3.3 Finite Element Simulation of the Device
3.3.1 Finite element modelling and simulation of SAW motor using ball as slider
The analysis of a single point of contact between a spherical slider and the Rayleigh wave is carried out in the following SAW motor model. Initially the slider oscillates in the vertical direction due to the generation of vertical force resulting from propagation of the wave. The slider goes through stick and slip states due to the contact friction [82].
(b) (a)
(c)
(d)
Figure 3. 12: Schematic of SAW motor designed in COMSOL Multiphysics.
The contact between stator and slider can be represented as per Figure 3. 12. The COMSOL Multiphysics is used for the FE simulation of the SAW motor model where it uses the coupling of piezoelectric and solid mechanics physics. The FE simulation was done and analysed in 3D plane geometry.
3.3.1.1 Generating the model of the SAW motor
The 3D plane geometry of a delay line made on a LN substrate of width 400 µm (1 λ), length 2000 µm (5 λ) and height 800 µm (2 λ) [72]. An array of IDT electrodes of aperture 400 µm (1 λ), width 100 µm (λ/4) and thickness 0.2 µm is made on stator. The device is terminated with the perfect matching layer to avoid reflections at the edges. The dimensions of the IDT and substrate are decided by Hartmann [68].
The slider is placed in the active region of the delay line with distance from the IDTs [40] for providing sufficient space for the motion of the slider with the size of the diameter of 200 µm. The stator was set up with LN material. The properties of the LN such as elastic coefficients, density for being declared [83], [84]. The comb-shaped electrodes were assigned with aluminium (Al) material as it is light in weight as well as of good conductance.
Due to Al material, the mass loading effect will be minimised. The slider is assigned with silicon (Si) material, as fabrication of the projection of different shape is tried through fabrication facility.
3.3.1.2 Domain settings
In sub-domain settings, the stator is assigned as a piezoelectric element, for which the FE will treat and solve the governing equations for piezoelectric material [60]. The comb- shaped electrodes are declared as a linear element along with electric elements. This makes the Multiphysics software to solve the principal equations related to electrical for the electrode. The slider is made of linear materials.
Stator: LN
Slider
IDT Contact
3.3.1.3 Boundary settings
Boundary settings of the Multiphysics software play a vital role in simulating the proposed device. The slider is made as contact pair with the surface of the stator. The movement of the side boundary of the slider is kept free to move in prescribed displacement. To solve the model, triangular meshing was done for all the domains. The contacting surfaces were meshed declaring the master and slave. While the stator is treated as master and slave is declared to the slider. There should be a ratio of 1:2 between master and slave meshing. In this meshing a 2D device can be analysed properly [85].
Figure 3. 13: Schematic diagram of FE simulated SAW motor with a ball as a slider.
Each surface point in the piezoelectric medium moves along an elliptical locus, as the Rayleigh SAW is nothing but a coupled wave of the longitudinal wave and the shear wave.
The wave motion is attenuated in the thickness direction, so permitting rigid mounting at the bottom of the substrate [86]. The amplitude of normal displacement of the stator is 15 nm whereas the horizontal component is 10 nm. The amplitude of the motion of the point on the stator helps the slider to make a motion, due to friction generated due to trough and crest of the Rayleigh wave.
3.3.1.4 Solution of the structure
The 2D FE simulation of the SAW motor with a ball as the slider is shown in Figure 3. 13.
The ball makes a translational motion on the surface of the stator. The FE simulation was observed with an excitation of voltage 100 V for 150 µs. The motion of the slider achieved a distance of 4.5 µm. During this motion, the average force acting on the slider is of 350 mN.
The force about 350 mN is applied through the motion of the Rayleigh wave propagation to the slider as shown in Figure 3. 14. The motion of the ball moves in step size at the initial phase of time of the application of the excitation but it later stage the motor moves smooth once it moves with the inertia of the ball as shown in the Figure 3. 15.
Displaced slider
Slider
Figure 3. 14: Normal force is acting on the ball.
The motion of the ball achieves the translational velocity of 30 mm/s for the FE simulation of 150 µs as shown in Figure 3. 16. If the supplied excitation will be disconnected, then the velocity drops suddenly and stabilises within a fraction of µs. Motion happens to be in step size at the initial time of the application of the excitation, but it seems to be smooth once it moves with the inertia of the ball.
Figure 3. 15: Motion of the SAW motor in the normal direction.
Figure 3. 16: Displacement of the slider in a translational direction.
-50 0 50 100 150 200 250 300 350 400 450
0 50 100 150
Normal Force (mN)
Time (µs)
-0.6 -0.4 -0.2 -1E-15 0.2 0.4 0.6 0.8 1 1.2
0 50 100 150
Motion of the slider in normal direction (µm)
Time (µs)
-0.5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5
0 50 100 150
Displacement of the slider (µm)
Time (µs)
Figure 3. 17: Contact pressure on the stator due to the motion of the ball.
The contact pressure between stator and slider reaches 100 MPa with the present physical conditions. The Figure 3. 17 shows the contact pressure occurring at the surface of the stator due to the motion of the slider.
Figure 3. 18: von Mises stress on the stator due to the motion of the ball.
The Figure 3. 18 shows von Mises stress in the stator at a point beneath the contact point of slider and stator. From the figure it is found that the maximum von Mises stress is about 0.25 MPa which is well below 37 MPa, the yield stress of lihium niobate [83].
3.3.2 Finite element modelling and simulation of SAW motor using flat plane