Info

Temperature, C

Fig. 12. Heating thermal cycles corresponding to an initial content of 40, 70 and 100% of martensite: the hysteretic volume is created using the sampling sets obtained for loads of 53, 107 and 160 MPa (Volkov, Trochu and Brailosvski, 1999).

S1IB6B, MPs

Temperature, C

Fig. 12. Heating thermal cycles corresponding to an initial content of 40, 70 and 100% of martensite: the hysteretic volume is created using the sampling sets obtained for loads of 53, 107 and 160 MPa (Volkov, Trochu and Brailosvski, 1999).

Fig. 13. Graph of Strain Level Versus Temperature for SMA

In order to implement a thermo mechanical model, only the transition from martensite to austenite was considered, and assumed to be linear according to Eq. (11). The reverse transformation could be formulated in an analogous manner.

where ei is the strain in the wire at the start of the transition. Notice that this equation defines the required temperature of the wire based on the required strain.

5. Controller design

The length of the wires and corresponding resistances allowed a 5V source to be used to drive enough current through the wires for the anticipated heating requirement. A pulse width modulation scheme was used to control the voltage applied to the wire and the temperature of the wire, with a 5V maximum. Using the strain time histories from the structural simulations run at 1Hz (tail beat frequency) as the input to the control law, a method was derived to compute the control files used by the ACE controller to move the tail. The update frequency of the control law was nominally set at 20 Hz, so 20 commands were needed over a 1 second time interval. To avoid damaging the wires, the wires on opposite sides of the tail are never actuated simultaneously. Consequently, the commands were computed for the time periods of decreasing strain. The strain during these time intervals was converted to a commanded temperature using Eq. (11). As an adequate approximation and to avoid complicated analysis, those temperatures were then converted to voltages using the required voltage at steady state conditions. While not strictly true, the solution of the differential heat equation for the controller was not warranted at this stage of development, and so the following equation was derived for the steady state temperature by dropping the transient term.

nD 2

^ V = J ^ Rl (T - Tj The actual entries in the control file were then determine by the following equation:

6. Mast drag prediction

In order to simplify the construction of the tow tank apparatus, the drag of the mast was not isolated from the load cells. Consequently, the drag of the mast must be known in order to determine to thrust of the fish. This value can be estimated both experimentally in the tow tank and by testing of the mast in isolation. Experimental testing introduces other effects, however, such as the vortices shed off the tip of the mast. For this reason, an analytic prediction was sought, using a potential flow panel method combined with boundary layer estimation.

The program DesignFoil (www.designfoil.com) implements a panel method for 2-D thick airfoils combined with boundary layer analysis based on the theory of T. von Karman and K. Pohlhausen. It also provides a good user interface for airfoil coordinate definition, and outputs coefficients of lift, drag, and pitching moment, given the coordinates of the airfoil and the Reynolds number. The coordinates of the mast were measured, and then fed into the program, interpolated at 200 points on the top and bottom of the section. It was found that the results from the program converged to a steady solution when more than 300 total points were used to define the airfoil. The results of this analysis are shown in Figure 14, with the following constants used for the mast and water:

l = 2.25" (mast chord length), s = 0.56m (submerged length of mast), Fd = cd I — pV Is I p = 1000 kg/m3 , v = 1.3x10-6 m2/s @ 10°C.

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