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

Abstract

The present invention relates to a design method for reducing the angular velocity of an IMU 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 an IMU under a rectangular impact load based on dynamics, the present invention establishes a linear motion dynamics differential equation based on the dynamics model of the IMU under a rectangular impact load; establishes an angular motion dynamics differential equation based on the dynamics model of the IMU under a rectangular impact load; establishes an IMU displacement equation; differentiates the IMU displacement equation to obtain an IMU velocity equation; establishes an IMU angle equation; differentiates the IMU angular velocity equation to obtain an IMU angular velocity equation; calculates the IMU angular velocity, and determines whether the IMU angular velocity meets the design requirements; if it does not meet the design requirements, adjusts the IMU structural parameters and shock absorber parameters until the design requirements are met. The present invention provides support for the structural design of the IMU and the design of the vibration reduction system, thereby improving the efficiency of the IMU structural design.

Description

Technical Field

[0001] The present invention belongs to the field of inertial navigation, and in particular 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 a core component of an inertial navigation system, the accuracy of the inertial measurement unit (IMU) directly impacts navigation performance. IMUs are often exposed to transient rectangular shock loads. These loads can cause the IMU's gyroscope to generate excessive angular velocity, which in turn affects the accuracy and reliability of the navigation system. Reducing the IMU's angular velocity under these loads is crucial for improving IMU accuracy in complex dynamic environments.

[0003] If the vibration reduction system's support center doesn't coincide with the IMU's center of mass, the rectangular impact load will produce not only linear motion but also angular motion, introducing a false angular velocity signal into the IMU. Accurately determining the angular motion caused by this linear motion during the initial design phase and then mitigating the IMU's angular velocity under rectangular impact loads through appropriate design has always been a key and challenging aspect of IMU design. To date, design methods for minimizing IMU angular velocity under rectangular impact loads have been empirical. Summary of the Invention

[0004] (1) Technical issues to be resolved

[0005] The technical problem to be solved by the present invention is how to provide a design method for dynamically reducing the angular velocity of the IMU under a rectangular impact load, so as to solve the problem of dynamically reducing the angular velocity of the IMU under a rectangular impact load.

[0006] (2) Technical solution

[0007] In order 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. The method comprises the following steps:

[0008] S1. Establish the linear motion dynamics differential equation based on the dynamic model under the IMU rectangular impact load;

[0009] S2. Establish the angular motion dynamics differential equation based on the IMU's dynamic model under rectangular impact load;

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

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

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

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

[0014] S7, calculating the IMU angular velocity based on the IMU structural parameters, the 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 structural parameters and shock absorber parameters until the design requirements are met.

[0017] (3) Beneficial effects

[0018] This paper proposes a design method for reducing the angular velocity of an IMU under rectangular impact loads based on dynamics. This method only requires adjusting the IMU structural parameters and shock absorber parameters to meet the IMU's technical requirements, eliminating the need for multiple finite element simulations. This method allows for rapid calculation of the IMU's angular velocity under rectangular impact loads during the initial design phase of the IMU design, ensuring that the IMU meets design requirements. This method simplifies the design process, shortens the design time, and improves the efficiency of IMU structural design. BRIEF DESCRIPTION OF THE DRAWINGS

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

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

[0021] Figure 3 Schematic diagram of the IMU model provided by an embodiment of the present invention;

[0022] Figure 4 Schematic diagram of the IMU dynamic model provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0023] In order to make the purpose, content and advantages of the present invention more clear, the specific implementation methods of the present invention are further described in detail below with reference to the accompanying drawings and examples.

[0024] The purpose of the present invention is to provide a design method for reducing the angular velocity of an IMU under a rectangular impact load based on dynamics, thereby improving the efficiency of IMU design and meeting the need for a successful product solution design in one go.

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

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

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

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

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

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

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

[0032] S7, calculating the IMU angular velocity based on the IMU structural parameters, the 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 the design requirements are not met, adjust the structural parameters and shock absorber parameters until the design requirements are met.

[0035] Preferably, in step S1, the IMU includes: an IMU structure 1 and a shock absorber assembly; 4 groups of shock absorber assemblies are installed on the IMU structure.

[0036] Preferably, in step S1 , the shock absorber assembly includes: a shock absorber 2 and a shock-absorbing sleeve 3 .

[0037] Preferably, step S1 includes: establishing a linear motion dynamics differential equation according to the IMU rectangular impact load dynamics model, as shown below:

[0038] (1)

[0039] Where: m is the mass of the IMU, in kg; k is the total stiffness of the shock absorber, in N / m; c is the total damping of the shock absorber, in Ns / m; z 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 center of mass and the shock absorber sleeve, in m / s; is the linear acceleration between the IMU center of mass and the shock absorber sleeve, in m / s 2 ; A is the magnitude of the rectangular impact load, in m / s 2 Preferably, step S2 includes: establishing an angular motion dynamics differential equation according to the IMU rectangular impact load dynamics model, as follows:

[0040] (2)

[0041] Where: I y The moment of inertia of the IMU around the y-axis, in kg.m 2 ; is the angular acceleration of the IMU around the y-axis, in rad / s 2 ; is the angular velocity of the IMU around the y-axis, in rad / s; θ y is the angle of the IMU around the y-axis, in rad; 2l is the installation distance between the two groups of shock absorbers in the x-direction, in m; e is the eccentricity between the shock absorber support center and the center of mass of the IMU, in m.

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

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

[0044] Preferably, step S3 includes:

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

[0046] (3)

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

[0048] Preferably, step S4 includes:

[0049] Differentiating the IMU displacement equation (3) yields 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), the IMU angle equation is established based on Duhamel integral. After simplification and calculation, it is as follows:

[0054] (5)

[0055] Where,

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

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

[0058] ;

[0059] f is the linear resonant frequency of the shock absorber, in Hz.

[0060] The derivation process is omitted here.

[0061] Preferably, step S6 includes:

[0062] The angular velocity equation is obtained by differentiating, simplifying and calculating the IMU angle equation (5), as follows:

[0063] (6)

[0064] The derivation process is omitted here.

[0065] Preferably, step S7 includes:

[0066] The angular velocity is calculated using formula (6) based on the IMU structural parameters, shock absorber parameters, and the magnitude of the rectangular impact load.

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

[0068] m (IMU mass), I y (IMU moment of inertia around the y-axis), 2l (the installation distance between the two sets of shock absorbers in the x-direction), and e (the eccentricity between the shock absorber support center and the center of mass).

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

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

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

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

[0073] (7)

[0074] Where α is the IMU angular velocity margin, The maximum angular velocity allowed for the IMU.

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

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

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

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

[0079] Example

[0080] The present invention provides a design method based on dynamics to reduce the angular velocity of IMU under rectangular impact load, the process is as follows: Figure 1 As shown, the following steps are included:

[0081] S1: According to the IMU rectangular impact dynamics model, the linear motion dynamics differential equation is established as follows:

[0082] (1)

[0083] Where m is the mass of the IMU structure, in kg; k is the total stiffness of the shock absorber, in N / m; c is the total damping of the shock absorber, in Ns / m; the z direction is the direction of the rectangular impact load; is the linear acceleration between the IMU center of mass and the shock absorber sleeve, in m / s 2 ; is the linear velocity between the IMU center of mass and the shock absorber sleeve, in units of m / s 2 ; z is the linear displacement between the IMU center of mass and the shock absorber sleeve, in m; A is the magnitude of the rectangular impact load, in m / s2 .

[0084] like Figure 4 As shown, e is the IMU installation fixed coordinate system, o1 is the IMU center of mass coordinate system, z=z1-z e ;

[0085] Figure 4 In the coordinate system o 1 ( x 1 y 1 z 1 ) is the IMU center of mass coordinate system, coordinate system o e ( x e y e z e ) is the IMU installation fixed coordinate system (or shock absorber sleeve coordinate system), o is the support center of the shock absorber. 2l for x The installation distance between the left and right shock absorbers, e is the eccentricity between the shock absorber support center and the IMU center of mass, m is the IMU mass, k / 2 is the stiffness of the left and right shock absorber groups, c / 2 is the damping ratio of the left and right shock absorbers, is the magnitude of the rectangular impact load.

[0086] S2: Establish the angular motion dynamics differential equation based on the IMU rectangular impact dynamics model;

[0087] (2)

[0088] Where, I y The moment of inertia of the IMU around the y-axis, in kg.m 2 ; is the angular acceleration of the IMU around the y-axis, in rad / s 2 ; is the angular velocity of the IMU around the y-axis, in rad / s; θ y is the angle of the IMU around the y-axis, in rad; 2l is the installation distance between the left and right shock absorbers in the x-direction, in m; e is the eccentricity between the shock absorber support center and the center of mass, in m.

[0089] S3: Based on formula (1), the displacement equation of the IMU is solved based on the Duhamel integral, as follows:

[0090] (3)

[0091] Where, ω n is the circular frequency of the linear vibration of the undamped system, in rad / s; ω d is the circular frequency of the linear vibration of the damped system, in rad / s; ζ is the total damping ratio of the linear vibration of the shock absorber; t is the rectangular impact load time, in s.

[0092] S4: Differentiate the IMU displacement equation (3) to obtain the IMU velocity equation, as follows:

[0093] (4)

[0094] S5: After substituting equations (3) and (4) into equation (2), the IMU angular velocity equation is established based on Duhamel integral. After simplification and calculation, it is as follows:

[0095] (5)

[0096] Where,

[0097] is the total damping ratio of IMU angular vibration;

[0098] is the angular vibration frequency of the IMU undamped system, in rad / s;

[0099] ;

[0100] f is the linear resonant frequency of the shock absorber, in Hz.

[0101] S6: Differentiate, simplify and calculate the IMU angle equation (5) to obtain the IMU angular velocity equation as follows:

[0102] (6)

[0103] S7: Calculate the IMU angular velocity using formula (6) based on the IMU structural parameters, vibration reduction parameters, and rectangular impact load magnitude.

[0104] S8: Determine whether the calculated IMU angular velocity margin meets the design requirements;

[0105] Specifically, the IMU angular velocity margin calculation formula is:

[0106] (7)

[0107] Where α is the IMU angular velocity margin, The maximum angular velocity allowed for the IMU.

[0108] 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.

[0109] Specifically, the IMU structural parameters are adjusted to increase the installation distance between the shock absorbers (2l), reduce the eccentricity between the shock absorber support center and the center of mass (e), and reduce the IMU moment of inertia around the y-axis (I y ) or a combination of one or more ).

[0110] Specifically, the adjustment of the shock absorber parameters is: increasing the shock absorber line resonant frequency (f), increasing the IMU line vibration total damping ratio (ζ), increasing the IMU angular vibration total damping ratio (ζ θ ) or a combination of one or more ).

[0111] Specifically, the premise of adjusting the IMU structural parameters and adjusting the shock absorber parameters in S9 is: selecting one or several parameter combinations for adjustment while meeting all the design requirements of the IMU.

[0112] Beneficial effects

[0113] The present invention provides a design method for reducing the angular velocity of an IMU under rectangular impact loads based on dynamics. This method only requires adjusting the IMU structural parameters and shock absorber parameters to meet the IMU's technical requirements, eliminating the need for multiple finite element simulations. This method allows for rapid calculation of the IMU's angular velocity under rectangular impact loads during the initial design phase of the IMU design, ensuring that the IMU meets design requirements. The present invention simplifies the design process, shortens the design time, and improves the efficiency of IMU structural design.

[0114] The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the technical principles of the present invention. These improvements and modifications should also be regarded as the scope of protection 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 based on the dynamic model under the IMU rectangular impact load; S2. Establish the angular motion dynamics differential equation based on the IMU's dynamic model under rectangular impact load; S3. Based on the online motion dynamics differential equation, the IMU displacement equation is established based on Duhamel integral; S4. Differentiate the IMU displacement equation to obtain the IMU velocity equation; S5. Substituting the IMU displacement equation and the IMU velocity equation into the angular motion dynamics differential equation, the IMU angle equation is established based on the Duhamel integral; S6. Differentiate the IMU angle equation to obtain the IMU angular velocity equation; S7, calculating the IMU angular velocity using the IMU angular velocity equation according to the IMU structural parameters, the shock absorber parameters, and the magnitude of the rectangular impact load; S8. Determine 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; in, In S1, the linear motion dynamics differential equation is established according to the dynamic 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 The direction is the rectangular impact load direction; z is the linear displacement between the IMU center of mass and the shock absorber sleeve, in meters; is the linear velocity between the IMU center of mass 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 ; In S2, the angular motion dynamics differential equation is established according to the dynamic model of the IMU under rectangular impact load, as shown in the following formula: （2） Where: I y For IMU orbit y Shaft moment of inertia, in Kg.m 2 ; For IMU orbit y The angular acceleration of the axis in units of rad / s 2 ; For IMU orbit y The angular velocity of the axis in rad / s ; θ y For IMU orbit y The angle of the axis in rad ; 2l for x The installation distance between the left and right shock absorbers, in units of m ; e is the eccentricity between the shock absorber support center and the IMU mass center, in units of m .

2. The design method for reducing the angular velocity of an IMU under a rectangular impact load based on dynamics according to 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-absorbing 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 S2, the IMU center of mass 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.

4. 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: The S3 includes: on the basis of formula (1), establishing the IMU displacement equation based on Duhamel integral, as follows: （3） Where, 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 damped system linear vibration, 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 ; τ is the time-integrated variable.

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: The S4 includes: Differentiating the IMU displacement equation (3) yields the IMU velocity equation, as follows: （4）。 6. The design method for reducing the angular velocity of an IMU under a rectangular impact load based on dynamics as claimed in claim 5, characterized in that: The S5 includes: After substituting equations (3) and (4) into equation (2), the IMU angle equation is established based on Duhamel integral. After simplification and calculation, it is shown as follows: （5） Where, 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 line resonant frequency of the shock absorber, in units of Hz .

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 S6 includes: The angular velocity equation is obtained by differentiating, simplifying and calculating the IMU angle equation (5), as follows: （6）。 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: In said S7, IMU structural parameters include: IMU mass 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 , circular frequency of linear vibration of undamped system ω n , the frequency of angular vibration of the IMU undamped system ω θ , total linear vibration damping ratio of shock absorber ζ , IMU angular vibration total damping ratio ζ θ ; In S8, the IMU angular velocity meets the design requirements: the IMU angular velocity margin is greater than 20%; The IMU angular velocity margin calculation formula is: （7） Where, α is the IMU angular velocity margin, The maximum angular velocity allowed for the IMU.

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: 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 adjustment of IMU structural parameters is 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 rotation y Shaft moment of inertia I y ; The adjustment of the shock absorber parameters is to increase 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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