Chapter 4
Electromagnetic analysis of MRF-based displays
4.1 Introduction
Heretofore we investigated on rheological properties of some controllable fluids and we explored the possibility of implementing heuristically haptic interfaces by using MRFs.
In this chapter some engineering investigations and improvements about the electromagnetic systems capable to energize the magnetorheological materials were reported.
After a theoretical introduction to the “Electromagnetic Inverse Problems” to which the proposed problem belongs, a simulation of the presented devices was carried out in order to verify its performance and to obtain some design criteria.
Then, taking into account the results of such simulations, a new system for the energization of MRF was developed and simulated by means of a Finite Elements (FE) code and some results in terms of field magnitude and its 2D/3D spatial
resolution are discussed.
Finally, the conclusive results obtained were used to develop a new 3D display for free-hand interactions, the HBB-II, which is presented in next chapter.
4.1.1 The inverse magnetic problem
The design of electromagnetic devices can be stated in mathematical terms as in- verse problems [52].
The proposed problem, in fact, belongs to the most general class of electromagne- tic problems, specifically called “Inverse Magnetic Problems” and so state: ”known the amplitude of magnetic flux density B specified in a limited spatial domain, de- termine a sources distribution capable to generate such field”. This problem is the reversal of the “Forward Magnetic Problem” related to the calculation of magnetic flux density B due to a given sources distribution.
Unfortunately, the problem of determining a set of electrical currents to realize the desired magnetic field and force distributions is less well understood.
On the other hand, the problem formulation presents serious difficulties related to the nature of its unknowns and specific physics quantities. The study is usually tailored according to the peculiar features of the problems to be solved [14].
According to their nature, the Inverse Problems can belong to two main classes:
• “Identification Problems”;
• “Synthesis Problems”.
The problem can be formulated as:
Ax = b (4.1)
where A is a continuous operator representing the source-effect through a functional relationship. For instance, in the classical case of electromagnetic problem, A is
4.1 Introduction
constituted by familiar formulas of electrodynamics, depending on the geometry of the system.
In the case of Identification Problem the aim is to determine the actual source x which produces the really existing effect b. Problems of this kind are typically met when b represents an experimentally measurable quantity; in this case, x exists and is unique.
In Synthesis Problems the source x is required to produce an effect approximat- ing as much as possible the specified b. Problems of this kind are typically met in those applications where the study is aimed at design of electromagnetic devices capable to produce specified effects.
These synthesis problems are often referred to as optimal design problems.
From a mathematical point of view they can be formulated as
min||Ax − b||2 (4.2)
where || − ||2 is a norm in the domain of the specified effect b.
Any x able to produce a close enough approximation of b in this norm represents a solution of the Synthesis Problems. The correct solution of the Identification Problem is definitively prevented due to the fact that the Inverse Problem is an
”Ill-posed” problem, not satisfying at least one of the conditions of the Hadamard’s for ”well-posed” problems, that are:
1. existence: the solution x exists for a given b;
2. uniqueness: the solution x is unique for a given b;
3. stability: the dependence of x on b is continuous in the neighbourhood of the solution in the two chosen norms of the domain of the specified effect b; that is for every ² > 0 e δ = δ(², b) > 0, exists so that:
||Ax1− b||2< δ ⇒ ||x1− x||1< ². (4.3)
The uniqueness of the solution of an Identification Problem requires that the information on b is consistent and the mathematical model A is adequate to describe and constrain the electromagnetic problem. On the contrary the Synthesis Problem generally presents a non-unique solution. Constrains are usually convenient, in order to better address the solution towards the optimal solution x. As described above, the problem to be solved belongs to the class of Synthesis Problems and deals about the simulation of an electromagnetic device capable to energize, with a specified field amplitude into a specified volume of MRF for realizing haptic interfaces. Since the values of field and resolution are not univocally determined, they can vary in an enough wide range and are specified by an arrangement between some parameters of the system (weight, thermal limits, etc.).
In line with the discussion, from an engineering point of view it is possible to simplify the Synthesis Problem by using an ”assumed” model through a numerical simulation.
4.2 FEM analysis
Historically, the Inverse Problem and, in particular, the Synthesis, have relatively neglected because electromagnetic actuators were built in symmetric geometries where an intuitive solution could designed.
The mathematical models for these electromagnetic problems are deriving from the Maxwell equations.
Currently, the use of mathematical modeling and numerical techniques in the in- dustrial design of electrical or electromagnetic machines, electrical actuators, trans- formers, etc. has gained popularity.
The basic idea of the nonlinear finite element formulation is to linearize the weak form of the equations of the problem and to solve these equations by discretising them, for example, by using the finite element method [86].
In this way the nonlinear optimisations, that are mathematically complex due
4.2 FEM analysis
to their ill-posedness and non-unique solutions can be easily tackled.
In order to characterize the ”assumed” model used to determine the device for the excitation of MRF, a numerical analysis was necessary to investigate the performance of the PG display and of the HBB-I device. In this way, taking into account the simulation results it is possible to carry out some design criteria that may be used for the characterization of a new device able to satisfy the specified performance. Since the behaviour of both MRF and ferromagnetic cores is highly nonlinear, an analytical method cannot perform an accurate investigation of the proposed system. All the following simulations were carried out by using a 3D code MEGA [60] developed at University of Bath (UK) and based on the Finite Elements Method (FEM). Such a code can take into account the B-H function for nonlinear materials, the leakage flux due to the presence of different magnetic paths in air, as well as the presence of different feeding coils. The code allowed to analyze the profile of the flux density B in the interested areas. In fig.4.1 the main step process used during the simulation setup is presented.
4.2.1 Field formulation: 3D Finite Elements Method (FEM) principle
In the used FEM code, the field formulation for regions with no source current, can be expressed in terms of total magnetic scalar potential ψ:
H = −∇ψ (4.4)
∇ · (µ∇ψ) = 0 (4.5)
Using the “reduced scalar potential” formulation for the regions containing source of current, it is possible to write
H = −∇φ + Hs (4.6)
Figure 4.1: FEMM Analysis process
and consequently
− ∇ · (µ∇ψ) + ∇ · (µHs) = 0. (4.7) Here µ is the non-linear function of the B-H characteristics and Hs is the field due to the source current calculated by using Biot-Savart law
Hs= 1 4π
Z J × ∇
µ1 r
¶
dV. (4.8)
Usually, a numerical simulation process is articulated by three steps (fig.4.1) describing of the physical phenomenon. A pre-processing phase allows to define the geometry of the model to be solved and to assign the material properties (the electrical and magnetic active sources), and the boundary conditions. The middle stage, after defining the data set describing the problem and a manual/automatic meshing algorithm, aims at solving the relevant Maxwell’s equations to obtain values for the magnetic field through the solution domain. The manual meshing of the
4.3 FEM analysis and optimization of the PG display
system is fundamental to obtain a better simulation of the problem. The final post- processing stage, through a graphical interface, displays the resulting fields (e.g. B, H) in terms of contour and density plots and provides energy densities and other electromagnetic quantities.
The design simulations of MRF-based devices were implemented taking care of respecting a few criteria:
• the magnetic field should be as uniform as possible within an MRF specimen in order to provide a fine rheological behaviour and to maximize the capability of discrimination of different compliances;
• the range of magnetic field should be compatible with MRF B-H and H-shear stress curves;
• the MRF specimen should be easily accessible in order to allow the hand to tactually explore freely and to perform stress relaxation and experimental tests.
The simulation led us to define specifications relative to the number of turns and current flowing into the coils in order to produce the maximum magnetic field in the gap containing the MRF according to its saturation phenomenon.
4.3 FEM analysis and optimization of the PG di- splay
The PG display presented in 3.3 was properly optimized by using the numerical code. The MRF is always positioned in the air-gap of an electromagnet within a latex sleeve allowing the pinch grasp manipulation [9]. The optimization was obtained by implementing a 2D simulation of the system with the presented MEGA software. In fig.4.2 a FEM simulation, in which we used the real B-H curves of MRF and steel experimentally evaluated and already reported in chapter 2.
Figure 4.2: Simulation of the Pinch Grasp (PG) display.
In this simulation we fixed 5100 AT (Ampere-turns). The color scale map in fig.4.2 shows the magnitude of the magnetic field within the ferromagnetic core and the air gap. The simulation needed to find the optimal structural param- eters/geometries and come to a fair compromise between the distribution of the magnetic field and the dissipated energy due to overheating. A comparison be- tween the theoretical and experimental values of magnetic field was performed. In particular we used a Gaussmeter (see fig.4.3) to measure the magnetic field in the air gap at different levels of current into coils and we compared the results with the behaviour given by the simulations.
4.3.1 Final PG hardware equipments
The device is comprised of three coils, whose main coil is composed of 1500 turns of copper wire having 0.85 mm in diameter, 0.03 Ω/m of electrical resistance and 0.5674 mm2in section. Other two secondary coils, located contiguously to the MRF volume, are composed of 1200 turns of copper wire having 0.45 mm in diameter, 0.11 Ω/m of electrical resistance and 0.1963 mm2 in section. The maximum current
4.3 FEM analysis and optimization of the PG display
Figure 4.3: Experimental Setup on the Pinch Grasp (PG) display.
Figure 4.4: Model and optimization of the Pinch Grasp (PG) display.
flowing through the main coil is 1.8 A and in the secondary coils is 1 A. These values, taking into account the overheating problem and the safety threshold of 3 A/mm2, are necessary to produce the maximum magnetic field magnitude of our interest. The different geometry of the coils allows to guarantee a strong and uniform magnetic field.
The ferromagnetic core is carbon steel AISI 1015 having a permeability around thousand more than the AISI 1040, a high level of saturation and low hysteresis.
The turns do not comes into direct contact with the ferromagnetic core, but are separated with a Teflon support. Each layer of the turns is covered with a special insulating material to ensure thermal and electrical isolation. The coils are fed by using separate generators. A rough control of the magnetic field within the MRF can be obtained by manually tuning the intensity of the electrical current in each coil.
A better resolution control was performed by using three analog outputs deriving from an acquisition card interfaced to a PC. The signals drive three voltage-current converters capable of properly feeding each coil. Basically, these converters present an operational amplifier that supplies a final power circuit, a push-pull section of bipolar power transistors (BD911 and BD912). The volume of MRF contained in the latex sleeve and allows for pinch grasp manipulation. This ferromagnetic ar- chitecture, permitted to better focus the magnetic field in a small gap-volume to modulate the rheology of the MRF with precision and good resolution in intensity.
In this way the magnetic field can be controlled within the fluid by varying the magnitude of electric current in order to tune the compliance of the fluid speci- men. An MRF volume of 20 cm3 allows an ergonomic manipulation and a good accessibility with the MRF specimen, reducing rigid constraints and facilitating the experimental tests. The fluid was excited with a magnetic field ranging between 0.0 and 0.35 T. A comparison between the theoretical and experimental analysis was performed showing good results. In particular, we used a Gaussmeter to measure the magnetic field in the air gap at different levels of current in the coils and we
4.4 FEM analysis of the HBB-I display
Figure 4.5: Preliminary HBB-I prototype.
compared the results with the behaviour given by the simulation.
4.4 FEM analysis of the HBB-I display
The preliminary prototype of the immersive MRF-based display (see fig. 5.1), named HBB-I, consisted of 16 cylindrical ferromagnetic cores, arranged in a matrix form of 4× 4 and placed below a plastic box with a square base. The magnetic field obtained by tuning the current into each coil, allows to materialize objects in the fluid with a given shape and compliance in a close range and with a specific resolution.
Here, a numerical analysis is performed on this prototype and some simulations of the magnetic field distributions are reported. Simulation results and the psy- chophysical analysis (reported in chapter 5) suggested some modifications in order to enhance performance of the preliminary prototypes.
One important HBB-I shortcomings, is the impossibility of creating 3D virtual objects which are, constrained to lie on a plane. On the basis of these considerations a new advanced design capable of overcoming this and other limitations of the previous prototype is here investigated. Fig.4.6 shows the FE model of the simulated device. During the modeling phase with FE software, taking into account the real complexity of the workspace and presence of two symmetry planes, only 1/4 of the
Figure 4.6: The whole FE model (left) and 14 of the FE model (right) of the HBB-I.
problem can be modeled (fig.4.6 right). In this case, simulations were carried out supposing linear B-H curve for both carbon steel core and MRF. Hence, in order to validate the numerical model by experimental measurements, a first simulation was performed setting to 1 the relative permeability of the MRF, that is supposing the box empty. The system was excited feeding the 8 centered coils with a constant electric current of 10 A, and a total number of about 24000 At. The flux density B was evaluated along the axis of a fixed coil (line A in fig.4.7 right).
Then, by using a portable Gaussmeter F.W. Bell/4048, equipped with accurate Hall sensor, some measurements were performed and the results are summarily reported in table 4.1. It can be seen that the maximum percentage error is about 8%, showing a good agreement between the simulated field and measured one.
The flux density B was evaluated along the axis of a fed coil (line A in fig.4.7
4.4 FEM analysis of the HBB-I display
Table 4.1: Comparison between FE analysis and experimental results.
Distance from the base coil Estimated B [T] Measured B [T] Error [%]
0 mm 0.15 T 0.146 T 3%
2 mm 0.13 T 0.12 T 8%
10 mm 0.06 T 0.057 T 5%
right) and between two consecutive coils (line B in fig.4.7 right).
The results show that the magnitude of flux density B, just outside the coils base, immediately decreases and at 1 cm far from the box base and the field is reduced of about 55% without MRF (=⇒ µr= 1).
A second simulation with the presence of MRF in the plastic box was performed in order to test the rheological behaviour of the system fully excited. Fig.4.8 shows the results in the same conditions of fig.4.7 with the MRF (=⇒ µr= 5).
Unfortunately the magnitude of B yet decreases, depending on the distance from the coils base and in this case, at about 1 cm far from the box base, the field is reduced of about 65%.
Regarding the rheological behaviour of the MRF, this gradient of magnetic field induces a proportional decreasing of the yield strength, smoothing the softness of the virtual object perceived.
On the other hand, it can be seen that the values of field B with the presence of MRF, are about twice the results obtained without MRF (Bf/Ba = 2.1).
This fact is due to the value of relative permeability of the MRF that is 5 times bigger than air. Furthermore, when the MRF is present, it is possible to note a better spatial distribution of the flux density B in the box.
A negative observation concerns the low values of field in the area between different coils (line B in fig.4.7 and fig.4.8); the flux density ”prefers” paths with low reluctance and, more easily, closes itself near the ferromagnetic cores (coaxial
Figure 4.7: Flux density B in the system (left) and profile of B along two different line (right) in air.
with coils) creating some field ”holes” in the areas between the coils, not easily eliminable.
From the results above discussed, it was possible to identify the guidelines to modify the old device HBB-I and improve its performance.
4.5 From the HBB-I to HBB-II
4.5.1 Design criteria
As a result of the FEM simulations, it is possible to report some general con- siderations on the main problems that have to be treated in the design of a new electromagnetic device capable of properly exciting a specified volume of MRF. A critical point regards the paths of the magnetic flux that, as clearly shows by the device [72], close themselves in air increasing the magnetic reluctance and, con- sequently, decreasing the magnetic field inside the MRF. However, some possible solutions at increasing the performance of the whole system are:
4.5 From the HBB-I to HBB-II
Figure 4.8: Flux density B in the system with MRF (left) and profile of B along two different line with MRF (right).
• reduction of the reluctance of the magnetic paths by the introduction of fer- romagnetic yokes and cores, properly positioned in the system, to close the magnetic flux path;
• increase of the number of ferromagnetic cores below the box to achieve a suitable spatial resolution.
In order to verify a real improvement of the system after the solutions above described, some simulations were carried out on new modified structures of the HBB-I. As shown in fig.4.9 (left), it was positioned a ferromagnetic sheet at a distance of about 5 cm above the box and linked to the cores below the box by means of two external ferromagnetic yokes. Fig.4.9 (right) shows the simulation results of this case. It can be seen an increase of the magnitude of the field B in the MRF along A and B lines, confirming the usefulness of the introduced solution.
Finally we considered the saturation of the used ferromagnetic materials whose non-linearity compromises the performance of the whole system. However, the choice of special materials and the possibility of increasing the transversal section
Figure 4.9: The modified HBB device (left) and profile of B along two different lines (right).
of the ferromagnetic yokes and columns could attenuate this problem.
Furthermore another design criterion regarded the dimensions of the MRF vol- ume to be energized. As discussed above, the relative permeability of such fluids, comparable to that of the air, leads to a huge magnetic reluctance with a decrease of magnetic field in the MRF. However, a compromise between an easy accessibility to the fluid, and the reduction of magnetic reluctance, allows to identify a proper height of the box. Then, it is possible to excite a parallelepiped of MRF with a two-dimensional spatial resolution related to the x−y axes of the plastic box, main- taining a constant height along z direction; the height of the excited fluid could be modified varying its volume in the box.
4.5.2 Possible new design of HBB display
Taking into account the previous simulations and considerations, it is possible to identify a new structure for the excitation of MRFs. Fig.4.10 shows a new device
4.5 From the HBB-I to HBB-II
Figure 4.10: Schematic representation of a possible new HBB device.
obtained by properly assembling ferromagnetic cores and feeding coils. The dimen- sions of the system are reported in fig.4.11 and they are regard an analytical design.
Fig.4.12 shows the device architecture without coils. The structures 1−10, 2−20and 3 − 30are used as base for the coils and to close the magnetic flux. All the cores are composed of ferromagnetic material AISI1015 with high magnetic permeability and with high saturation threshold in order to reduce its transversal section. In fig.4.13 is shown a particular of the section 4 − 40 activated. Such system is composed of two hollow ferromagnetic parallelepiped boxes with a series of little ferromagnetic
”pistons” winded by coils of about 2500 At for a fine control of the magnitude res- olution. Above each parallelepiped box is mounted an auxiliary system (not shown in the figures) able to move each piston along the vertical direction; when all the pistons are at rest (inside the box), the reluctance of the magnetic path, closed
Figure 4.11: The main dimensions of the new system HBB in cm.
along the line A − A0, is very high and the value of flux in the fluid is negligible;
on the contrary, when two opposed pistons are pushed out of the box (see fig.4.11), the airgap along the magnetic path is reduced and it results in an increase of mag- netic flux in a specified region of fluid corresponding to the x − y position of the pistons. In this way the electric current in the coils modulates the value of field and, instead, the spatial resolution is controlled by the exit and the input of each couple of pistons. Since such resolution is linked to the total number of the pistons, for the device reported in figures, the number of the pistons is 25 arranged as a 5 × 5 matrix with a total cover area of 81%. They regard the base surface of the box containing the MRF (the old device has a cover area of 14%, considering only the ferromagnetic core section, and of 55%, considering also the coil system). In order to increase the field uniformity in the fluid along the z direction, the plastic box containing the MRF is positioned in the center line between the two opposed systems 4 − 40.
4.5 From the HBB-I to HBB-II
Figure 4.12: Schematic representation of the new HBB device without coils.
4.5.3 Energization of the new HBB system
In order to better define the feeding system of the device and taking into account the indication obtained in previous chapter about the number of the Ampere-turns for the energization of the MRF, a deeper non-linear analysis of the magnetic circuit was performed. The study here performed takes into account the workspace of the device and the dimensions of its parts. Fig.4.12 and fig.4.13 show the system operating with an excited couple of pistons and fig.4.14 shows the equivalent magnetic circuit drawn on it. Since the different elements of the network are referred to the Hopkinson’s law, the terms <f e, <f lu, <p, and <a represent, respectively, the magnetic reluctance of the ferromagnetic cores, of the MRF, of the piston and of the airgap; the terms N1I1, N2I2 and NpIp instead, represent the magnetomotive forces (m.m.f.) of the
Figure 4.13: Particular of the A − A0 part during the energization.
different coils in the system. The analysis, based on the magnetic circuits’ theory by considering negligible the leakage flux, was carried out by means of a simple code and written in MATLAB software. Using the ”mesh method” to solve the network of fig.4.14, it is possible to obtain a set of equivalent magnetic equilibrium equations:
N1I1+ 2N2I2= (<f e+ 2<If e+ 2<IIf e+ 2<a12 +<flu12 )Φ1+ (2<IIf e)Φ2− (2<a12 +<flu12 )Φ3− (0)Φ4
N1I1+ 2N2I2= (2<IIf e)Φ1+ (<f e+ 2<If e+ 2<IIf e+ 2<a12 +<flu12 )Φ2+ (0)Φ3− (2<a12 +<flu12 )Φ4
2NpIp= −2(<a12 +<flu12 )Φ1+ 0Φ2+ (<p+ 2<Ia+ <f lu+ 2<a12 +<flu12 )Φ3+ (<p+ 2<Ia+ <f lu)Φ4
2NpIp= (0)Φ1− (2<a12 +<flu12 )Φ2+ (2<p+ 2<Ia+ <f lu)Φ3+ (2<p+ 2<Ia+ <f lu+<a12 +<flu12 )Φ4
where the terms divided by 12 represent the total reluctance of 12 branches in parallel. The figure takes into account the symmetry of the system: 12+12+1 = 25 pistons. Now, introducing the matrix form, the set of equations becomes:
[N I]4x1= [<]4x4[Φ]4x1. (4.9)
Finally, substituting some indicative values for the dimensions of the device and with a total number of 17500 At, it is possible to obtain a value of flux density
4.5 From the HBB-I to HBB-II
Figure 4.14: The equivalent magnetic circuit of new HBB design.
B = 0.6 T in the fluid. It can be seen that this value of B, that is about the same of those calculated in section, was obtained with less than half of Ampere-turns;
this difference is due to the presence of the ferromagnetic cores and pistons capable to reduce the reluctance of the system and to address the flux in a specified zone of the fluid.
4.5.4 The advanced FEM simulated model
Since this analysis was performed neglecting the leakage flux in the airgap of the system, the real number of Ampere-turns will be surely greater than the calculated one. However, when more than one piston is in action, due to the magnetic interac- tion between them, the analytical solution is not suitable and accurate results can be obtained only by using numerical methods.
Furthermore, the symmetry of the system allows simulating only 1/8 of the whole device. The shape of the device and its particular use suggested the possibility to modify the plastic box containing the fluid. As a result of different evaluations about the experimental tests concerning the MRF, it is possible to image the plastic box
Figure 4.15: Plastic box for MRF-based displays with a latex glove.
in a cubic shape with a square base of 20cm × 20cm and an height equal to the distance between two opposed active pistons (about 15 cm). On the other hand, in order to allow a good accessibility of the fluid, the box contains in the inner side a latex glove able to handle the magnetically excited fluid as shown in fig.4.15.
Although this modification doesn’t change the shape of the electromagnetic device, the height of the plastic box, full of MRF, reduces the reluctance of the airgap and allows a better operation of the system. On the contrary, the presence of the latex glove inside the fluid modifies its magnetic permeability, introducing some problems related to the field distribution that should be taken into account during the simulations. Finally, the number of pistons was increased from 25 to 49 (7 × 7) to obtain a fine resolution control. Indeed, to characterize the behaviour of the device in terms of field magnitude and its spatial resolution, several simulations were carried out and some results are here presented.
Fig.4.16 shows a 3D view of the simulated device (left) and a cut (right) inside it.
It is possible to see the coils around the ferromagnetic cores, the matrix of pistons and the MRF within the box. Fig.4.17 shows the matrix of pistons above the plastic
4.5 From the HBB-I to HBB-II
Figure 4.16: 3D view of the simulated device (left) and a cut inside the system (right).
box containing the MRF. Each piston, called Pi,j, can be identified with the indexes i, j, of the spatial distribution; for example, taking into account the symmetry of the system, the central piston is named P1,1. Fig.4.18 shows the device with an insertion of a ferromagnetic sheet around the box containing the fluid at a distance of about 4 − 5 cm. This modification could increase the magnetic field resolution in the MRF. Fig.4.23 shows the 1/8 of the device that, for the symmetry of system, was really simulated. It can be seen the mesh of the FEM model with the presence of the ferromagnetic sheet. Finally fig.4.20 shows the particular conic shape of the pistons head in order to better address the magnetic flux in the fluid.
4.5.5 Main simulations results
Fig.4.21 shows the flux density B in the fluid at z = 0 at the intersection of the MRF with a plane orthogonal at the box’s height in the center zone of the fluid, when only one couple of pistons are in action (specifically piston P1,1already shown in fig.4.17 and its opposed). In this case no ferromagnetic sheet is present in the
Figure 4.17: Perspective view of the pistons distribution.
device. The profile of B is considered along the red line indicated in figure. The maximum value of the field in the fluid is about two times that of the minimum (Bmax/Bmin ≈ 2). Fig.4.22 shows the flux density B in the same condition as before but with the ferromagnetic sheet around the fluid. In this case, the ratio between the maximum and minimum value in the field is about eight times, being Bmax/Bmin ≈ 8. Since the introduction of the ferromagnetic sheet in the system is due to some considerations about the leakage flux, fig.4.23 shows the behaviour of the vector B in the whole space occupied by the device. Fig.4.24 zooms in the area of interest and shows how the sheet collects the leakage flux that, in this way, doesn’t interest the volume of fluid out of the pistons. In order to simulate the presence of the latex glove in the fluid (see fig.4.15), some modelings and simulations were carried out. Fig.4.25 shows the flux density B in same condition as in fig.4.22 but with a hand inside the fluid, modeled by changing the relative permeability from 5 to 1. In this case, the ratio between the maximum and minimum value of the field in the fluid is about 8.5 times: Bmax/Bmin ≈ 8.5 with a higher value of field magnitude and a better 2D spatial resolution. Fig.4.26 shows the behaviour
4.5 From the HBB-I to HBB-II
Figure 4.18: The device with a ferromagnetic sheet.
of the vector B in presence of the hand. Finally, a last simulation with more than one piston in action was performed in order to evaluate the field in the fluid. In particular, in this case the active pistons are the red (P1,1) and the green ones (P1,2 and P1,20 ) with their opposed. The result is shown in fig.4.27. It can be seen that the value of the field is about 0.55 Tesla. Furthermore, due to the presence of the MRF, when a couple of pistons is “in action”, an attractive magnetic force acts between the pistons and the MRF. Such magnetic force was simulated and its value is approximately 2.8 N for each active piston. According to this value an electromagnetic actuator necessary to move each piston along its axial direction in order to reach an active piston (near the fluid) or a rest position (far from the fluid) should be considered.
Taking into account the general considerations and the results previously pre- sented, another design of a new Haptic Black Box display, capable of improving the ability of the MRF to mimic the rheology of some materials was examined. A schematic view of the whole system with the main dimensions is shown in fig.4.28.
This configuration represents an evolution of the previous design of the HBB device.
Figure 4.19: 1/8 of the FEM model of the device.
The main improvements concerned the reduction of the overall dimensions.
Also in this case due to the symmetry of the device only 1/8 of the domain can be modeled (fig.4.29). The simple modeling allowed us to reduce the complexity of the FEM simulations without compromise the numerical results.
Different simulations were performed and they confirmed a similar energization respect the previous designs. In fig.4.30 an exemplificative simulation of the archi- tecture, when the central couple of pistons is active with the presence of MRF, is reported.
4.5 From the HBB-I to HBB-II
Figure 4.20: Particular of the pistons with the conic shape head.
Figure 4.21: Flux density in the fluid at z = 0, without ferromagnetic sheet.
Figure 4.22: Flux density in the fluid at z = 0, with ferromagnetic sheet.
Figure 4.23: Vector B in the whole space occupied by the device.
4.5 From the HBB-I to HBB-II
Figure 4.24: The operation of ferromagnetic sheet.
Figure 4.25: Flux density in the fluid at z = 0, with ferromagnetic sheet and with the hand inside it.
Figure 4.26: Vector B in the volume near the fluid in presence of the ferromagnetic sheet and of the hand.
Figure 4.27: Flux density in the fluid at z = 0 with 3 active pistons.
4.5 From the HBB-I to HBB-II
Figure 4.28: Architecture of a new design of HBB.
Figure 4.29: Symmmetry of the new design of HBB.
Figure 4.30: Simulation of the new design of HBB.
