**By R. Belmans**

## Design of electrostatic micro motors

**Scaling analysis shows that as size is reduced,** electrostatic designs become advantageous over the electromagnetic versions that dominate at dimensions starting in the millimetre range. The electrostatic micro motors studied here are based on the principal of variable capacitance. The operation principle is very simple. A voltage on the stator electrodes induces a charge on a conducting rotor and in response the rotor moves to minimise the electrostatic field energy.

**The most inexpensive fabrication technology** of electrostatic micro machines is a thin film process for planar structures. Therefore, such rotating actuators are extremely flat and the generated forces are very low. The motor with its outer dimensions is shown in Fig. 10.26. Fig. 10.27 shows its corresponding three-dimensional finite element model. In this case of geometrical symmetry, the mesh is extruded in an angular direction to build up the three-dimensional structure (Fig. 10.27b).

**Fig. 10.26. Detailed construction and outer dimensions of the studied axial field electrostatic micro motor.**

**Fig. 10.27. a) Axial field electrostatic micro motor model and b) the base planes rotated in angular extrusion direction.**

**Radial field type machines are also feasible.** When the same height of the machine is considered, the surface that contributes to the interaction between stator and rotor is much smaller. However, the problem is that only very small forces can be generated. Using a radial type of interaction and the LIGA production technique, allowing the fabrication of higher microstructures, results in higher torque values. This technique is very expensive. More inexpensive alternatives are developed but are not capable of supplying the same depth of the rotor. Fig. 10.28 shows the three-dimensional finite element model of a radial field micro motor.

**However,** both types of motor can be analysed in an analogue way. The electrostatic energy stored in the model is evaluated and serves as data to obtain the parameters of an equivalent circuit.

**Fig. 10.28. Radial field electrostatic micro motor with FEM model.**

The use of this equivalent circuit model enables calculation of the forces of the motor operated with various voltage cycles without new computationally expensive FEM analyses.

**The desired parameters in the equivalent circuit are the values** C of the capacity between the single components of the geometry as indicated in Fig. 10.29. The equivalent circuit in Fig. 10.29 consists of 12 capacitances, twice the number of stator electrodes. The capacitance of each capacitor varies with the rotor position.

**Fig. 10.29. Definition of the elements of the equivalent circuit for a 6/8 pole radial field electrostatic micro motor.**

**To avoid axial forces on the rotor shaft,** the motor must be excited symmetrically. Fig. 10.30 shows the possible symmetric excitations of a motor with 6 stator electrodes. The grey electrodes are excited by 1 V and the rotor electrodes are set to ground potential 0 V.

**Fig. 10.30. Possible symmetrical excitation sequence to perform one revolution of the rotor.**

**By applying different** excitation cycles to the equivalent circuit, the torque characteristics versus rotor position can be calculated. Using the principles of virtual work, the torque is found by partial differentiating of energy with respect to the angle of rotation:

**Fig. 10.31. Potential solution of the radial cross-section of the axial field motor.**

**Fig. 10.32. Potential solution of the radial field type micro motor.**