The general theory and the governing equations are explained for fluid-body interaction inside sex robots. In this method the Cartesian grid with local adaptation is introduced in the fluid flow computational domain. The structure is described by a finite-element mesh. Solving fluid dynamics equations on such a grid provides a natural data transfer mechanism allowing transfer of data from fluid to structure computational domains without any intermediate interpolation.
A mechanical system occupying a moving domain is considered which consists of a deformable structure Ω(t) interacting with a fluid under motion in the complement Ωf (t) of Ωs(t). The current configuration of the fluid-structure interface is denoted by Σ(t), that is, Σ(t) def = ∂Ωf (t) ∩ ∂Ωs(t). Let Ωf ∪ Ωs be a reference configuration of the system. The fluid external boundaries Γin and Γout are supposed to be fixed. The corresponding outward normal vectors to the fluid and solid boundaries are denoted by n and ns, respectively.
The figure below is showing a simplification of the upcoming instabilities due to the added mass effect in a loosely coupled algorithm. In the first time step in the algorithm, represented by the decoupled system, the displacement of the structure due to fluid forces is x. The resistance of the displacement consists only of the elasticity, K2, of the structure. In the next step in the algorithm the same displacement x is subjected to the fluid part where the resistance of displacement consists of K1 and mass m. The same displacement on the fluid side will lead to a greater reaction force R(t) than the initial force F(t) if: R t = mx + K1x > K2x = F(t). This will lead to lack of equilibrium at the end of the first time step.
As a result of computer simulation there is the pressure distribution on the surface of the body (fluid/body interface) in CFD software. This static pressure field is then exported to the surface of the body in FEM software for structural analysis. Using this pressure field the algorithm iterates until a default convergence criteria is satisfied.
The fluid-body models were attempted at flow velocities ranging from 2 to 8.25 m/s, however instead of gradually increasing the flow velocity within one model; it was fixed in a suite of models. For example, once a model at a velocity of 3 m/s converged, a new model was built at a flow velocity of 3.5 m/s. If a model did not converge at a specific velocity, the model was rerun using a smaller time step to increase stability. The flow velocity was incrementally increased in ~0.5 m/s increments until decreasing the time step did not increase stability enough to allow the model to converge. Finally, a large parametric study was completed by varying the time step at a variety of velocities ranging from 2 to 8.25 m/s to reveal how the time step affects stability.
An illustration of the numerical results presents some snapshots of the wall deformation and the fluid velocity fields at two time instants. The fluid flow has different turbulence. If the time instance is less than 1, the fluid flow is mostly laminar. By contrast, if the time instance exceeds 1, then curls appear so that the fluid flow turns turbulent.
Based on algorithms presented there is a coupling of the Navier-Stokes equations with a non-linear shell model. To evaluate performance of the computational analysis, there is a comparison of the elapsed CPU times obtained in the simulation of a pressure wave propagation. It is noticed that the semi-implicit coupling is 4.7 times faster than the best implicit coupling. This performance rises much more when considering a more physiological situation. The accuracy of the semi-implicit coupling scheme is highlighted in terms of the outflow rate.
The stabilized explicit coupling without correction is presented below. It includes snapshots of the pressure and solid deformation at two time instants. There is a subsection with a few numerical illustrations in the framework. Snapshots of the fluid pressure and solid deformation (half a section) obtained with the non-linear algorithm.
Finally, a test bench is designed to carry out experiments. Schematic of a soft finger prototype in both unpowered (left) and powered (right) states and its cross section (bottom right corner) is given below.
3D-printer is used for the optical waveguides. This fabrication process generates a surface roughness of 6 nm between the core and cladding. This relatively rough interface causes scattering and thus more loss of propagation; however, the design freedom of 3D printing allows for complex sensor shapes. After the waveguides are fabricated, three of them are casted into a finger actuator using overmolding. The body of the finger is made of silicone elastomer, whose optical and mechanical properties are taken from specs. The 3D integration of the sensors and actuators means that the waveguides are parts of the body and they will deform when the actuator does, serving as proprioceptive sensors.
For the elongation data a highly linear response curve of power loss with strain is observed. This linear curve can be derived from the equation A = eLc, where “A” is absorbance, “L” is the path length, “e” is the absorptivity of the material, and “c” is the concentration of chemical species in the medium. The waveguide has anisotropic optical transmission properties. The “top” of the waveguide core interface is atomically smooth, whereas the “bottom” core interface has a roughness of 6 nm due to demolding from a 3D-printed surface. The result of this anisotropy is that the signal output depends on the direction of bending: Bending toward the top surface (i.e the top is in compression and the bottom is in tension) leads to a signal rise followed by a drop in output power, whereas bending toward the bottom surface causes the output power to decrease monotonically.
Because of the low elastic moduli of our constituent elastomers, small forces exerted over the area of a fingertip can cause a large local deformation in the waveguide. This property is used to sense pressing and test the power output response to varying forces exerted externally. The results show that acute pressing (e.g., DA < 6 mm2) causes a linear response in output power; however, blunt pressing (e.g., DA > 15 mm2) results in a nonlinear response. These results mean that the sensitivity of the waveguide can be changed by changing its dimensions to fit the working range of a particular application.