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A novel design of a microelectromechanical systems (MEMS) control moment gyroscope (MCMG) was proposed in this paper in order to generate a torque output with a magnitude of 10^{−6} N·m. The MCMG consists of two orthogonal angular vibration systems, ^{−8} N·m. The element with four MCMGs could generate a torque of 5 × 10^{−8} N·m. The torque output could reach a magnitude of 10^{−6} N·m when the frequency was improved from 1,000 Hz to 10,000 Hz. Using arrays of 4 × 4 effective elements on a 1 kg spacecraft with a standard form factor of 10 cm × 10 cm × 10 cm, a 10 degrees attitude change could be achieved in 26.96 s.

Miniature, low cost, and autonomous spacecrafts have been the focus of NASA since 1992 [

There are two fundamental ways to control the attitude of spacecrafts, either by applying external torques through technologies such as thrusters [

The working principles of RW, CMG, and VSCMG are very similar. When a torque is exerted on the wheel, an equal and opposite reaction torque is applied to the spacecraft. RWs are electric motor driven rotors made to spin in the direction opposite to that required to re-orient the spacecraft [

The conventional CMGs were large in size, mechanically complex, and expensive. Many efforts have been made to obtain mini-CMGs to satisfy the needs of small satellites with a weight of 1–20 kg [

The major challenge to realize the RW or CMG through MEMS technologies lies in the miniaturization of traditional momentum wheels. Eunjeong Lee proposed a fully rotating miniature flywheel based on high temperature superconductor technology for nano satellites [^{−12} N·m. Obviously, this vibration-based miniature CMG eliminates the need for advanced bearings. It is quite a promising attitude control technology. However, the magnitude of the torque was too small to change the attitude of a sub-kg spacecraft. In this paper, we designed a MCMG in detail using a feasible micromachining process flow. Furthermore, the maximum torque output was largely improved, which would bring forth possible applications in sub-kg spacecrafts.

The working principle of the MCMG is similar, yet precisely opposite, to that of conventional MEMS Coriolis vibratory gyroscopes (CVG). MCMGs uses Coriolis effect to influence the outside world, while MEMS CVGs use Coriolis effect to sense the outside world. The proposed MCMG is actually a single gimbal CMG. For development equations of the torque output, two reference frames, _{g}_{g}_{g}_{s}_{s}_{s}_{g}_{g}_{g}

If a rotation is applied to the spinning disc about _{g}_{g}

In the proposed MCMG, angular sinusoidal vibrations substitute the angular rotations. The angular displacements of rotor and gimbal in corresponding frames can be expressed as following:
_{r}_{g}

Substituting

It is obvious that the amplitude of the output torque is proportional to the inertial moment of spinning disc

MCMG consists of two orthogonal angular vibration systems,

Wire pads for comb drives are usually located at fixed combs. This can, however, not be used for MCMGs. The vibration of the SOI sandwich will break off the wires. To solve this problem, the ‘link structure’ (

A process flow is proposed to realize such a MCMG structure as shown in

This process flow has three advantages at least. In contrast with the surface process [

Based on the aforementioned design scheme, we gave a group of major parameters with their feasible values as shown in _{1} and _{2}, and the voltages applied on the gimbal’s two electrodes of the parallel plate actuator were _{3} and _{4}. The expressions of the voltages are listed in

Transient analysis results of the MCMG are shown in ^{−8} N·m. The rotor’s kinetic energy in the MCMG can be calculated by the equation as following.

The maximum instantaneous energy that the rotor sustained is just the maximum kinetic energy of the rotor. According to ^{−7} J. The power of a single MCMG can also be obtained from the transient analysis results. The total power of four voltage sources, _{1}, _{2}, _{3} and _{4}, was about 0.26 mW as shown in

The output torque of the designed MCMG can be enhanced further in several ways. It is very efficient to enhance the torque output by increasing the resonant frequency, since the torque is proportional to square of the frequency. As for the current design, if we improved the resonant frequency from 1000 Hz to 10,000 Hz, then the torque output could reach a magnitude of 10^{−6} N·m. Increasing inertial moment of the rotor means to augment the size of the whole MCMG. However, the size of a chip is usually restricted by the corresponding micromachining process. The layout area for the MCMG with 3 microns as the critical dimension is usually limited to 1.0 cm × 1.0 cm approximately. Another way is to increase the driving voltages to enlarge the angular vibration amplitude of both rotor and gimbal. However, the pull-in phenomenon of parallel plate capacitor actuators [

In order to meet the requirements of practical attitude control, parasitic torque and fluctuations of torque output for MCMG need to be eliminated or smoothed. The parasitic torque is generated due to change of the gimbal momentum. A configuration of two-MCMG pairs with an opposite phase can cancel the parasitic torque effectively (

According to _{1} = ^{2} _{2} = ^{2} (^{2} _{r}A_{g}

All in all, in order to solve the two problems mentioned above, an array configuration using four MCMGs as an effective MCMG element, in which the torques are generated with a phase difference of ^{−8} N·m.

A 1 kg cubic spacecraft with a standard form factor of 10 cm × 10 cm × 10 cm [^{−6} N·m. Then the spacecraft can change its attitude around three axes in Cartesian coordinate system. Using such a configuration, a 10-degree attitude change, a five-degree acceleration phase and a five-degree deceleration phase [

In this paper, a novel concept of MEMS control moment gyroscope was designed and simulated, and a possible process flow was also presented. The performance of the MCMG was projected to have a torque output of 2.5 × 10^{−8} N·m, even larger to a magnitude of 10^{−6} N·m. The proposed four-MCMG array configuration with a phase difference of 90 degrees between every two MCMGs was proved very effective to null out the parasitic torque and smooth the output torque. Through a proper configuration, the MCMG could be used to generate a torque output that is big enough to change the attitude for the sub-kg spacecraft.

The authors gratefully acknowledge Chinese Hi-Tech Research and Development Program’s financial support (Contract No.2009AA04Z320), Xi’an Applied Materials Innovation Fund of China’s financial support (No. XA-AM-200801), and Chinese National Science Foundation’s financial support (Contract No. 60976087).

Schematic of a single gimbal CMG.

(a) Top view of MCMG. (b) Cross section of MCMG. (c) Solid model of MCMG. (The figures are not to scale).

The designed link structure to supply electronic voltage.

The proposed process flow for the MCMG.

The system level model of MCMG established in Architect.

(a) AC analysis results of the rotor. (b) AC analysis results of the gimbal.

(a) Transient analysis results of the MCMG. (b) A closer view of the results.

The power of voltage sources in a MCMG.

Cancellation of the parasitic torque by the MCMG pair with an opposite phase.

The array configuration with four MCMGs as an element.

The array configuration of MCMG elements on a spacecraft.

Major parameters for the MCMG.

Length of gimbal | Thickness of gimbal | Length of gimbal beam | Width of gimbal beam | Thickness of dioxide layer | |

Length of rotor beam | Width of rotor beam | Thickness of rotor | Inner diameter of pie plate | Outer diameter of pie plate | |

Length of pie plate | Comb finger length | Comb finger width | Comb finger gap | Comb finger overlap | |

_{1} = 25 + 25 sin(2_{2} = 25 + 25 sin(2 | |||||

_{3} = 50 + 50 sin(2_{4} = 50 + 5 sin(2 |