Vibration isolation design method for optical fiber strapdown inertial navigation system of helicopter

Abstract

The invention discloses a vibration isolation design method for an optical fiber strapdown inertial navigation system of a helicopter, and belongs to the technical field of vibration isolation design for optical fiber strapdown inertial navigation systems of large helicopters.The vibration isolation design method comprises the steps that eight-point vibration isolation layout design with three symmetric planes is adopted for the inertial navigation system based on motion decoupling; establishing a random dynamical model of the inertial navigation system based on a substructure method of a frequency response function; sine acceleration excitation in a helicopter vibration power spectrum is converted into narrow-band random vibration, on this basis, the influence of the shock absorber rigidity parameter on the root-mean-square acceleration response of the inertial navigation system is analyzed, and the shock absorber rigidity parameter when the root-mean-square acceleration response is minimum is obtained under the condition that the main paddle frequency is fully considered according to the influence rule. The method can solve the problems of repeated iteration, low efficiency, incapability of directly judging the vibration isolation effect of the system and the like in the frequency avoiding method in the traditional vibration isolation design of the helicopter inertial navigation system.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of vibration isolation technology of helicopter fiber-optic strapdown inertial navigation system, and particularly relates to a vibration isolation design method of helicopter fiber-optic strapdown inertial navigation system. BACKGROUND

[0002] Helicopters have irreplaceable roles in the fields of rescue, drug and smuggling suppression, medical aid and military strikes due to their hovering, low-speed maneuvering and ability to operate in complex environments. The inertial navigation system (INS) is the core device of helicopter flight control and attitude stabilization, and its accuracy is significantly affected by the vibration environment of the machine body. Unlike fixed-wing aircraft, the vibration environment of a helicopter is mainly characterized by low-level wideband random vibration superimposed with strong Sine-on-Random (SOR) vibration. This vibration is mainly generated by components such as rotors, tail rotors and engine transmission shafts. If the natural frequency of the inertial navigation system is close to the frequency of these Sine-on-Random vibrations, the amplitude will be amplified by more than 10 times, and the vibration characteristics will not only seriously affect the measurement accuracy of the inertial navigation system, but also cause fatigue cracks in the structural components.

[0003] In order to improve the measurement accuracy of the inertial navigation system in the vibration environment, the inertial navigation system usually adopts passive vibration isolation design. The vibration isolation design of the helicopter inertial navigation system needs to specially consider the SOR frequency spectrum characteristics of its vibration environment. Due to the presence of multiple significant Sine-on-Random excitation frequencies in the environment, the traditional frequency avoidance design principle cannot simultaneously suppress the vibration transmission of all key frequencies, so it is difficult to directly evaluate the effectiveness of the vibration isolation system. This results in the current vibration isolation design process of the inertial navigation system often needing to go through multiple iterative design and test verification, which is long in cycle and low in efficiency. Therefore, the vibration isolation design of the inertial navigation system under the specific SOR vibration environment of the helicopter has become a key technical problem to be solved.

[0004] When analyzing the random vibration response of the inertial navigation system, it is generally simplified as a linear system. According to the linear random vibration theory, the calculation of the power spectral density of the linear system response is crucial to the calculation of the frequency response function of the system. In the vibration isolation design process of the inertial navigation system, the iterative adjustment of the damper stiffness will change the overall dynamic characteristics of the system. At this time, whether using the direct method or the modal superposition method to calculate the frequency response function, there is a problem of high calculation cost and low efficiency, which is particularly significant for complex structures. For structures that only undergo local changes, the substructure synthesis method based on the frequency response function has a significant advantage. This method can conveniently analyze the frequency response function of the structure after local changes without the need to reconstruct the frequency response function of the unchanged components, thereby effectively improving the calculation efficiency. SUMMARY

[0005] The technical problem solved by the present application is to provide a helicopter optical fiber strapdown inertial navigation system vibration isolation design method, which solves the problems of existing technologies of traditional frequency avoidance vibration isolation design methods of helicopter inertial navigation systems, such as repeated iteration, low efficiency and inability to directly evaluate the vibration isolation effect of the system.

[0006] In order to solve the above technical problems, the technical scheme adopted by the present application is as follows: a helicopter optical fiber strapdown inertial navigation system vibration isolation design method, comprising the following steps:

[0007] Step 1: based on motion decoupling, an eight-point vibration isolation layout design with three symmetrical surfaces is adopted for the inertial navigation system;

[0008] Step 2: a random dynamics model of the inertial navigation system in step 1 is established based on the substructure method of frequency response function;

[0009] Step 3: the sine acceleration excitation in the helicopter vibration power spectrum is converted into narrow-band random vibration, and on this basis, the influence of the damper stiffness parameter on the root mean square acceleration response of the inertial navigation system is analyzed, and the damper stiffness parameter at the minimum root mean square acceleration response is obtained under the condition of fully considering the main shaft frequency.

[0010] Further, the vibration isolation layout method in step 1 is as follows:

[0011] Considering the elastic support of the inertial measurement unit IMU, a coordinate system Oxyz is established at the geometric center position of the inertial measurement unit IMU, and the motion differential equation of the inertial navigation system is:

[0012] (1),

[0013] Among them, , , respectively represent the three axial accelerations measured by the inertial navigation system when the carrier moves, , , respectively represent the angular accelerations of the inertial navigation system around the three axes, is the mass matrix of the system, and the specific form is:

[0014] (2),

[0015] In the formula, m represents the mass of the inertial measurement unit IMU, I xx , I yy , I zz represent the moments of inertia of the inertial measurement unit IMU around the center of mass, I xy , I xz , I yz represent the inertia products of the inertial measurement unit IMU, , , the position coordinates of the center of mass of the inertial measurement unit IMU;

[0016] is the stiffness matrix of the system, and has the form

[0017] (3)

[0018] wherein , , respectively represent the position coordinates of the elastic support, , , represents the stiffness of the three main elastic axes of the elastic support, and subscript i represents the i-th damper;

[0019] Assuming that the oyz plane is the symmetry plane of the vibration isolation system, then

[0020] (4)

[0021] Assuming that the oxz plane is the symmetry plane of the vibration isolation system, then

[0022] (5)

[0023] Assuming that the oxy plane is the symmetry plane of the vibration isolation system, then

[0024] (6)

[0025] Therefore, in order to make a vibration isolation system completely realize stiffness decoupling, the following conditions need to be met:

[0026] (7)

[0027] The corresponding vibration isolation system needs to have three symmetry planes, and the installation form that meets the decoupling condition of formula (7) is an eight-point vibration isolation mode.

[0028] If the parameters of each damper are consistent, the stiffness matrix of the vibration isolation system is a diagonal matrix, and has the form

[0029] (8)

[0030] wherein x, y and z respectively represent the three elastic main axes of the damper, sym represents the symmetry of the stiffness matrix K, , and respectively represent the stiffness of the damper along the elastic main axes x, y and z.

[0031] Further, the method for establishing the random dynamic model of the inertial navigation system in step 2 is as follows:

[0032] The inertial navigation system is divided into substructure A and substructure B, substructure A is a support structure, i.e. a case, substructure B includes an IMU support, a quartz accelerometer and an optical fiber gyroscope, and the connecting structure between the two includes eight rubber dampers;

[0033] For substructure A, the main excitation is external load and interface force Therefore, the frequency response equation between the interface node displacement and the excitation is obtained as follows:

[0034] (15),

[0035] In the formula, subscript c represents the interface node, i represents the internal node, represents the displacement frequency response function, which is obtained by the modal superposition method, and the displacement frequency response function between any two points of the structure is as follows:

[0036] (16),

[0037] In the formula, , , respectively represent the mode shape, frequency and damping ratio of the nth mode of the structure, N is the number of modes reserved for modal analysis, and respectively represent the displacement components of the mode shape of the nth mode of the structure in s and t degrees of freedom;

[0038] For substructure B, the main excitation is interface force Therefore, the frequency response equation between the internal node displacement, the interface node displacement and the excitation is obtained as follows:

[0039] (17),

[0040] In the analysis, the damper is simplified as a spring-damping system, and according to the displacement coordination condition and the force balance condition, the following equation is obtained:

[0041] (18),

[0042] In the formula, is the impedance of the damper, which is expressed as:

[0043] (19),

[0044] In the formula, represents the first the stiffness matrix of the rth vibration absorber, r represents the number of vibration absorbers, r = 1, 2, …, 8, is the structural damping coefficient of the vibration absorber;

[0045] The frequency response relationship between the interface node displacement of the substructure B and the external excitation is obtained as follows:

[0046] (20),

[0047] The displacement response of the internal node of the substructure B is considered as the sum of the rigid body motion of the interface node and the elastic motion relative to the interface, and the rigid body motion of the interface node reflects the advantages and disadvantages of the vibration absorber. According to the rigid body kinematics theory, the rigid body motion of the interface node is described by the response of a reference point, that is:

[0048] (21),

[0049] In the formula, is the displacement response of the reference point, is a conversion matrix, and its form is:

[0050] (22),

[0051] In the above formula, is:

[0052] (23),

[0053] In the formula, , , is the position coordinate of the reference point, , , is the position coordinate of the mounting point of the rth vibration absorber;

[0054] The displacement response of the reference point is obtained by using the least square principle is:

[0055] (24),

[0056] Therefore, the acceleration response of the reference point is obtained as follows:

[0057] (25),

[0058] The frequency response function between the acceleration response of the reference point and the structure subjected to the excitation is finally obtained as follows:

[0059] (26),

[0060] where f represents the excitation frequency of the helicopter vibration environment to the inertial navigation system.

[0061] Further, the acceleration power spectrum corresponding to the sinusoidal excitation in step 3 is:

[0062] (9),

[0063] where, is the quality factor, , is the sinusoidal excitation frequency, is the excitation amplitude of, is the Heaviside function, and the lower limit frequency of the frequency bandwidth and the upper limit are respectively:

[0064] (10),

[0065] Since the wideband random vibration response is expressed as a linear relationship in a double logarithmic coordinate, the acceleration power spectral density of the wideband random vibration is obtained as:

[0066] (11),

[0067] Thus, the combined vibration of the inertial navigation system mounted on the helicopter is converted into random vibration, and the power spectral density thereof is the superposition of the narrowband acceleration power spectrum and the wideband acceleration power spectrum, expressed as:

[0068] (12).

[0069] The root mean square acceleration calculation method is to obtain the self-power spectral density of the reference point acceleration response is:

[0070] (27),

[0071] where, represents the mass of the mass element at the excitation point, represents the diagonal element of ;

[0072] In order to evaluate the effect of the inertial navigation isolation system, the root mean square acceleration value of the interface reference point in the excitation frequency band is defined as is

[0073] (28),

[0074] where, represents the acceleration self-power spectral density of the reference point in the i-th direction.

[0075] The present application has the following advantages: compared with the prior art, the present application is directed to the problem of optical fiber strapdown inertial navigation system, and proposes a vibration isolation design method suitable for helicopter inertial navigation system. The method is based on the motion decoupling principle, and adopts an eight-point vibration isolation layout with three symmetrical surfaces. Then, the frequency response function substructure method is applied to establish a random dynamics model of the inertial navigation system, and the sinusoidal acceleration excitation in the helicopter vibration environment is equivalent to narrow-band random vibration. On this basis, the influence of the stiffness parameters of the vibration absorber on the root mean square acceleration response of the system is analyzed, and the optimal stiffness parameters are selected according to the response minimization principle. The method can solve the problems of the frequency avoidance method in the traditional vibration isolation design of the helicopter inertial navigation system, such as repeated iteration, low efficiency, and inability to directly evaluate the vibration isolation effect of the system. BRIEF DESCRIPTION OF DRAWINGS

[0076] Figure 1 Figure 1 is a diagram of the dynamics model of the inertial navigation system with elastic support;

[0077] Figure 2 Figure 5 is a schematic diagram of an eight-point vibration isolation mode;

[0078] Figure 3 Figure 6 is a vibration spectrum diagram of the helicopter wideband random superposition of sine combination;

[0079] Figure 4 Figure 7 is a schematic diagram of the main structure of the optical fiber strapdown inertial navigation system;

[0080] Figure 5 Figure 8 is a schematic diagram of the substructure dynamics model of the inertial navigation system;

[0081] Figure 6 Figure 9 is a finite element model diagram of substructure A;

[0082] Figure 7 Figure 10 is a finite element model diagram of substructure B;

[0083] Figure 8 Figure 11 is a diagram of the connecting structure (vibration absorber);

[0084] Figure 9 Figure 12 is a vibration power density spectrum curve after conversion;

[0085] Figure 10 Figure 13 is a relationship curve of the stiffness parameters of the vibration absorber on the root mean square acceleration of the vibration response of the inertial navigation vibration isolation system;

[0086] Figure 11 Figure 14 is a diagram of the vibration test device of the inertial navigation vibration isolation system

[0087] Figure 12 Figure 15 is the acceleration amplitude-frequency curve of the inertial navigation vibration isolation system designed by the traditional method along the X-axis, Y-axis and Z-axis

[0088] Figure 13 Acceleration amplitude-frequency curve of the inertial navigation isolation system designed by the new method along the X-axis, Y-axis and Z-axis

[0089] Figure 14 Acceleration power spectral density curve of the inertial navigation isolation system designed by the traditional method along the X-axis, Y-axis and Z-axis

[0090] Figure 15 Acceleration power spectral density curve of the inertial navigation isolation system designed by the new method along the X-axis, Y-axis and Z-axis DETAILED DESCRIPTION

[0091] The application will be further explained in conjunction with the drawings of the specification, so as to be better understood by those skilled in the art.

[0092] The vibration environment of the helicopter inertial navigation system mainly shows the characteristics of low-level wideband random vibration superimposed on strong sinusoidal vibration. Since the environment contains multiple significant sinusoidal excitation frequencies, it is difficult to directly evaluate the effectiveness of the isolation system by using the traditional frequency avoidance design principle because it cannot simultaneously suppress the vibration transmission of all key frequencies. Therefore, the application proposes an isolation design method suitable for the helicopter inertial navigation system. Taking a certain fiber-optic strapdown inertial navigation system as the research object, first, an eight-point isolation layout with three symmetric surfaces is designed for the inertial navigation system based on motion decoupling. Then, a random dynamics model of the inertial navigation system is established based on the substructure method of frequency response function. Next, the sinusoidal acceleration excitation in the helicopter vibration power spectrum is converted into narrowband random vibration. On this basis, the influence of the damper stiffness parameter on the root mean square acceleration response of the inertial navigation system is analyzed. According to the influence law, the damper stiffness parameter is obtained when the root mean square acceleration response is minimized under the condition of fully considering the main propeller frequency. Then, the simulation and experimental comparison of the isolation system composed of the obtained damper parameters are carried out. The simulation and experimental results both show that the isolation design method of the helicopter inertial navigation system proposed by the application is feasible.

[0093] Embodiment 1: As shown in the figure, a helicopter fiber-optic strapdown inertial navigation system isolation design method comprises the following steps: Figures 1-12

[0094] Step 1: An eight-point isolation layout with three symmetric surfaces is designed for the inertial navigation system based on motion decoupling.

[0095] The isolation layout method based on motion decoupling in step 1 is as follows: When designing the inertial navigation isolation system, since the stiffness of the elastic support is much smaller than that of the inertial measurement unit IMU (inertial measurement unit, IMU) body, the inertial measurement unit IMU is usually assumed to be a rigid body. The inertial navigation isolation system can be simplified as an elastic supported IMU. Considering that Figure 1 ​The inertial measurement unit (IMU) is elastically supported, a coordinate system Oxyz is established at the geometric center of the IMU, and the motion differential equation of the inertial navigation vibration isolation system is as follows:

[0096] (1),

[0097] wherein, , , respectively represent three axial accelerations measured by the inertial navigation system during carrier motion, , , respectively represent angular accelerations of the inertial navigation system around three axes, is a mass matrix of the system, and the specific form is as follows:

[0098] (2),

[0099] wherein, m represents the mass of the inertial measurement unit (IMU), I xx , I yy and I zz represent the moments of inertia of the inertial measurement unit (IMU) around the center of mass, I xy , I xz and I yz represent the products of inertia of the inertial measurement unit (IMU), , and represent the position coordinates of the center of mass of the inertial measurement unit (IMU);

[0100] is a stiffness matrix of the system, and the specific form is as follows:

[0101] (3),

[0102] wherein, , and respectively represent the position coordinates of the elastic supports, , and represent the stiffnesses of three main elastic axes of the elastic supports, and the subscript i represents the i-th vibration damper;

[0103] As can be seen from equation (2), the center of mass of the IMU should be coincided with the geometric center thereof during design, so as to minimize the coupling between linear vibration and angular vibration of the IMU. In addition, by reasonably arranging the elastic supports, the system has a specific symmetry plane, and the decoupling of partial linear vibration and angular vibration of the system can also be realized. In the following, the elastic coupling characteristics of the orthogonal elastic support system with different numbers of symmetry planes will be analyzed in sequence.

[0104] Case 1: Orthogonal elastic support with one symmetry plane

[0105] Assuming that the oyz plane is the symmetry plane of the vibration isolation system, then:

[0106] (4),

[0107] Case 2: Orthogonal elastic support with two symmetry planes

[0108] Based on Case 1, assuming that the oxz plane is the symmetry plane of the vibration isolation system, then:

[0109] (5),

[0110] Case 3: Orthogonal elastic support with three symmetry planes

[0111] Based on Cases 1 and 2, assuming that the oxy plane is the symmetry plane of the vibration isolation system, then:

[0112] (6),

[0113] Therefore, to make a vibration isolation system completely realize stiffness decoupling, the following conditions need to be met:

[0114] (7),

[0115] The corresponding vibration isolation system needs to have three symmetry planes, and the installation form that meets the decoupling condition of formula (7) is shown in Figure 2 , which is an eight-point vibration isolation mode.

[0116] The stiffness matrix of the vibration isolation system is a diagonal matrix, and if the parameters of each damper are consistent, its form is

[0117] (8),

[0118] In the formula, x, y and z respectively represent the three elastic principal axes of the damper, sym represents the symmetry of the stiffness matrix K, 、 and respectively represent the stiffness of the damper along the elastic principal axes x, y and z.

[0119] In summary, the optical fiber strapdown inertial navigation system of the application adopts an eight-point orthogonal elastic support mode, which can well suppress the coupling between linear vibration and angular vibration.

[0120] Step 2: Establish the random dynamics model of the inertial navigation system in step 1 based on the substructure method of frequency response function;

[0121] The typical vibration environment of a helicopter inertial navigation system is as shown in Figure 3The figure shows. In the figure, f1~f4 are 4-order sinusoidal constant frequency, A1~A4 are sinusoidal acceleration amplitude, W0 and W1 are wideband random vibration acceleration power spectrum density.

[0122] In processing the above vibration spectrum, the sinusoidal acceleration excitation is usually converted into narrowband acceleration power spectrum. The acceleration power spectrum corresponding to the sinusoidal acceleration excitation is:

[0123] (9),

[0124] In the formula, Q is the quality factor, , f is the sinusoidal excitation frequency, A is the excitation amplitude of, n=1, 2, 3, 4, H is the Heaviside function. The lower limit frequency of the corresponding frequency bandwidth and the upper limit frequency are

[0125] (10),

[0126] Since the wideband random vibration response is expressed as a linear relationship in double logarithmic coordinates, the acceleration power spectrum density of the wideband random vibration can be obtained as

[0127] (11),

[0128] The combined vibration borne by the inertial navigation system installed on the helicopter is converted into random vibration, and the power spectrum density thereof is the superposition of the narrowband acceleration power spectrum and the wideband acceleration power spectrum, which is expressed as

[0129] (12),

[0130] The base acceleration excitation borne by the inertial navigation isolation system can be converted into external load by the large mass method, and has:

[0131] ,

[0132] In the formula, M represents the excitation point mass, which is generally 10 6 times the mass of the inertial navigation system.

[0133] Therefore, the inertial navigation system bearing the base acceleration excitation can be regarded as a single-input multi-output linear system, and the relationship between the power spectrum density of the output response and the power spectrum density of the input is:

[0134] (14),

[0135] where superscript denotes the conjugate matrix, superscript denotes the transpose of a matrix, is the frequency response function between input and output.

[0136] Since the power spectral density of the excitation of the inertial navigation system is known, the key of the vibration response analysis of the system is the calculation of the frequency response function.

[0137] The frequency response function is established based on the substructure synthesis method of the frequency response function:

[0138] The typical structural model of the fiber-optic strapdown inertial navigation system is shown in Fig. 4. The whole fiber-optic strapdown inertial navigation system is mainly composed of a case (supporting structural member), shock absorber, IMU, circuit board and receiver, and the IMU is mainly composed of a bracket, fiber-optic gyroscope and quartz accelerometer. The structural model shown in Fig. 4 is equivalent to the substructure dynamics model of the inertial navigation system shown in Fig. 5. According to the principle of substructure division, the structure on both sides of the connecting structure is generally divided into substructures. Therefore, the above system can be divided into substructures A and B. Substructure A is the case and the receiver, circuit board mounted thereon, and substructure B contains the bracket, quartz accelerometer and fiber-optic gyroscope, and the connecting structure between the two contains eight rubber shock absorbers. Figure 4 Figure 5 For substructure A, the main excitation is external load and interface force

[0139] Therefore, the frequency response equation between the interface node displacement and the excitation is obtained as:

[0140] (15),

[0141] where subscript c represents the interface node, i represents the internal node, represents the displacement frequency response function, which is obtained by using the modal superposition method, and the displacement frequency response function between any two points of substructure A is:

[0142] (16),

[0143] where , and respectively represent the mode shape, frequency and damping ratio of the nth order mode of the structure, N is the number of modes reserved for modal analysis, and respectively represent the displacement components of the mode shape of the nth order mode of the structure at s and t degrees of freedom;

[0144] For substructure B, the main excitation is the interface force​​ Therefore, the frequency response equations between the internal nodal displacements, the interface nodal displacements, and the excitation are obtained as follows:

[0145] (17)

[0146] In the analysis, the vibration damper is simplified as a spring-damped system. Based on the displacement compatibility condition and the force balance condition, the following equation is obtained:

[0147] (18)

[0148] In the formula, The damper impedance is expressed as:

[0149] (19)

[0150] In the formula, Representing the The stiffness matrix of each vibration damper, where r represents the number of vibration dampers, r = 1, 2, ..., 8. This refers to the structural damping coefficient of the vibration damper;

[0151] Therefore, the frequency response relationship between the interface node displacements of substructure B and the external excitation is obtained as follows:

[0152] (20)

[0153] The displacement response of the internal nodes of substructure B is considered as the sum of the rigid body motion of the interface nodes and the elastic motion relative to the interface. The rigid body motion of the interface nodes reflects the quality of the vibration damper. According to rigid body kinematics theory, the rigid body motion of the interface nodes is described by the response at a certain reference point, that is:

[0154] (twenty one),

[0155] In the formula, Displacement response at reference point The transformation matrix has the following form:

[0156] (twenty two),

[0157] In the above formula for:

[0158] (twenty three),

[0159] In the formula, , and The coordinates of the reference point are... , and Let r be the coordinates of the installation point of the r-th vibration isolator;

[0160] The displacement response of the reference point is obtained using the least squares principle. for:

[0161] (twenty four),

[0162] Therefore, the acceleration response at the reference point is:

[0163] (25)

[0164] The final frequency response function between the acceleration response at the reference point and the excitation borne by the structure is:

[0165] (26)

[0166] In the formula, f represents the excitation frequency applied to the inertial navigation system by the helicopter vibration environment.

[0167] Step 3: Convert the sinusoidal acceleration excitation in the helicopter vibration power spectrum into narrowband random vibration. Based on this, analyze the influence of the damper stiffness parameters on the root mean square acceleration response of the inertial navigation system. According to the influence law, under the condition of fully considering the main rotor frequency, obtain the damper stiffness parameters with the minimum root mean square acceleration response.

[0168] The root mean square acceleration is calculated as follows: According to equation (14), the self-power spectral density of the acceleration response at the reference point is obtained. for:

[0169] (27)

[0170] In the formula, This represents the mass of the mass element at the excitation point. express The diagonal elements;

[0171] To evaluate the effectiveness of the inertial navigation vibration reduction system, the root mean square acceleration value of the interface reference point within the excitation frequency band is defined. for:

[0172] (28)

[0173] In the formula, This represents the autopower spectral density of the acceleration at the reference point in the i-th direction.

[0174] To illustrate the effectiveness of the present invention, the following simulation experiment was conducted:

[0175] 1. Establishment of the finite element model of the inertial navigation system:

[0176] In establishingFigure 4 When modeling the inertial navigation system using the finite element method (FEM), reasonable and necessary geometric simplifications are performed (such as removing unnecessary rounded corner features). The chassis support structure is simulated using second-order tetrahedral elements. Bolted connections are simulated using beam elements. In the analysis, the circuit boards and receiver on the chassis are treated as non-structural masses; the fiber optic gyroscope and quartz accelerometer are simplified as lumped mass elements and coupled to the support using rigid constraints. The rubber vibration damper between the chassis and the IMU is simplified as a spring-damped system, and its mass effect is ignored. The FEM models corresponding to substructures A and B are shown below. Figure 6 and Figure 7 As shown, the two are connected by a rubber shock absorber, and their positions are determined by... Figure 8 As shown by the black dots in the image.

[0177] The vibration environment parameters of the helicopter inertial navigation system used are shown in Table 1.

[0178]

[0179] Based on the vibration environment parameters in Table 1, and according to equations (9) to (14), the converted vibration power density spectrum curve is as follows: Figure 9 As shown.

[0180] The analysis assumes a structural damping coefficient of 0.02 for the chassis and support, and a structural damping coefficient of 0.2 for the vibration damper. Simultaneously, it considers the three-dimensional isostiffness characteristics of the vibration damper, with a stiffness range of 5~25 N / mm. The influence of variations in the vibration damper stiffness parameters on the root mean square acceleration response of the inertial navigation isolation system is calculated, and the results are as follows. Figure 10 As shown in the figure, AX, AY, and AZ represent the root mean square accelerations of the inertial navigation vibration isolation system along the X-axis, Y-axis, and Z-axis, respectively.

[0181] Depend on Figure 10 It can be seen that the influence of changes in the damper stiffness parameter on the root mean square acceleration response of the inertial navigation vibration isolation system along the X, Y, and Z axes shows a basically consistent trend, which verifies the effectiveness of the eight-point vibration isolation layout design in achieving decoupling. Furthermore, the system's root mean square acceleration response exhibits a trend of first decreasing and then increasing with increasing damper stiffness, rather than a monotonic change. Therefore, under the premise of meeting design feasibility, the system's root mean square acceleration should be minimized when selecting the damper stiffness parameter. Simulation calculations show that the root mean square acceleration response is minimized when the stiffness parameter is approximately 11 N / mm. Considering the manufacturing and processing factors and stiffness errors of the rubber damper, a damper with a measured stiffness parameter of 13 N / mm was actually selected.

[0182] The helicopter inertial navigation isolation system design traditionally adopts the anti-frequency method, which is mainly based on finite element software and test, and the natural frequency of the system is changed by adjusting the stiffness of the damper to avoid the excitation frequency. According to the traditional anti-frequency method, the natural frequency of the system is 60 Hz, and the corresponding damper stiffness parameter is 23.5 N / mm. The corresponding root mean square acceleration AX, AY, AZ of the system is 7.70g, 7.78g, 7.76g respectively. Obviously, the design effect of the new method is better than that of the traditional method. Figure 10

[0183] 2. Test verification

[0184] 2.1 Sinusoidal sweep test

[0185] In order to compare the natural frequency of the inertial navigation isolation system designed by the two methods, the sweep vibration test is carried out on the inertial navigation isolation system designed by the traditional method and the new method respectively. The acceleration sensor is attached to the center of the IMU, and the test device is shown in Figure 11 , and the vibration direction is X axis, Y axis and Z axis respectively.

[0186] The input condition of the vibration test is sinusoidal sweep vibration, the sweep mode is logarithmic sweep, the sweep rate is 1 oct / min, and the acceleration amplitude is 1g. The acceleration transmissibility amplitude-frequency curve of the inertial navigation isolation system designed by the traditional method is shown in Figure 12 . The acceleration transmissibility amplitude-frequency curve of the inertial navigation isolation system designed by the new method is shown in Figure 13 .

[0187] From Figure 12 and Figure 13 , it can be seen that the acceleration amplitude-frequency curves of the inertial navigation isolation systems designed by the two methods along the X axis, Y axis and Z axis are basically coincident, which verifies that the inertial navigation system adopts the eight-point isolation device layout design based on motion decoupling, and the non-coincidence part is mainly caused by the installation error and the damper stiffness parameter error. The resonant frequencies of the X axis, Y axis and Z axis of the inertial navigation isolation system designed by the traditional method are 68 Hz, 66 Hz and 64 Hz respectively, and the maximum acceleration transmissibility of the X axis, Y axis and Z axis is 4.55, 4.75 and 4.65 respectively. The natural frequencies of the X axis and Z axis of the inertial navigation isolation system designed by the new method are both 48 Hz, and the Y axis is 51 Hz. The maximum acceleration transmissibility of the X axis, Y axis and Z axis is 4.45, 4.35 and 4.45 respectively. Obviously, the natural frequency of the inertial navigation isolation system designed by the new method is smaller than that of the traditional method, and the maximum acceleration transmissibility is also smaller. The natural frequencies of the X axis, Y axis and Z axis of the two methods are successfully avoided from the fourth order sinusoidal excitation frequency.

[0188] 2.2 Wideband random + sinusoidal combined vibration test

[0189] ​In order to compare the root mean square acceleration responses of the inertial navigation isolation systems designed by the two methods, vibration tests are respectively conducted on the inertial navigation isolation systems designed by the traditional method and the new method. The acceleration sensors are attached to the center of the IMU, and the vibration tests are conducted according to the vibration spectrum in FIG. 5 and the parameters in Table 1. The vibration directions are X-axis, Y-axis and Z-axis respectively, and the test time of each axis is 900s. The acceleration power spectral density curves of the inertial navigation isolation system designed by the traditional method along the X-axis, Y-axis and Z-axis are shown in FIG. Figure 14 The acceleration power spectral density curves of the inertial navigation isolation system designed by the new method along the X-axis, Y-axis and Z-axis are shown in FIG. Figure 15 .

[0190] From Figure 14 and Figure 15 , it can be seen that the vibration response curves of the inertial navigation isolation systems designed by the traditional method and the new method along the X-axis, Y-axis and Z-axis are basically consistent, which also verifies that the eight-point isolator layout decoupling design is adopted for the inertial navigation system. There is strong energy response near the four frequencies of ① 6.77Hz, ② 27.1Hz, ③ 54.1Hz and ④ 81.2Hz in the two figures. Referring to Figure 5 , the energy mutations at the four places are mainly caused by the response changes of the four-order sinusoidal constant frequency f1~f4 in Table 1, which also directly reflects the SOR spectrum characteristics of the helicopter vibration environment. After 90Hz, the acceleration power spectral response decreases rapidly with the increase of frequency, and the isolation effect is obvious. Then the root mean square accelerations of the vibration response curves of the system along the X-axis, Y-axis and Z-axis are respectively calculated Figure 14 and Figure 15 , and the comparison results are shown in Table 2.

[0191]

[0192] From the data in Table 2, compared with the root mean square accelerations of the inertial navigation isolation system designed by the traditional method along the X-axis, Y-axis and Z-axis, the AX, AY and AZ calculated by the new method are respectively reduced by 26.9%, 24.4% and 24.7%, which is obviously better than the traditional method. It shows that the new method is feasible.

[0193] Conclusion: Aiming at the problem of low efficiency and repeated iteration in the frequency-avoiding method of traditional vibration isolation design for helicopter inertial navigation system (INS), a new vibration isolation design method is proposed. Firstly, based on the motion decoupling principle, an eight-point vibration isolation layout with three symmetrical surfaces is adopted. Then, the random dynamics model of the INS is established by using the frequency response function substructure method, and the sinusoidal acceleration excitation in the helicopter vibration environment is converted into narrow-band random vibration. On this basis, the influence of the stiffness parameters of the damper on the root mean square (RMS) acceleration response of the system is analyzed, and the optimal stiffness parameters are selected according to the response minimization principle. To verify the effectiveness of the method, comparative tests are carried out on the INS vibration isolation systems designed by the new method and the traditional method. The sine sweep test shows that the natural frequencies of the X, Y and Z axes of the two systems successfully avoid the fixed-frequency excitation. The wide-band random superimposed sine combined test proves that the RMS acceleration response of the new method is significantly better than that of the traditional method, and the vibration isolation performance is significantly improved. The test results fully verify the feasibility and engineering superiority of the method proposed in this paper.

Claims

1. A vibration isolation design method for a helicopter fiber optic strapdown inertial navigation system, characterized in that, Includes the following steps: Step 1: Based on motion decoupling, an eight-point vibration isolation layout with three symmetrical planes is designed for the inertial navigation system; Step 2: Establish the stochastic dynamic model of the inertial navigation system in Step 1 based on the substructure method of the frequency response function; Step 3: Convert the sinusoidal acceleration excitation in the helicopter vibration power spectrum into narrowband random vibration. Based on this, analyze the influence of the damper stiffness parameters on the root mean square acceleration response of the inertial navigation system. According to the influence law, obtain the damper stiffness parameters with the minimum root mean square acceleration response under the condition of fully considering the main rotor frequency.

2. The vibration isolation design method for a helicopter fiber optic strapdown inertial navigation system according to claim 1, characterized in that, The vibration isolation layout method in step 1 is as follows: Considering an inertial measurement unit (IMU) with elastic support, a coordinate system Oxyz is established at the geometric center of the IMU. The differential equation of motion for the inertial navigation system is: （1）， in, , , These represent the three axial accelerations measured by the inertial navigation system during the carrier's motion. , , These represent the angular accelerations of the inertial navigation system about the three axes, respectively. The system's quality matrix has the following specific form: （2）， In the formula, m represents the mass of the inertial measurement unit (IMU), and I... xx I yy and I zz I represents the moment of inertia of the inertial measurement unit (IMU) about its center of mass. xy I xz and I yz The inertial product representing the inertial measurement unit (IMU) , and Represents the position coordinates of the centroid of the inertial measurement unit (IMU); The system's stiffness matrix is ​​given by: （3）， In the formula, , and These represent the position coordinates of the elastic support. , and This represents the stiffness of the three principal elastic axes of the elastic support, with the subscript i indicating the i-th damper. This indicates that the stiffness matrix K is symmetric, meaning that the formulas for the corresponding positions of the upper right and lower left corners of the matrix are the same. Assuming the oyz plane is the plane of symmetry of the vibration isolation system, then: （4）， Assuming the oxz plane is the plane of symmetry of the vibration isolation system, then we have: （5）， Assuming the oxy plane is the plane of symmetry of the vibration isolation system, then: （6）， Therefore, for a vibration isolation system to achieve complete stiffness decoupling, the following conditions must be met: （7）， The corresponding vibration isolation system needs to have three symmetrical planes and be installed in a manner that satisfies the decoupling condition of formula (7). This vibration isolation system is an eight-point vibration isolation mode. If the parameters of each vibration damper are identical, the stiffness matrix of the vibration isolation system is a diagonal matrix, in the form of: （8）， In the formula, x, y, and z represent the three elastic principal axes of the vibration damper, and sym indicates that the stiffness matrix K is symmetric. , and These represent the stiffness of the damper along the elastic principal axes x, y, and z, respectively.

3. The vibration isolation design method for a helicopter fiber optic strapdown inertial navigation system according to claim 2, characterized in that, The method for establishing the stochastic dynamic model of the inertial navigation system in step 2 is as follows: The inertial navigation system is divided into substructure A and substructure B. Substructure A is the supporting structure, i.e., the chassis. Substructure B includes the IMU bracket, quartz accelerometer and fiber optic gyroscope. The connection structure between the two includes eight rubber vibration dampers. For substructure A, the main excitation it bears is external load. and interface force Therefore, the frequency response equation between the interface node displacement and the excitation is obtained as follows: （15）， In the formula, the subscript c represents the interface node, and i represents the internal node. The displacement frequency response function, obtained using the modal superposition method, is given by: （16）， In the formula, , , Let represent the mode shape, frequency, and damping ratio of the nth mode of the structure, respectively, where N is the number of modes retained in the modal analysis. and These represent the displacement components of the nth mode shape of the structure at the s and t degrees of freedom, respectively. For substructure B, the main excitation it experiences is interfacial force. Therefore, the frequency response equations between the internal nodal displacements, the interface nodal displacements, and the excitation are obtained as follows: （17）， In the analysis, the vibration damper is simplified as a spring-damped system. Based on the displacement compatibility condition and the force balance condition, the following equation is obtained: （18）， In the formula, The damper impedance is expressed as: （19）， In the formula, This represents the stiffness matrix of the r-th vibration damper, where r represents the number of vibration dampers, r = 1, 2, ..., 8. This refers to the structural damping coefficient of the vibration damper; Therefore, the frequency response relationship between the interface node displacements of substructure B and the external excitation is obtained as follows: （20）， The displacement response of the internal nodes of substructure B is considered as the sum of the rigid body motion of the interface nodes and the elastic motion relative to the interface. According to rigid body kinematics, the rigid body motion of the interface nodes is described by the response at a certain reference point, i.e.: （21）， In the formula, Displacement response at reference point The transformation matrix has the following form: （22）， In the above formula for: （23）， In the formula, , , The coordinates of the reference point are... , , Let be the coordinates of the installation point of the r-th vibration isolator; The displacement response of the reference point is obtained using the least squares principle. for: （24）， Therefore, the acceleration response at the reference point is: （25）， The final frequency response function between the acceleration response at the reference point and the excitation borne by the structure is: （26）， In the formula, f represents the excitation frequency applied to the inertial navigation system by the helicopter vibration environment.

4. The vibration isolation design method for a helicopter fiber optic strapdown inertial navigation system according to claim 3, characterized in that, The acceleration power spectrum corresponding to the sinusoidal acceleration excitation in step 3 is: （9）， In the formula, For quality factors, , The frequency of the sinusoidal excitation is... For the excitation amplitude, For the Heaviside function, the lower limit frequency of the corresponding bandwidth. and upper limit The frequencies are respectively: （10）， The acceleration power spectral density of the broadband random vibration is obtained as follows: （11）， The combined vibrations experienced by the inertial navigation system installed on the helicopter are converted into random vibrations, and its power spectral density is the superposition of the narrowband acceleration power spectrum and the broadband acceleration power spectrum, expressed as: （12）。 5. The vibration isolation design method for a helicopter fiber optic strapdown inertial navigation system according to claim 4, characterized in that, The root mean square acceleration calculation method in step 3 is as follows: obtain the self-power spectral density of the acceleration response at the reference point. for: （27）， In the formula, This represents the mass element at the excitation point. express The diagonal elements; Define the root mean square acceleration value of the interface reference point within the excitation frequency band. for （28）， In the formula, This represents the autopower spectral density of the acceleration at the reference point in the i-th direction.

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