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EMS Structural simulation of Magnetic micro-actuator design for tactile display

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A variety of developed actuation mechanisms are used for the reproduction of tactile sensation in haptic devices. In this paper, the proposedtactile micro-actuator is based on Micro-magneto-mechanical systems. It allows high deflection of its deformable active surfacesunder high magnetic forces.Hence, the use of a high mechanically resistant elastomeric material, was successfully processedas an alternative to classical PDMS, in such tactile applications.

The proposed model is composed of an array of pulse-driven magnetostatic micro-actuators with 2 mm pitch.It proved to be a relevant choice for a hybriddesign, joining micro-engineering and microfabrication techniques.This permits to reach large deformations without any deterioration of the mechanism.

Figure 1 shows the structure of the studied tactile device.

4×4 micro-actuator array: mounting and integration into its packaging

Figure 1 - 4×4 micro-actuator array: mounting and integration into its packaging [2].

Problem description

The Magnetostatic micro-actuator array proposed in this paper is composed of 4 × 4 individually driven micro-actuatorswith a resolution of 2mm. Each designconsists of two parts: a first part constituted of a mobile elastomeric membrane made of PDMS based on a Silicon substrate holding a micromagnet at its center. The second part is holding a fixed copper coil underneath the magnet and surrounding a ferromagnetic core. The whole dimensions are detailed in table 1.

Figure 2: a). Cross-sectional view of the tactile micro-actuator [1] b) 3D CAD design

Figure 2 - a). Cross-sectional view of the tactile micro-actuator [1] b) 3D CAD design.

Table1 : Components  dimensions

Component Dimensions (mm)
Coil Inner diameter Outer diameter Height
0.5 1.2 1.8
PDMS membrane Length height Width
2 2 0.8
Substrate Outer part Length Height Width
2 2 0.8
Inner part Inner Diameter Outer diameter Thickness
1.2 1.7 0.8
Magnet Diameter Height
1 0.5
Core Diameter Height
0.5 1.8
Gap between coil and magnet 0.4

Simulation setup

The main goal of the study is to compute and visualize the PDMS-membrane deflection produced by the magnetic actuation forces of the Coil-Magnet interaction. A FEM simulation was performed by coupling the magnetostatic module of EMS to structural analysis.

The following steps define the required simulation setup:

1.Select the appropriate materials:

Table 2: Material properties  
Part Material Density
(Kg/m cubed)
Magnetic permeability Electrical conductivity
Elastic Modulus
Poissons ratio Magnetization
Coercivity (A/m)
Remanence (T)
Coil Copper (Cu) 8900 0.99 5.7 E+07 Not required Not required
Membrane PDMS 1030 1.38 0 2E+6 0.49
Substrate Silicon (Si) 2329 1 0 159E+9 0.27
Core Permalloy (NiFe) Not required 82000 0 Not required 
Magnet Neodymium-Iron-Boron (NdFeB) 1.175 0 954929

2.Electromagnetic Inputs:

The inductor coil is defined as a woundcoil defined by table 3:

Table 3: Coil properties.
  Number of turns Wire diameter (mm). RMS current ammplitude (A)
Wound coil-1 48 0.15 0.8


 3.Mechanical boundary conditions:

Fixed boundary conditions are applied to the four lateral sides of the PDMS membrane, as shown in the figure 3:


Figure 3: Applied mechanical boundary conditions.


The mesh of the deformed part (Elastomeric membrane) should be refined to get accurate magnetic force calculation and to guarantee enough elements for stress and deformation computing. The figure below shows the whole meshed model with a fine mesh control applied to the top parts.

Figure 4 - a). The whole meshed model b). Bottom View.


A multi physics simulation was performed using EMS tool allowed the determination of the magnetic force resulting from the interaction between the magnet and the coil. The obtained results are shown in figures below.

The magnetic flux distribution, for both core and magnet part, is visualized through figure 5.


Figure 5 - Magnetic flux distribution across a). the core and b). the magnet parts.

Table 4: EMS Results table of the virtual work defining the coil-magnet interaction.

  Fx-axis (N) Fy-axis (N) Fz-axis (N)
Virtual Work - 1

The correlation between the Reference [1] and EMS results appears very well through the obtained results of the magnetic actuation force and the maximum deflection value of the PDMS membrane. Table 5 shows this agreement:

Table 5: Comparative table between EMS and Reference [1] results.

Results EMS Reference [1]
Actuation force (mN) 5.18 5
Maximum deflection (µm) 108.9 108.6

Under the influence of the magnetic forces acting on it, the membrane is bending towards its center with a significant deflection magnitude, as shown in figure6. 


Figure 6 - Section plot of theResultant displacement of the membrane.



This paper presents the investigation of the advances in magnetostatic micro-actuation and polymer-based MEMS processing. The characterization of such type of tactile display actuators showed good performance and satisfaction in terms of generated forces and deflections at small scales, with respect to low power consumption.
The obtained EMS results confirm the ability of Magnetostatic micro-mechanisms to fulfill the satisfaction of tactile sensation in haptic devices, independently of actuation frequency.


[1].Streque, Jeremy, et al. "New magnetic microactuator design based on PDMS elastomer and MEMS technologies for tactile display." IEEE Transactions on Haptics 3.2 (2010): 88-97.
[2]. Streque, J., et al. "Pulse-driven magnetostatic micro-actuator array based on ultrasoft elastomeric membranes for active surface applications." Journal of Micromechanics and Microengineering 22.9 (2012): 095020.