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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 signal mass piezoelectric six-degrees-of-freedom (six-DOF) accelerometer is put forward in response to the need for health monitoring of the dynamic vibration characteristics of high grade digitally controlled machine tools. The operating principle of the piezoelectric six-degrees-of-freedom accelerometer is analyzed, and its structure model is constructed. The numerical simulation model (finite element model) of the six axis accelerometer is established. Piezoelectric quartz is chosen for the acceleration sensing element and conversion element, and its static sensitivity, static coupling interference and dynamic natural frequency, dynamic cross coupling are analyzed by ANSYS software. Research results show that the piezoelectric six-DOF accelerometer has advantages of simple and rational structure, correct sensing principle and mathematic model, good linearity, high rigidity, and theoretical natural frequency is more than 25 kHz, no nonlinear cross coupling and no complex decoupling work.

Many motion controlled and measured systems, such as vehicles, automatic navigation, earthquake prediction devices, robot control systems, health monitoring of machine tools and other areas require determination of spatial vibration characteristics. This spatial vibration information can be described by the six-DOF acceleration motion. Six-axis accelerometers which can perform the simultaneous measurement of the six spatial components (three translational and three rotational) of acceleration are used as important sensing elements for detecting spatial vibration information.

At present, six-DOF acceleration sensing methods can be classified into the single-mass-spring-damper six-axis acceleration sensing approach (SPMSD approach) and the integrated six-axis acceleration sensing approach based on multiple single-axis accelerometers (MSAAs approach) [

According to the type of conversion element used, the six-axis accelerometers based on the SPMSD approach can be classified into elastic style [

According to the number of single-axis accelerometers used, six-DOF accelerometers based on the MSAAs approach can be classified into six-single-axis accelerometer style and nine-single-axis accelerometer style [

In order to overcome the shortcomings of the six axis accelerometer based on the SPMSD and MSAAs approaches, in this paper, a novel six-DOF accelerometer sensing principle based on a single inertial mass is presented. Piezoelectric quartz is chosen for the force sensing element and conversion element. The operating principle of the proposed six-axis accelerometer is analyzed, a structure model is built, a numerical finite element model of the piezoelectric six-DOF accelerometer is set up, and its static sensitivity, static coupling interference and dynamic natural frequency, and dynamic cross coupling are analyzed by ANSYS software. The research results show that the measurement principle of the piezoelectric six-DOF accelerometer is correct.

The mechanical structure of the piezoelectric six-DOF accelerometer is shown in

The spatial layout structure schematic of the quartz chip groups within the piezoelectric six-axis accelerometer is shown in _{x}_{y}_{z}_{x}_{y}_{z}_{X}_{Y}_{Z}_{X}_{Y}_{Z}^{0}-crystals are distributed on the nodes of X and Y axes and the quartz crystal chip groups distribution circle, and are used for the measurement of _{x}_{y}_{z}^{0}-crystals are distributed on other locations and are used for the measurement of _{z}_{x}_{y}

Due to the influence of the piezoelectric six-axis accelerometer structure, the layout of the quartz chip group, the quantity and production level (among other factors), the arrangement of the quantity of quartz crystal cells and the production level, the actual conditions do not fully meet the above assumption in practice. Therefore, the acceleration transfer coefficients of _{ax}_{,}_{ay}_{,}_{az}_{,}_{amx}_{,}_{amy}_{and}_{amz}

To simplify the analysis, the following assumptions are adopted: the rigidities of the quartz crystal chip groups are identical, with equal sensitivity and symmetry uniform distribution. The inertial mass is a rigid body with the same stiffness in all directions, equal sensitivity, and uniform distribution. The directions of _{z}_{x}_{y}_{x}_{y}_{z}

_{1}-X_{1}Y_{1}Z_{1} denotes the installation layout position coordinate system of quartz crystal chip groups. The quartz crystal chip groups are arranged along the same circle with radius is R, the distance between the quartz chip group 2 and 4 is r = Rcos45°, and the distance between the centroid of inertial mass and the surface of quartz crystal chip groups is b, the inertial force that generated by acceleration acting on each quartz crystal chip groups can be expressed by

According to

As can be seen from _{y}_{x}_{x}_{y}

To verify the effectiveness of the piezoelectric six-axis accelerometer structure model, ANSYS software is used to pre-assess the piezoelectric six-DOF accelerometer's static and dynamic characteristics. ANSYS software has powerful analysis capability in the coupled field, which is the preferred software in the field of piezoelectric analysis. However, its physical model modeling function is weak, making it unsuitable for creating complex physical models. So the analysis process of the six-DOF accelerometer primarily applies a modeling approach and load application method.

In the first step, the physical structural model of the piezoelectric six-axis accelerometer is built with CAD software (

This approach includes the installation constraints and acceleration loading on the piezoelectric six-axis accelerometer. The constraints set adhere to the sensor's installation status and the preload force is applied through a section of the inertial mass. The degree of freedom of the pedestal's mounting surface is zero. The measured accelerations are applied to the key point, which is established on the Z axis and located in the same plane as the upper surface of the inertial mass. Additionally, the key point and the upper surface of the inertial mass are built in the rigid region.

In the piezoelectric coupled field process based on the ANSYS software, the potential difference between the surface of piezoelectric quartz crystal chip can be obtained, so in the paper, the relationship between the potential difference and the acceleration was selected instead of the relationship between the acceleration input and the potential output. _{x}_{y}_{z}_{x}_{y}_{z}

_{x}_{y}_{z}^{2}) in the _{x}^{2}) in the _{y}^{2}) in the _{z}_{y}_{x}_{x}_{y}

Research on the piezoelectric six-DOF accelerometer's dynamic characteristics involves the study of its natural frequency. Modal analysis, harmonic analysis and other methods based on ANSYS software can be used to estimate the natural frequency of the six-axis accelerometer.

To study the amplitude frequency characteristics of the piezoelectric six-DOF accelerometer, the harmonic analysis method was chosen.

_{y}_{x}_{x}_{y}

In this paper, the feasibility of the six-DOF acceleration sensing principle based on the SPMSD approach has been explored. On this basis, the principle and characteristics of the six-DOF acceleration sensing method based on signal mass piezoelectric six axis accelerometer has been proposed and analyzed. According to the research results, the following conclusions can be obtained:

The six-axis acceleration sensing principle and the structure of the single inertial mass piezoelectric six-DOF accelerometer can effectively provide the 6-axis acceleration information.

Due to the influence of the six-DOF accelerometer's spatial structure, there are some cross coupling interferences of six-axis accelerometer take place in the _{y}_{x}_{x}_{y}

According to the one-dimensional miniature piezoelectric accelerometer research approach of the literature [

Compared with commercial single or multi-axis linear accelerometers or angular accelerometers, although the sensitivity of piezoelectric six axis accelerometer is slightly lower, its natural frequency is expected to increase 2–5 times.

This work is supported by the National High Technology Research and Development Program of China (863 Program) (No. 2012AA040107), the Natural Science Foundation Project of ChongQing China CSTC (No.CSTC2012JJA40024), the Fundamental Research Funds for the Central Universities (No. 1061120131205).

The authors declare no conflict of interest.

Schematic diagram of the 6-axis accelerometer. (

Block diagram of the sensor's structure.

Piezoelectric six-DOF sensor's input acceleration and output voltage curve. (

Inherent vibration modes of the piezoelectric six-DOF accelerometer. (

The amplitude-frequency response curve of piezoelectric six-DOF accelerometer. (

The strain cloud of six-DOF accelerometer's core parts and quartz crystal chip groups under the composite loads.

Main structural parameters of the six-DOF accelerometer model.

^{3}) | |||||
---|---|---|---|---|---|

Inertial mass | 10 | 46 | 1Cr18Ni9Ti | 2.1e11 | 7,900 |

Mounting boss | 4 | 46 | 1Cr18Ni9Ti | 2.1e11 | 7,900 |

Mounting pedestal | 4 | 50 | 1Cr18Ni9Ti | 2.1e11 | 7,900 |

Quartz crystal chip | 2 | 10 | SiO_{2} |
8.0e10 | 2,650 |

Simulation results of static sensitivity and cross coupling.

| ||||||
---|---|---|---|---|---|---|

Ax(V/g) | 0.697 | 0.15% | −0.06% | 0.80% | 61.84% | −0.07% |

Ay(V/g) | −0.03% | 0.695 | 0.03% | −61.78% | 0.41% | −0.07% |

Az(V/g) | 0.00% | −0.01% | 0.792 | 0.12% | 0.10% | 0.11% |

AMx(V/(rad/s^{2})) |
0.00% | −60.93% | v0.12% | 0.00174 | −0.52% | 0.06% |

AMy(V/(rad/s^{2})) |
60.93% | 0.11% | −0.06% | 0.80% | 0.00174 | −0.06% |

AMz(V/(rad/s^{2})) |
0.07% | 0.07% | 0.17% | −0.03% | −0.03% | 0.00302 |

Simulation results of modal analysis.

1 | 25,107 | The linear vibration of inertial mass along the X-axis |

2 | 25,132 | The linear vibration of inertial mass along the Y-axis |

3 | 26,685 | The rotational vibration of inertial mass along the Z-axis |

4 | 40,327 | The folded vibration of inertial mass along the bisector of X and Y-axis |

5 | 40,493 | The folded vibration of inertial mass along the Y-axis |

6 | 43,046 | The linear vibration of the outer edge of inertial mass along the Z-axis |

Analytical results of composite loads.

Ax | 490 m/s^{2} |
133.111 V | 488.70 m/s^{2} |
0.27% |

Ay | 490 m/s^{2} |
−62.731 V | 491.09 m/s^{2} |
−0.22% |

Az | 490 m/s^{2} |
−39.512 V | 489.48 m/s^{2} |
0.11% |

AMx | 92,395 rad/s^{2} |
140.746 V | 92,464.11 rad/s^{2} |
−0.07% |

AMy | 92,395 rad/s^{2} |
182.008 V | 92,501.62 rad/s^{2} |
−0.12% |

AMz | 65,333 rad/s^{2} |
−197.244 V | 65,332.21 rad/s^{2} |
0.00% |