external force. Upon heating past the transition temperature of the alloy, the phase of the material changes to austentite, a phase with high elastic modulus and yield strength, and due to the training process will attempt to return to the remembered shape. The transition temperature can be tailored by the alloying and heat treatment process to obtain a value between -100°C and 100°C. Nitinol can be obtained in a variety of forms, including thin film, rod and bar, tube, and wire stock. It is usually sold in its as formed state, and must undergo a complex heat treatment process in order to "train" it and thereby attain its memory. The process consists of heating and coiling cycles over which the material is strained from its remembered state, and must be repeated over 50 times.

Nitinol has been made available by Mondo-Tronics in pre-trained wire form, making integration into various robotics projects quite strait forward. The commercial name is either "Muscle Wires" or "Flexinol." The wires are available in a number of diameters ranging from 37^m up to 0.375mm, and are actuated by passing a current directly through the length of the wire. Larger wires can exert higher forces, however require correspondingly higher currents for Joule heating and are not capable of fast cycling. Low and high temperature wires are available with transition temperatures of 70°C and 90°C respectively, and care must be taken to avoid overheating which destroys the wires. The low temperature

wires were considered here due to the fact that they will be immersed in water that ensure adequate heat transfer for cooling. (Note that operating the wires in water is advertised to permit over 10 times the frequency of operation compared to operation in air due to increased convective cooling.) A number of the salient properties are listed in Table 1 below for the candidate wires. The Flexinol 300 series were selected to ensure adequate force is available for actuation.

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