Error Analysis Method of Liquid Ring Angular Accelerometer under Variable Linear Acceleration Conditions

Abstract

The present invention provides a method for analyzing the error of a liquid ring angular accelerometer under variable linear acceleration conditions. When establishing an error model for the liquid ring angular accelerometer under variable linear acceleration conditions, the influence of the compressibility of the working fluid is taken into account. Therefore, the model can be applied to the error analysis of the angular accelerometer under high-frequency variable linear acceleration excitation. The present invention establishes a linear vibration influence model based on a mass-spring-damper system. The model can be iteratively solved using the Newton-Euler method, has a high calculation speed, and can realize real-time calculation and analysis of the linear vibration influence. The present invention can perform numerical simulation prediction on the error of the liquid ring angular accelerometer under variable linear acceleration conditions. The prediction results of the error model can be used to compensate for the error of the liquid ring angular accelerometer under variable linear acceleration conditions, thereby ensuring its operating reliability in high dynamic conditions.

Description

Technical Field

[0001] The present invention relates to the technical field of angular accelerometers, and in particular to an error analysis method for a liquid ring angular accelerometer under variable linear acceleration conditions. Background Art

[0002] The liquid ring angular accelerometer is an inertial sensor capable of directly measuring angular acceleration. It has broad application prospects in areas such as high-dynamic aircraft attitude control, vehicle rollover warning, and earthquake monitoring. The liquid ring angular accelerometer consists of an annular cavity, a liquid mass, a solid-state converter, metal electrodes, and a conditioning circuit. When an external angular acceleration is input, inertia causes relative motion between the annular cavity and the liquid mass, creating a pressure differential across the solid-state converter. The solid-state converter is a porous dielectric structure composed of sintered glass microspheres. Due to the interfacial double-layer effect, a double-layer structure with opposite polarity exists between the microspheres and the liquid. This pressure differential causes the liquid to flow through the solid-state converter, causing the double-layer at the solid-liquid interface to move in a directional manner, generating a streaming current. This current is then passed through the metal electrodes and conditioning circuitry, ultimately outputting an electrical signal. In tests, the liquid ring angular accelerometer demonstrated a wide measurement range, wide bandwidth, and good environmental adaptability. Its excellent overall performance makes it suitable for attitude measurement of highly dynamic vehicles.

[0003] However, high-dynamic motion often involves highly dynamic changes in multiple parameters, including attitude, velocity, and position. If linear motion, such as linear acceleration and jerk, affects the angular accelerometer's measurements, the accuracy and reliability of the angular acceleration measurements will be significantly reduced. Therefore, angular accelerometers must be insensitive to linear acceleration and other factors. Research has found that while linear acceleration has a minimal impact on liquid ring angular accelerometers, rapid and dramatic changes in linear acceleration can introduce errors into the liquid ring's angular acceleration measurements. Therefore, it is necessary to study the error model for liquid ring angular accelerometers under varying linear acceleration conditions and analyze the errors. Summary of the Invention

[0004] In view of this, an object of the present invention is to provide an error analysis method for a liquid ring angular accelerometer under variable linear acceleration conditions, which has a fast calculation speed and can improve the measurement accuracy of the angular accelerometer.

[0005] A method for analyzing an error of a liquid ring angular accelerometer under variable linear acceleration conditions comprises:

[0006] Step 1: for the annular cavity of the angular liquid ring accelerometer, slice the annular cavity along a direction parallel to the plane where the annular cavity is located, and approximately make the shape of the fluid in each layer equivalent to a circular cylinder;

[0007] Step 2: Equivalent the fluid system of each layer of the annular cylinder to a two-dimensional mass-spring-damper system;

[0008] Step 3: Set the simulation time and linear speed excitation signal;

[0009] Step 4: Use the Newton-Euler method to solve the resultant force on the solid-phase converter under the linear velocity excitation signal.

[0010] Step 5: Calculate the pressure difference of the liquid at both ends of the solid phase converter.

[0011] Preferably, in step 1, let R represent the radius of the annular cavity, r c Represents the diameter of the circular cross section of the inner cavity of the annular cavity; uniformly slice the annular cavity along the plane parallel to the annular cavity, and divide it into w layers, and each layer is approximately equivalent to a circular cylinder; let h represent the height of each layer of circular cylinder, then

[0012] Preferably, the specific method of step 2 is:

[0013] For each layer of the annular cylinder, divide it evenly along the axial direction of the annular cavity into q+1 parts, and divide it evenly along the radial direction into n+1 parts. Let each axial division be represented by a row, and each radial division be represented by a column. Then m ij represents the mass of the particles in the axial i-th row and radial j-th column, where the outermost particles are boundary particles and the others are internal fluid particles. Figure 2 As shown, the mass formula of the internal fluid particle is:

[0014]

[0015] Where i = 0, 1…q, j = 0, 1…n, ρ represents the density of the fluid, and d represents the cross-sectional width of the current layered ring cylinder;

[0016] Establish a plane rectangular coordinate system, set the center of the annular cavity as the coordinate origin, the direction from the origin to the solid phase converter as the positive direction of the x-axis, the direction perpendicular to the solid phase converter as the positive direction of the y-axis, and the z-axis direction is determined by the x-axis and y-axis according to the right-hand screw rule, as follows: Figure 2 As shown. The initial position coordinates of the particle in the i-th row and j-th column in the plane rectangular coordinate system are Considering the boundary layer problem, the position of each particle is first defined in the polar coordinate system, and then converted to the plane rectangular coordinate system. The coordinate definition of the initial position of the particle in the polar coordinate system is As shown in formulas (2) and (3):

[0017]

[0018]

[0019] According to the conversion relationship between polar coordinates and plane rectangular coordinates, the initial position of the particle is calculated as

[0020]

[0021] Adjacent masses in each row and column are connected by springs and dampers, which are axial springs, axial dampers, radial springs, and radial dampers respectively. The spring coefficient is determined by the bulk elastic modulus of the liquid.

[0022] The axial springs connect the masses in different rows in each column. The axial springs in each column have the same spring constant. The axial springs and spring constants of the jth column, ith row to i+1th row can be expressed as K (i,i+1),j ; Radial springs connect the masses in different columns in each row. The radial springs in each row have the same spring coefficient. The radial springs and their spring coefficients in the i-th row, j-th column to j+1-th column can be expressed as K i,(j,j+1) ;L i,(j,j+1),0 represents the initial length of the axial spring between the jth column and the j+1th column in the i-th row, L (i,i+1),j,0 represents the initial length of the radial spring between the i-th row and the i+1-th row in the j-th column, which is calculated based on the initial position coordinates of the mass points at both ends of the spring;

[0023] For axial springs, the formula for calculating the spring rate is:

[0024]

[0025] where K l represents the bulk modulus of the working fluid;

[0026] For radial springs, the formula for calculating the spring constant is:

[0027]

[0028] Use c i,(j,j+1) The damping coefficient of the axial damping between the jth column and the j+1th column in the i-th row is expressed as c (i,i+1),j,0 represents the damping coefficient of the radial damping between the i-th row and the i+1-th row in the j-th column. The damping coefficient is an empirical parameter determined based on prior knowledge.

[0029] Preferably, the specific method of step 3 is:

[0030] Assume the total simulation time is T and the simulation time step is d t , simulation steps n t =T / d t During the simulation time, the carrier moves along the y-axis direction. t is defined as the simulation time. The linear velocity of the linear motion along the y-axis direction at time t can be expressed as vy (t), v y (0)=0.

[0031] Preferably, the specific method of step 4 is:

[0032] Step 4.1, parameter initialization, initial time t = 0, the initial position of the particle is Initial velocity of each particle At the initial moment, the spring length is equal to the original length of the spring, and the system is at rest;

[0033] Step 4.2. Calculate the length of all springs at time t: At time t, the position of the mass point in row i and column j is Speed is The acceleration is The length of the spring from row i, column j to column j+1 at time t is expressed as L i,(j,j+1),t , and its calculation formula is:

[0034]

[0035] The length of the spring in row i and column j-1 to column j at time t is represented by L i,(j-1,j),t , and its calculation formula is:

[0036]

[0037] The length of the spring in the jth column, ith row to i+1th row at time t is expressed as L (i,i+1),j,t , and its calculation formula is:

[0038]

[0039] The length of the spring in the jth column, i-1th row to ith row at time t is expressed as L (i-1,i),j,t , and its calculation formula is:

[0040]

[0041] Step 4.3. Calculate the internal fluid particle acceleration at time t

[0042] make represents the sum of the spring force and damping force in the i-th row, j-th column and j-1-th column at time t; represents the sum of the spring force and damping force in the i-th row, j-th column and j+1-th column at time t; represents the sum of the spring force and the damping force in the jth column, ith row and i-1th row at time t; It represents the sum of the spring force and the damping force in the jth column, the ith row and the i+1th row at time t. The calculation formula is shown in formula (11-14):

[0043]

[0044]

[0045]

[0046]

[0047] According to Newton's second law, for the internal fluid particle m in row i and column j i,j , and its acceleration is calculated as:

[0048]

[0049] Step 4.4. Calculate the forces acting on the boundary particles at both ends of the solid-phase converter The calculation formula is:

[0050]

[0051] Among them, Fx * i,j (t) and Fy * i,j (t) represents the components of the force on the particle at row i and column j in the x-axis and y-axis directions respectively;

[0052] Step 4.5. Update the internal fluid particle velocity and location The update formula is:

[0053]

[0054]

[0055] Step 4.6. Update the velocity and position of the boundary particles. The motion state of the carrier is used as the boundary condition of the fluid system. Therefore, the velocity update equation and position update equation of the boundary particles are:

[0056]

[0057]

[0058] Step 4.7, update the current simulation time t = t + 1, and determine whether it exceeds the set simulation time, that is, whether t + 1 > n tIf yes, the simulation is completed; otherwise, go to Step 4.2 and perform the iterative calculation at the next moment, specifically:

[0059] The position at time t+1 is obtained using formula (18) and formula (20) Use formulas (7)-(10) to update the spring length at time t+1; use the spring length at time t+1 and the position at time t+1 to get the spring length at time t+1. Formulas (11)-(14) are used to update the sum of the spring force and the damping force at time t+1; then, the acceleration at time t+1 is updated using formula (15), and the force on the boundary particle at time t+1 is calculated using formula (16);

[0060] Finally, use formula (18) to formula (20) to update the position at the next moment;

[0061] And so on, enter the iterative calculation of the next moment until t+1>n t .

[0062] Preferably, the specific method of step 5 is:

[0063] According to the net external force on the solid-phase converter in the mass-spring system, the pressure difference of the liquid at both ends of the actual solid-phase converter is calculated. For each moment t obtained above, the calculation formula for the pressure difference ΔP(t) at both ends of the solid-phase converter caused by the acceleration condition is:

[0064]

[0065] The present invention has the following beneficial effects:

[0066] The present invention provides a method for analyzing the error of a liquid ring angular accelerometer under variable linear acceleration conditions. When establishing the error model of the liquid ring angular accelerometer under variable linear acceleration conditions, the influence of the compressibility of the working fluid is taken into account. Therefore, the model can be applied to the error analysis of angular accelerometers under high-frequency variable linear acceleration excitation.

[0067] The present invention establishes a linear vibration influence model based on a mass-spring-damper system. The model can be solved iteratively using the Newton-Euler method, has a fast calculation speed, and can realize real-time calculation and analysis of linear vibration influence.

[0068] The present invention can perform numerical simulation prediction on the error of the liquid ring angular accelerometer under variable linear acceleration conditions. The prediction results of the error model can be used to compensate for the error of the liquid ring angular accelerometer under variable linear acceleration conditions, thereby ensuring its working reliability in high dynamic conditions. BRIEF DESCRIPTION OF THE DRAWINGS

[0069] Figure 1Schematic diagram of the layered equivalent of a liquid ring angular accelerometer as a circular cylinder.

[0070] Figure 2 Schematic diagram of a two-dimensional mass-spring-damper system.

[0071] Figure 3 Flowchart for solving the Newton-Euler method.

[0072] Figure 4 It is the simulation result of the pressure difference across the solid-phase converter under variable linear acceleration conditions (instantaneous linear acceleration step excitation). DETAILED DESCRIPTION

[0073] The present invention is described in detail below with reference to the accompanying drawings and embodiments.

[0074] The error analysis method of the liquid ring angular accelerometer under the condition of variable linear acceleration includes the following steps:

[0075] Step 1: For the annular cavity of the angular liquid ring accelerometer, ignore the linear vibration effect perpendicular to the plane of the annular cavity and only consider the measurement error introduced by the linear acceleration parallel to the solid-phase converter (set in the cross section of the annular cavity). Figure 1 As shown, the annular cavity is sliced along the direction parallel to the plane where the annular cavity is located, and the fluid shape of each layer is approximately equivalent to a circular cylinder. A two-dimensional model is established for each layer of the circular cylinder for analysis, specifically:

[0076] Let R be the radius of the annular cavity, r c Represents the diameter of the circular cross section of the inner cavity of the annular cavity. Slice the annular cavity uniformly along the plane parallel to the annular cavity, and divide it into w layers. Each layer is approximately equivalent to a circular cylinder, and the empirical parameter is w = 7; let h represent the height of each layer of circular cylinder, then Let d s (s=1,2…w) represents the cross-sectional width of the layered ring cylinder.

[0077] Step 2: Ignore the movement of the fluid in the direction perpendicular to the plane of the annular cavity and treat the fluid system of each layer of the annular cylinder as a two-dimensional mass-spring-damper system. The mass of the liquid is equivalent to the mass, the bulk elastic modulus of the liquid is equivalent to the elastic coefficient of the spring, and the viscous force inside the liquid is equivalent to the damping between the masses. The specific parameters are defined as:

[0078] For each layer of the annular cylinder, divide it evenly along the axial direction of the annular cavity into q+1 parts, and divide it evenly along the radial direction into n+1 parts. Let each axial division be represented by a row, and each radial division be represented by a column. Then m ij(i=0,1…q,j=0,1…n) represents the mass of the particles in the axial i-th row and radial j-th column, where the outermost particles are boundary particles; the others are internal fluid particles. Figure 2 As shown, the mass formula of the internal fluid particle is:

[0079]

[0080] Where ρ represents the density of the fluid, and d represents the cross-sectional width of the current layered annular cylinder. The values of q and n are determined by the annular cavity structural parameters R and d, and are adjusted based on the results of simulation experiments to select the most appropriate values. The empirical parameters are q = 47 and n = 4.

[0081] Establish a plane rectangular coordinate system, set the center of the annular cavity as the coordinate origin, the direction from the origin to the solid phase converter as the positive direction of the x-axis, the direction perpendicular to the solid phase converter as the positive direction of the y-axis, and the z-axis direction is determined by the x-axis and y-axis according to the right-hand screw rule, as follows: Figure 2 As shown. The initial position coordinates of the particle in the i-th row and j-th column in the plane rectangular coordinate system are Considering the boundary layer problem, we first define the position of each particle in the polar coordinate system (the polar coordinate system has the same origin as the plane coordinate system established above, and the polar axis direction is the x-axis direction), and then transform it into the plane rectangular coordinate system. The coordinate definition of the initial position of the particle in the polar coordinate system is: As shown in formulas (2) and (3).

[0082]

[0083]

[0084] According to the conversion relationship between polar coordinates and plane rectangular coordinates (as shown in formula (4)), the initial position of the particle can be calculated as

[0085]

[0086] Adjacent masses in each row and column are connected by springs and dampers: axial springs, axial dampers, radial springs, and radial dampers. The spring constants are determined by the bulk modulus of the fluid. In this model, the working fluid is equivalent to a mass-spring-damper system.

[0087] The axial springs connect the masses in different rows in each column. The axial springs in each column have the same spring constant. The axial springs and spring constants of the jth column, ith row to i+1th row can be expressed as K (i,i+1),j ; Radial springs connect the masses in different columns in each row. The radial springs in each row have the same spring coefficient. The radial springs and their spring coefficients in the i-th row, j-th column to j+1-th column can be expressed as Ki,(j,j+1) . L i,(j,j+1),0 represents the initial length of the axial spring between the jth column and the j+1th column in the i-th row, L (i,i+1),j,0 The initial length of the radial spring between the i-th row and the i+1-th row in the j-th column can be calculated based on the initial position coordinates of the mass points at both ends of the spring.

[0088] For axial springs, the formula for calculating the spring rate is:

[0089]

[0090] where K l represents the bulk modulus of the working fluid.

[0091] For radial springs, the formula for calculating the spring constant is:

[0092]

[0093] Use c i,(j,j+1) The damping coefficient of the axial damping between the jth column and the j+1th column in the i-th row is expressed as c (i,i+1),j,0 represents the damping coefficient of the radial damping between the i-th row and the i+1-th row in the j-th column. The damping coefficient is an empirical parameter determined based on prior knowledge.

[0094] Step 3: Set the simulation time and linear velocity excitation signal. Assume the total simulation time is T and the simulation time step is d. t , so the number of simulation steps n t =T / d t (Set d t It must be divisible by T). During the simulation time, the carrier moves along the y-axis, and t is defined as (t=0,1…n t ) represents the simulation time, and the linear velocity of the linear motion in the y-axis direction at time t can be expressed as v y (t), to ensure that the simulation starts from a stable state, v y (0)=0.

[0095] Step 4: Use the Newton-Euler method to calculate the resultant force on the solid-phase converter under the linear velocity excitation signal. The specific calculation steps are as follows:

[0096] Step 4.1, parameter initialization, time t = 0. Therefore, the initial position of the particle is Initial velocity of each particle At the initial moment, the spring length is equal to the original length of the spring, and the system is at rest;

[0097] Step 4.2. Calculate the length of all springs at time t. At time t, the position of the mass point in row i and column j is Speed is The acceleration is The length of the spring from row i, column j to column j+1 at time t can be expressed as L i,(j,j+1),t , and its calculation formula is:

[0098]

[0099] The length of the spring in row i and column j-1 to column j at time t can be expressed as L i,(j-1,j),t , and its calculation formula is:

[0100]

[0101] The length of the spring in the jth column, ith row to i+1th row at time t can be expressed as L (i,i+1),j,t , and its calculation formula is:

[0102]

[0103] The length of the spring from column j, row i-1 to row i at time t can be expressed as L (i-1,i),j,t , and its calculation formula is:

[0104]

[0105] Step 4.3. Calculate the internal fluid particle acceleration at time t

[0106] make represents the sum of the spring force and damping force in the i-th row, j-th column and j-1-th column at time t; represents the sum of the spring force and damping force in the i-th row, j-th column and j+1-th column at time t; represents the sum of the spring force and the damping force in the jth column, ith row and i-1th row at time t; It represents the sum of the spring force and the damping force in the jth column, the ith row and the i+1th row at time t. The calculation formula is shown in formula (11-14):

[0107]

[0108]

[0109]

[0110]

[0111] According to Newton's second law, for the internal fluid particle m in row i and column j i,j , and its acceleration is calculated as:

[0112]

[0113] Step 4.4. Calculate the forces acting on the boundary particles at both ends of the solid-phase converter The calculation formula is:

[0114]

[0115] Among them, Fx * i,j (t) and Fy * i,j (t) represents the components of the force on the particle at the i-th row and j-th column in the x-axis and y-axis directions respectively.

[0116] Step 4.5. Update the internal fluid particle velocity and location The update formula is:

[0117]

[0118]

[0119] Step 4.6. Update the velocity and position of the boundary particles. The motion state of the carrier is used as the boundary condition of the fluid system. Therefore, the velocity update equation and position update equation of the boundary particles are:

[0120]

[0121]

[0122] Step 4.7, update the current simulation time t = t + 1, and determine whether it exceeds the set simulation time, that is, whether t + 1 > n t If yes, the simulation is completed; otherwise, go to Step 4.2 and perform the iterative calculation at the next moment, specifically:

[0123] The position at time t+1 is obtained using formula (18) and formula (20) Use formulas (7)-(10) to update the spring length at time t+1; use the spring length at time t+1 and the position at time t+1 to get the spring length at time t+1. Formulas (11)-(14) are used to update the sum of the spring force and the damping force at time t+1; then, the acceleration at time t+1 is updated using formula (15), and the force on the boundary particle at time t+1 is calculated using formula (16);

[0124] Finally, use formula (18) to formula (20) to update the position at the next moment;

[0125] And so on, enter the iterative calculation of the next moment until t+1>n t .

[0126] Step 5: Calculate the pressure difference of the liquid at both ends of the solid-phase converter. Based on the net external force on the solid-phase converter in the mass-spring system, calculate the pressure difference of the liquid at both ends of the actual solid-phase converter. For each moment t obtained above, the calculation formula for the pressure difference ΔP(t) at both ends of the solid-phase converter caused by the acceleration condition is:

[0127]

[0128] Analyze the error of liquid ring angular accelerometer based on pressure difference ΔP(t).

[0129] Example:

[0130] In this embodiment, the ring cavity radius R of the liquid ring angular accelerometer is 0.02m, and the inner diameter of the ring cavity is r c =0.003m, the working liquid is water, considering that there may be a small amount of gas mixed in the working liquid, so the bulk modulus K of the working liquid l =2.2×10 7 Pa. Figure 1 As shown in the figure, the ring cavity is divided into 7 layers along the normal direction of the ring cavity plane. Taking the modeling of the fourth layer as an example for analysis, the cross-sectional width of the layer is d = 0.003.

[0131] The annular cavity is divided into 48 rows along the axial direction and 5 columns along the radial direction, i.e., q = 47, n = 4. According to the mass formula (1) of the internal fluid particles and the boundary particles, the mass of each internal particle is set;

[0132] According to the conversion relationship between polar coordinates and plane rectangular coordinates (as shown in formula (4)), the initial position of the particle can be calculated as

[0133] The spring constants of the axial spring and radial spring are set according to formulas (5) and (6), and the initial length of each spring is calculated according to the initial positions of the masses at both ends of the spring. The damping coefficient is set according to prior knowledge.

[0134] Set the simulation time and linear velocity excitation signal. Assume the total simulation time is T = 0.02s and the simulation time step is d t =0.000001s, simulation step number n t =T / d t During the simulation time, the carrier moves along the y-axis, and the linear velocity of the linear motion along the y-axis at time t is

[0135] The Newton-Euler method is used to solve the resultant force on the solid-phase converter under linear velocity excitation. The specific calculation steps are as follows:

[0136] Step 4.1, parameter initialization, time t = 0. Therefore, the initial position of the particle is Initial velocity of each particle At the initial moment, the spring length is equal to the original length of the spring, and the system is at rest;

[0137] Step 4.2. Calculate the length of all springs at time t. At time t, the position of the mass point in row i and column j is Speed is The acceleration is The length of the spring from row i, column j to column j+1 at time t can be expressed as L i,(j,j+1),t , which is calculated as formula (7); the length of the spring in the i-th row and the j-1th column to the j-th column at time t can be expressed as L i,(j-1,j),t , which is calculated as formula (8); the length of the spring from the jth column and the ith row to the i+1th row at time t can be expressed as L (i,i+1),j,t , which is calculated as formula (9); the length of the spring from the jth column, the i-1th row to the ith row at time t can be expressed as L (i-1,i),j,t , and its calculation formula is formula (10).

[0138] Step 4.3. Calculate the sum of the spring force and the damping force at time t according to formula (11-14), and then calculate the internal fluid particle acceleration at time t according to formula (15)

[0139] Step 4.4. Calculate the force on the boundary particles at both ends of the solid-phase converter according to formula (16):

[0140] Step 4.5: Update the internal fluid particle velocity according to formulas (17) and (18) and location

[0141] Step 4.6, update the boundary particle velocity and position according to formula (19) and (20);

[0142] Step 4.7, update the current simulation time t = t + 1, and determine whether it exceeds the set simulation time, that is, whether t + 1 > n t If yes, then complete the simulation; otherwise go to Step 4.2.

[0143] The force magnitude of each particle at each moment is stored, and the pressure difference of the liquid at both ends of the solid-phase converter is calculated according to formula (21). Therefore, the simulation results of the pressure difference at both ends of the solid-phase converter under the condition of variable linear acceleration (instantaneous linear acceleration step excitation) are as follows: Figure 4 shown.

[0144] In summary, the above are only preferred embodiments of the present invention and are not intended to limit the scope of protection of the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A method for error analysis of a liquid ring angular accelerometer under variable linear acceleration conditions, characterized in that: include: Step 1: Slice the annular cavity of the liquid ring angular accelerometer along a direction parallel to the plane of the annular cavity, and approximately make the shape of the fluid in each layer equivalent to a circular cylinder; Step 2: Equivalent the fluid system of each layer of the annular cylinder to a two-dimensional mass-spring-damper system. The specific method is as follows: For each layer of the annular cylinder, divide it evenly along the axial direction of the annular cavity into q+1 parts, and divide it evenly along the radial direction into n+1 parts. Let each axial division be represented by a row, and each radial division be represented by a column. Then m ij represents the mass of the particles in the axial i-th row and radial j-th column, where the outermost particles are boundary particles and the others are internal fluid particles. The mass formula of the internal fluid particles is: Where i = 0, 1…q, j = 0, 1…n, ρ represents the density of the fluid, and d represents the cross-sectional width of the current layered ring cylinder; Establish a plane rectangular coordinate system, set the center of the annular cavity as the coordinate origin, the direction from the origin to the solid phase converter as the positive direction of the x-axis, the direction perpendicular to the solid phase converter as the positive direction of the y-axis, and the z-axis direction is determined by the x-axis and y-axis according to the right-hand screw rule; the initial position coordinates of the particle in the i-th row and j-th column in the plane rectangular coordinate system are Considering the boundary layer problem, the position of each particle is first defined in the polar coordinate system, and then converted to the plane rectangular coordinate system. The coordinate definition of the initial position of the particle in the polar coordinate system is As shown in formulas (2) and (3): According to the conversion relationship between polar coordinates and plane rectangular coordinates, the initial position of the particle is calculated as Adjacent masses in each row and column are connected by springs and dampers, which are axial springs, axial dampers, radial springs, and radial dampers respectively. The spring coefficient is determined by the bulk elastic modulus of the liquid. The axial springs connect the masses in different rows in each column. The axial springs in each column have the same spring constant. The axial springs and spring constants of the jth column, ith row to i+1th row can be expressed as K (i,i+1),j ; Radial springs connect the masses in different columns in each row. The radial springs in each row have the same spring coefficient. The radial springs and their spring coefficients in the i-th row, j-th column to j+1-th column can be expressed as K i,(j,j+1) ;L i,(j,j+1),0 represents the initial length of the axial spring between the jth column and the j+1th column in the i-th row, L (i,i+1),j,0 represents the initial length of the radial spring between the i-th row and the i+1-th row in the j-th column, which is calculated based on the initial position coordinates of the mass points at both ends of the spring; For axial springs, the formula for calculating the spring rate is: where K l represents the bulk modulus of the working fluid; For radial springs, the formula for calculating the spring constant is: Use c i,(j,j+1) The damping coefficient of the axial damping between the jth column and the j+1th column in the i-th row is expressed as c (i,i+1),j,0 represents the damping coefficient of the radial damping between the i-th row and the i+1-th row in the j-th column. The damping coefficient is an empirical parameter determined based on prior knowledge. Step 3: Set the simulation time and linear speed excitation signal; Step 4: Use the Newton-Euler method to calculate the magnitude of the resultant force on the solid-phase converter under the linear velocity excitation signal; Step 5: Calculate the pressure difference of the liquid at both ends of the solid phase converter.

2. The error analysis method of a liquid ring angular accelerometer under variable linear acceleration conditions according to claim 1, characterized in that: In step 1, let R represent the radius of the annular cavity, r c Represents the diameter of the circular cross section of the inner cavity of the annular cavity; uniformly slice the annular cavity along the plane parallel to the annular cavity, and divide it into w layers, and each layer is approximately equivalent to a circular cylinder; let h represent the height of each layer of circular cylinder, then 3. The error analysis method of a liquid ring angular accelerometer under variable linear acceleration conditions according to claim 1, characterized in that: The specific method of step 3 is: Assume the total simulation time is T and the simulation time step is d t , simulation steps n t =T / d t During the simulation time, the carrier moves along the y-axis direction. t is defined as the simulation time. The linear velocity of the linear motion along the y-axis direction at time t can be expressed as v y (t), v y (0)=0.

4. The error analysis method of a liquid ring angular accelerometer under variable linear acceleration conditions according to claim 1, characterized in that: The specific method of step 4 is: Step 4.1, parameter initialization, initial time t = 0, initial position of the particle is Initial velocity of each particle At the initial moment, the spring length is equal to the original length of the spring, and the system is at rest; Step 4.

2. Calculate the length of all springs at time t: At time t, the position of the mass point in row i and column j is Speed is The acceleration is The length of the spring from row i, column j to column j+1 at time t is expressed as L i,(j,j+1),t , and its calculation formula is: The length of the spring in row i and column j-1 to column j at time t is represented by L i,(j-1,j),t , and its calculation formula is: The length of the spring in the jth column, ith row to i+1th row at time t is expressed as L (i,i+1),j,t , and its calculation formula is: The length of the spring in the jth column, i-1th row to ith row at time t is expressed as L (i-1,i),j,t , and its calculation formula is: Step 4.

3. Calculate the internal fluid particle acceleration at time t make represents the sum of the spring force and damping force in the i-th row, j-th column and j-1-th column at time t; represents the sum of the spring force and damping force in the i-th row, j-th column and j+1-th column at time t; represents the sum of the spring force and the damping force in the jth column, ith row and i-1th row at time t; It represents the sum of the spring force and the damping force in the jth column, the ith row and the i+1th row at time t. The calculation formula is shown in formula (11-14): According to Newton's second law, for the internal fluid particle m in row i and column j i,j , and its acceleration is calculated as: Step 4.

4. Calculate the forces acting on the boundary particles at both ends of the solid-phase converter The calculation formula is: Among them, Fx * i,j (t) and Fy * i,j (t) represents the components of the force on the particle at row i and column j in the x-axis and y-axis directions respectively; Step 4.

5. Update the internal fluid particle velocity and location The update formula is: Step 4.

6. Update the velocity and position of the boundary particles. The motion state of the carrier is used as the boundary condition of the fluid system. Therefore, the velocity update equation and position update equation of the boundary particles are: Step 4.7, update the current simulation time t = t + 1, and determine whether it exceeds the set simulation time, that is, whether t + 1 > n t If yes, the simulation is completed; otherwise, go to Step 4.2 and perform the iterative calculation at the next moment, specifically: The position at time t+1 is obtained using formula (18) and formula (20) Use formulas (7)-(10) to update the spring length at time t+1; use the spring length at time t+1 and the position at time t+1 to get the spring length at time t+1. Formulas (11)-(14) are used to update the sum of the spring force and the damping force at time t+1; then, the acceleration at time t+1 is updated using formula (15), and the force on the boundary particle at time t+1 is calculated using formula (16); Finally, use formula (18) to formula (20) to update the position at the next moment; And so on, enter the iterative calculation of the next moment until t+1>n t .

5. The error analysis method of a liquid ring angular accelerometer under variable linear acceleration conditions according to claim 4, characterized in that: The specific method of step 5 is: According to the net external force on the solid-phase converter in the mass-spring system, the pressure difference of the liquid at both ends of the actual solid-phase converter is calculated. For each moment t obtained above, the calculation formula for the pressure difference △P(t) at both ends of the solid-phase converter caused by the acceleration condition is:

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