Design method for reducing IMU angular velocity under rectangular impact load based on dynamics

Abstract

The invention relates to a design method for reducing an IMU angular velocity under a rectangular impact load based on dynamics, and belongs to the field of inertial navigation. In order to solve the problem of reducing the angular velocity of the IMU under the rectangular impact load based on dynamics, a linear motion dynamics differential equation is established according to a kinetic model under the rectangular impact load of the IMU; establishing an angular motion dynamic differential equation according to the dynamic model under the IMU rectangular impact load; establishing an IMU displacement equation; differentiating the IMU displacement equation to obtain an IMU speed equation; establishing an IMU angle equation; differentiating the IMU angular velocity equation to obtain the IMU angular velocity equation; the IMU angular velocity is calculated, and whether the IMU angular velocity meets the design requirement or not is judged; and if the design requirements are not met, adjusting IMU structure parameters and shock absorber parameters until the design requirements are met. According to the invention, support is provided for the structural design of the IMU and the design of a damping system, and the structural design efficiency of the IMU is improved.

Description

Technical Field

[0001] The present invention belongs to the field of inertial navigation, and particularly relates to a design method for reducing the angular velocity of an IMU under a rectangular impact load based on dynamics. Background Art

[0002] As the core component of an inertial navigation system, the accuracy of an inertial measurement unit (IMU) directly affects the navigation performance. The IMU often faces an instantaneous rectangular impact load environment. The rectangular impact load will cause the gyroscope of the IMU to generate additional angular velocity, thereby affecting the accuracy and reliability of the navigation system. Reducing the angular velocity of the IMU under the rectangular impact load is crucial for improving the accuracy of the IMU in a complex dynamic environment.

[0003] If the support center of the damping system does not coincide with the centroid of the IMU, when excited by a rectangular impact load, not only linear motion will be generated, but also angular motion will be generated, introducing a pseudo-angular velocity signal to the IMU. How to accurately solve the angular motion caused by linear motion at the initial stage of design, and then reduce the angular velocity of the IMU under the rectangular impact load through corresponding design has always been the focus and difficulty of IMU design. So far, the design method for reducing the angular velocity of the IMU under the rectangular impact load is still in an empirical state. Summary of the Invention

[0004] (I) Technical Problems to be Solved

[0005] The technical problem to be solved by the present invention is how to provide a design method for reducing the angular velocity of an IMU under a rectangular impact load based on dynamics to solve the problem of reducing the angular velocity of an IMU under a rectangular impact load based on dynamics.

[0006] (II) Technical Solutions

[0007] To solve the above technical problems, the present invention proposes a design method for reducing the angular velocity of an IMU under a rectangular impact load based on dynamics, and the method includes the following steps:

[0008] S1. Establish a linear motion dynamics differential equation according to the dynamics model of the IMU under a rectangular impact load;

[0009] S2. Establish an angular motion dynamics differential equation according to the dynamics model of the IMU under a rectangular impact load;

[0010] S3. Establish an IMU displacement equation based on the Duhamel integral;

[0011] S4. Differentiate the IMU displacement equation to obtain the IMU velocity equation;

[0012] S5. Establish an IMU angle equation based on the Duhamel integral;

[0013] S6. Differentiate the IMU angle equation to obtain the IMU angular velocity equation;

[0014] S7. Calculate the IMU angular velocity based on the IMU structure parameters, shock absorber parameters, and the magnitude of the rectangular impact load;

[0015] S8. Determine whether the IMU angular velocity meets the design requirements;

[0016] S9. If the design requirements are not met, adjust the structure parameters and shock absorber parameters until the design requirements are satisfied.

[0017] (III) Beneficial Effects

[0018] The present invention proposes a design method for reducing the IMU angular velocity under a rectangular impact load based on dynamics. The present invention only needs to adjust the IMU structure parameters and shock absorber parameters on the premise of meeting the IMU technical requirements, without performing finite element simulations multiple times. It can quickly calculate the IMU angular velocity under a rectangular impact load at the initial stage of the IMU scheme design, ensuring that the IMU meets the design requirements. The design process of the present invention is simple, time-consuming, and improves the efficiency of IMU structure design. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] Figure 1 is a flowchart of the design method for reducing the IMU angular velocity under a rectangular impact load based on dynamics in an embodiment of the present invention;

[0020] Figure 2 is a schematic diagram of the rectangular impact load provided in an embodiment of the present invention;

[0021] Figure 3 is a schematic diagram of the IMU model provided in an embodiment of the present invention;

[0022] Figure 4 is a schematic diagram of the IMU dynamics model provided in an embodiment of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0023] To make the objectives, contents, and advantages of the present invention clearer, the following further describes in detail the specific embodiments of the present invention with reference to the drawings and embodiments.

[0024] The objective of the present invention is to provide a design method for reducing the IMU angular velocity under a rectangular impact load based on dynamics, which improves the IMU design efficiency and meets the need for a successful product scheme design at one time.

[0025] To achieve the above objective, the present invention provides a design method for reducing the IMU angular velocity under a rectangular impact load based on dynamics, which specifically includes the following steps:

[0026] S1. Establish a linear motion dynamics differential equation based on the IMU dynamics model under a rectangular impact load;

[0027] S2. Establish the angular motion dynamic differential equation based on the dynamic model of the IMU under rectangular impact load;

[0028] S3. Establish the IMU displacement equation based on the Duhamel integral;

[0029] S4. Differentiate the IMU displacement equation to obtain the IMU velocity equation;

[0030] S5. Establish the IMU angle equation based on the Duhamel integral;

[0031] S6. Differentiate the IMU angle equation to obtain the IMU angular velocity equation;

[0032] S7. Calculate the IMU angular velocity according to the IMU structure parameters, shock absorber parameters, and the magnitude of the rectangular impact load;

[0033] S8. Determine whether the IMU angular velocity meets the design requirements;

[0034] S9. If it does not meet the design requirements, adjust the structure parameters and shock absorber parameters until the design requirements are met.

[0035] Preferably, in step S1, the IMU includes: IMU structure 1 and shock absorber assembly; Four groups of shock absorber assemblies are installed on the IMU structure.

[0036] Preferably, in step S1, the shock absorber assembly includes: shock absorber 2 and shock absorber bushing 3.

[0037] Preferably, step S1 includes: establishing the linear motion dynamic differential equation according to the dynamic model of the IMU under rectangular impact load, as shown in the following formula:

[0038] (1)

[0039] In the formula: m is the mass of the IMU, with the unit of Kg; k is the total stiffness of the shock absorber, with the unit of N / m; c is the total damping of the shock absorber, with the unit of N.s / m; the z direction is the direction of the rectangular impact load; z is the linear displacement between the centroid of the IMU and the shock absorber bushing, with the unit of m; is the linear velocity between the centroid of the IMU and the shock absorber bushing, with the unit of m / s; is the linear acceleration between the centroid of the IMU and the shock absorber bushing, with the unit of m / s 2 ; A is the magnitude of the rectangular impact load, with the unit of m / s 2 . Preferably, step S2 includes: establishing the angular motion dynamic differential equation according to the dynamic model of the IMU under rectangular impact load, as shown in the following formula:

[0040] (2)

[0041] Where: I y is the moment of inertia of the IMU rotating about the y-axis, with the unit of Kg·m 2 ; is the angular acceleration of the IMU rotating about the y-axis, with the unit of rad / s 2 ; is the angular velocity of the IMU rotating about the y-axis, with the unit of rad / s; θ y is the angle of the IMU rotating about the y-axis, with the unit of rad; 2l is the installation distance between the left and right groups of shock absorbers in the x direction, with the unit of m; e is the eccentricity between the support center of the shock absorber and the centroid of the IMU, with the unit of m.

[0042] Preferably, in step S2, the centroid of the IMU is the mass center of the IMU structure.

[0043] Preferably, in step S2, the support center of the shock absorber is the geometric center of the 4 groups of shock absorbers.

[0044] Preferably, step S3 includes:

[0045] Based on the formula (1), an IMU displacement equation is established based on the Duhamel integral, as follows:

[0046] (3)

[0047] Where, ω n is the circular frequency of the linear vibration of the IMU undamped system, with the unit of rad / s; ω d is the circular frequency of the linear vibration of the damped system, with the unit of rad / s; ζ is the total damping ratio of the linear vibration of the shock absorber; t is the impact time of the rectangular impact load, with the unit of s; is the time integration variable. The derivation process is omitted here.

[0048] Preferably, step S4 includes:

[0049] Differentiating the IMU displacement equation (3) gives the IMU velocity equation, as follows:

[0050] (4)

[0051] The derivation process is omitted here.

[0052] Preferably, step S5 includes:

[0053] After substituting equations (3) and (4) into equation (2), an IMU angle equation is established based on the Duhamel integral, and after simplification and calculation, it is as follows:

[0054] (5)

[0055] In the formula,

[0056] is the total damping ratio of the angular vibration of the IMU;

[0057] is the frequency of the angular vibration of the undamped system of the IMU, with the unit of rad / s;

[0058] ;

[0059] f is the linear resonance frequency of the shock absorber, with the unit of Hz.

[0060] The derivation process is omitted here.

[0061] Preferably, step S6 includes:

[0062] Differentiate, simplify and calculate the IMU angle equation (5) to obtain the angular velocity equation as follows:

[0063] (6)

[0064] The derivation process is omitted here.

[0065] Preferably, step S7 includes:

[0066] Calculate the angular velocity according to the IMU structure parameters, shock absorber parameters, and rectangular impact load magnitude through formula (6).

[0067] Preferably, in step S7, the IMU structure parameters include:

[0068] m (IMU mass), I y (the moment of inertia of the IMU rotating about the y-axis), 2l (the installation distance between the left and right groups of shock absorbers in the x direction), e (the eccentricity between the shock absorber support center and the centroid).

[0069] Preferably, in step S7, the shock absorber parameters include:

[0070] f (the linear resonance frequency of the shock absorber), ω n (the circular frequency of the linear vibration of the undamped system), ω θ (the frequency of the angular vibration of the undamped system of the IMU), ζ (the total damping ratio of the linear vibration of the shock absorber), ζ θ (the total damping ratio of the angular vibration of the IMU).

[0071] Preferably, the IMU angular velocity in step S8 meets the design requirement: the IMU angular velocity margin is greater than 20%.

[0072] Preferably, the formula for calculating the IMU angular velocity margin described in step S8 is:

[0073] (7)

[0074] In the formula, α is the IMU angular velocity margin, is the maximum allowable angular velocity of the IMU.

[0075] Preferably, if the design requirements are not met in step S9, the IMU structure parameters and the shock absorber parameters are adjusted until the design requirements are met.

[0076] Preferably, the adjustment of the IMU structure parameters described in step S9 is: increasing the installation distance (2l) between the shock absorbers, reducing the eccentricity (e) between the shock absorber support center and the center of mass, and reducing the moment of inertia of the IMU about the y-axis (I y ).

[0077] Preferably, the adjustment of the shock absorber parameters described in step S9 is: increasing the linear resonance frequency (f) of the shock absorber, increasing the total linear vibration damping ratio (ζ) of the IMU, and increasing the total angular vibration damping ratio (ζ θ ) of the IMU.

[0078] Preferably, the premise for adjusting the IMU structure parameters and the shock absorber parameters described in step S9 is: selecting one or several parameters for adjustment on the premise of meeting all the design requirements of the IMU.

[0079] Embodiment

[0080] The present invention provides a design method for reducing the IMU angular velocity under rectangular impact loads based on dynamics, and its process is as Figure 1 shown, including the following steps:

[0081] S1: Establish a linear motion dynamics differential equation according to the dynamics model of the IMU under rectangular impact, as follows:

[0082] (1)

[0083] In the formula, m is the mass of the IMU structure, with the unit of Kg; k is the total stiffness of the shock absorber, with the unit of N / m; c is the total damping of the shock absorber, with the unit of N.s / m; the z direction is the direction of the rectangular impact load; is the linear acceleration of the IMU center of mass relative to the shock absorber bushing, with the unit of m / s 2 ; is the linear velocity of the IMU center of mass relative to the shock absorber bushing, with the unit of m / s 2 ; z is the linear displacement of the IMU center of mass relative to the shock absorber bushing, with the unit of m; A is the magnitude of the rectangular impact load, with the unit of m / s2 .

[0084] As Figure 4 shown, o e is the IMU installation fixed coordinate system, o1 is the IMU centroid coordinate system, z = z1 - z e ; Figure 4 In, the coordinate system o 1 ( x 1 y 1 z 1 ) is the IMU centroid coordinate system, and the coordinate system o e ( x e y e z e ) is the IMU installation fixed coordinate system (or shock absorber bushing coordinate system), o is the shock absorber support center, 2l is x the installation distance between the left and right groups of shock absorbers, e is the eccentricity between the shock absorber support center and the IMU centroid, m is the IMU mass, k / 2 are the stiffnesses of the left and right groups of shock absorbers, c / 2 are the damping ratios of the left and right groups of shock absorbers, is the magnitude of the rectangular impact load.

[0085] S2: Establish the angular motion dynamic differential equation according to the IMU dynamic model under rectangular impact;

[0086] (2)

[0087] In the formula, I y is the moment of inertia of the IMU about the y-axis, with the unit of Kg.m 2 ; is the angular acceleration of the IMU about the y-axis, with the unit of rad / s 2 ; is the angular velocity of the IMU about the y-axis, with the unit of rad / s; θ y is the angle of the IMU about the y-axis, with the unit of rad; 2l is the installation distance between the left and right groups of shock absorbers in the x direction, with the unit of m; e is the eccentricity between the shock absorber support center and the centroid, with the unit of m.

[0088] S3: Based on Equation (1), solve the displacement equation of the IMU using the Duhamel integral, as shown below:

[0089] (3)

[0090] where ω n is the circular frequency of the linear vibration of the undamped system, with the unit of rad / s; ω d is the circular frequency of the linear vibration of the damped system, with the unit of rad / s; ζ is the total damping ratio of the linear vibration of the shock absorber; t is the time of the rectangular impact load, with the unit of s.

[0091] S4: Differentiate the displacement equation (3) of the IMU to obtain the velocity equation of the IMU, as shown below:

[0092] (4)

[0093] S5: Substitute Equation (3) and Equation (4) into Equation (2), and then establish the angular velocity equation of the IMU based on the Duhamel integral. After simplification and calculation, it is as shown below:

[0094] (5)

[0095] where

[0096] is the total damping ratio of the angular vibration of the IMU;

[0097] is the angular vibration frequency of the undamped system of the IMU, with the unit of rad / s;

[0098] ;

[0099] f is the linear resonance frequency of the shock absorber, with the unit of Hz.

[0100] S6: Differentiate, simplify and calculate the IMU angle equation (5) to obtain the angular velocity equation of the IMU, as shown below:

[0101] (6)

[0102] S7: Calculate the angular velocity of the IMU according to the IMU structure parameters, damping parameters, and rectangular impact load magnitude through Equation (6).

[0103] S8: Determine whether the calculated angular velocity margin of the IMU meets the design requirements;

[0104] Specifically, the calculation formula for the angular velocity margin of the IMU is:

[0105] (7)

[0106] where α is the IMU angular velocity margin, and is the maximum allowable angular velocity of the IMU.

[0107] S9: If the design requirements are not met, adjust the IMU structure parameters and the shock absorber parameters until the design requirements are satisfied.

[0108] Specifically, the adjustment of the IMU structure parameters includes increasing the installation distance (2l) between the shock absorbers, reducing the eccentricity (e) between the shock absorber support center and the centroid, and reducing the moment of inertia of the IMU about the y-axis (I y ) in one or more combinations.

[0109] Specifically, the adjustment of the shock absorber parameters is: increasing the linear resonance frequency (f) of the shock absorber, increasing the total linear vibration damping ratio (ζ) of the IMU, and increasing the total angular vibration damping ratio (ζ θ ) in one or more combinations.

[0110] Specifically, the premise for adjusting the IMU structure parameters and the shock absorber parameters in S9 is: select one or several parameter combinations for adjustment on the premise of meeting all the design requirements of the IMU.

[0111] Beneficial effects

[0112] The present invention provides a design method for reducing the IMU angular velocity under rectangular impact loads based on dynamics. Only by adjusting the IMU structure parameters and the shock absorber parameters on the premise of meeting the IMU technical requirements, there is no need to perform finite element simulations multiple times. The IMU angular velocity under rectangular impact loads can be quickly calculated at the initial stage of the IMU scheme design to ensure that the IMU meets the design requirements. The design process of the present invention is simple and time-consuming, and improves the efficiency of the IMU structure design.

[0113] The above are only the preferred embodiments of the present invention. It should be noted that for those of ordinary skill in the art, without departing from the technical principle of the present invention, several improvements and deformations can be made, and these improvements and deformations should also be regarded as the protection scope of the present invention.

Claims

1. A design method for reducing the angular velocity of an IMU under a rectangular impact load based on dynamics, characterized in that: The method comprises the following steps: S1. Establish the linear motion dynamics differential equation according to the dynamic model under the IMU rectangular impact load; S2, establish the angular motion dynamics differential equation according to the dynamic model under the IMU rectangular impact load; S3, establish IMU displacement equation based on Duhamel integral; S4, differentiating the IMU displacement equation to obtain the IMU velocity equation; S5. Establish the IMU angle equation based on Duhamel integral; S6. Differentiate the IMU angle equation to obtain the IMU angular velocity equation; S7, calculating the IMU angular velocity according to the IMU structural parameters, the shock absorber parameters, and the magnitude of the rectangular impact load; S8, judging whether the IMU angular velocity meets the design requirements; S9. If the design requirements are not met, adjust the structural parameters and shock absorber parameters until the design requirements are met.

2. The design method for reducing the angular velocity of an IMU under a rectangular impact load based on dynamics as claimed in claim 1, characterized in that: In S1, the IMU comprises: an IMU structure (1) and a shock absorber assembly; four groups of shock absorber assemblies are installed on the IMU structure; and the shock absorber assembly comprises: a shock absorber (2) and a shock absorber bushing (3).

3. The design method for reducing the angular velocity of an IMU under a rectangular impact load based on dynamics as claimed in claim 1, characterized in that: In S1, a linear motion dynamics differential equation is established according to the dynamics model under the IMU rectangular impact load, as shown in the following formula: （1） Where: m is the IMU mass, in units of Kg ; k is the total stiffness of the shock absorber, in units of N / m; c is the total damping of the shock absorber, in N. s / m ; z Direction is the direction of the rectangular impact load; z is the linear displacement between the center of mass of the IMU and the shock absorber sleeve, in m; is the linear velocity between the IMU mass center and the shock absorber sleeve, in m / s; is the linear acceleration between the IMU center of mass and the shock absorber sleeve, in units of m / s 2 ; A is the magnitude of the rectangular impact load, in units of m / s 2 .

4. The design method for reducing the angular velocity of an IMU under a rectangular impact load based on dynamics as claimed in claim 3, characterized in that: In S2, the angular motion dynamics differential equation is established according to the dynamics model under the IMU rectangular impact load, as shown in the following formula: （2） Where: I y For IMU y Shaft moment of inertia, in Kg.m 2 ; For IMU y The angular acceleration of the axis in rad / s 2 ; For IMU y The angular velocity of the axis in rad / s ; θ y For IMU y The angle of the axis in rad ; 2l for x The installation distance between the left and right shock absorbers, in m ; e is the eccentricity between the shock absorber support center and the IMU mass center, in units of m .

5. The design method for reducing the angular velocity of an IMU under a rectangular impact load based on dynamics as claimed in claim 4, characterized in that: In S2, the IMU centroid is the mass center of the IMU structure, and the shock absorber support center is the geometric center of the four groups of shock absorbers.

6. The design method for reducing the angular velocity of an IMU under a rectangular impact load based on dynamics as claimed in claim 4, characterized in that: The S3 includes: on the basis of formula (1), establishing the IMU displacement equation based on Duhamel integral, as follows: （3） In the formula, ω n is the circular frequency of the undamped system linear vibration, in units of rad / s ; ω d is the circular frequency of the linear vibration of the damped system, in units of rad / s ; ζ is the total damping ratio of the shock absorber’s linear vibration; t is the impact time of the rectangular impact load, in units of s ; is the time-integrated variable.

7. The design method for reducing the angular velocity of an IMU under a rectangular impact load based on dynamics as claimed in claim 6, characterized in that: The S4 includes: Differentiating the IMU displacement equation (3) yields the IMU velocity equation, as follows: （4）。 8. The design method for reducing the angular velocity of an IMU under a rectangular impact load based on dynamics as claimed in claim 7, characterized in that: The S5 includes: After substituting equation (3) and equation (4) into equation (2), the IMU angle equation is established based on Duhamel integral. After simplification and calculation, it is shown as follows: （5） In the formula, is the total damping ratio of the IMU angular vibration; is the frequency of the angular vibration of the IMU undamped system, in units of rad / s ; ； f is the vibration absorber line resonant frequency, in Hz .

9. The design method for reducing the angular velocity of an IMU under a rectangular impact load based on dynamics as claimed in claim 8, characterized in that: The S6 includes: The angular velocity equation is obtained by differentiating, simplifying and calculating the IMU angle equation (5), as follows: （6）。 10. The design method for reducing the angular velocity of an IMU under a rectangular impact load based on dynamics as claimed in claim 9, characterized in that: In the S7, IMU structural parameters include: IMU quality m ,IMU winding y Shaft moment of inertia I y , x Installation distance between the left and right shock absorbers 2l , the eccentricity between the shock absorber support center and the center of mass e ; The shock absorber parameters include: shock absorber line resonance frequency f , the circular frequency of the linear vibration of the undamped system ω n , the frequency of angular vibration of the IMU undamped system ω θ , total damping ratio of linear vibration of shock absorber ζ , IMU angular vibration total damping ratio ζ θ ; In S8, the IMU angular velocity meets the design requirement that: the IMU angular velocity margin is greater than 20%; The IMU angular velocity margin calculation formula is: （7） In the formula, α is the IMU angular velocity margin, The maximum angular velocity allowed for the IMU.

11. The design method for reducing the angular velocity of an IMU under a rectangular impact load based on dynamics as claimed in claim 10, characterized in that: In S9, if the design requirements are not met, the IMU structural parameters and the shock absorber parameters are adjusted until the design requirements are met; The IMU structural parameters are adjusted as follows: increasing the installation distance between the shock absorbers 2l , reduce the eccentricity between the shock absorber support center and the center of mass e , reduce IMU y Shaft moment of inertia I y ; The adjustment of the shock absorber parameters is: increasing the shock absorber line resonance frequency f , Improve the total vibration damping ratio of IMU line ζ , improve the total damping ratio of IMU angular vibration ζ θ .

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