A design method of inertial navigation vibration isolation system for helicopter vibration environment

Abstract

This invention discloses a design method for an inertial navigation system (INS) vibration isolation system for helicopter vibration environments, belonging to the technical field of INS vibration isolation system design for helicopter vibration environments. The method includes the following steps: Step 1, based on the differential equation of motion of a single-degree-of-freedom isolation system under basic acceleration excitation, constructing an analytical model of the root-mean-square acceleration (RMS) of the INS vibration isolation system under SOR excitation; Step 2, based on this model, analyzing the variation of the RMS acceleration and response power of the system with the natural frequency of the isolation system under sinusoidal vibration, broadband random vibration, and both superimposed excitation conditions, and determining the optimal natural frequency of the isolation system according to the principle of minimizing response. This invention can effectively reduce the maximum error and standard deviation of the yaw, pitch, and roll angles of the INS, verifying the effectiveness of the design method.

Description

Technical Field

[0001] This invention relates to the field of inertial navigation vibration isolation system design technology, and specifically to a design method for an inertial navigation vibration isolation system for helicopter vibration environments. Background Technology

[0002] Helicopters, as a special type of aircraft, possess unique capabilities such as vertical takeoff and landing, omnidirectional maneuvering, hovering, and ultra-low-altitude ground-hugging flight. Inertial navigation systems (INS) are crucial core components for helicopter flight control and attitude stabilization, playing a key role in ensuring flight safety and mission execution capabilities under complex environmental conditions. Compared to fixed-wing aircraft, helicopters exhibit significantly different vibration environments, characterized by low-level broadband random vibration superimposed with intense sinusoidal fixed-frequency vibration, i.e., a Sine-on-Random (SOR) vibration environment. In this environment, when the structural dynamics of the INS coincide with or are close to the external excitation frequency, the system's vibration response is significantly amplified, potentially leading to structural damage or functional failure in severe cases. Therefore, the rational design and optimization of INS vibration isolation systems under helicopter vibration conditions has become a critical research issue for ensuring structural integrity and measurement accuracy.

[0003] Researchers have conducted systematic studies and made corresponding progress on the design of vibration isolation systems for helicopter inertial navigation systems. The literature “Ren Yan, Fang Jiancheng, Xu Rui. Vibration-resistant design and real-time filtering method for helicopter fiber optic gyroscope IMU [J]. Journal of Beijing University of Aeronautics and Astronautics, 2013, 39(4):437-441” establishes a mathematical model of the vibration isolation system for a helicopter fiber optic IMU (Inertial Measurement Unit). Through optimized design, it achieves decoupling of linear motion and angular motion channels, effectively suppressing the transmission of high-frequency harmful vibrations. The literature “Feng Shiwei, Zhi Yinzhou, Li Yong, et al. Random vibration response and linear-angular coupling error analysis of inertial measurement units [J]. Journal of Chinese Inertial Technology, 2025, 33(12):1175-1182” establishes a three-dimensional model of the linear-angular coupling error of IMU multi-point vibration isolation, providing theoretical guidance for the vibration isolation design and linear-angular coupling suppression of inertial navigation systems. The literature “Cheng Guoda, Qu Xiaodong, Zhang Yi. Research on Vibration Performance Improvement of Airborne Strapdown Inertial Navigation System [J]. Journal of Astronautics, 2024, 45(4):532-539” derives the spatial six-degree-of-freedom matrix vibration differential equation of airborne inertial navigation system and establishes a numerical solution model for the vibration equation of inertial navigation system. On this basis, the influence of batch stiffness consistency and stiffness anisotropy of vibration damper is analyzed. However, existing research is mostly focused on the design of inertial navigation vibration isolation system under broadband random vibration environment, and relatively little attention is paid to the SOR characteristics that are common in helicopter vibration environment. Systematic research on this type of composite vibration environment is still relatively limited in the literature. Summary of the Invention

[0004] The technical problem to be solved by this invention is to provide a design method for an inertial navigation vibration isolation system for helicopter vibration environment, which can effectively reduce the maximum error and standard deviation of the inertial navigation system's heading angle, pitch angle and roll angle, and verify the effectiveness of the design method.

[0005] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is: a design method for an inertial navigation vibration isolation system oriented towards the vibration environment of helicopters, comprising the following steps:

[0006] Step 1: Based on the differential equation of motion of a single-degree-of-freedom vibration isolation system under basic acceleration excitation, construct an analytical model of the root mean square acceleration of the inertial navigation vibration isolation system under SOR excitation.

[0007] Step 2: Based on the model, analyze the variation of the root mean square acceleration and response power of the system with the natural frequency of the vibration isolation system under sinusoidal vibration, broadband random vibration and the superposition of the two excitation conditions, and determine the optimal natural frequency of the vibration isolation system according to the principle of minimizing response.

[0008] Furthermore, the analytical model construction method in step 1 above is as follows:

[0009] After decoupling, the inertial navigation vibration isolation system is approximately equivalent to a single-degree-of-freedom vibration system with six independent motion directions (i.e., the six faces of the IMU). The foundation of the single-degree-of-freedom vibration isolation system is subjected to acceleration excitation. The differential equation of motion of the single-degree-of-freedom vibration isolation system is expressed as:

[0010] (1),

[0011] In the formula, m, k, and c represent the mass of the IMU, the stiffness of the damper, and the damping coefficient, respectively; x, and These represent the absolute displacement, velocity, and acceleration of the IMU, respectively. , and These are the basic excitation displacement, velocity, and acceleration, respectively;

[0012] Introducing relative displacement Equation (1) is transformed into:

[0013] (2),

[0014] In the formula, , ;

[0015] Using equation (2), we get:

[0016] (3),

[0017] Under basic acceleration random excitation, the root mean square (RMS) value of the acceleration response is used as the core evaluation index of the system's response. Based on random vibration theory, the value of the autocorrelation function of a stationary random process at zero time shift is the RMS value of the response. Therefore, the RMS value of the system's absolute acceleration response is expressed as:

[0018] (4),

[0019] In the formula, For x r The autocorrelation function of , using the Wiener-Khinchin theorem, has the following relationship:

[0020] (5),

[0021] In the formula, Indicates the fundamental acceleration excitation frequency. It is the one-sided self-power spectral density of the system's relative displacement, obtained by solving the random vibration response of a single-input, single-output system, and its expression is:

[0022] (6),

[0023] In the formula, The one-sided self-power spectral density of the basic acceleration excitation, The frequency response function of the system is:

[0024] (7),

[0025] Combining equations (4)-(7), the mean square value of the absolute acceleration of the inertial navigation vibration isolation system under random acceleration excitation is:

[0026] (8),

[0027] In the formula, T is the absolute acceleration transmissibility of the system, which is a function of β, expressed as:

[0028] (9),

[0029] For broadband random vibrations for:

[0030] (10)

[0031] In the formula, and These represent the acceleration power spectral density values ​​corresponding to the starting and ending frequencies of the broadband random vibration segment, respectively. For sinusoidal excitation, for:

[0032] (11),

[0033] In the formula, f i The acceleration amplitude corresponding to the i-th order sinusoidal vibration (i = 1, 2, 3, 4). Represents the Dirac function;

[0034] According to equation (8), the mean square value of the absolute acceleration generated by the sinusoidal excitation is obtained as follows:

[0035] (12)

[0036] In the formula, , Let represent the excitation frequency of the i-th order sinusoidal vibration. Therefore, the root mean square value of the absolute acceleration of the inertial navigation isolation system under helicopter vibration conditions is expressed as:

[0037] (13)

[0038] The integral term in the formula is calculated using numerical integration.

[0039] Furthermore, the specific implementation method of step 2 above is as follows: within the set range of 30-70 Hz for the natural frequency of the inertial navigation vibration isolation system, calculate the relationship curves of the root mean square acceleration of the system with the natural frequency of the vibration isolation system under sinusoidal vibration excitation, broadband random vibration excitation, and the superposition of the two excitations respectively:

[0040] Based on equations (8) and (12), the relationship curves between the system power and the natural frequency of the inertial navigation isolation system under sinusoidal excitation frequencies f1, f2, f3, f4 and broadband random vibration excitation were calculated respectively. Under random excitation of the foundation acceleration, the system response is usually represented by the root mean square value of the acceleration response. Based on equation (13), the relationship curve between the root mean square acceleration and the system's natural frequency was calculated, and the natural frequency corresponding to the minimum root mean square response was selected as the optimal natural frequency.

[0041] The beneficial effects of this invention are as follows: Compared with the prior art, this invention proposes a design method for inertial navigation system vibration isolation systems oriented towards this type of vibration environment. Based on the differential equations of motion of a single-degree-of-freedom system under basic acceleration excitation, this method derives an analytical model of the root-mean-square acceleration of the inertial navigation system vibration isolation system under superimposed excitation of sinusoidal vibration and broadband random vibration. A finite element model is established to verify the analytical model, confirming its correctness. Furthermore, the variation of the root-mean-square acceleration and power of the system with natural frequency under sinusoidal vibration, broadband random vibration, and their superimposed excitation conditions is analyzed. Based on the principle of minimizing the root-mean-square response, the optimal natural frequency of the vibration isolation system is determined. This invention can effectively reduce the maximum error and standard deviation of the heading angle, pitch angle, and roll angle of the inertial navigation system, verifying the effectiveness of this design method. Attached Figure Description

[0042] Figure 1 The spectrum is a mixture of broadband random vibration and sinusoidal vibration of a helicopter.

[0043] Figure 2 This diagram shows the common vibration damper layout for inertial navigation vibration isolation systems.

[0044] Figure 3 This is a model diagram of a single-degree-of-freedom vibration isolation system.

[0045] Figure 4 This is a schematic diagram of the main structure of a strapdown inertial navigation system.

[0046] Figure 5 A finite element model diagram of an inertial navigation system;

[0047] Figure 6 This is the equivalent acceleration power spectral density plot;

[0048] Figure 7 The curve of root mean square acceleration as a function of natural frequency (comparison between finite element method and the method of this application);

[0049] Figure 8 The curves show the variation of root mean square acceleration with the natural frequency of the inertial navigation vibration isolation system under three vibration conditions;

[0050] Figure 9 The curves showing the variation of system power with the natural frequency of the inertial navigation vibration isolation system under different excitations;

[0051] Figure 10 Schematic diagram of the SOR vibration test device for inertial navigation isolation system;

[0052] Figure 11 The acceleration power spectral density curves of the system in Scheme 1 along the X, Y, and Z axes are shown.

[0053] Figure 12The acceleration power spectral density curves of the system in Scheme 2 along the X, Y, and Z axes are shown.

[0054] Figure 13 is a comparison of the heading angle error curves of the inertial navigation system;

[0055] Figure 14 is a comparison of the pitch angle error curves of the inertial navigation system;

[0056] Figure 15 is a comparison of the roll angle error curves of the inertial navigation system. Detailed Implementation

[0057] The present invention will be further explained and described below with reference to the accompanying drawings to enable those skilled in the art to better understand it.

[0058] To address the impact of superimposed broadband random vibration and sinusoidal vibration excitation on the design of inertial navigation system (INS) vibration isolation systems in helicopter vibration environments, a design method for such vibration isolation systems is proposed. This method is based on the differential equations of motion of a single-degree-of-freedom system under foundation acceleration excitation, deriving an analytical model of the root-mean-square (RMS) acceleration of the system under the superposition of sinusoidal and broadband random vibrations. Using a fiber-optic strapdown INS as the research object, the established model was verified using the finite element method (FEM), and the results show good agreement between the analytical model and the FEM calculation results. Furthermore, the variation laws of the system's RMS acceleration and power with natural frequency under different excitation conditions were analyzed. The results show that the variation law of the system's RMS acceleration is mainly dominated by the power change caused by sinusoidal excitation, while the influence of random vibration components on the overall response is relatively small. Based on the principle of minimizing the system's RMS response, the optimal natural frequency of the vibration isolation system was determined. The designed vibration isolation system was verified through SOR vibration tests. The results show that, compared with the traditional frequency avoidance method, the vibration isolation system designed by the proposed method reduces the root mean square acceleration in the X, Y, and Z axes by 26.9%, 24.4%, and 24.7%, respectively. Simultaneously, it reduces the maximum errors of the inertial navigation system's heading angle, pitch angle, and roll angle by 82.6%, 89.9%, and 26.2%, respectively, and the standard deviations by 82.7%, 90.5%, and 12.3%, respectively. The research results demonstrate that this method can effectively improve the vibration isolation performance of the helicopter inertial navigation system. The specific scheme is described in Example 1. Before introducing the scheme, the following content regarding the random vibration response of the helicopter inertial navigation vibration isolation system will be introduced.

[0059] The random vibration response of a helicopter inertial navigation vibration isolation system: Helicopter vibration is mainly caused by aerodynamic alternating loads generated by rotating components such as the main rotor and tail rotor. Its typical vibration mixture spectrum is as follows: Figure 1 As shown in the figure, f1-f4 are the main frequency components of the fourth-order sinusoidal vibration, and A1-A4 are the corresponding acceleration amplitudes; W0 and W1 are the broadband random vibration acceleration power spectral densities.

[0060] In the design of inertial navigation vibration isolation systems, the layout of the vibration dampers is a primary consideration. Common layout methods for airborne inertial navigation vibration isolation systems include spatial eight-point layout, planar four-point layout, spatial four-point layout, and chair-shaped four-point layout, etc. Figure 2 As shown.

[0061] When the elastic center of the vibration isolation system coincides with the center of mass of the IMU, and both the elastic principal axis and the inertial principal axis are aligned with the analysis coordinate axes, the system's stiffness matrix and mass matrix are both diagonal matrices, thus achieving complete decoupling. In practical design, decoupling is usually achieved through measures such as symmetrical layout of the vibration dampers and reducing the deviation between the elastic center and the center of mass of the vibration isolation system. The decoupled system can be approximately equivalent to six independent single-degree-of-freedom vibration systems, thus enabling simplified analysis and design of the system based on single-degree-of-freedom vibration isolation theory. Traditional vibration damper design methods are widely used in engineering based on this idea.

[0062] Example 1: As Figure 1-15 As shown, a design method for an inertial navigation vibration isolation system for helicopter vibration environments includes the following steps:

[0063] Step 1: Based on the differential equation of motion of a single-degree-of-freedom vibration isolation system under basic acceleration excitation, construct an analytical model of the root mean square acceleration of the inertial navigation vibration isolation system under SOR excitation.

[0064] The analytical model construction method is as follows:

[0065] After decoupling, the inertial navigation vibration isolation system is approximately equivalent to a single-degree-of-freedom vibration system with six independent motion directions. The decoupling of the inertial navigation vibration isolation system is considered... Figure 3 The single-degree-of-freedom vibration isolation system model shown is illustrated. The foundation of the single-degree-of-freedom vibration isolation system is subjected to acceleration excitation. The differential equation of motion of the single-degree-of-freedom vibration isolation system is expressed as follows:

[0066] (1),

[0067] In the formula, m, k, and c represent the mass of the IMU, the stiffness of the damper, and the damping coefficient, respectively; x, and These represent the absolute displacement, velocity, and acceleration of the IMU, respectively. , and These are the basic excitation displacement, velocity, and acceleration, respectively;

[0068] Introducing relative displacement Equation (1) is transformed into:

[0069] (2),

[0070] In the formula, , ;

[0071] Using equation (2), we get:

[0072] (3),

[0073] Under basic acceleration random excitation, the root mean square (RMS) value of the acceleration response is used as the core evaluation index of the system's response. Based on random vibration theory, the value of the autocorrelation function of a stationary random process at zero time shift is the RMS value of the response. Therefore, the RMS value of the system's absolute acceleration response is expressed as:

[0074] (4),

[0075] In the formula, For x r The autocorrelation function of , using the Wiener-Khinchin theorem, has the following relationship:

[0076] (5),

[0077] In the formula, Indicates the fundamental acceleration excitation frequency. It is the one-sided self-power spectral density of the system's relative displacement, obtained by solving the random vibration response of a single-input, single-output system, and its expression is:

[0078] (6),

[0079] In the formula, The one-sided self-power spectral density of the basic acceleration excitation, The frequency response function of the system is:

[0080] (7),

[0081] Combining equations (4)-(7), the mean square value of the absolute acceleration of the inertial navigation vibration isolation system under random acceleration excitation is:

[0082] (8),

[0083] In the formula, T is the absolute acceleration transmissibility of the system, which is a function of β, expressed as:

[0084] (9),

[0085] for Figure 1 The broadband random vibration shown for:

[0086] (10)

[0087] In the formula, and These represent the acceleration power spectral density values ​​corresponding to the starting and ending frequencies of the broadband random vibration segment, respectively. For sinusoidal excitation, for:

[0088] (11),

[0089] In the formula, f i The acceleration amplitude corresponding to the i-th order sinusoidal vibration (i = 1, 2, 3, 4). Represents the Dirac function;

[0090] According to equation (8), the mean square value of the absolute acceleration generated by the sinusoidal excitation is obtained as follows:

[0091] (12)

[0092] In the formula, , Let represent the i-th order sinusoidal vibration frequency. Therefore, the root mean square value of the absolute acceleration of the inertial navigation vibration isolation system under helicopter vibration conditions is expressed as:

[0093] (13)

[0094] The integral terms in the formula are calculated using numerical integration;

[0095] Step 2: Based on the model, analyze the variation of the root mean square acceleration and response power of the system with the natural frequency of the vibration isolation system under sinusoidal vibration, broadband random vibration and the superposition of the two excitation conditions, and determine the optimal natural frequency of the vibration isolation system according to the principle of minimizing response.

[0096] The specific implementation method in step 2 above is as follows: within the set range of 30-70 Hz for the natural frequency of the inertial navigation vibration isolation system, calculate the relationship curves of the root mean square acceleration of the system with the natural frequency of the vibration isolation system under sinusoidal vibration excitation, broadband random vibration excitation, and the superposition of the two excitations respectively.

[0097] Based on equations (8) and (12), the relationship curves of system power with natural frequency of inertial navigation vibration isolation system under sinusoidal excitation frequencies f1, f2, f3, f4 and broadband random vibration excitation were calculated respectively. Under random excitation of foundation acceleration, the response of inertial navigation vibration isolation system is usually evaluated by the root mean square value of acceleration response. Based on equation (13), the relationship curve of root mean square acceleration with natural frequency of system was calculated, and the natural frequency corresponding to the minimum value of root mean square response was selected as the optimal natural frequency.

[0098] Performance analysis and design of inertial navigation vibration isolation system: The structural model of the inertial navigation system used in this application is as follows: Figure 4 As shown. The system mainly consists of an IMU, rubber vibration dampers, a chassis (support structure), a circuit board, and a receiver. The IMU is composed of a fiber optic gyroscope, a bracket, and a quartz accelerometer.

[0099] To verify the effectiveness of the analytical model constructed in step 1 above, the root mean square acceleration response of the inertial navigation vibration isolation system under SOR excitation conditions was calculated using the finite element method. The model was established as follows: Figure 5 In the finite element model of the inertial navigation system shown, necessary simplifications were made to the structural geometry. The chassis and support structure were discretized using solid elements (tetrahedral, hexahedral, and wedge-shaped elements), and bolted connections were simulated using beam elements. During the analysis, components such as the circuit boards and receivers inside the chassis were treated as non-structural masses; the fiber optic gyroscope and quartz accelerometer were simplified as lumped mass elements and coupled to the support through rigid constraints. The rubber vibration damper between the chassis and the IMU was modeled using spring-damped elements, while neglecting the influence of its own mass on the system's dynamic characteristics. The final finite element model contains a total of 4,449,663 elements.

[0100] The vibration environment parameters of the helicopter inertial navigation system used in this application are shown in Table 1. The root mean square acceleration of the mixed spectrum is 4.3 g, of which the root mean square acceleration of the broadband random vibration is 2.5 g.

[0101] Table 1. Main parameters of vibration environment for helicopter inertial navigation system

[0102]

[0103] Because the random vibration response of a structure has statistical characteristics, unlike the deterministic sinusoidal vibration response analysis, it usually requires probabilistic and statistical methods for characterization. Therefore, for the mixed-spectrum excitation of a helicopter SOR vibration environment, the finite element method is difficult to directly calculate the response. It is typically necessary to convert the sinusoidal acceleration excitation into an equivalent narrowband acceleration power spectral density. Based on the vibration environment parameters given in Table 1, the equivalent acceleration power spectral density curve obtained after the conversion is shown below. Figure 6 As shown.

[0104] In the response analysis, only the damping effect of the vibration damper is considered, and the structural damping coefficient is taken as 0.2. The natural frequency of the inertial navigation vibration isolation system is generally selected at around 50 Hz. In order to find the optimal solution, the natural frequency setting range is expanded to ±40%, that is, the range of 30Hz-70Hz.

[0105] Since the basic excitation is the acceleration power spectral density, the calculation method of equation (8) needs to be used during the comparative verification. The root mean square acceleration response of the inertial navigation isolation system along the X, Y, and Z axes is calculated as a function of the system's natural frequency using both the finite element method and the method of this application, as shown below. Figure 7 As shown in the figure, since the vibration damper adopts a three-dimensional equal stiffness design, the dynamic characteristics of the method in this application are completely consistent in the three axes. Therefore, the root mean square acceleration response results in the three directions are the same. Only the calculation results for one direction are shown in the figure.

[0106] from Figure 7 As can be seen, after decoupling design, the calculation results of the finite element method in the three directions are basically consistent, indicating that the system is highly decoupled with only weak coupling effects. Meanwhile, the curves of the root mean square acceleration response in the three directions obtained by the finite element method as a function of the natural frequency are in good agreement with the calculation results of the analytical model in this application, and the trends are consistent. This result verifies the correctness and effectiveness of the analytical model in this application. Compared with the finite element method, the method in this application significantly improves computational efficiency while ensuring computational accuracy, and is therefore more suitable for parameter analysis and optimization design of inertial navigation vibration isolation systems.

[0107] According to equation (13), within the set range of 30-70 Hz for the natural frequency of the inertial navigation vibration isolation system, the relationship curves of the root mean square acceleration of the system with the natural frequency of the vibration isolation system under sinusoidal vibration excitation, broadband random vibration excitation, and superposition of the two excitations are calculated respectively. The calculation results are as follows: Figure 8 As shown.

[0108] Depend on Figure 8 It can be seen that under helicopter vibration conditions, the root mean square acceleration (RMS) of the system exhibits a "decreasing-increasing-decreasing" pattern with increasing natural frequency of the inertial navigation isolation system. Under sinusoidal vibration excitation only, the RMS acceleration shows a similar trend, with a smaller difference in numerical level. This indicates that under SOR excitation, the system response is mainly controlled by the sinusoidal excitation component. Although the RMS acceleration caused by broadband random vibration increases with increasing natural frequency, its contribution to the overall system response is relatively limited, especially in the low-frequency region.

[0109] To further reveal the formation mechanism of the above response law, calculations were performed according to equations (8) and (12). For the calculation process corresponding to equation (8), since its expression is an integral form with respect to frequency and it is difficult to obtain an analytical solution, a numerical integration method was used to solve it. Specifically, within the given frequency parameter range, the integration interval was discretized, a sufficiently small frequency step size was selected, and the integrand was accumulated point by point using the trapezoidal integration method to obtain the system power response value. For the calculation process corresponding to equation (12), since it is an explicit analytical expression, numerical substitution calculations can be performed directly. That is, after determining the values ​​of each parameter (including the excitation amplitude, the ratio of the excitation frequency to the system natural frequency, etc.), the sinusoidal excitation frequency was substituted into equation (12) in turn, and the corresponding system power value was calculated point by point. Based on this, the relationship curves of the sinusoidal excitation frequencies f1, f2, f3, f4 and the system power with the natural frequency of the inertial navigation isolation system under broadband random vibration excitation conditions were obtained, as shown in the figure. Figure 9 As shown in the figure, the variation law and formation mechanism of system power under different excitation conditions are significantly different: Under sinusoidal excitation, when the excitation frequency is f1, the system power remains basically unchanged because it is much lower than the system's natural frequency; when the excitation frequency is f2, as the system's natural frequency increases, the excitation frequency gradually moves away from the system's natural frequency, and the system power shows a gradual decreasing trend; when the excitation frequency is f3, the system power shows a trend of first increasing and then decreasing with the change of the natural frequency, which is due to the excitation frequency gradually approaching and crossing the system's natural frequency; while when the excitation frequency is f4, because it is always close to the system's natural frequency, the system power continues to increase with the increase of the natural frequency. In contrast, under broadband random vibration excitation, the system power generally shows a trend of gradually increasing with the increase of the natural frequency.

[0110] In summary, the above analysis shows that under SOR excitation, the variation of the system's root mean square acceleration is mainly dominated by the power variation caused by sinusoidal excitation, while the random vibration component has a relatively small impact on the overall response. This result reasonably explains the power response from the perspective of power response. Figure 8 The formation mechanism of the root mean square acceleration variation law was studied, and a basis was provided for the rational selection of the natural frequency of the inertial navigation vibration isolation system.

[0111] Traditionally, helicopter inertial navigation vibration isolation system design employs the frequency avoidance method, which requires the natural frequency of the isolation system to maintain a frequency interval of at least 10% from the main sinusoidal fixed-frequency excitation f1-f4. Based on the vibration environment parameters given in Table 1, the natural frequency of the isolation system determined using the frequency avoidance method is 60 Hz. Figure 8It can be seen that when the system's natural frequency is 60 Hz, the corresponding root-mean-square acceleration is 7.7 g, which does not reach the minimum value of the system response. Based on the principle of response minimization, the natural frequency of the vibration isolation system is determined to be 43 Hz using the method proposed in this study. At this point, the system's root-mean-square acceleration is minimized to 5.4 g. Compared with the frequency avoidance method, the root-mean-square acceleration of the vibration isolation system is reduced by 29.9%, indicating that the proposed method can effectively improve the vibration reduction performance of the vibration isolation system.

[0112] Considering the impact of vibration damper manufacturing errors on system parameter matching, the theoretical design results were appropriately modified in the engineering implementation. The vibration damper stiffness matched using the method proposed in this application is 13.3 N / mm, corresponding to a natural frequency of 45 Hz for the vibration isolation system; while the vibration damper stiffness matched using the frequency avoidance method is 23.5 N / mm, corresponding to a natural frequency of 60 Hz for the vibration isolation system. Vibration isolation systems will be constructed using vibration dampers with the above two stiffness parameters respectively. For ease of description, the vibration isolation system with parameters determined based on the frequency avoidance method is designated as Scheme 1, and the vibration isolation system with parameters determined using the method proposed in this paper is designated as Scheme 2. The vibration isolation performance of the two schemes will be compared and verified through SOR vibration tests.

[0113] In summary, this application proposes a design method for an inertial navigation system (INS) vibration isolation system designed for helicopter vibration environments. First, based on the differential equations of motion of a single-degree-of-freedom isolation system under foundation acceleration excitation, an analytical model of the root-mean-square (RMS) acceleration of the INS vibration isolation system under SOR excitation is derived. This analytical model is then verified using the finite element method. Based on this model, the variation of the system's RMS acceleration and response power with the natural frequency of the isolation system under sinusoidal vibration, broadband random vibration, and both superimposed excitation conditions is analyzed. The optimal natural frequency of the isolation system is determined based on the principle of minimizing the response. Finally, SOR vibration tests are conducted to compare and verify the performance of the INS vibration isolation system designed using traditional frequency avoidance design methods and the method proposed in this application.

[0114] To demonstrate the effectiveness of the present invention, the following SOR vibration test was conducted:

[0115] 1. Comparison and verification of root mean square acceleration response

[0116] To compare the vibration isolation performance of the two design schemes, SOR vibration tests were conducted on them. To facilitate direct measurement of the acceleration response at the simulated load center, a simulated load was used instead of the actual IMU in the test. This simulated load maintained consistency with the real IMU in key parameters such as mass, damper mounting method, number of dampers, and interface dimensions. An accelerometer was positioned at the geometric center of the simulated load to measure the system response. The schematic diagram of the vibration test setup is shown below. Figure 10As shown, the chassis is located on the upper surface of the vibration table and is fixedly connected to the vibration table by bolts. The IMU is located inside the chassis and is connected to the chassis by rubber vibration dampers. The test parameters are set according to the vibration environment given in Table 1. Excitation is applied along the three axes of X, Y and Z respectively, and the test time in each direction is 900 s.

[0117] The acceleration power spectral density (PSD) curves of the system in Scheme 1 along the X, Y, and Z directions are as follows: Figure 11 As shown, the corresponding results for Scheme 2 are as follows: Figure 12 As shown.

[0118] Depend on Figure 11 and Figure 12 It can be seen that the PSD curves of the systems obtained by the two design methods are basically the same in the X, Y, and Z directions, indicating that after the decoupling design is completed, the dynamic characteristics of the vibration isolation system in each direction are relatively consistent, and it can be analyzed and designed approximately as a single-degree-of-freedom vibration system.

[0119] Furthermore, in the PSD curves of both design schemes, obvious spectral peaks appear near ① 6.77 Hz, ② 27.1 Hz, ③ 54.1 Hz, and ④ 81.2 Hz. These four spectral peaks are mainly caused by the fourth-order sinusoidal fixed-frequency excitation f1-f4 in Table 1, reflecting the SOR spectral characteristics of the helicopter vibration environment.

[0120] contrast Figure 11 and Figure 12 It was also found that the curves of the two schemes showed consistent trends in the low-frequency range, with a very small agreement error; in the mid-to-high frequency range, the spectral peak amplitude of Scheme 1 was significantly higher than that of Scheme 2, indicating that the method proposed in this application has a more significant effect on attenuating the resonance response. Further research... Figure 11 and Figure 12 The root mean square acceleration of the system is obtained by integrating the PSD curve shown, and the comparison results are shown in Table 2.

[0121] Table 2 Comparison of Root Mean Square Acceleration Parameters of Inertial Navigation Vibration Isolation Systems

[0122]

[0123] As shown in Table 2, the root mean square acceleration (RMSE) of both schemes is significantly higher than that of the input spectrum. This is mainly because the inertial isolation system primarily targets the high-frequency components of broadband random vibrations, while it can only achieve a certain degree of vibration reduction for sinusoidal excitation. Compared to Scheme 1, Scheme 2 reduces the RMS acceleration in the X, Y, and Z directions by 26.9%, 24.4%, and 24.7%, respectively, indicating that the design method proposed in this application has a more significant advantage in vibration reduction and isolation performance. Furthermore, the data in the table also shows that, due to the three-dimensional equal stiffness design of the vibration damper, the test results in the X and Z directions are basically consistent, while the RMS acceleration test value in the Y direction is about 15% higher than that in the X and Z directions, showing a relatively significant deviation. This difference may mainly stem from the fact that the Y direction is more sensitive to installation errors (such as the connection state between the specimen and the vibration table and the preload of the vibration damper). Future work will focus on optimizing the installation process and assembly control to further reduce the test deviation in this direction and improve the consistency and reliability of the test results.

[0124] 2. Comparison and verification of attitude and bearing errors

[0125] Attitude standard deviation and maximum error are important indicators for evaluating the performance of inertial navigation vibration isolation systems. Figure 4 The fiber optic strapdown inertial navigation system platform shown was used for attitude calculation, and the two inertial navigation system designs were compared and verified. The experiment was conducted according to the vibration environment parameters given in Table 1, with the vibration direction vertically upward and a duration of 900 s. The attitude output data of the inertial navigation system was monitored in real time during the vibration process. The heading angle error curves, pitch angle error curves, and roll angle error curves of the two designed inertial navigation systems are shown below. Figure 13 , Figure 14 and Figure 15 As shown.

[0126] Depend on Figure 13 — Figure 15 It can be seen that during the SOR vibration test, after 900 s of attitude parameter monitoring, the attitude calculation errors of both schemes gradually increased over time. This is mainly due to the continuous accumulation of inherent errors of the inertial navigation system during the integration calculation process.

[0127] The comparison results of the maximum error are shown in Table 3, and the comparison results of the standard deviation are shown in Table 4. Compared with Scheme 1, Scheme 2 reduced the maximum error in the heading angle, pitch angle, and roll angle directions by 82.6%, 89.9%, and 26.2%, respectively, and the corresponding standard deviations were reduced by 82.7%, 90.5%, and 12.3%, respectively.

[0128] The above results show that Scheme 2 is significantly better than Scheme 1 in terms of attitude error control, indicating that the vibration isolation system parameters determined by the design method proposed in this application can effectively improve the attitude calculation accuracy of the inertial navigation system under SOR vibration environment.

[0129] Table 3 Comparison of Maximum Attitude and Void Error Results of Inertial Navigation System

[0130]

[0131] Table 4 Comparison of Standard Deviation Results of Inertial Navigation System Attitude and Bearing

[0132]

[0133] In summary, considering the characteristics of broadband random vibration and sinusoidal vibration superposition in the vibration environment of helicopter inertial navigation systems, a design method for inertial navigation vibration isolation systems for this type of vibration environment is proposed. This method, based on the differential equations of motion of a single-degree-of-freedom system under foundation acceleration excitation, derives an analytical model of the root-mean-square acceleration (RMS) of the inertial navigation isolation system under superposition excitation of sinusoidal vibration and broadband random vibration. Taking a certain type of helicopter fiber-optic strapdown inertial navigation system as the research object, a finite element model was established to verify the analytical model. The results show that the curves of the RMS acceleration in the X, Y, and Z directions as a function of natural frequency calculated by the finite element method are basically consistent with the analytical results, verifying the correctness of the established model. Based on this, the variation laws of the system's RMS acceleration and power with natural frequency under sinusoidal vibration, broadband random vibration, and their superposition excitation conditions are further analyzed. The results show that the change in the system's RMS acceleration is mainly dominated by the power change caused by sinusoidal excitation, while the random vibration component has a relatively small impact on the overall response. Based on the principle of minimizing the RMS response, the optimal natural frequency of the isolation system is determined. Finally, SOR vibration tests were conducted on the inertial navigation system (INS) vibration isolation systems obtained based on the frequency avoidance method and the analytical design method, respectively. The test results show that the vibration isolation system obtained by the analytical design method has a smaller root mean square acceleration, and its vibration isolation effect is significantly better than that of the frequency avoidance method. Furthermore, this method can effectively reduce the maximum error and standard deviation of the INS' heading angle, pitch angle, and roll angle, verifying the effectiveness of the design method.

[0134] It should be noted that the method of this application does not depend on a specific vibration isolator layout. The established root mean square acceleration analytical model is applicable to the combined vibration environment of helicopter broadband random vibration and sinusoidal vibration superposition. Therefore, it has certain universality and engineering application value, and can provide theoretical basis and technical reference for the vibration isolation design of helicopter inertial navigation system.

Claims

1. A design method for an inertial navigation vibration isolation system for helicopter vibration environments, characterized in that, Includes the following steps: Step 1: Based on the differential equation of motion of a single-degree-of-freedom vibration isolation system under basic acceleration excitation, construct an analytical model of the root mean square acceleration of the inertial navigation vibration isolation system under SOR excitation. Step 2: Based on the model, analyze the variation of the root mean square acceleration and response power of the system with the natural frequency of the vibration isolation system under sinusoidal vibration, broadband random vibration and the superposition of the two excitation conditions, and determine the optimal natural frequency of the vibration isolation system according to the principle of minimizing response.

2. The design method for an inertial navigation vibration isolation system for helicopter vibration environment according to claim 1, characterized in that, The method for constructing the analytical model in step 1 is as follows: After decoupling, the inertial navigation vibration isolation system is approximately equivalent to a single-degree-of-freedom vibration system with six independent motion directions. The foundation of the single-degree-of-freedom vibration isolation system is subjected to acceleration excitation. The differential equation of motion of the single-degree-of-freedom vibration isolation system is expressed as: （1）， In the formula, m, k, and c represent the mass of the IMU, the stiffness of the damper, and the damping coefficient, respectively; x, and These represent the absolute displacement, velocity, and acceleration of the IMU, respectively. , and These are the basic excitation displacement, velocity, and acceleration, respectively; Introducing relative displacement Equation (1) is transformed into: （2）， In the formula, , ; Using equation (2), we get: （3）， Under basic acceleration random excitation, the root mean square (RMS) value of the acceleration response is used as the core evaluation index of the system's response. Based on random vibration theory, the value of the autocorrelation function of a stationary random process at zero time shift is the RMS value of the response. Therefore, the RMS value of the system's absolute acceleration response is expressed as: （4）， In the formula, For x r The autocorrelation function of , using the Wiener-Khinchin theorem, has the following relationship: （5）， In the formula, Indicates the fundamental acceleration excitation frequency. It is the one-sided self-power spectral density of the system's relative displacement, obtained by solving the random vibration response of a single-input, single-output system, and its expression is: （6）， In the formula, The one-sided self-power spectral density of the basic acceleration excitation, The frequency response function of the system is: （7）， Combining equations (4)-(7), the mean square value of the absolute acceleration of the inertial navigation vibration isolation system under random acceleration excitation is: （8）， In the formula, T is the absolute acceleration transmissibility of the system, which is a function of β, expressed as: （9）， For broadband random vibrations for: （10）， In the formula, and These represent the acceleration power spectral density values ​​corresponding to the starting and ending frequencies of the broadband random vibration segment, respectively. For sinusoidal excitation, for: （11）， In the formula, f i The acceleration amplitude of the i-th order sinusoidal vibration (i = 1, 2, 3, 4). Represents the Dirac function; According to equation (8), the mean square value of the absolute acceleration generated by the sinusoidal excitation is obtained as follows: （12）， In the formula, , Let represent the excitation frequency of the i-th order sinusoidal vibration. Therefore, the root mean square value of the absolute acceleration of the inertial navigation isolation system under helicopter vibration conditions is expressed as: （13）， The integral term in the formula is calculated using numerical integration.

3. The design method for an inertial navigation vibration isolation system for helicopter vibration environment according to claim 2, characterized in that, The specific implementation method in step 2 is as follows: within the set range of 30-70 Hz for the natural frequency of the inertial navigation vibration isolation system, calculate the relationship curves of the root mean square acceleration of the system with the natural frequency of the vibration isolation system under sinusoidal vibration excitation, broadband random vibration excitation and the superposition of the two excitations respectively. According to equations (8) and (11), calculate the relationship curves of the system power with the natural frequency of the inertial navigation vibration isolation system under sinusoidal excitation frequencies f1, f2, f3, f4 and broadband random vibration excitation respectively. Under the random excitation of the base acceleration, the response of the inertial navigation vibration isolation system is usually evaluated by the root mean square value of the acceleration response. Based on equation (13), calculate the relationship curve of the root mean square acceleration with the natural frequency of the system, and select the natural frequency corresponding to the minimum value of the root mean square response as the optimal natural frequency.

Images