阅读说明：本技术 一种石英圆柱谐振子第二次谐波误差的化学修调方法 (Chemical trimming method for second harmonic error of quartz cylindrical harmonic oscillator ) 是由 潘瑶 陶云峰 贾永雷 谭中奇 金世龙 杨开勇 罗晖 于 2020-05-11 设计创作，主要内容包括：本发明属于振动陀螺技术领域,公开了一种石英圆柱谐振子第二次谐波误差的化学修调方法,所述方法包括步骤：A、通过扫频方法获得谐振子的本征频率、频率裂解和固有刚性轴方位；B、根据谐振子的本征频率、质量、振幅比,计算谐振子的第二次谐波误差值；C、根据化学修形的浸没深度、倾斜角度、谐振子的第二次谐波误差值和化学刻蚀液的刻蚀速率计算化学修形时间；D、根据化学修形时间,利用化学刻蚀液沿低频轴方位间隔180°的两个位置上对谐振子刻蚀。通过在谐振子n＝1模态的低频轴方位去除特定质量来降低第二次谐波误差值,该方法能够进一步改善谐振子的一致性和对称性,降低输出信号中的噪声,提高圆柱振动陀螺的精度。(The invention belongs to the technical field of vibrating gyros and discloses a chemical trimming method for second harmonic errors of quartz cylindrical harmonic oscillators, which comprises the following steps: A. obtaining the eigenfrequency, frequency cracking and inherent rigid axis orientation of the harmonic oscillator by a frequency sweeping method; B. calculating a second harmonic error value of the harmonic oscillator according to the eigenfrequency, the mass and the amplitude ratio of the harmonic oscillator; C. calculating chemical modification time according to the immersion depth and the inclination angle of the chemical modification, the second harmonic error value of the harmonic oscillator and the etching rate of the chemical etching liquid; D. and etching the harmonic oscillator at two positions which are spaced by 180 degrees along the low-frequency axis by using chemical etching liquid according to the chemical modification time. The second harmonic error value is reduced by removing the specific mass in the low-frequency axis direction of the harmonic oscillator n-1 mode, the method can further improve the consistency and symmetry of the harmonic oscillator, reduce the noise in an output signal and improve the precision of the cylindrical vibration gyro.)

1. A chemical trimming method for second harmonic errors of quartz cylindrical harmonic oscillators is characterized by comprising the following steps:

s1: determining the inherent rigid axis orientation and the frequency cracking value of a quartz cylinder shell harmonic oscillator n-1 mode;

1.1) obtaining the eigenfrequency of a harmonic oscillator n-1 mode by adopting a frequency sweeping method;

1.2) exciting the harmonic oscillator to vibrate by using a sinusoidal signal of the eigenfrequency of the harmonic oscillator;

1.3) rotating the harmonic oscillator, and finding out the position with the maximum amplitude under stable vibration, wherein the position is the position of one inherent rigid shaft of the n-1 mode, and the included angle between the position of the other inherent rigid shaft and the position of the other inherent rigid shaft is 90 degrees;

1.4) measuring the eigenfrequencies along two inherently rigid axes, respectively, wherein the inherently rigid axis with the higher eigenfrequency is oriented as the high frequency axis, the inherently rigid axis with the lower eigenfrequency is oriented as the low frequency axis, and the eigenfrequencies ω of the high frequency axis and the low frequency axis are measured₁、ω₂The difference is the frequency cracking value delta f;

s2: determining a second harmonic error value of the harmonic oscillator according to the vibration characteristic parameters of the harmonic oscillator;

2.1) determining the defect quality of defective cylindrical harmonic oscillator

The method comprises the steps of enabling a resonance ring of a main vibration part of a cylindrical shell harmonic oscillator to be equivalent to a circular ring model, adding an ideal mass point with the mass of m to be equivalent to an actual defect harmonic oscillator, and enabling the defect harmonic oscillator with the ratio of radial amplitude to tangential amplitude of lambda to vibrate along an inherent rigid axis at two eigenfrequencies omega₁、ω₂Respectively expressed as:

wherein M is₀Quality of harmonic oscillator without defects, omega₀The resonance is the eigenfrequency of a non-defective harmonic oscillator n-1 mode;

determining the relation between the defect quality and the mode eigenfrequency of the harmonic oscillator n-1 as follows:

2.2) determining the second harmonic error value in the defect quality

Determination of harmonic oscillator radial and tangential by experimentThe amplitude ratio λ is obtained by the displacement, and the eigenfrequency ω of the high-frequency axis of the harmonic oscillator is measured according to the step S1₁And eigenfrequency ω of the low frequency axis₂And determining the eigenfrequency omega of the non-defective harmonic oscillator by finite element simulation₀Determining the mass M of the actual defect harmonic oscillator through experiments, and further determining the defect mass value of the harmonic oscillator; since the second harmonic error of the harmonic oscillator defect is the main source of n-1 mode frequency cracking, the defect quality of n-1 mode is approximately equal to the second harmonic error value of the harmonic oscillator defect quality;

s3: determining the modification quality according to the second harmonic error value of the harmonic oscillator defect quality;

removing shape-modifying mass m in n-1 mode low-frequency axis direction_tTo eliminate the second harmonic error of the defect quality of the defective harmonic oscillator and shape the quality m_tThe relationship between the second harmonic error value and the harmonic oscillator vibration characteristic parameter is as follows:

s4: determining chemical modification time according to the second harmonic error value of the harmonic oscillator defect quality and the chemical modification parameters;

determining modification time t according to the second harmonic error value of the defect harmonic oscillator determined in the step S2 by combining the immersion depth h and the chemical modification parameter of the inclination angle α;

the shape modification time t is as follows:

wherein m is₂The second harmonic mass value in the mass is removed in the primary chemical modification, v is the etching rate of the chemical etching liquid, ρ is the material density of the harmonic oscillator, R is the outer diameter of the harmonic oscillator, α is the inclination angle of the harmonic oscillator, t is the modification time,

selecting proper immersion depth and inclination angle according to the harmonic oscillator second harmonic error value determined in the step S2, and calculating corresponding modification time;

s5, adjusting the rotating table and the angle adjusting mechanism to a preset position according to the inclination angle α and the immersion depth h selected in the step S3, installing the cylindrical shell harmonic oscillator on the harmonic oscillator installing seat, and aligning the low-frequency axis position of the harmonic oscillator n-1 mode to the zero scale line of the rotating table;

s6: operating the vertical displacement table to enable the harmonic oscillator to be immersed in the chemical etching liquid by the depth h, adjusting the rotating table to rotate the harmonic oscillator by 180 degrees after the etching time t/2, and continuing to etch for the time t/2; after the chemical etching of the second position is finished, adjusting the vertical displacement table, and moving the harmonic oscillator out of the chemical etching liquid;

s7: steps S1-S6 are repeated until the harmonic oscillator n-1 modal frequency cracking decreases to the required value.

Technical Field

The invention belongs to the technical field of vibrating gyros, and particularly relates to a chemical trimming method for second harmonic errors of quartz cylindrical harmonic oscillators.

Background

The cylindrical shell vibrating gyroscope is a solid-state gyroscope for detecting angular velocity by using the inertia effect of standing waves on a vibrating shell, has the advantages of high precision, long service life, low power consumption, small volume, low cost and the like, has wide application prospect in the field of inertia, and is a research hotspot at present. The basic working principle is as follows: the cylindrical shell harmonic oscillator generates standing wave vibration along the excitation direction under the excitation of the working frequency. When an external angular velocity is input, a new standing wave vibration is generated at a position forming an angle of 45 degrees with the excitation direction due to the existence of Coriolis force, the superposition of the two standing wave vibrations can lead the vibration mode of the harmonic oscillator to generate precession, and the precession is demodulated to obtain the magnitude of the external input angular velocity.

The quartz cylinder shell harmonic oscillator is a core device of the cylinder shell vibration gyro, and the quality factor and the frequency cracking of the quartz cylinder shell harmonic oscillator can directly influence the overall performance of the gyro. However, due to the complex three-dimensional structure, material characteristics and processing technology of the harmonic oscillator, the actually processed harmonic oscillator always has different degrees of defects such as non-uniform wall thickness, non-uniform density and structural damage. The above defects can seriously affect the consistency and symmetry of the harmonic oscillator, and further cause the vibration frequency along the two eigen main axes of the harmonic oscillator to change, and the difference value is the frequency cracking value. The size of the frequency cracking value is determined by the size of the harmonic oscillator defect, and the main axis direction of the mode is determined by the spatial distribution of the harmonic oscillator defect. The existence of frequency cracking can cause errors in the output signals of the gyroscope, the accuracy of the gyroscope is seriously influenced, and therefore, the frequency cracking must be reduced through modification.

These defects on the harmonic oscillator can be expressed as multiple harmonic superpositions by fourier expansion. In the harmonic expansion of defects, the first fourth harmonic error is the main cause of gyroscopic errors and performance degradation. The fourth harmonic error of the harmonic defect is a main factor causing the harmonic n-2 mode frequency cracking, and the second harmonic error is a main factor causing the harmonic n-1 mode frequency cracking. The first, second and third harmonic errors cause the mass center of the harmonic oscillator working in the n-2 mode to move, and the movement of the mass center increases the support loss of the harmonic oscillator and causes the quality factor of the harmonic oscillator to be non-uniform. Since n-2 mode frequency splitting is a main source of vibration gyro errors, the prior art only focuses on the adjustment of the fourth harmonic error of the harmonic oscillator. However, for the high-precision vibration gyro, even if the harmonic oscillator completes the trimming of the fourth harmonic error, the second harmonic error will cause the remarkable deterioration of the gyro performance, and the precision of the vibration gyro is severely limited. Therefore, further improvement and development is required in the art.

Disclosure of Invention

The technical problem to be solved by the invention is as follows: in order to reduce the second harmonic error value of the quartz cylinder shell harmonic oscillator and further improve the performance of the harmonic oscillator, a chemical trimming method for the second harmonic error of the quartz cylinder harmonic oscillator is provided. The method is based on a chemical modification system, a relation between a second harmonic error value of a harmonic oscillator and a chemical modification parameter is established, and a certain mass is removed from the low-frequency axis direction of the harmonic oscillator n-1 mode to reduce the frequency cracking value of the cylindrical shell harmonic oscillator n-1 mode, so that the second Fourier harmonic error value of the quartz cylindrical shell harmonic oscillator is reduced.

The technical scheme provided by the invention is as follows:

a chemical trimming method for second harmonic error of quartz cylinder harmonic oscillator comprises the following steps:

s1: determining the inherent rigid axis orientation and the frequency cracking value of a quartz cylinder shell harmonic oscillator n-1 mode;

1.1) obtaining the eigenfrequency of a harmonic oscillator n-1 mode by adopting a frequency sweeping method;

1.2) exciting the harmonic oscillator to vibrate by using a sinusoidal signal of the eigenfrequency of the harmonic oscillator;

1.3) rotating the harmonic oscillator, and finding out the position with the maximum amplitude under stable vibration, wherein the position is the position of one inherent rigid shaft of the n-1 mode, and the included angle between the position of the other inherent rigid shaft and the position of the other inherent rigid shaft is 90 degrees;

1.4) measuring the eigenfrequencies along two inherently rigid axes, respectively, wherein the inherently rigid axis with the higher eigenfrequency is oriented as the high frequency axis, the inherently rigid axis with the lower eigenfrequency is oriented as the low frequency axis, and the eigenfrequencies ω of the high frequency axis and the low frequency axis are measured₁、ω₂The difference is the frequency cracking value delta f;

as shown in fig. 1, the mode shape of the cylindrical resonator n-1 mode is such that the angle between the two inherent stiffness axes is 90 °.

S2: determining a second harmonic error value of the harmonic oscillator according to the vibration characteristic parameters of the harmonic oscillator;

2.1) determining the defect quality of defective cylindrical harmonic oscillator

The method comprises the steps of enabling a resonance ring of a main vibration part of a cylindrical shell harmonic oscillator to be equivalent to a circular ring model, adding an ideal mass point with the mass of m to be equivalent to an actual defect harmonic oscillator, and enabling the defect harmonic oscillator with the ratio of radial amplitude to tangential amplitude of lambda to vibrate along an inherent rigid axis at two eigenfrequencies omega₁、ω₂Respectively expressed as:

wherein M is₀Quality of harmonic oscillator without defects, omega₀The resonance is the eigenfrequency of a non-defective harmonic oscillator n-1 mode;

determining the relation between the defect quality and the mode eigenfrequency of the harmonic oscillator n-1 as follows:

2.2) determining the second harmonic error value in the defect quality

Measuring the radial and tangential displacements of the harmonic oscillator by experiment to obtain an amplitude ratio lambda, and measuring the eigenfrequency omega of the high-frequency axis of the harmonic oscillator according to the step S1₁And eigenfrequency ω of the low frequency axis₂And determining the eigenfrequency omega of the non-defective harmonic oscillator by finite element simulation₀Determining the mass M of the actual defect harmonic oscillator through experiments, and further determining the defect mass value of the harmonic oscillator; since the second harmonic error of the harmonic oscillator defect is the main source of n-1 mode frequency cracking, the defect quality of n-1 mode is approximately equal to the second harmonic error value of the harmonic oscillator defect quality;

s3: determining the modification quality according to the second harmonic error value of the harmonic oscillator defect quality;

removing shape-modifying mass m in n-1 mode low-frequency axis direction_tTo eliminate the second harmonic error of the defect quality of the defective harmonic oscillator and shape the quality m_tThe relationship between the second harmonic error value and the harmonic oscillator vibration characteristic parameter is as follows:

s4: determining chemical modification time according to the second harmonic error value of the harmonic oscillator defect quality and the chemical modification parameters;

determining modification time t according to the second harmonic error value of the defect harmonic oscillator determined in the step S2 by combining the immersion depth h and the chemical modification parameter of the inclination angle α;

the shape modification time t is as follows:

wherein m is₂The mass value of the second harmonic in the mass removed in the primary chemical modification is V, the etching rate of the chemical etching liquid is V, rho is the material density of the harmonic oscillator, R is the outer diameter of the harmonic oscillator, α is the inclination angle of the harmonic oscillator,

selecting proper immersion depth and inclination angle according to the harmonic oscillator second harmonic error value determined in the step S2, and calculating corresponding modification time;

s5, adjusting the rotating table and the angle adjusting mechanism to a preset position according to the inclination angle α and the immersion depth h selected in the step S3, installing the cylindrical shell harmonic oscillator on the harmonic oscillator installing seat, and aligning the low-frequency axis position of the harmonic oscillator n-1 mode to the zero scale line of the rotating table;

s6: operating the vertical displacement table to enable the harmonic oscillator to be immersed in the chemical etching liquid by the depth h, adjusting the rotating table to rotate the harmonic oscillator by 180 degrees after the etching time t/2, and continuing to etch for the time t/2; after the chemical etching of the second position is finished, adjusting the vertical displacement table, and moving the harmonic oscillator out of the chemical etching liquid;

s7: steps S1-S6 are repeated until the harmonic oscillator n-1 modal frequency cracking decreases to the required value.

The method comprises the steps of establishing a relation between vibration characteristic parameters of the cylindrical shell harmonic oscillator and a second harmonic error value based on a chemical modification technology, determining chemical modification time according to the second harmonic error value and the characteristics of a chemical modification system, and removing specific mass at two positions 180 degrees apart in the low-frequency axis direction of the harmonic oscillator to achieve the purpose of reducing the second harmonic error value of the cylindrical harmonic oscillator.

Compared with the prior art, the invention has the advantages that:

the chemical trimming method for the second harmonic error of the quartz cylinder harmonic oscillator provided by the invention has the advantages of high trimming precision, high efficiency and low cost, and can effectively reduce the second harmonic error of the cylinder shell harmonic oscillator, thereby meeting the requirement of a high-precision vibration gyro navigation system on a high-performance harmonic oscillator.

Drawings

Fig. 1 is a schematic diagram of a quartz cylinder shell harmonic oscillator n-1 mode shape in the present invention;

fig. 2 is a geometric schematic diagram of the chemical modification of a resonator with a quartz cylindrical shell, wherein α is the inclination angle of the resonator, 2 β is the zenith angle of the immersed part of the resonator, h is the immersion depth of the resonator, R is the outer diameter of the resonator, and O is the center of a circle of the end surface of a supporting column of the resonator;

FIG. 3 is a schematic view of a chemical modification system of the present invention;

fig. 4 is a flowchart of a second harmonic error trimming method for a quartz cylinder shell harmonic oscillator according to the present invention.

Illustration of the drawings:

in FIG. 3, 1-a thermostatic solution tank; 2-chemical etching liquid; 3-a cylindrical shell harmonic oscillator; 4-harmonic oscillator mounting seat; 5-rotating the platform; 6-an angle adjusting mechanism; 7-an adapter plate; 8-vertical displacement table.

Detailed Description

The following further describes the embodiments of the present invention with reference to the drawings.

The quartz cylindrical shell harmonic oscillator modification system comprises a constant-temperature solution tank 1, a chemical etching solution 2, a cylindrical shell harmonic oscillator 3, a harmonic oscillator mounting seat 4, a rotating platform 5, an angle adjusting mechanism 6, an adapter plate 7 and a vertical displacement platform 8, as shown in FIG. 3; the harmonic oscillator 3 is arranged on the harmonic oscillator mounting seat 4 and connected to the rotary table 5; the angle adjusting mechanism 6 is mounted on a vertical displacement table 8 through an adapter plate 7.

The constant-temperature solution tank 1 is made of polytetrafluoroethylene and is used for storing a chemical etching solution with strong corrosivity and keeping the chemical etching solution at a constant temperature.

The chemical etching liquid 2 consists of 49 mass percent of HF solution and 40 mass percent of NH₄Solution F was prepared as 10: 1, has a stable etch rate for fused silica, typically 0.00637 um/s.

The rotating table 5 is used for rotating the harmonic oscillator by 180 degrees to a second etching position after the harmonic oscillator completes etching at one position.

The angle adjusting mechanism 6 is used for adjusting the included angle between the harmonic oscillator and the chemical etching liquid 2 to reach a preset inclination angle α;

the vertical displacement table 8 is used for adjusting the distance from the lowest point of the harmonic oscillator to the liquid level of the chemical etching liquid 2 so as to reach a preset immersion depth h.

Fig. 4 shows an embodiment of trimming the second harmonic error of the quartz cylinder shell harmonic oscillator by using the chemical trimming system, which includes the following steps:

s1: determining the inherent rigid axis orientation and the frequency cracking value of a quartz cylinder shell harmonic oscillator n-1 mode;

1.1) obtaining the eigenfrequency of a harmonic oscillator n-1 mode by adopting a frequency sweeping method: the supporting columns of the cylindrical shell harmonic oscillators are fixed by the harmonic oscillator mounting seats 4, and the eigenfrequencies of two-order vibration modes of the harmonic oscillators which form 90 degrees with each other are respectively obtained by a frequency sweeping method. In this example, according to the simulation result of the eigenfrequency of the harmonic oscillator, the eigenfrequency ω of the non-defective harmonic oscillator n-1 mode₀Is 3658.836 Hz. The harmonic oscillator is swept in a frequency range of 1000Hz-6000Hz to obtain a harmonic oscillator frequency response curve, and a harmonic oscillator n-1 modal frequency response peak is found. Then, frequency sweeping is carried out again in the range of the frequency +/-10 Hz so as to obtain the accurate eigenfrequency of the harmonic oscillator n-1 mode;

1.2) exciting the harmonic oscillator to vibrate by using a sinusoidal signal of the eigenfrequency of the harmonic oscillator;

1.3) rotating the harmonic oscillator, and finding out the position with the maximum amplitude under stable vibration, wherein the position is the position of one inherent rigid shaft of the n-1 mode, and the included angle between the position of the other inherent rigid shaft and the position of the other inherent rigid shaft is 90 degrees;

1.4) measuring the eigenfrequencies along two inherently rigid axes respectively: measuring to obtain the eigenfrequency omega of the harmonic oscillator high-frequency axis₁3138.037Hz, eigenfrequency ω of the low frequency axis₂3132.251Hz, and the initial frequency cracking value delta f of the harmonic oscillator is 5.786 Hz;

s2: determining a second harmonic error value of the harmonic oscillator according to the vibration characteristic parameters of the harmonic oscillator;

2.1) determining the defect quality of the defective cylindrical harmonic oscillator: the ratio lambda between the radial amplitude and the tangential amplitude of the harmonic oscillator was experimentally determined to be 2.03. The mass M of the harmonic oscillator was measured by a precision balance to be 3149.31 mg. Further, determining the defect mass of the harmonic oscillator to be 12.98mg according to the formula (2);

2.2) determining a second harmonic error value in the defect quality; the defect quality of the harmonic oscillator is approximately equal to the second harmonic error, and the second harmonic error value is 12.98 mg;

s3: root of herbaceous plantAnd determining the modification quality according to the second harmonic error value of the harmonic oscillator defect quality. Determining the modification mass m according to the formula (3)_t9.53 mg;

according to the structural characteristics of the chemical modification system in the embodiment, the inclination angle α is determined to be 45 degrees, the immersion depth h is determined to be 1mm, and the modification time t is determined to be 1496S according to a formula (4);

s5: the inclination angle of the harmonic oscillator is adjusted to 45 degrees through the angle adjusting mechanism 6, and the vertical displacement table 8 is adjusted to enable the lowest point of the harmonic oscillator to be 50mm away from the liquid level of the ionization etching solution 2. Mounting a harmonic oscillator with known inherent rigidity axis orientation on a harmonic oscillator mounting seat 4 and aligning the low-frequency axis orientation with a zero scale mark of a rotating table 5;

s6: and adjusting the vertical displacement platform 8 to reduce the height of the harmonic oscillator by 51mm according to the immersion depth h of the harmonic oscillator. And when the etching time reaches 748s, adjusting the vertical displacement platform 8 to enable the harmonic oscillator to rise by 51mm, and adjusting the rotating platform 5 to enable the harmonic oscillator to rotate 180 degrees to reach a second etching position. The height of the harmonic oscillator is reduced by 51mm by adjusting the vertical displacement table 8. When the etching time reaches 748s, adjusting the vertical displacement table 8 to move the harmonic oscillator out of the chemical etching liquid 2;

s7: steps S1-S6 are repeated until the harmonic oscillator n-1 modal frequency cracking decreases to the required value.

The protection scope of the present invention is not limited to the above embodiments, and all technical solutions belonging to the idea of the present invention belong to the protection scope of the present invention.