A piezoelectric ceramic multi-position self-calibration device and method for an intrinsically safe inertial navigation system

Abstract

The application relates to a piezoelectric ceramic multi-position self-calibration device and method for an intrinsic inertial navigation system, and relates to the technical field of inertial navigation system calibration.The self-calibration device comprises a base, a double-shaft piezoelectric driving assembly, a rotating unit and an angle measuring unit, the base is used for fixing the self-calibration device on a downhole platform or other fixing equipment, the double-shaft piezoelectric driving assembly comprises X-axis and Y-axis piezoelectric ceramic drivers and a flexible hinge, the rotating unit comprises a rotating shaft and a rotating platform, the rotating platform is used for mounting the inertial navigation system, and the angle measuring unit is arranged on the rotating platform and is used for monitoring the rotating angle in real time.The device and method of the application can meet the multi-position calibration angle of the inertial navigation system through the inverse piezoelectric effect of the piezoelectric ceramic.

Description

Technical Field

[0001] This invention relates to the field of inertial navigation system calibration technology, and in particular to an intrinsically safe inertial navigation system piezoelectric ceramic multi-position self-calibration device and method for use in underground coal mining scenarios. Background Technology

[0002] The underground environment of coal mines is extremely harsh, posing a severe challenge to the calibration of inertial navigation systems. The temperature at the underground working face is typically maintained at 25-35°C, with relative humidity reaching 80-95%. In deeper mines, the temperature can reach 30°C to 50°C, and humidity increases with mining depth. Underground roadways have small cross-sections, resulting in narrow and congested working spaces. In some coal mining faces, the space is even more cramped, restricting personnel movement and making equipment operation difficult.

[0003] Calibration of inertial navigation systems is a key technology to ensure their accurate operation in downhole environments. Traditional calibration methods mainly include the six-position method and the twelve-position method. The six-position method involves pointing the x, y, and z axes upwards and downwards, resulting in six positions. It can only calibrate the zero bias and scale factor of the X, Y, and Z axes, totaling six parameters. The twelve-position method includes 36 axes.

[0004] Existing calibration methods for mining inertial navigation systems typically require fixing the system to a calibration turntable and collecting initial alignment data in four directions, static calibration data in 12 directions, and dynamic calibration data in four directions. However, this traditional mechanical calibration method has many limitations in the underground environment: firstly, the underground space is narrow, making it difficult to deploy large calibration turntables; secondly, the underground environment is harsh, and mechanical devices are easily affected by dust and humidity, reducing accuracy; and thirdly, traditional calibration methods require disassembling the inertial navigation system from the equipment, affecting normal production operations.

[0005] Furthermore, in underground coal mine transportation scenarios, the inertial navigation system uses three-axis accelerometers and gyroscopes to measure the vehicle's acceleration, angular velocity, and attitude angles in real time, combining this with dead reckoning algorithms to achieve continuous positioning. The collaborative positioning technology of inertial navigation and odometry further optimizes accuracy; experiments show that the measurement error of the working face straightness can be controlled within 90mm. This places higher demands on the calibration accuracy of the inertial navigation system.

[0006] Piezoelectric ceramics exhibit unique technological advantages in the field of inertial navigation system calibration. The piezoelectric nano-rotary stage, driven by the inverse piezoelectric effect of piezoelectric ceramics, uses an input voltage to induce nanoscale deformation in the material, offering nanoscale resolution, frictionless operation, and ultrafast response speed, perfectly meeting the requirements of IMU calibration. The piezoelectric nano-rotary stage can generate and stabilize extremely small angular steps (microradian level) to accurately calibrate sensor nonlinear errors, etc. Piezoelectric drive offers millisecond-level response speed and the advantages of being nonmagnetic and frictionless.

[0007] Currently, the application of piezoelectric ceramics in inertial navigation system calibration is mainly concentrated in laboratory environments, and there is still a gap in dedicated calibration devices for harsh downhole environments. In particular, key technical issues such as how to utilize the inverse piezoelectric effect of piezoelectric ceramics to achieve dual-axis rotation to meet the self-calibration requirements of inertial navigation systems, and how to combine piezoelectric ceramics with flexible hinges to achieve large-angle torsion, still require further technological breakthroughs.

[0008] More importantly, the underground environment contains severe explosive gases and dust. When the concentration of methane (CH4) released from the coal seam reaches 5%-16%, it poses an explosion hazard, and the concentration of combustible coal dust generated during mining and transportation reaches 30-2000 g / m³. 3 Furthermore, there is an explosion risk when suspended, posing a double explosion risk. Therefore, underground equipment must meet stringent intrinsically safe explosion-proof standards. The core requirement is that the electrical sparks or thermal effects generated by the circuit under normal and fault conditions cannot ignite explosive mixtures. Combustible gases such as methane and coal dust exist in underground mines, requiring all electrical equipment to meet intrinsically safe explosion-proof standards. The core of this standard is to limit the energy of the electrical sparks generated by the circuit under any normal or fault condition, ensuring that it is insufficient to ignite specific hazardous gases (for example, the minimum ignition energy of methane, a Class IIC gas, is approximately 200 μJ). Intrinsically safe equipment prevents ignition by limiting circuit energy; key parameters include the maximum permissible current (I0.05). max ), maximum allowable voltage (U) max ) and maximum allowable power (P) max The equipment must pass intrinsically safe explosion-proof certification, adopt a sealed structure and anti-interference communication protocol (such as CAN bus), and the protection level should reach IP65 or above. Summary of the Invention

[0009] The main technical problems to be solved by this invention include:

[0010] Traditional mechanical rotating devices suffer from problems such as large size, low precision, and difficult maintenance in downhole environments. Precise dual-axis rotational motion requires the use of the inverse piezoelectric effect of piezoelectric ceramics. One of the technical problems this invention aims to solve is how to design a dual-axis rotating device that utilizes the inverse piezoelectric effect of piezoelectric ceramics to meet the angle requirements of multi-position calibration in inertial navigation systems.

[0011] According to existing technology, the maximum static rotation angle of piezoelectric torsion devices is typically between 4.935 mrad (approximately 0.28°) and 2.73°, which is far from meeting the rotation angle requirement of over 90° required for inertial navigation system calibration. How to combine piezoelectric ceramics with flexible hinges to achieve large-angle torsion, especially solving the problem of the torsion angle limitation of piezoelectric torsion devices, is also one of the technical problems that this invention aims to solve.

[0012] Intrinsically safe equipment must pass intrinsically safe explosion-proof certification, adopt a sealed structure and anti-interference communication protocol, and have a protection level of IP65 or higher. Ensuring that the entire device meets the explosion-proof requirements of intrinsically safe downhole environments, including key technical indicators such as circuit energy limits, enclosure protection level, and temperature control, are also issues that need to be considered.

[0013] In addition, it is necessary to consider how to achieve the engineering application of the device, including the rationality of the structural design, the feasibility of the manufacturing process, and the economy of cost control.

[0014] To address the above problems, the present invention provides a piezoelectric ceramic multi-position self-calibration device for an inertial navigation system. The device includes: a base, a biaxial piezoelectric drive assembly, a rotation unit, and an angle measurement unit. The base is used to fix the self-calibration device to a downhole platform or other fixed equipment. The biaxial piezoelectric drive assembly includes an X-axis piezoelectric drive assembly and a Y-axis piezoelectric drive assembly, respectively used to control the rotational motion of the rotation unit around the X-axis and Y-axis. The X-axis piezoelectric drive assembly includes an X-axis piezoelectric ceramic actuator and an X-axis flexible hinge; the Y-axis piezoelectric drive assembly includes a Y-axis piezoelectric ceramic actuator and a Y-axis flexible hinge. The rotation unit includes a rotation axis and a rotation platform. The rotation axis is fixedly connected to the X-axis flexible hinge and the Y-axis flexible hinge. The rotation platform is used to mount the inertial navigation system. The angle measurement unit is disposed on the rotation platform and is used to monitor the rotation angle in real time.

[0015] Furthermore, both the X-axis and Y-axis flexible hinges are multi-segment flexible hinge structures, which are composed of multiple flexible hinge segments connected in series.

[0016] Furthermore, the X-axis and Y-axis flexible hinges are integrally formed with the rotating unit using a single machining process.

[0017] Furthermore, a metal substrate is also included between the base and the biaxial piezoelectric drive assembly for fixing the piezoelectric drive assembly to the base.

[0018] Furthermore, both the X-axis and Y-axis piezoelectric ceramic actuators are composed of multiple piezoelectric ceramic sheets stacked together. The piezoelectric ceramic sheets are fixed to the metal substrate by epoxy resin bonding to form a piezoelectric stack structure.

[0019] Furthermore, the base is designed with a sealed chamber for installing the control circuit of the piezoelectric ceramic actuator, and the control circuit meets the intrinsically safe explosion-proof requirements.

[0020] Furthermore, the X-axis piezoelectric drive assembly also includes an X-axis limiting device, and the Y-axis piezoelectric drive assembly also includes a Y-axis limiting device.

[0021] Furthermore, the self-calibration device and the inertial navigation system being calibrated are placed in a sealed housing. Both the inertial navigation system and the self-calibration device meet the intrinsically safe equipment requirements, and the sealed housing is designed with an IP65 protection rating.

[0022] Furthermore, the device also includes an electrical interface for connecting to an external control system.

[0023] Further, the method includes the following steps: S1. Calibration initialization: The inertial navigation system is installed on a rotating platform, all electrical interfaces are connected, and the self-calibration device performs initialization operations after the inertial navigation system starts or the control system receives a calibration command; S2. Initial position calibration: The inertial navigation system is placed in the initial position, and the data output by the angle measurement unit at this time is recorded as the calibration reference; S3. Angle planning: The control system loads the pre-stored calibration position sequence; S4. Rotation control: The rotation unit is controlled to move according to the angle sequence planned in S3; S5. Data acquisition: Inertial navigation system data is acquired after each calibration position stabilizes; S6. Determining whether all positions are completed: If not, return to S4. The selection of rotation positions should ensure that the main attitudes within the working range of the inertial navigation system are covered; S7. Data processing: The acquired data is preprocessed, including filtering and noise reduction; S8. Parameter estimation: The error parameters of the inertial navigation system are estimated using the least squares method or other optimization algorithms; S9. Error compensation: Substitute the parameters estimated in S8 into the inertial navigation system calibration mathematical model for error compensation, and fuse the data from multiple measurements; S10. Calibration verification: Verify the calibration effect through experiments, and recalibrate if the requirements are not met.

[0024] Further, S8 includes: S81. Establishing and compensating for the error model of the inertial navigation system, wherein the error model includes accelerometer error, gyroscope error, temperature error, lever error, and installation error; S82. Establishing observation equations for multi-position calibration, wherein error parameters are estimated by measuring gravitational acceleration and Earth's rotation angular velocity under different attitudes; S83. Continuously optimizing the estimated error parameters using the least squares method or iterative calculation.

[0025] Further, S9 includes: S91. Simplifying the error model of inertial navigation under small-angle rotation; S92. Using Kalman filtering or particle filtering algorithms to fuse the data from multiple measurements using the simplified error model, thereby further improving the estimation accuracy of parameters.

[0026] Further, the specific steps of S3 and S4 are as follows: (1) Receive calibration instructions and determine the target rotation angle and rotation axis; (2) Calculate the required control voltage according to the target rotation angle; (3) Output control voltage and convert the digital signal into an analog voltage signal through a D / A converter; (4) The piezoelectric ceramic deforms and generates a torsional torque under the action of voltage; (5) The flexible hinge amplifies the displacement and amplifies the small deformation of the piezoelectric ceramic into a larger rotation angle; (6) Angle feedback detection and the angle sensor monitors the rotation angle in real time; (7) Closed-loop control and compare the actual angle with the target angle to adjust the control voltage; (8) Determine whether the target angle has been reached. If not, return to step (2) to continue adjustment.

[0027] The beneficial effects of this invention are:

[0028] 1. A novel combination of the inverse piezoelectric effect of piezoelectric ceramics and flexible hinges has been achieved: This invention is the first to combine the inverse piezoelectric effect of piezoelectric ceramics with flexible hinge technology, applying it to the self-calibration field of inertial navigation systems. This combination fully leverages the high precision and fast response characteristics of piezoelectric ceramics, while simultaneously solving the problem of small output displacement of piezoelectric ceramics through the elastic amplification effect of the flexible hinge.

[0029] 2. Innovative Structural Design of a Dual-Axis Rotation Device: This invention designs a dual-axis rotation device based on piezoelectric ceramics, achieving independent rotation control of the X and Y axes through two sets of orthogonally arranged piezoelectric ceramic actuators. This design can meet the requirements of inertial navigation systems for multi-position calibration at different angular positions, and has advantages such as small size, high precision, and fast response compared to traditional mechanical rotation devices.

[0030] 3. Innovative Method to Solve the Limitation of Piezoelectric Torsion Angle: Addressing the issue of small torsion angles in piezoelectric torsion devices, this invention proposes an innovative method for multi-position combination calibration. By decomposing large-angle rotations into multiple small-angle rotations and combining this with optimized calibration algorithms, multi-point positioning functionality is achieved under the torsion angle limitation of piezoelectric torsion devices.

[0031] 4. Innovative Solution for Intrinsically Safe Explosion-Proof Design: This invention fully considers the special requirements of the intrinsically safe environment underground in its device design. Through measures such as circuit energy limitation, sealing structure design, and temperature control, it ensures that the entire device meets the explosion-proof standards for underground coal mines. In particular, the intrinsically safe circuit is adopted in the circuit design of the piezoelectric ceramic actuator, limiting the maximum energy output of the circuit.

[0032] 5. Innovative design concept suitable for engineering applications: The design of this invention fully considers the needs of engineering applications. In terms of structural design, it adopts a modular design concept, which facilitates manufacturing, installation and maintenance. In terms of material selection, it adopts corrosion-resistant and impact-resistant materials suitable for the downhole environment. In terms of cost control, it reduces manufacturing costs through optimized design. Attached Figure Description

[0033] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the structures shown in these drawings without creative effort.

[0034] Figure 1 This is a schematic diagram of the overall structure of the piezoelectric ceramic multi-position self-calibration device of the present invention;

[0035] Figure 2 This is a front view of the piezoelectric ceramic actuator and flexible hinge structure of the present invention;

[0036] Figure 3 This is a top view of the piezoelectric ceramic actuator and flexible hinge structure of the present invention;

[0037] Figure 4 This is a flowchart illustrating the working principle of the piezoelectric ceramic biaxial rotation of the present invention.

[0038] Figure 5 This is a flowchart illustrating the piezoelectric ceramic multi-position calibration process of the inertial navigation system of the present invention.

[0039] The realization of the objective, functional features and advantages of the present invention will be further explained in conjunction with the embodiments and with reference to the accompanying drawings. Detailed Implementation

[0040] Exemplary embodiments will now be described in detail, examples of which are illustrated in the accompanying drawings. When the following description relates to the drawings, unless otherwise indicated, the same numerals in different drawings denote the same or similar elements. The embodiments described in the following exemplary embodiments do not represent all embodiments consistent with this disclosure. Rather, they are merely examples of apparatuses and methods consistent with some aspects of this disclosure as detailed in the appended claims.

[0041] The terms "first," "second," etc., used in this disclosure and in the claims are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate so that the embodiments of this disclosure described herein can be implemented, for example, in orders other than those illustrated or described herein.

[0042] Furthermore, the terms “comprising” and “having”, and any variations thereof, are intended to cover non-exclusive inclusion, such that a process, method, system, product, or apparatus that includes a series of steps or units is not necessarily limited to those steps or units that are explicitly listed, but may include other steps or units that are not explicitly listed or that are inherent to such process, method, product, or apparatus.

[0043] Multiple, including two or more.

[0044] And / or, it should be understood that, for the purposes of this disclosure, the term "and / or" is merely a description of the relationship between related objects, indicating that three relationships can exist. For example, A and / or B can represent three situations: A exists alone, A and B exist simultaneously, and B exists alone.

[0045] The basic principle of this invention, which utilizes the inverse piezoelectric effect of piezoelectric ceramics to achieve biaxial rotational motion, is as follows: when an electric field is applied in the polarization direction of the piezoelectric ceramic, it undergoes mechanical deformation, including elongation, shortening, or torsion. In this invention, the torsional deformation of the piezoelectric ceramic is primarily used to generate rotational torque.

[0046] 1. Principle of the Inverse Piezoelectric Effect of Piezoelectric Ceramics: The inverse piezoelectric effect of piezoelectric ceramics refers to the rearrangement of the internal electric dipole moments when an external electric field is applied, leading to mechanical deformation of the material. For torsional piezoelectric ceramic actuators, applying a voltage to the electrodes generates shear stress, causing torsional deformation of the material. The torsional angle θ is proportional to the applied voltage V, which can be expressed as θ = k·V, where k is the torsional coefficient.

[0047] The mechanism for dual-axis rotation: This invention employs two sets of piezoelectric ceramic actuators to control the rotational motion of the X-axis and Y-axis respectively. Each set of piezoelectric ceramic actuators consists of multiple piezoelectric ceramic sheets arranged in a specific manner. For X-axis rotation control, when a voltage is applied to the X-axis piezoelectric ceramic actuator, the piezoelectric ceramic generates a torsional torque around the X-axis, which is transmitted to the rotating platform through a flexible hinge mechanism, causing the platform to rotate around the X-axis. The control principle for the Y-axis is the same as that for the X-axis. By controlling the magnitude and direction of the voltage of the two sets of actuators, the rotating platform can achieve rotational motion in any direction.

[0048] The mechanism of torsional moment generation in piezoelectric ceramics is based on shear strain in the inverse piezoelectric effect. When an electric field is applied in a specific direction to the piezoelectric ceramic, a shear stress T is generated, which is proportional to the electric field strength E: T = e·E, where e is the piezoelectric stress constant. This shear stress generates a shear strain γ within the piezoelectric ceramic, which in turn produces a torsional moment M. The magnitude of the torsional moment depends on the geometry, material parameters, and applied voltage of the piezoelectric ceramic.

[0049] For a piezoelectric ceramic torsional actuator with a circular cross-section, the torsional torque M can be expressed as: , where d 36 denoted as the piezoelectric strain constant, V as the applied voltage, r as the average radius of the piezoelectric ceramic, t as the thickness of the piezoelectric ceramic, G as the shear modulus, and h as the polarization direction length of the piezoelectric ceramic (electrode spacing).

[0050] Dual-axis coordinated control strategy: To achieve precise dual-axis rotation control, this invention employs a closed-loop control system. An angle sensor monitors the angular position of the rotating platform in real time and compares it with a set value, forming a feedback control loop. The control system adjusts the voltage of the piezoelectric ceramic actuator based on the deviation signal, achieving precise angle control.

[0051] In practical applications, rotational motion at different angles can be achieved by controlling the voltage phase difference between two sets of piezoelectric ceramic actuators. For example, when the voltage phase difference between the two sets of actuators is 90°, a circular rotational motion can be achieved; when the phase difference is 0° or 180°, a straight-line oscillating motion can be achieved.

[0052] This invention establishes a complete mathematical model of a piezoelectric ceramic torsion device. This model is based on the constitutive equation of piezoelectric materials and the theory of elasticity, and can accurately describe the electromechanical coupling characteristics of the device.

[0053] I. Mathematical Model of Piezoelectric Ceramic Torsion Device

[0054] (1) Constitutive equation of piezoelectric ceramics: The constitutive equation of piezoelectric ceramics describes the coupling relationship between mechanical and electrical quantities. For the piezoelectric torsional mode, the equation can be expressed as follows:

[0055]

[0056] (1)

[0057] Where S is the strain tensor, T is the stress tensor, E is the electric field intensity, D is the electric displacement, and s E d is the elastic compliance coefficient under a constant electric field, and d is the piezoelectric strain constant matrix. is the dielectric constant under constant stress.

[0058] For a toroidal piezoelectric ceramic torsional actuator, in cylindrical coordinates, the dominant stress component is the shear stress T. θz The corresponding strain component is the shear strain S. θz When an electric field E is applied axially to the piezoelectric ceramic... Z At this time, according to the inverse piezoelectric effect, shear strain will occur:

[0059] (2)

[0060] Where, d 36 E is the piezoelectric strain constant (unit: m / V). Z S represents the axial electric field strength (unit: V / m). θz It is a dimensionless strain.

[0061] (2) Calculation model of torsional torque: The relationship between the torsional torque M generated by the piezoelectric ceramic torsional actuator and the applied voltage V can be calculated by the following formula:

[0062] (3)

[0063] Where r is the average radius of the piezoelectric ceramic, t is the thickness of the piezoelectric ceramic, G is the shear modulus, and h is the length of the polarization direction of the piezoelectric ceramic (electrode spacing). This formula (3) shows that the torsional torque is related to the piezoelectric constant d 36 The voltage V is directly proportional to the cube of the radius r and inversely proportional to the thickness t. Therefore, increasing the radius or decreasing the thickness of the piezoelectric ceramic can significantly improve the torsional torque.

[0064] Corrected formula considering actual efficiency:

[0065] (4)

[0066] In the formula, η is the efficiency coefficient (considering hysteresis, losses, etc., with a typical value of 0.8-0.95).

[0067] (3) Elastic Model of Flexible Hinge: The elastic deformation of a flexible hinge can be described using the bending theory of beams. For a straight circular flexible hinge, its torsional stiffness K can be expressed as:

[0068] (5)

[0069] Where E is the elastic modulus of the material, approximately 2 × 10⁻⁶ for stainless steel. 11 Pa and b are the widths of the hinge, t h Let t be the hinge thickness and l be the hinge length. This formula applies to hinges with a thickness of t. h Much smaller than length l (t) h A straight circular flexible hinge with l < 0.1, when t h When / l>0.1, nonlinear correction needs to be considered:

[0070] (6)

[0071] In the formula, α is the correction factor (typical value 0.2-0.5).

[0072] When a torsional moment M is applied, the flexible hinge produces a torsional angle. for:

[0073] (7)

[0074] (4) Overall model of the piezoelectric torsion device: Considering the characteristics of the piezoelectric ceramic actuator and the flexible hinge, in the overall mathematical model of the piezoelectric torsion device, θ piezo With θ hinge Since they are in series, the total torsional angle is determined by the magnification factor of the flexible hinge, and the expression is:

[0075] (8)

[0076] Where, θ total Let θ be the total torsional angle. piezo M is the torsional angle directly generated by the piezoelectric ceramic. amplification This is the magnification factor for the flexible hinge.

[0077] The magnification factor is shown in the following formula:

[0078] (9)

[0079] Where L1 is the distance from the point of action of the piezoelectric ceramic to the center of the hinge, L2 is the distance from the center of the hinge to the rotating platform, and β is the structural efficiency coefficient (0.9-0.98).

[0080] Total magnification of multi-stage magnification (each stage has the same magnification):

[0081] (10)

[0082] In the formula: n is the magnification level.

[0083] (5) Dynamic characteristic model: The dynamic characteristics of the piezoelectric torsion device can be described by a second-order vibration system:

[0084] (11)

[0085] Where J is the system's moment of inertia. c is the damping coefficient K total The total stiffness of the system M(t) is the applied torsional moment.

[0086] The system's natural angular frequency ω n The damping ratios ζ and ζ are respectively:

[0087]

[0088] ζ (12)

[0089]

[0090] Critical damping coefficient :

[0091] (13)

[0092] II. Mathematical Model of Biaxial Rotational Motion

[0093] The dual-axis rotation device of the present invention involves rotational motion in two orthogonal directions, and it is necessary to establish a corresponding mathematical model to describe the coupling relationship and coordinated control strategy of the dual-axis motion.

[0094] (1) Kinematic model of biaxial rotation: Let the rotation angles in the X-axis and Y-axis directions be θ respectively. x and θ y The attitude of the rotating platform is described using Euler angles. This invention involves dual-axis rotation (X and Y), first rotating about the Y axis by θ. y Then rotate θ around the X-axis x The order.

[0095] For a dual-axis rotating device, the main rotational motions involve the X and Y axes, and the corresponding rotation matrices are:

[0096] (14)

[0097] (15)

[0098] When two rotations occur simultaneously, the total rotation matrix is:

[0099] (16)

[0100] Rotation matrix multiplication does not satisfy the commutative law; the above expression indicates that the matrix must first be rotated θ around the Y-axis. y Then rotate θ around the X-axis x If the rotation is first around the X-axis and then around the Y-axis, the rotation matrix is: Since the two have different postures, in this embodiment of the invention, the rotation order is Y first and then X.

[0101] (2) Coupling effect of biaxial motion: In actual biaxial rotational systems, there is a coupling effect between the two rotating axes. This coupling mainly originates from the asymmetry of the mechanical structure and installation errors. The coupling effect can be described by the coupling matrix C:

[0102] (17)

[0103] Where, θ x eff and θy eff θ is the actual rotation angle. x cmd and θ y cmd Let C be the command rotation angle, and C be the coupling matrix.

[0104] The general form of the coupling matrix C is:

[0105] (18)

[0106] Among them, c xy c is the coupling coefficient between the X-axis and the Y-axis. yx c is the coupling coefficient between the Y-axis and the X-axis. xy c represents the angle of rotation of the Y-axis when the X-axis rotates by a unit angle. yx Similarly; ideally, c xy =c yx =0, the actual value is generally less than 0.01 (1%).

[0107] (3) Dual-axis coordinated control model: To achieve precise dual-axis rotation control, a coordinated control model needs to be established. Let the control voltages of the two piezoelectric ceramic actuators be V. x and V y According to the mathematical model of the piezoelectric torsion device, we have:

[0108]

[0109] (19)

[0110] Where, k x and k y These are the voltage-angle conversion coefficients for the X and Y axes, respectively. For the error term caused by temperature, δ(V): voltage nonlinearity error term.

[0111] In practical control, the required control voltage needs to be calculated based on the target rotation angle:

[0112] (20)

[0113] In the formula: θ ref From the target angle.

[0114] Considering the dynamic characteristics and control delay of the system, the control algorithm needs to adopt predictive control or feedforward control strategies to improve response speed and control accuracy.

[0115] For complex rotational trajectories, such as circular or spiral trajectories, it is necessary to establish corresponding trajectory planning models.

[0116] III. Mathematical Model for Inertial Navigation System Calibration

[0117] The present invention also establishes a mathematical model for the calibration of an inertial navigation system applicable to a piezoelectric ceramic self-calibration device. This model takes into account the characteristics of small-angle rotation and the statistical characteristics of multiple measurements.

[0118] (1) Error Model of Inertial Navigation System: The error model of inertial navigation system includes the accelerometer error model and the gyroscope error model. The accelerometer error model can be expressed as:

[0119] (twenty one)

[0120] in, The measured value is from the accelerometer. For the true acceleration, ΔKa is a 3×3 scaling factor and installation error matrix, where the diagonal elements represent the scaling factor error and the off-diagonal elements represent the installation error. The zero bias error vector For measuring white noise, I is a 3×3 identity matrix. , , , Both are 3×1 vectors, expanded as follows:

[0121] (twenty two)

[0122] The error model of a gyroscope can be expressed as:

[0123] (twenty three)

[0124] in, This is the measurement value from the gyroscope. For true angular velocity, This is a 3×3 scaling factor and installation error matrix, where the diagonal elements represent scaling factor errors and the off-diagonal elements represent installation errors. This is the drift error vector. Measure white noise for a gyroscope.

[0125] Simplified form (ignoring installation errors):

[0126] (twenty four)

[0127] The error model includes accelerometer error, gyroscope error, temperature error, lever arm error, and installation error, etc. The installation error is ignored in the above error model formula, and the lever arm error and temperature error can be compensated in the host computer software.

[0128] (2) Observation equations for multi-position calibration: In multi-position calibration, error parameters are estimated by measuring gravitational acceleration and Earth's rotational angular velocity under different attitudes. Under static calibration conditions, the accelerometer should measure the local gravitational acceleration, and the gyroscope should measure the component of Earth's rotational angular velocity in the carrier coordinate system.

[0129] For the i-th calibration position, the accelerometer's observation equation is:

[0130] (25)

[0131] For the i-th calibration position, the gyroscope's observation equation is:

[0132] (26)

[0133] In the formula:

[0134] Gravity vector (navigation coordinate system);

[0135] Earth's rotational angular velocity, ;

[0136] Gravitational acceleration;

[0137] L: Local latitude.

[0138] in, Let be a 3×3 orthogonal rotation matrix from the navigation coordinate system to the vehicle coordinate system, satisfying (The inverse matrix is ​​equal to the transpose matrix), g is the gravitational acceleration vector. Let be the Earth's rotational angular velocity vector. and To measure noise, the navigation coordinate system n adopts the North-East (NED) coordinate system, and the vehicle coordinate system b adopts the Front-Up-Right (FRU) coordinate system.

[0139] (3) Model simplification under small-angle rotation: Considering the torsion angle limitation of the piezoelectric torsion device, the angle of each rotation is usually small (less than 10°), so a small-angle approximation can be used: ,

[0140] In the case of small angles, the rotation matrix can be simplified to:

[0141] ;

[0142] (27)

[0143] This simplification can greatly simplify the calculation process and improve the real-time performance of the calibration algorithm.

[0144] Approximate error analysis: when When (0.087 rad), the approximation error is <0.1%; when At (0.175 rad), the approximation error is <0.5%.

[0145] (4) Data fusion model for multiple measurements: Due to the calibration strategy of multiple small-angle rotations, it is necessary to fuse the data from multiple measurements. The least squares method is used, and the objective function is:

[0146] (28)

[0147] Weighted matrix W a and W g It is usually taken as the inverse matrix of the measurement noise covariance matrix:

[0148]

[0149]

[0150] By minimizing the objective function J, the error parameters of the inertial navigation system can be estimated.

[0151] (5) Observability analysis of calibration parameters: The observability of calibration parameters determines the accuracy and stability of parameter estimation. Under small-angle rotation conditions, some parameters may become unobservable or poorly observable.

[0152] Observability matrix:

[0153] (29)

[0154] Where: h i is the i-th observation output (or measurement); p is the parameter vector to be identified; It is h i The gradient (or Jacobian row vector) of the parameter vector p.

[0155] Observability criterion: if Then all parameters are observable;

[0156] like If so, then there are unobservable parameters.

[0157] Note: rank( ) represents the amount of information (dimension) that can be independently determined from the observed data, dim( The rank of the matrix represents the total number of parameters to be identified. If the rank of the matrix is ​​equal to the number of parameters, it means that each parameter can be uniquely determined by the observed data. If the rank is less than the number of parameters, then there are some parameters that cannot be distinguished from the data (i.e., there are parameters that are not identifiable).

[0158] IV. Error Analysis and Compensation Model

[0159] This invention establishes a complete error analysis and compensation model for evaluating calibration accuracy and performing error compensation, ensuring that the calibration results of the inertial navigation system meet the accuracy requirements for downhole applications.

[0160] (1) Analysis of the sources of calibration error: The calibration error mainly comes from the following aspects: hysteresis error of piezoelectric ceramic actuator, elastic deformation error of flexible hinge, measurement error of angle sensor, temperature and vibration interference of downhole environment, and model error of calibration algorithm, etc. The measurement error of angle sensor can be seen in the index of selected sensor. The relative hysteresis error of vibration interference of downhole environment and model error of calibration algorithm can be ignored. Among them, the hysteresis error of piezoelectric ceramic is the main factor affecting calibration accuracy, and its hysteresis rate is usually between 5% and 10%. The elastic deformation error of flexible hinge can be compensated by temperature error, because this is mainly the error caused by deformation due to temperature.

[0161] (2) Establishment of the error compensation model: To improve calibration accuracy, a corresponding error compensation model needs to be established. For the hysteresis error of piezoelectric ceramics, the Preisach hysteresis model is used for compensation. This model can accurately describe the hysteresis characteristics of piezoelectric ceramics. The expression of the Preisach hysteresis model is:

[0162] (30)

[0163] in, For Preisach density function, Let α be the unit hysteresis operator, and let β be the upper and lower thresholds of the hysteresis characteristic, respectively.

[0164] Simplified implementation (piecewise linear model):

[0165] (31)

[0166] In the formula: K up ,b up : Slope of the ascending branch and bias; k down ,b down : Slope of the descending branch and bias.

[0167] Hysteresis compensation algorithm:

[0168] (32)

[0169] Where: V cmd : The ideal voltage corresponding to the desired output angle (assuming no hysteresis);

[0170] The voltage correction term added to compensate for the hysteresis effect depends on the previous state (θ). prev V prev (and the direction of voltage change).

[0171] To address temperature errors, a polynomial fitting method is used to establish a temperature compensation model. Let the temperature be T, and the torsional angle error of the piezoelectric ceramic be Δθ(T), then the temperature compensation model is:

[0172] (33)

[0173] Where: θ raw The angle is the original measurement or calculation (without temperature compensation). T0 is the fitting coefficient for the temperature error, and T0 is the reference temperature (usually taken as the room temperature during calibration).

[0174] Typical second-order model:

[0175] (34)

[0176] This is the specific implementation of formula (33) when n=2. .

[0177] Temperature sensitivity coefficient: (unit: ppm / °C)

[0178] Where k is the torsional stiffness, TC k It is the temperature coefficient of the material / structure.

[0179] (3) Steps for implementing error compensation:

[0180] The steps for error compensation include: first, measuring error data under different voltages and temperatures through experiments; second, establishing an error model based on the measurement data and determining the model parameters; third, integrating the error model into the calibration algorithm, calculating and compensating for the error in real time during the calibration process; and finally, verifying the compensation effect through experiments and continuously optimizing the error model parameters.

[0181] In an embodiment of the present invention, see Figure 1 The present invention relates to a piezoelectric ceramic dual-axis rotating device structure. This structure adopts a modular design and mainly includes core components such as a base, an X-axis piezoelectric drive assembly, a Y-axis piezoelectric drive assembly, a flexible hinge mechanism, and a rotating platform. Specifically:

[0182] (1) Base: The base is the basic support structure of this device. It is made of high-strength stainless steel and has good corrosion resistance and impact resistance (maintaining a certain rigidity and stability). The base is provided with mounting holes for fixing the entire device firmly to the downhole platform or equipment base with bolts. The base is also provided with standard mounting interfaces, which can be used with the mounting bracket of the downhole inertial navigation system to achieve fast, accurate and reliable mechanical docking.

[0183] The base has a sealed chamber for installing the control circuit of the piezoelectric ceramic actuator, ensuring that the circuit meets intrinsically safe explosion-proof requirements.

[0184] (2) X-axis piezoelectric drive assembly: The X-axis piezoelectric drive assembly is responsible for controlling the rotational motion of the rotating platform around the X-axis. This assembly includes an X-axis piezoelectric ceramic actuator, an X-axis flexible hinge mechanism, and an X-axis limiting device. X-axis piezoelectric ceramic actuator: Responsible for controlling the rotational motion of the rotating platform around the X-axis. The X-axis piezoelectric ceramic actuator is composed of multiple piezoelectric ceramic sheets stacked together, using high-performance piezoelectric materials such as PZT-5H, which have a large piezoelectric coefficient. The piezoelectric ceramic sheets are fixed to the metal substrate by epoxy resin bonding to form a piezoelectric stack structure.

[0185] (3) Y-axis piezoelectric drive assembly: The structure of the Y-axis piezoelectric drive assembly is similar to that of the X-axis, and it is responsible for controlling the rotational motion of the rotary platform around the Y-axis. The X-axis and Y-axis piezoelectric drive assemblies are orthogonally arranged to ensure that the two rotation axes are perpendicular to each other, which meets the orthogonality requirements of the inertial navigation system calibration. Y-axis piezoelectric ceramic actuator: It is responsible for controlling the rotational motion of the rotary platform around the Y-axis. Its structure is the same as that of the X-axis actuator, and it is orthogonally arranged with the X-axis actuator.

[0186] (4) Flexible hinge mechanism: This includes an X-axis flexible hinge and a Y-axis flexible hinge, connecting the X-axis and Y-axis piezoelectric ceramic actuators and the rotating platform, respectively. The flexible hinge mechanism is a key component connecting the piezoelectric ceramic actuator and the rotating platform. The flexible hinge mechanism and the piezoelectric ceramic actuator are connected using epoxy resin adhesive, while the flexible hinge and the rotating platform are integrally molded using a single processing technology. This flexible hinge mechanism amplifies the minute displacement of the piezoelectric ceramic through elastic deformation. Preferably, this invention employs a straight circular flexible hinge or an asymmetrical triangular arc-shaped flexible hinge structure.

[0187] The design parameters of a flexible hinge include hinge thickness t, length l, and width b, which directly affect the torsional angle and the magnitude of the output torque. According to the theoretical model of a flexible hinge, the flexible deformation angle α around the z-axis... z With torque M z The relationship is: M z = K z ·α z K zThis represents the torsional stiffness of the flexible hinge. By optimizing the structural parameters of the flexible hinge, precise control of the torsional angle can be achieved. The magnification factor of the flexible hinge can be calculated using the lever principle: magnification factor M = L2 / L1, where L1 is the distance from the point of action of the piezoelectric ceramic actuator to the center of the hinge, and L2 is the distance from the center of the hinge to the rotating platform.

[0188] (5) Rotating Platform: The rotating platform is used to install the inertial navigation system (IMU). It is made of lightweight aluminum alloy and has good rigidity and stability. The rotating platform is equipped with a standard inertial navigation system installation interface, which can be adapted to different models of inertial navigation systems. A high-precision angle sensor is set at the center of the platform for real-time monitoring of the rotation angle.

[0189] (6) Angle sensor: Installed on the rotating platform, coaxial with the inertial measurement unit, used to monitor the rotation angle in real time, using a high-precision optical encoder or capacitive sensor.

[0190] (7) Sealed housing: The protective housing of the entire device is designed with an IP65 protection rating to prevent dust from entering and water from entering.

[0191] (8) Electrical interfaces: including power interfaces, signal interfaces, communication interfaces, etc., used to connect to external control systems.

[0192] See Figure 2 and Figure 3 The connection structure between the piezoelectric ceramic actuator and the flexible hinge is shown in detail. The piezoelectric ceramic sheet stack consists of multiple piezoelectric ceramic sheets (such as PZT-5H) stacked together. The metal substrate is used to fix the piezoelectric ceramic stack and is made of stainless steel. The electrodes and electrode leads are used to connect the drive circuit and are made of high-temperature resistant wires. Since the piezoelectric ceramic requires a voltage input of +5V and -5V to achieve bending, the drive circuit needs to convert the input voltage. The X-axis flexible hinge body is connected to the rotating platform and achieves rotational motion through flexible deformation. The Y-axis flexible hinge structure is the same as the X-axis flexible hinge, but the direction is orthogonal.

[0193] The structural design of the entire device fully considers the special requirements of the downhole environment and adopts a compact structural layout to ensure that complex dual-axis rotation functions can be achieved within a limited space.

[0194] This invention organically combines piezoelectric ceramics with flexible hinges. The elastic deformation of the flexible hinge amplifies the minute displacements of the piezoelectric ceramics, achieving large-angle torsional motion. This combination fully utilizes the high precision characteristics of piezoelectric ceramics and the amplification effect of the flexible hinge, which is one of the core innovations of this invention. Key features include:

[0195] 1. Magnification Principle of Flexible Hinges: A flexible hinge is a mechanical structure with elasticity that transmits motion and force through its own elastic deformation. In this invention, the flexible hinge is used as a connection mechanism between the piezoelectric ceramic actuator and the rotating platform. Its main function is to amplify the minute torsional displacement generated by the piezoelectric ceramic into a larger rotation angle.

[0196] The magnification factor of a flexible hinge depends primarily on its geometric parameters and material properties. For a straight circular flexible hinge, its torsional stiffness K can be expressed as: This formula is applicable to straight circular flexible hinges with a thickness t much smaller than the length l (t / l<0.1). When t / l>0.1, nonlinear correction needs to be considered. Here, E is the elastic modulus of the material, b is the width of the hinge, t is the thickness of the hinge, and l is the length of the hinge.

[0197] The relationship between the torsional angle θ and the applied torque M is as follows: When the torque generated by the piezoelectric ceramic acts on the flexible hinge, a torsional angle is produced. By adjusting the geometric parameters of the flexible hinge, the torsional angle can be precisely controlled.

[0198] 2. Integrated Design of Piezoelectric Ceramic and Flexible Hinge: This invention adopts an integrated design concept, combining the piezoelectric ceramic actuator with the flexible hinge mechanism. Specifically, the piezoelectric ceramic actuator is connected to the flexible hinge through mechanical fixing or adhesive bonding to form a single integrated drive unit.

[0199] In terms of structural design, the piezoelectric ceramic actuator is mounted on the fixed end of the flexible hinge, while the rotating platform is connected to the free end of the flexible hinge. When the piezoelectric ceramic generates a torsional torque, this torque is transmitted to the rotating platform through the flexible hinge, causing the platform to rotate. The design of the flexible hinge needs to consider factors such as stress concentration and fatigue life to ensure that it will not fail during long-term use.

[0200] 3. Multi-segment flexible hinge structure: To further improve the torsion angle, this invention proposes a multi-segment flexible hinge structure. This structure consists of multiple flexible hinge segments connected in series, each with a certain magnification factor. Through the cascading amplification of multiple hinge segments, a larger overall magnification factor can be achieved.

[0201] Assuming the magnification factor of each flexible hinge segment is... M l Then the total magnification factor after cascading n hinge segments is... M total = M l nFor example, if the magnification of each hinge segment is 10, then the total magnification of three cascaded hinge segments can reach 1000 times.

[0202] 4. Selection of Flexible Hinge Material: The choice of flexible hinge material has a significant impact on the performance of the entire device. This invention uses high-strength, high-elastic-modulus materials such as stainless steel or titanium alloy to manufacture the flexible hinge. These materials have good corrosion resistance and are suitable for use in downhole environments.

[0203] The elastic modulus E and yield strength R of the material e These are two key parameters. The elastic modulus determines the stiffness of the flexible hinge, while the yield strength determines the maximum allowable deformation. To obtain a large magnification factor, a material with a low elastic modulus needs to be selected, but at the same time, the yield strength of the material must be high enough to avoid plastic deformation during operation. See also... Figure 4 The working principle flow of the piezoelectric ceramic biaxial rotation device of the present invention is as follows:

[0204] 1. System initialization: including parameter settings, sensor calibration, communication establishment, etc.;

[0205] The parameter settings include: initial parameter settings for driving the flexible hinge to the initial position after the piezoelectric ceramic is powered on, and initial parameter settings for entering the working mode after the inertial navigation system starts power-on self-test; input of lever arm error and installation error information; sensor calibration refers to the angle sensor returning to zero position to ensure that the inertial navigation system and the rotating platform are at the zero position; communication establishment is the host computer receiving the output data of the inertial navigation system.

[0206] 2. Receive calibration instructions and determine the target rotation angle and rotation axis;

[0207] 3. Calculate the required control voltage. Based on the target angle and the voltage-angle conversion coefficient, calculate Vx and Vy. In actual control, the specific method for calculating the required control voltage based on the rotation angle is as follows:

[0208] For example, the target angle is = = 45°, calibration parameter is k x = k y = 0.5 ° / V, in the coupling matrix c_{xy} = 0.005, c_{yx} = 0.003, then

[0209]

[0210]

[0211] Temperature and nonlinear error are temporarily ignored. Then the ideal voltage V x_ideal =Vy_ideal = 45° / 0.5° / V = ​​90 V, perform feedforward decoupling (substitute into formula 20):

[0212]

[0213] Due to the presence of coupling, the actual voltage required to achieve 45 degrees on both axes (approximately 89.55V) is slightly lower than the 90V calculated without considering coupling, because the rotation of one axis "helps" the other axis rotate through coupling.

[0214] 4. Output control voltage, converting digital signals into analog voltage signals via a D / A converter;

[0215] 5. When piezoelectric ceramics deform, they generate torsional torque under voltage.

[0216] 6. Flexible hinges amplify displacement, turning the minute deformation of piezoelectric ceramics into a larger rotation angle;

[0217] 7. Angle feedback detection: The angle sensor monitors the rotation angle in real time;

[0218] 8. Closed-loop control: compare the actual angle with the target angle and adjust the control voltage accordingly;

[0219] 9. Determine if the target angle has been reached. If not, return to step 3 to continue adjusting.

[0220] 10. The angle is stable, and the voltage remains stable after the target angle is reached, while waiting for the inertial navigation system to collect data.

[0221] See Figure 5 The complete workflow diagram for multi-position calibration of the present invention is as follows:

[0222] 1. Calibration preparation: Install the inertial navigation system on the rotating platform, connect all electrical interfaces, and after the system is powered on or the controller receives the external calibration command, the intrinsically safe control and processing unit performs initialization operations, including parameter zeroing, circuit self-test, and verification of communication links of each module, to ensure that the intrinsically safe IMU, piezoelectric ceramic multi-axis precision positioning stage, angle sensor and other components are working properly;

[0223] Among them: parameter zeroing is to ensure that the parameters read by the inertial navigation system are the parameters of this measurement; circuit self-test is to confirm that there are no short circuits or open circuits in the circuit; and communication link verification of each module is to send verification data to verify that the communication is working properly.

[0224] 2. Initial position calibration: Record the sensor's initial position; place the inertial navigation system at the initial position and record the sensor output data at this time as the calibration reference.

[0225] 3. Angle Planning: After the data system is powered on, the pre-stored calibration position sequence is loaded. In this embodiment, eight calibration positions are selected: Position 1: Pitch +90°, Azimuth 0°; Position 2: Pitch -90°, Azimuth 0°; Position 3: Pitch 0°, Azimuth +90°; Position 4: Pitch 0°, Azimuth -90°; Position 5: Pitch +45°, Azimuth +45°; Position 6: Pitch +45°, Azimuth -45°; Position 7: Pitch -45°, Azimuth +45°; Position 8: Pitch -45°, Azimuth -45°.

[0226] 4. Rotation control: Control the movement of the rotating platform according to the planned angle sequence; control the rotating platform to rotate at small angles through a piezoelectric torsion device, with each rotation angle being Δθ, and the rotation direction can be the X-axis, Y-axis, or Z-axis direction;

[0227] 5. Data Acquisition: Acquire inertial navigation system data after stabilization at each calibration position;

[0228] 6. Determine if all positions have been completed. If not, return to step 4. The selection of rotation positions must ensure that they cover the main attitudes within the operating range of the inertial navigation system.

[0229] 7. Data Processing: Preprocess the collected data, including filtering and noise reduction;

[0230] 8. Parameter estimation: The least squares method or other optimization algorithms are used to estimate the inertial navigation error parameters. The error parameters of the inertial navigation include the zero bias, scale factor, and installation error of the accelerometer, and the zero bias, scale factor, and drift of the gyroscope.

[0231] The parameter estimation includes the following steps:

[0232] (1) Establish the error model of the inertial navigation system: The error model of the inertial navigation system includes the accelerometer error model and the gyroscope error model;

[0233] (2) Establish observation equations for multi-position calibration: In multi-position calibration, error parameters are estimated by measuring gravitational acceleration and Earth's rotation angular velocity under different attitudes;

[0234] (3) Simplify the model by rotating it at a small angle;

[0235] (4) Since the calibration strategy of multiple small-angle rotations is adopted, the data from multiple measurements need to be fused. In this embodiment, the least squares method is adopted, and the objective function is: see formula (28). By minimizing the objective function J, the error parameters of the inertial navigation system can be estimated;

[0236] 9. Error Compensation: The estimated parameters are substituted into the inertial navigation system for error compensation. The steps for error compensation include: First, measuring error data under different voltages and temperatures through experiments; Second, establishing an error model based on the measured data and determining the model parameters; Third, integrating the error model into the calibration algorithm, calculating the error in real time during the calibration process and compensating for it. The calibration error mainly comes from the following aspects: the hysteresis error of the piezoelectric ceramic actuator, the elastic deformation error of the flexible hinge, the measurement error of the angle sensor, the temperature and vibration interference of the downhole environment, and the model error of the calibration algorithm. Among them, the hysteresis error of the piezoelectric ceramic is one of the main factors affecting the calibration accuracy. Its hysteresis rate is usually between 5% and 10%. For the hysteresis error of the piezoelectric ceramic, the Preisach hysteresis model is used for compensation, and the compensation is carried out according to formulas (30)-(32); for the temperature error, the polynomial fitting method is used to establish a temperature compensation model, and the compensation is carried out according to formulas (33)-(34).

[0237] 10. Calibration and verification: Verify the calibration effect through experiments. If the requirements are not met, recalibrate.

[0238] In summary, to address the limitation of the torsion angle of piezoelectric torsion devices, this invention proposes an innovative multi-position calibration strategy. By combining multiple small-angle rotations and optimizing the calibration algorithm, the requirements for multi-point positioning of the inertial navigation system are met without requiring a single large-angle rotation.

[0239] The basic principle of multi-position calibration: Calibration of inertial navigation systems typically requires data acquisition at multiple different attitude positions to determine the sensor's error parameters. According to existing technology, commonly used calibration methods include the 6-position method and the 12-position method. The 6-position method places the x, y, and z axes upwards and downwards, for a total of six positions; the 12-position method, based on the 6-position method, performs mirror measurements at each position to compensate for interference caused by the tilt of the placement surface. For the piezoelectric torsion device of this invention, due to the limited single torsion angle, large-angle rotations above 90° cannot be directly achieved. Therefore, a strategy of multiple small-angle rotations is needed, using a combination of multiple rotations and measurements to cover the required angle range.

[0240] Angle decomposition and path planning: This invention decomposes large-angle rotations into multiple small-angle rotation steps. Specifically, a 90° rotation is decomposed into n small angle increments Δθ, the size of which depends on the maximum torsion angle of the piezoelectric torsion device. For example, if the maximum torsion angle of the piezoelectric torsion device is 0.22° (intrinsically safe operation at 24V), then 90° can be decomposed into 41 rotation steps of 0.22°; if the maximum torsion angle is 22° (after 3-stage amplification), then it can be decomposed into 5 rotation steps of 4.5°.

[0241] In terms of path planning, this invention employs a spiral or stepped rotation path to ensure coverage of the entire spherical space. After each rotation step, the system stabilizes for a period of time to allow vibration decay before data acquisition. The design of the rotation sequence must consider the observability of the inertial navigation system's error parameters, ensuring that each error parameter is adequately excited.

[0242] Optimized design of the calibration algorithm: To adapt to calibration methods involving multiple small-angle rotations, this invention optimizes the traditional calibration algorithm. The main optimization measures include:

[0243] 1. Improvement of the error model: Establish an error model suitable for small-angle rotation, taking into account the nonlinear effects of the rotation angle and the influence of cumulative error.

[0244] 2. Data fusion algorithm: Kalman filtering or particle filtering methods are used to fuse data from multiple measurements to improve the estimation accuracy of calibration parameters.

[0245] 3. Iterative optimization algorithm: Employ the least squares method or other optimization algorithms, such as iterative calculations, to continuously optimize the calibration parameters and reduce estimation errors. Each iteration adjusts the parameters based on the previous result until the convergence condition is met.

[0246] 4. Robust design: Consider uncertainties such as noise interference and model error in the algorithm design to improve the robustness of the calibration results.

[0247] The core technical solution of this invention is to combine the inverse piezoelectric effect of piezoelectric ceramics with a flexible hinge to design a dual-axis rotating piezoelectric torsion device for multi-position self-calibration of inertial navigation systems. The device mainly includes a base, a piezoelectric ceramic actuator, a flexible hinge mechanism, and a rotating platform, among other key components.

[0248] In terms of achieving dual-axis rotation, this invention employs two sets of piezoelectric ceramic actuators to control rotational motion in two orthogonal directions. Each set of piezoelectric ceramic actuators consists of multiple stacked piezoelectric ceramic sheets, generating torsional torque by applying voltage. The inverse piezoelectric effect of piezoelectric ceramics refers to the rearrangement of internal electric dipole moments when an external electric field is applied to the piezoelectric ceramic, resulting in mechanical deformation of the material. The deformation (ΔL) is proportional to the applied voltage (V), mathematically expressed as ΔL = d·V, where d is the piezoelectric constant.

[0249] In terms of flexible hinge design, this invention uses a flexible hinge as the connection mechanism between the piezoelectric ceramic actuator and the rotating platform. The elastic deformation of the flexible hinge amplifies the minute displacement of the piezoelectric ceramic, achieving large-angle torsional motion. The design parameters of the flexible hinge include hinge thickness, length, and width, which directly affect the torsional angle and the magnitude of the output torque.

[0250] Regarding multi-position calibration, considering the torsion angle limitation of the piezoelectric torsion device, this invention proposes a multi-position combination calibration method. When the piezoelectric torsion device cannot be torn more than 90°, a large-angle position change can be achieved by combining multiple small-angle rotations. Combined with the optimization of the calibration algorithm, this method meets the requirements of multi-point positioning of the inertial navigation system.

[0251] Furthermore, the device of this invention must meet the stringent explosion-proof requirements of intrinsically safe underground environments, which is crucial to ensuring the safe operation of the equipment underground. The design of intrinsically safe equipment must comply with the relevant requirements of the GB3836 series standards and coal mine safety regulations.

[0252] Circuit energy limitation design: The core requirement of intrinsically safe equipment is that the electrical sparks or thermal effects generated by the circuit under normal and fault conditions cannot ignite an explosive mixture. According to GB3836.4 standard, key parameters for intrinsically safe equipment include the maximum permissible current (IA). max ), maximum allowable voltage (U) max ) and maximum allowable power (P) max ).

[0253] In terms of circuit design, this invention employs an intrinsically safe circuit, limiting the maximum energy output of the circuit through components such as current-limiting resistors and Zener diodes. The piezoelectric ceramic actuator's drive circuit uses a low-voltage power supply, with a maximum voltage not exceeding 24V and a maximum current not exceeding 100mA. For methane-based explosive gases, the maximum permissible energy of the intrinsically safe circuit is typically no more than 20μJ, corresponding to a current-limiting resistor of not less than 28.8kΩ at 24V (according to E=U 2 ( / (2R) derivation), ensuring that no spark energy sufficient to ignite the gas will be generated under fault conditions.

[0254] Enclosure Protection Design: The enclosure of the device of this invention is made of high-strength aluminum alloy or stainless steel, providing excellent sealing performance. The enclosure protection rating reaches IP65 or higher, preventing dust ingress and water intrusion. According to standard requirements, an IP65 protection rating means that the equipment can prevent the accumulation of harmful dust and withstand water spray from all directions.

[0255] Temperature Control Design: The surface temperature of intrinsically safe equipment must be strictly controlled within a specified range. Downhole methane environments correspond to temperature groups T1-T4. The maximum surface temperature for group T1 is no more than 450℃, and for group T4, it is no more than 135℃. This device is adapted to group T4 requirements, with the maximum surface temperature controlled below 135℃, making it more suitable for use in high-risk downhole environments. In downhole environments, equipment must consider not only its own heat generation but also the influence of ambient temperature. This invention achieves temperature control through the following measures: First, low-power piezoelectric ceramic actuators and control circuits are selected to reduce self-heating; second, a heat dissipation design is adopted, with heat sinks or ventilation holes on the casing; third, a temperature monitoring circuit is installed, automatically cutting off the power supply when the temperature exceeds the set value.

[0256] Explosion-proof certification requirements: The device of this invention must pass an explosion-proof certificate, with the explosion-proof mark being Ex ia I Ma. The equipment must also have the coal mine safety product safety mark MA, which is a prerequisite for the equipment to be installed underground.

[0257] During the certification process, the equipment needs to pass a series of rigorous tests, including spark ignition tests, temperature tests, enclosure strength tests, and sealing performance tests. In particular, the spark ignition test requires passing 10 discharge verifications to ensure that no sparks that could ignite explosive gases will be generated under any circumstances.

[0258] Special Design of Intrinsically Safe Circuit: Considering the unique characteristics of piezoelectric ceramic actuators, this invention incorporates special protection measures in its circuit design. Piezoelectric ceramics exhibit capacitive properties, generating instantaneous large currents during charging and discharging. To prevent sparking from these instantaneous currents, a buffer circuit and a current-limiting circuit are included in the circuit.

[0259] Meanwhile, to ensure safety in the event of cable breakage or short circuit, the circuit incorporates multiple protection mechanisms, including overvoltage protection, overcurrent protection, and short circuit protection. These protection circuits are independent of each other, so even if one fails, the others will still function normally.

[0260] The sequence numbers of the above embodiments of the present invention are for descriptive purposes only and do not represent the superiority or inferiority of the embodiments.

[0261] Through the above description of the embodiments, those skilled in the art can clearly understand that the above implementation methods can be implemented by means of software plus necessary general-purpose hardware platforms. Of course, they can also be implemented by hardware, but in many cases the former is a better implementation method. Based on this understanding, the technical solution of the present invention, in essence, or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product is stored in a storage medium (such as ROM / RAM, magnetic disk, optical disk), and includes several instructions to cause a terminal (which may be a mobile phone, computer, server, air conditioner, or network device, etc.) to execute the methods described in the various embodiments of the present invention.

[0262] The embodiments of the present invention have been described above with reference to the accompanying drawings. However, the present invention is not limited to the specific embodiments described above. The specific embodiments described above are merely illustrative and not restrictive. Those skilled in the art can make many other forms under the guidance of the present invention without departing from the spirit and scope of the claims. All of these forms are within the protection scope of the present invention.

Claims

1. A piezoelectric ceramic multi-position self-calibration device for inertial navigation systems, characterized in that, The device includes: a base, a biaxial piezoelectric drive assembly, a rotation unit, and an angle measuring unit, wherein: The base is used to fix the self-calibration device to the downhole platform; The biaxial piezoelectric drive assembly is fixed to the base. The biaxial piezoelectric drive assembly includes an X-axis piezoelectric drive assembly and a Y-axis piezoelectric drive assembly, which are used to control the rotational motion of the rotating unit around the X-axis and Y-axis, respectively. The X-axis piezoelectric drive assembly includes an X-axis flexible hinge, and the Y-axis piezoelectric drive assembly includes a Y-axis flexible hinge. The rotating unit includes a rotating shaft and a rotating platform. The rotating shaft is fixedly connected to the X-axis flexible hinge and the Y-axis flexible hinge. The rotating platform is used to install the inertial navigation system. The angle measurement unit is mounted on the rotating platform and is used to monitor the rotation angle of the inertial navigation system in real time. Both the X-axis and Y-axis flexible hinges are multi-segment flexible hinge structures, which are composed of multiple flexible hinge segments connected in series. The X-axis piezoelectric drive assembly further includes an X-axis piezoelectric ceramic actuator, and the Y-axis piezoelectric drive assembly further includes a Y-axis piezoelectric ceramic actuator. Both the X-axis and Y-axis piezoelectric ceramic actuators are composed of multiple piezoelectric ceramic sheet stacks. The piezoelectric ceramic actuator is connected to the flexible hinge by mechanical fixing or adhesive bonding to form an integral drive unit; When the piezoelectric ceramic generates a torsional torque, the torque is transmitted to the rotating platform through the flexible hinge, causing the platform to rotate. Elastic model of flexible hinge: The elastic deformation of a flexible hinge can be described by the bending theory of beams, and its torsional stiffness K can be expressed as: where E is the elastic modulus of the material, b is the width of the hinge, t h is the thickness of the hinge, and l is the length of the hinge. This formula is valid for straight circular flexure hinges when t h / l < 0.1, and a nonlinear correction is needed when t h / l > 0.

1. In the formula, α is the correction coefficient; Taking into account the characteristics of the piezoelectric ceramic actuator and the flexible hinge, in the overall mathematical model of the piezoelectric torsion device, θ piezo With θ hinge Since they are in series, the total torsional angle is determined by the magnification factor of the flexible hinge, and the expression is: Where, θ total Let θ be the total torsional angle. piezo M is the torsional angle directly generated by the piezoelectric ceramic. amplification This is the magnification factor for the flexible hinge; The magnification factor is shown in the following formula: Where L1 is the distance from the point of action of the piezoelectric ceramic to the center of the hinge, L2 is the distance from the center of the hinge to the rotating platform, and β is the structural efficiency coefficient.

2. The multi-position self-calibration device according to claim 1, characterized in that, The flexible hinges of the X-axis and Y-axis are integrally formed with the rotating unit using a single machining process.

3. The multi-position self-calibration device according to claim 1, characterized in that, A metal substrate is also included between the base and the biaxial piezoelectric drive assembly for fixing the biaxial piezoelectric drive assembly to the base.

4. The multi-position self-calibration device according to claim 3, characterized in that, The piezoelectric ceramic sheet is fixed to the metal substrate by epoxy resin bonding to form a piezoelectric stack structure.

5. The multi-position self-calibration device according to claim 4, characterized in that, The base has a sealed chamber for installing the control circuit of the X-axis and Y-axis piezoelectric ceramic actuators. The control circuit meets the intrinsically safe explosion-proof requirements.

6. The multi-position self-calibration device according to claim 1, characterized in that, The X-axis piezoelectric drive assembly further includes an X-axis limiting device, and the Y-axis piezoelectric drive assembly further includes a Y-axis limiting device.

7. The multi-position self-calibration device according to claim 1, characterized in that, The self-calibration device and the inertial navigation system being calibrated are housed in a sealed enclosure. Both the inertial navigation system and the self-calibration device meet the intrinsically safe equipment requirements. The sealed enclosure is designed with an IP65 protection rating.

8. The multi-position self-calibration device according to claim 1, characterized in that, The device also includes an electrical interface for connecting to an external control system.

9. A method for multi-position self-calibration of piezoelectric ceramics for inertial navigation systems, characterized in that, The method is implemented using the self-calibration device according to any one of claims 1-8, and the method includes the following steps: S1. Calibration and initialization: Install the inertial navigation system on the rotating platform, connect all electrical interfaces, and after the inertial navigation system starts or the control system receives the calibration command, the self-calibration device performs the initialization operation; S2. Initial position calibration: The inertial navigation system is placed at the initial position, and the data output by the angle measurement unit at this time is recorded as the calibration reference; S3. Angle planning: The control system loads a pre-stored calibration position sequence; S4. Rotation control: Control the movement of the rotating unit according to the angle sequence planned in S3; S5. Data Acquisition: Acquire inertial navigation system data after stabilization at each calibration position; S6. Determine if all positions have been completed; if not, return to S4. S7. Data processing: Preprocessing the collected data, including filtering and noise reduction; S8. Parameter estimation: The least squares method is used to estimate the error parameters of the inertial navigation system. S9. Error compensation: Substitute the parameters estimated in S8 into the mathematical model for inertial navigation system calibration to compensate for errors in the preprocessed acquired data, and perform fusion processing on the data from multiple measurements. S10. Calibration and verification: Verify the calibration effect through experiments. If the requirements are not met, recalibrate.

10. The self-calibration method according to claim 9, characterized in that, S8 includes: S81. Establish an error model for the inertial navigation system and compensate for it. The error model includes accelerometer error, gyroscope error, temperature error, lever error, and installation error. S82. Establish observation equations for multi-position calibration, in which error parameters are estimated by measuring gravitational acceleration and Earth's rotation angular velocity under different attitudes; S83. Continuously optimize the estimated error parameters using the least squares method or iterative calculation.

11. The self-calibration method according to claim 10, characterized in that, S9 includes: S91. Simplify the error model for inertial navigation under small-angle rotation; S92. The data from multiple measurements using the simplified error model are fused using Kalman filtering or particle filtering algorithms to further improve the accuracy of parameter estimation.

12. The self-calibration method according to claim 9, characterized in that, The specific steps of S3 and S4 are as follows: (1) Receive calibration instructions and determine the target rotation angle and rotation axis; (2) Calculate the required control voltage based on the target rotation angle; (3) Output control voltage, which converts the digital signal into an analog voltage signal through a D / A converter; (4) The piezoelectric ceramic deforms and generates a torsional moment under the action of voltage; (5) Flexible hinges amplify displacement, turning the tiny deformation of piezoelectric ceramics into a larger rotation angle; (6) Angle feedback detection: the angle sensor monitors the rotation angle in real time; (7) Closed-loop control: compare the actual angle with the target angle and adjust the control voltage accordingly; (8) Determine whether the target angle has been reached. If not, return to step (2) to continue adjusting.

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