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This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/3.0/).

A novel multi-fork z-axis gyroscope is presented in this paper. Different from traditional quartz gyroscopes, the lateral electrodes of the sense beam can be arranged in simple patterns; as a result, the fabrication is simplified. High sensitivity is achieved by the multi-fork design. The working principles are introduced, while the finite element method (FEM) is used to simulate the modal and sensitivity. A quartz fork is fabricated, and a prototype is assembled. Impedance testing shows that the drive frequency and sense frequency are similar to the simulations, and the quality factor is approximately 10,000 in air. The scale factor is measured to be 18.134 mV/(°/s) and the nonlinearity is 0.40% in a full-scale input range of ±250 °/s.

The quartz gyroscope is an important sensor used in various civil and military applications [

The organization of the paper is as follows: first a brief description of the principle and structure is provided in the Introduction section. Device modeling is discussed in Section 2. Theoretical analysis and simulation are introduced in Section 3. Fabrication and signal detection methods are described in Section 4, while experimental test results are presented in Section 5, and the summary and conclusions are given in the last section.

The working principle of a quartz gyroscope is based on the Coriolis effect. In this paper, we present a z-axis gyroscope. The structure of the drive fork and sense fork are shown in

When the drive forks are driven, a vibration is induced along the x-axis based on the inverse piezoelectric effect, while an opposite vibration occurs on the four drive forks in x-axis direction. The drive mode is shown in

Therefore, the following benefits can be determined when comparing the gyroscope presented in this paper with a traditional y-axis gyroscope:

The fabrication of the electrode is easy: it can sense the angular rate without complex electrodes.

The thickness of the wafer has little effect on the mode frequency; thus, the wafer can be made thinner, but the shock resistance should be considered.

The symmetry of this structure can suppress the effects of the linear acceleration and cross-coupling,

In addition, when compared to other z-axis gyroscopes [

The most basic design goal is to obtain the appropriate resonant frequency; One beam of the drive mode is shown in _{n}_{n}

From this equation, it is possible to express the resonant equation, as below:
_{1} and _{2} represent the length of the left and right parts of the cross beam.

The Transfer Matrix Method [_{1} and _{2} can cause a resonant frequency change in the sense mode. The different beam has four elements ^{T}

First, considering the beam section from point 0 to point 1, the following equations can be derived [

Next, considering the point mass from the left of point 1 to the right of point 1, the following equations can be obtained:

From Equations ^{T}

Using the same method, the relationship from point 1 to point 2 can be written as

Using the boundary conditions of the beam, which are expressed in

The state vector of the left point on the beam can be expressed as in

Thus,

A system of homogeneous Equations can be obtained from the above result that are expressed in _{i}

The results calculated in MATLAB are shown in _{22},

From the above analysis, it is possible to draw a couple of conclusions.

As the length of the cross beam increases the sense mode frequency will decrease. As the width increases the sense mode frequency will increase. As the _{1}:_{2} ratio increases the sense mode frequency will increase.

As the distance between the drive fork and the sense fork decreases, the sense mode frequency will become higher.

Finite element method (FEM) analysis is used to perform modelling and simulation. The frequency change with different dimension of the fork is simulated as shown in

It can be seen from

These results can be used to design the dimensions of a structure. From the simulation, the dimensions of the chip are set as shown in

From the above analysis, the following conclusions can be drawn:

The drive mode frequency is determined by the drive fork dimensions.

Sense mode frequency is dominated by the width and length of the cross beam.

Changes in the drive fork and sense fork will change the equivalent mass, and affect the frequency of the sense mode.

The position of the sense fork will change the frequency of the sense mode.

To obtain the highest sensitivity, the sensitivity can be expressed by _{r}_{d}_{s} is the sensitivity phase, _{r}_{d}_{x}_{0} is the drive displacement, and _{s}

The output of the gyroscope is the charge signal; so, the result can be simulated in ANSYS software. The voltage sensitivity result is shown in

The fabrication process is shown in _{4}F (40 wt % aqueous solution) (concentration ratio of the HF and NH_{4}F is 1:2) is used to etch the quartz at 50 °C for 48 h. Long etching time can give rise to good etch result, while it is limited by the Cr/Au films adhesive force on the quartz wafer (

From _{d}_{s}

The signal detection method is shown in

The testing system is shown in

In this paper, the modeling, simulation, fabrication, and performance characterization of a kind of multi fork z-axis quartz gyroscope are presented. With the proposed scheme, the fabrication process on the lateral electrode can be simplified compared to traditional quartz gyroscopes. Benefiting from the multi fork design, a higher sensitivity than possible with some other z-axis quartz gyroscopes is obtained. The structure is etched from a z-cut quartz wafer. The drive mode frequency is measured to be about 11 kHz and the quality factor is about 10,000 in air at atmospheric pressure, indicating the gyroscope can function in air without the need for a vacuum package. The experimentally obtained scale factor is 18.137 mV/(°/s) and the nonlinearity is 0.40% in the range of ±250 °/s. The sensitivity is higher than 0.05 °/s at the bandwidth of 50 Hz.

Thanks for the grants of School of Optoelectronics in Beijing Institute of Technology. This work is supported by Natural Science Foundation of China (Grant No. 61027007).

The authors declare no conflict of interest.

Vibration modes and electrode distribution of a traditional gyroscope. (

Structure and electrode distribution. (

Vibration modes of the gyroscope. (

(

The relationship between frequency and various dimensions, (_{1}:l_{2}

The effect of different fork dimension on the frequency. (

The dimensions of the chip.

Simulation of voltage sensitivity.

Fabrication process.

Packaged device.

Impendence testing. (

Signal detection process; (

Testing system.

Output with different input angular rate with ±0.1 °/s, ±0.5 °/s, ±1 °/s, ±5 °/s, ±10 °/s, ±20 °/s, ±40 °/s, ±60 °/s, ±80 °/s, ±100 °/s, ±120 °/s, ±140 °/s, ±160 °/s, ±180 °/s, ±200 °/s, ±220 °/s, ±240 °/s, ±250 °/s.

Statistical output with different input angular rate.

Sensitivity test.

The dimensions of the chip (μm).

Length of drive fork | 7,030 | Width of drive fork | 790 |

Length of sense fork | 6,400 | Width of sense fork | 800 |

_{1} |
1,230 | _{2} |
1,420 |

Thickness of fork | 500 |

Simulation data with different angular rates.

0 | — | — |

1 | 1.243 × 10^{−5} |
−0.207 |

2 | 2.485 × 10^{−5} |
−0.204 |

5 | 6.214 × 10^{−5} |
−0.203 |

10 | 1.243 × 10^{−4} |
−0.203 |

Values of the drive mode and sense mode of the fork.

_{0} (pF) |
_{1} (pF) |
_{1} (kΩ) |
_{1} (kH) | |||
---|---|---|---|---|---|---|

Drive mode | 11.185 | 11,735 | 6.631 | 0.017 | 71.450 | 11.931 |

Sense mode | 11.324 | 7,697 | 7.131 | 0.005 | 345.485 | 37.387 |