A method for estimating the acceleration of the center of mass of a rigid body

Abstract

The invention discloses a method for estimating the acceleration of the center of mass of a rigid body, and belongs to the technical field of automobile dynamics analysis. The estimation method comprises the steps of: S1: selecting N first marking points on the rigid body to obtain the corresponding coordinates and accelerations; S2: substituting the coordinates and accelerations of the N first marking points into the acceleration equation to estimate the acceleration of the center of mass of the rigid body; S3: selecting M second marking points on the rigid body to obtain the corresponding coordinates and actual accelerations; according to the estimated center of mass acceleration in step S2, substituting the coordinates of the M second marking points into the acceleration equation to obtain the estimated acceleration; S4: comparing the estimated acceleration of each second marking point with the actual acceleration to determine whether the errors of the two are within the allowable range; S5: if the errors of the M second marking points are all within the allowable range, the method for estimating the acceleration of the center of mass is reliable. The estimation method of the invention can obtain the acceleration of the center of mass of a rigid body simply and quickly, and has important engineering value.

Description

Technical Field

[0001] The invention relates to the technical field of automobile dynamics analysis, and in particular to a method for estimating the acceleration of the center of mass of a rigid body. Background Art

[0002] As competition in the automotive industry becomes increasingly fierce, users have higher and higher requirements for vehicle dynamics. Since the center of mass position and center of mass acceleration of a vehicle are crucial to the vehicle's handling stability and comfort, it is of great significance to obtain accurate center of mass position and center of mass acceleration, whether in the simulation process related to vehicle dynamics or in the actual testing process.

[0003] However, due to the irregular shape of the rigid body or the uneven performance, the center of mass position of the rigid body is often unable to be determined. Or, although the center of mass position can be determined, the center of mass acceleration sensor cannot be installed at the center of mass position and can only be arranged at an approximate position, resulting in the inability to accurately obtain the center of mass acceleration. In this case, the consistency between the simulation and the actual test cannot be guaranteed, which is not conducive to the relevant vehicle dynamics analysis.

[0004] Therefore, it is urgent to provide a method for estimating the acceleration of the center of mass of a rigid body to solve the above problems. Summary of the invention

[0005] The purpose of the present invention is to provide a method for estimating the acceleration of the center of mass of a rigid body, which can accurately obtain the acceleration of the center of mass of the rigid body and solve the problem that the physical motion characteristics of the center of mass cannot be directly measured in actual engineering.

[0006] In order to achieve the above objectives, the following technical solutions are provided:

[0007] A method for estimating the acceleration of a rigid body mass center comprises the following steps:

[0008] S1: Select N first marking points on the rigid body, and obtain the accelerations of the N first marking points in the fixed coordinate system and the coordinates of the N first marking points in the fixed coordinate system; wherein N ≥ 4; the fixed coordinate system is a coordinate system fixed to the rigid body;

[0009] S2: Substitute the coordinates and accelerations of the N first marked points in step S1 into the acceleration equation Estimate the center of mass acceleration a0 of the rigid body;

[0010] in,

[0011]

[0012] T represents the direction cosine matrix of the fixed coordinate system relative to the fixed coordinate system, represents the second-order derivative of T with respect to time t, t 11 =(cosψcosθ)″,t12 =(cosψsinθsinφ-cosφsinψ)″,t 13 =(sinψsinφ+cosφcosψsinθ)″,t 21 =(cosθsinψ)″,t 22 =(cosψcosφ+sinψsinφsinθ)″,t 23 =(cosφsinψsinθ-cosψsinφ)″,t 31 =(-sinθ)″,t 32 =(cosθsinφ)″,t 33 =(cosθcosφ)″, where θ=θ(t) is the angle between the y-axis of the fixed coordinate system and the Y-axis of the fixed coordinate system, and is a function of time t. Similarly, φ=φ(t) is the angle between the x-axis of the fixed coordinate system and the X-axis of the fixed coordinate system, and ψ=ψ(t) is the angle between the z-axis of the fixed coordinate system and the Z-axis of the fixed coordinate system; a x0 、a y0 、a z0 are the components of the mass center acceleration a0 in the fixed coordinate system; P is an arbitrary marked point on the rigid body, O is the mass center of the rigid body, ρ represents the coordinate of the vector OP in the fixed coordinate system, and ρ remains unchanged during the motion of the rigid body;

[0013] S3: Select M second marking points on the rigid body and obtain their actual acceleration a in the fixed coordinate system P and the coordinates in the fixed coordinate system; according to the estimated center of mass acceleration a0 in step S2, the coordinates of the M second marking points are substituted into the acceleration equation to obtain the estimated acceleration a P ′; where M ≥ 1;

[0014] S4: Compare the estimated acceleration a of each second marking point obtained in step S3 P ′ and its actual acceleration a P , determine the error between the two Δ = a P ′-a P Is it within the permitted range?

[0015] S5: If the errors Δ of the M second marking points are all within the allowable range, it is considered that the estimation method of the center of mass acceleration is reliable.

[0016] Furthermore, the acceleration equation in step S2 is obtained by the following steps:

[0017] Q1: In a fixed coordinate system, the position of any marker point P on a rigid body is expressed by the following equation:

[0018] R=R0+r

[0019] in, Represents the coordinates of the marker point P in the fixed coordinate system, represents the coordinates of the center of mass O of the rigid body in the fixed coordinate system, represents the coordinates of the vector OP in the fixed coordinate system;

[0020] According to the relative position relationship between the fixed coordinate system and the fixed coordinate system, r can also be expressed by the following formula: r = T*ρ, where: Therefore, R can also be expressed as: R = R0 + T*ρ;

[0021] Q2: Find the second-order derivative of R=R0+T*ρ with respect to time t, that is, We can get the acceleration equation That is to say

[0022] Furthermore, the value of N is 4.

[0023] Furthermore, N takes a value greater than 4; in step S2, each four different first marking points among the N first marking points correspond to a center of mass acceleration a0, and at this time, the average value of all the center of mass accelerations a0 is used as the final center of mass acceleration a0.

[0024] Furthermore, in step S5, the allowable range of the error Δ is the actual acceleration a P 5%.

[0025] Furthermore, the value of M is 2.

[0026] Furthermore, in step S1, the rigid body is established by simulation software.

[0027] Furthermore, in step S1, the rigid body is a solid.

[0028] Furthermore, the coordinates and acceleration of the first marking point and the second marking point are acquired by simulation software or acquired on a physical body.

[0029] Furthermore, the first marking point and the second marking point do not overlap.

[0030] Compared with the prior art, the present invention has the following beneficial effects:

[0031] This estimation method mainly provides an acceleration equation. According to the acceleration equation, we only need to select a number of marked points and substitute their coordinate values ​​and acceleration values ​​to estimate the center of mass acceleration of the rigid body. The estimation method is simple and fast. At the same time, a verification step is also set in the estimation method to ensure the reliability of the center of mass acceleration estimation method. Since the above estimation method can obtain accurate center of mass acceleration, it solves the problem that the physical motion characteristics of the center of mass cannot be directly measured in actual engineering, and therefore has important engineering value. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] Figure 1 is a flow chart of a method for estimating the acceleration of the center of mass of a rigid body in an embodiment of the present invention;

[0033] Figure 2 Schematic diagram of a rigid body in different coordinate systems in an embodiment of the present invention. DETAILED DESCRIPTION

[0034] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Generally, the components of the embodiments of the present invention described and shown in the drawings here can be arranged and designed in various different configurations.

[0035] Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the invention claimed for protection, but merely represents selected embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0036] It should be noted that similar reference numerals and letters denote similar items in the following drawings, and therefore, once an item is defined in one drawing, further definition and explanation thereof is not required in subsequent drawings.

[0037] In the description of the present invention, it should be noted that the terms "upper", "lower", "left", "right", "vertical", "horizontal", "inside", "outside", etc. indicate positions or positional relationships based on the positions or positional relationships shown in the accompanying drawings, or are the positions or positional relationships in which the inventive product is usually placed when in use. They are only for the convenience of describing the present invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore cannot be understood as limiting the present invention. In addition, the terms "first", "second", "third", etc. are only used to distinguish the description, and cannot be understood as indicating or implying relative importance. In the description of the present invention, unless otherwise specified, "multiple" means two or more.

[0038] In the description of the present invention, it is also necessary to explain that, unless otherwise clearly specified and limited, the terms "disposed" and "connected" should be understood in a broad sense, for example, it can be a fixed connection, a detachable connection, or an integral connection; it can be a mechanical connection or an electrical connection. For ordinary technicians in this field, the specific meanings of the above terms in the present invention can be understood according to specific circumstances.

[0039] In the present invention, unless otherwise clearly specified and limited, a first feature being "above" or "below" a second feature may include that the first and second features are in direct contact, or may include that the first and second features are not in direct contact but are in contact through another feature between them. Moreover, a first feature being "above", "above" and "above" a second feature includes that the first feature is directly above and obliquely above the second feature, or simply indicates that the first feature is higher in level than the second feature. A first feature being "below", "below" and "below" a second feature includes that the first feature is directly below and obliquely below the second feature, or simply indicates that the first feature is lower in level than the second feature.

[0040] Embodiments of the present invention are described in detail below, examples of which are shown in the accompanying drawings, wherein the same or similar reference numerals throughout represent the same or similar elements or elements having the same or similar functions. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present invention, and cannot be understood as limiting the present invention.

[0041] This embodiment discloses a method for estimating the acceleration of the center of mass of a rigid body. Figure 1 and Figure 2 As shown, the estimation method specifically includes the following steps:

[0042] S1: Select N first marking points on the rigid body, and obtain the accelerations of the N first marking points in the fixed coordinate system and the coordinates of the N first marking points in the fixed coordinate system; wherein N ≥ 4; the fixed coordinate system is a coordinate system fixed to the rigid body;

[0043] S2: Substitute the coordinates and accelerations of the N first marked points in step S1 into the acceleration equation Estimate the center of mass acceleration a0 of the rigid body;

[0044] in,

[0045]

[0046] T represents the fixed coordinate system (i.e. Figure 2 The xyz coordinate system in the image is relative to the fixed coordinate system (i.e. Figure 2 The direction cosine matrix of the XYZ coordinate system in the image, the fixed coordinate system is the coordinate system fixed to the rigid body; represents the second-order derivative of T with respect to time t, t 11 =(cosψcosθ)″,t 12 =(cosψsinθsinφ-cosφsinψ)″,t 13 =(sinψsinφ+cosφcosψsinθ)″,t 21 =(cosθsinψ)″,t 22=(cosψcosφ+sinψsinφsinθ)″,t 23 =(cosφsinψsinθ-cosψsinφ)″,t 31 =(-sinθ)″,t 32 =(cosθsinφ)″,t 33 =(cosθcosφ)″, where θ=θ(t) is the angle between the y-axis of the fixed coordinate system and the Y-axis of the fixed coordinate system, and is a function of time t. Similarly, φ=φ(t) is the angle between the x-axis of the fixed coordinate system and the X-axis of the fixed coordinate system, and ψ=ψ(t) is the angle between the z-axis of the fixed coordinate system and the Z-axis of the fixed coordinate system; a x0 、a y0 、a z0 are the components of the center of mass acceleration a0 in the fixed coordinate system; P is an arbitrary marked point on the rigid body, O is the center of mass of the rigid body, ρ represents the coordinate of the vector OP in the fixed coordinate system, and ρ remains unchanged during the motion of the rigid body.

[0047] After step S2, the method for estimating the acceleration of the center of mass of a rigid body disclosed in this embodiment further includes the following steps:

[0048] S3: Select M second marking points on the rigid body and obtain their actual acceleration a in the fixed coordinate system P and the coordinates in the fixed coordinate system; according to the estimated center of mass acceleration a0 in step S2, the coordinates of the M second marking points are substituted into the acceleration equation to obtain the estimated acceleration a P ′; where M ≥ 1;

[0049] S4: Compare the estimated acceleration a of each second marking point obtained in step S3 P ′ and its actual acceleration a P , determine the error between the two Δ = a P ′-a P Is it within the permitted range?

[0050] S5: If the errors Δ of the M second marking points are all within the allowable range, it is considered that the estimation method of the center of mass acceleration is reliable.

[0051] Steps S3-S5 are a process of verifying the reliability of the estimation result obtained in step S2.

[0052] The method for estimating the center-of-mass acceleration of a rigid body provided in this embodiment mainly provides an acceleration equation. According to the acceleration equation, it is only necessary to select a number of marking points and substitute their coordinate values ​​and acceleration values ​​to estimate the center-of-mass acceleration of the rigid body. The estimation method is simple and fast. At the same time, a verification step is also provided in the estimation method to ensure the reliability of the above-mentioned method for estimating the center-of-mass acceleration. Since the above-mentioned estimation method can obtain accurate center-of-mass acceleration, it solves the problem that the physical motion characteristics of the center of mass cannot be directly measured in actual engineering projects, and therefore has important engineering value.

[0053] Figure 2 In the figure, the solid arrow represents the fixed coordinate system XYZ, and the dotted arrow represents the fixed coordinate system xyz. The position of the fixed coordinate system is relatively fixed; while the fixed coordinate system is the coordinate system of the rigid body itself, the fixed coordinate system is fixed relative to the rigid body, but the position of the fixed coordinate system will change with the displacement of the rigid body, that is, at each moment t, the position of the fixed coordinate system relative to the fixed coordinate system changes; in this embodiment, the direction cosine matrix T of the fixed coordinate system relative to the fixed coordinate system is used to establish the relationship between the two coordinate systems. Optionally, the center of mass O of the rigid body can be used as the origin of the fixed coordinate system. Furthermore, since the rigid body is moving all the time, its center of mass acceleration a0 at each moment t is different. The center of mass acceleration estimated in this embodiment is the acceleration of the center of mass O of the rigid body in the fixed coordinate system at moment t.

[0054] refer to Figure 2 , the acceleration equation in step S2 is obtained by the following steps:

[0055] Q1: In a fixed coordinate system, the position of any marker point P on a rigid body is expressed by the following equation:

[0056] R=R0+r

[0057] in, Represents the coordinates of the marker point P in the fixed coordinate system, represents the coordinates of the center of mass O of the rigid body in the fixed coordinate system, represents the coordinates of the vector OP in the fixed coordinate system;

[0058] According to the relative position relationship between the fixed coordinate system and the fixed coordinate system, r can also be expressed by the following formula: r = T*ρ, where: Therefore, R can also be expressed as: R = R0 + T*ρ;

[0059] Q2: Find the second-order derivative of R=R0+T*ρ with respect to time t, that is, We can get the acceleration equation That is to say

[0060] From the acceleration equation in Q2 From the specific matrix form, we can see that there are a x0 、a y0 、a z0 ,t 11 ,t 12 ,t 13 ,t 21 ,t 22 ,t 23 ,t 31 ,t 32 and t 33 There are 12 unknown quantities in total. Therefore, we only need to know the coordinates of the four marked points and their accelerations, and then plug them into the acceleration equation to completely determine these 12 unknown quantities, that is, to obtain the center of mass acceleration of the rigid body. Therefore, in step S1 of this embodiment, the number of first marking points N is set to be greater than or equal to 4; when the value of N is 4, the center-of-mass acceleration a0 of a rigid body can be obtained. However, when the value of N is greater than 4, according to step S2, each of the four different first marking points in the N first marking points corresponds to a center-of-mass acceleration a0. At this time, the average value of all the center-of-mass accelerations a0 is used as the final center-of-mass acceleration a0, that is, a center-of-mass acceleration a0 is obtained by averaging, which can further improve the reliability of the center-of-mass acceleration estimation.

[0061] Furthermore, in step S5, the allowable range of the error Δ is acceleration a P The setting of 5% can fully guarantee the reliability of the method for estimating the acceleration of the center of mass of a rigid body proposed in this embodiment.

[0062] It is worth noting that the first marking point and the second marking point should not overlap, otherwise the subsequent verification process is meaningless. Specifically, in step S3, M takes a value of 2, that is, two second marking points are selected, and their coordinates and accelerations are brought into the acceleration equation for full verification.

[0063] Furthermore, the rigid body described in step S1 can be established in the simulation software or can be an entity. The coordinates and accelerations of the corresponding marking points can be obtained in the simulation software or can be obtained on the entity. Specifically, the acceleration of the marking points on the entity is obtained by arranging an acceleration sensor on the entity; even, the coordinates of the marking points can be obtained in the simulation software, and the corresponding acceleration is obtained by arranging an acceleration sensor at the marking point of the entity for actual measurement; since the rigid body in the estimation method can be established in the simulation software or can be an actual object, the consistency between the simulation and the actual test can be guaranteed during the vehicle dynamics analysis, which has great engineering value and is conducive to the relevant vehicle dynamics analysis.

[0064] Substitute the specific data of the marker points below to explain the above estimation method in detail:

[0065] First, select four first marking points on the rigid body. The coordinates and accelerations of the four first marking points are expressed in the following matrix:

[0066]

[0067] Substitute the data in the above two equations into the acceleration equation In this paper, we can get the following matrix equation:

[0068]

[0069] The matrix equation is rearranged as follows:

[0070] first step:

[0071]

[0072] Step 2:

[0073]

[0074] Then we can find the 12 unknown quantities a x0 、a y0 、a z0 ,t 11 ,t 12 ,t 13 ,t 21 ,t 22 ,t 23 ,t 31 ,t 32 ,t 33 The specific value of the center of mass acceleration a0 is estimated.

[0075] In order to verify the accuracy of the above estimation, a second marked point [100 350 0] is selected for verification. The actual acceleration a of the second marked point is P Substitute the coordinates of the second marking point and the specific values ​​of the 12 unknown quantities obtained by calculation into the acceleration equation. In the calculation, the estimated acceleration a is obtained P ′ is [-0.3806 -276.9849 142.8870], compared with a P ′ and a P , it can be obtained that each component of the error Δ is within the allowable range of 5%, so the estimation method of the center of mass acceleration provided by this embodiment is reliable. Further, M can take the value of 2, so a second marking point is selected for verification, and the coordinates and acceleration a of this second marking point areP are [-50 350 0] and [5.1513 -256.189 172.1333] respectively; for the second marked point, the same method is used to obtain the estimated acceleration a P ′ is [5.1448 -255.5187 171.7337], compared with a P ′ and a P It can be obtained that each component of the error Δ is also within the allowable range of 5%, verifying that the estimation method of the center of mass acceleration provided by this embodiment is still reliable.

[0076] Note that the above are only preferred embodiments of the present invention and the technical principles used. Those skilled in the art will understand that the present invention is not limited to the specific embodiments described herein, and that various obvious changes, readjustments and substitutions can be made by those skilled in the art without departing from the scope of protection of the present invention. Therefore, although the present invention has been described in more detail through the above embodiments, the present invention is not limited to the above embodiments, and may include more other equivalent embodiments without departing from the concept of the present invention, and the scope of the present invention is determined by the scope of the appended claims.

Claims

1. A method for estimating the acceleration of a rigid body center of mass, characterized in that: The steps include: S1: Select N first marking points on the rigid body, and obtain the accelerations of the N first marking points in the fixed coordinate system and the coordinates of the N first marking points in the fixed coordinate system; wherein N ≥ 4; the fixed coordinate system is a coordinate system fixed to the rigid body; S2: Substitute the coordinates and accelerations of the N first marked points in step S1 into the acceleration equation Estimate the center of mass acceleration a0 of the rigid body; in, T represents the direction cosine matrix of the fixed coordinate system relative to the fixed coordinate system, represents the second-order derivative of T with respect to time t, t 11 =(cosψcosθ)″, t 12 =(cosψsinθsinφ-cosφsinψ)″,t 13 =(sinψsinφ+cosφcosψsinθ)″, t 21 =(cosθsinψ)″, t 22 =(cosψcosφ+sinψsinφsinθ)″, t 23 =(cosφsinψsinθ-cosψsinφ)″,t 31 =(-sinθ)″, t 32 =(cosθsinφ)″, t 33 =(cosθcosφ)″, where θ=θ(t) is the angle between the y-axis of the fixed coordinate system and the Y-axis of the fixed coordinate system, and is a function of time t. Similarly, φ=φ(t) is the angle between the x-axis of the fixed coordinate system and the X-axis of the fixed coordinate system, and ψ=ψ(t) is the angle between the z-axis of the fixed coordinate system and the z-axis of the fixed coordinate system; a x0 、a y0 、a z0 are the components of the center-of-mass acceleration a0 in the fixed coordinate system; P is an arbitrary marked point on the rigid body, O is the center of mass of the rigid body, ρ represents the coordinate of the vector OP in the fixed coordinate system, and ρ remains unchanged during the motion of the rigid body; S3: Select M second marking points on the rigid body and obtain their actual acceleration a in the fixed coordinate system P and the coordinates in the fixed coordinate system; according to the estimated center of mass acceleration a0 in step S2, the coordinates of the M second marking points are substituted into the acceleration equation to obtain the estimated acceleration a P ′; where M ≥ 1; S4: Compare the estimated acceleration a of each second marking point obtained in step S3 P ′ and its actual acceleration a P , determine the error between the two Δ = a P ′-a P Is it within the permitted range? S5: If the errors Δ of the M second marking points are all within the allowable range, it is considered that the estimation method of the center of mass acceleration is reliable.

2. The method for estimating the acceleration of the center of mass of a rigid body according to claim 1, characterized in that: The acceleration equation in step S2 is obtained by the following steps: Q1: In a fixed coordinate system, the position of any marker point P on a rigid body is expressed by the following equation: R=R0+r in, Represents the coordinates of the marker point P in the fixed coordinate system, represents the coordinates of the center of mass O of the rigid body in the fixed coordinate system, represents the coordinates of the vector OP in the fixed coordinate system; According to the relative position relationship between the fixed coordinate system and the fixed coordinate system, r is expressed by the following formula: r = T*ρ, where: Therefore, R is expressed as: R = R0 + T*ρ; Q2: Find the second-order derivative of R=R0+T*ρ with respect to time t, that is, Get the acceleration equation Right now 3. The method for estimating the acceleration of the center of mass of a rigid body according to claim 1, characterized in that: The value of N is 4.

4. The method for estimating the acceleration of the center of mass of a rigid body according to claim 1, characterized in that: The value of N is greater than 4; in step S2, each four different first marking points among the N first marking points correspond to a center of mass acceleration a0, and at this time, the average value of all the center of mass accelerations a0 is used as the final center of mass acceleration a0.

5. The method for estimating the acceleration of the center of mass of a rigid body according to claim 1, characterized in that: In step S5, the allowable range of error Δ is the actual acceleration a P 5%.

6. The method for estimating the acceleration of the center of mass of a rigid body according to claim 1, characterized in that: The value of M is 2.

7. The method for estimating the acceleration of the center of mass of a rigid body according to claim 1, characterized in that: In step S1, a rigid body is created by simulation software.

8. The method for estimating the acceleration of the center of mass of a rigid body according to claim 1, characterized in that: In step S1, the rigid body is a solid.

9. The method for estimating the acceleration of the center of mass of a rigid body according to claim 1, characterized in that: The coordinates and acceleration of the first marking point and the second marking point are acquired by simulation software or on a physical object.

10. The method for estimating the acceleration of the center of mass of a rigid body according to claim 1, characterized in that: The first marking point and the second marking point do not overlap.

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