CN116819637A - Gravitation effect compensation method and system - Google Patents
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Abstract
The invention provides a gravitational effect compensation method and a gravitational effect compensation system, and belongs to the field of spatial gravitational wave detection. The method comprises the steps of obtaining the mass distribution of a spacecraft, calculating the gravitation effect of the spacecraft on the internal inspection mass serving as an inertial sensor probe, and determining the gravitation effect quantity exceeding the gravitation effect requirement; calculating the gravitation multipole field of the spacecraft, and designing a compensation mass block of each check mass according to the spatial distribution characteristics of different orders of spherical harmonics; calculating the gravitation effect value of the compensation mass block on the checking mass and adjusting the mass of the compensation mass block to enable the gravitation effect value to meet the requirement; the shape and the size of the compensation mass are designed according to the space which can be compensated in the spacecraft, so that the compensation mass block can be installed in the spacecraft. The invention uses the orthogonality of the sphere multipole expansion basis function to decouple translational acceleration and gravitational gradient effect in different directions caused by gravitational effect, and can realize the purpose of respective compensation.
Description
Technical Field
The invention belongs to the field of space gravitational wave detection, and particularly relates to a gravitational effect compensation method and system.
Background
Einstein 1915 proposed a generalized relativity theory, which theoretically predicts gravitational waves. However, due to technical limitations, humans did not detect gravitational waves on the ground for the first time in 2016. Sensitive frequency of different gravitational wave detection methodsSegment-to-segment, spatial gravitational wave detection frequency band pair 10 -4 The gravitational wave sensitivity of the frequency band of 1Hz can detect gravitational waves and the like from star-level black holes, dense double stars of the Galangal system, early universe, and the like, can generate obvious pushing effect on physical research, and simultaneously relates to a plurality of fields of precision measurement science and technology.
The basic principle of space gravitational wave detection is that three satellites are utilized to enter laser interference ranging of an inter-satellite inertial reference check mass, each satellite comprises two check masses serving as inertial references, the movement of the check masses which are kept in a free state by tracking of a spacecraft in the direction of an inter-satellite ranging sensitive axis is controlled by a non-dragging control technology, and the check masses are kept near the balance position under the action of electrostatic suspension control force and moment in the direction of a non-sensitive axis. The residual disturbance acceleration resolution index requirement of the space gravitational wave detection plan on the inspection quality is metThe gravitational effects of the spacecraft on the inspection mass include translational acceleration, rotational acceleration, gravitational gradient and the like, and are one of the main sources of disturbance force/moment to which the inspection mass is subjected, and can influence residual acceleration noise of the inspection mass from various aspects.
The control thrust of the spacecraft without dragging and the electrostatic suspension control force of the inspection mass are limited to a certain extent, and in order to ensure that the spacecraft and the inspection mass can be in a normal control state, the inspection mass is required to be subjected to the gravitation effect of the spacecraft and cannot exceed a certain limit. Because the mass of the spacecraft is large, if the mass distribution of the spacecraft is not specially designed, the gravitation effect of the spacecraft on the internal test mass of the spacecraft is often large in the initial situation, and the gravitation effect influence needs to be reduced by optimizing the mass distribution design and adding a compensation mass block.
The gravitational effect quantity mainly comprises gravitational acceleration of the test mass in three orthogonal translational directions and six independent gravitational gradient components, which are all related to the mass and the position of the compensation mass, and when the compensation mass is added, all gravitational effect values are often changed, so that the selection of the mass and the position of the compensation mass is complicated. Meanwhile, the space in which the compensation mass block can be added in the spacecraft is limited, the distribution position is not regular, and the compensation mass block is convenient to install, so that the difficulty of designing the specific shape of the compensation mass block is increased. It is therefore a difficult problem how to easily and efficiently design the mass and position of the compensating mass.
Disclosure of Invention
Aiming at the defects of the prior art, the invention aims to provide a gravity effect compensation method and a gravity effect compensation system, and aims to solve the problem that the mass and the position of a compensation mass block cannot be conveniently and effectively designed in the existing spacecraft gravity compensation.
To achieve the above object, in a first aspect, the present invention provides a gravitational effect compensation method, comprising the steps of:
under the condition that the volume of the second object is not ignored, determining a first gravitation effect value of the first object to the second object, comparing the first gravitation effect value with a preset gravitation effect threshold, and determining a second gravitation effect value exceeding the preset gravitation effect threshold; wherein the second object is located inside the first object; the gravitational effect value includes gravitational acceleration and gravitational gradient;
grid dividing the first object to obtain a plurality of point masses, and determining a first attractive multipole field of the first object to the second object based on attractive multipole fields of the second object by each point mass under the condition of neglecting the volume of the second object; wherein the gravitational multipole field is related to the mass of the point mass, the distance from the center of the second object and spherical harmonics, and the spatial distribution corresponding to different orders of the spherical harmonics is different;
determining a comparison relationship between the first attractive multipole field and a third attractive force effect value of the first object on the second object under the condition of neglecting the volume of the second object; determining a second gravitation multipole field corresponding to a second gravitation effect value based on the second gravitation effect value and the comparison relation and neglecting the second object volume corresponding to the second gravitation effect value, designing at least one compensation mass block at a proper position in the first object according to the spatial symmetry distribution corresponding to the spherical harmonic function and the spatial distribution condition of the object in the first object, and designing the mass of each compensation mass block according to the comparison relation so as to enable the third gravitation multipole field corresponding to all the compensation mass blocks to counteract the second gravitation multipole field under the condition of neglecting the second object volume;
and under the condition that the volume of the second object is not ignored, adjusting the mass of each compensation mass block so that the fourth gravitation effect value of all the compensation mass blocks on the second object and the second gravitation effect value are mutually counteracted to compensate the gravitation effect of the first object on the second object.
It should be noted that "first" and "second" and the like are used herein to distinguish between different objects, and are not used to describe a particular order of objects. For example, the first and second gravitational effects values, etc. are used to distinguish between different gravitational effects values and not to describe a particular order of gravitational effects values, and accordingly, the first and second objects, etc. are also used to distinguish between different objects and not to describe a particular order of objects.
For the convenience of the reader, the applicant shall describe the multiple gravitation effect values and the multiple gravitation multipole fields involved in the scheme of the invention in a unified way:
first attraction effect value: not neglecting all attractive force effect values of the first object on the second object under the condition of the second object volume;
second attraction effect value: the gravitation effect value of the first object to the second object exceeding the preset threshold value under the condition of not neglecting the second object volume is not ignored;
third attraction effect value: ignoring all attractive force effect values of the first object at the center of the second object in the case of the second object volume;
fourth attraction effect value: the gravitation effect value of the compensating mass block on the second object under the condition of the second object volume is not ignored;
first attractive multipole field: neglecting an attractive multipole field of a first object at a center of a second object in the case of a second object volume;
a second attractive multipole field: ignoring the gravitation multipole field of the part exceeding the requirement corresponding to the second gravitation effect value under the condition of the second object volume;
third attractive multipole field: the attractive multipole field of the compensating mass to the second object is ignored in the case of the second object volume.
In one possible implementation, the method further comprises the steps of:
the shape and size of the compensating mass are designed according to the available space in the first object and the mass of the compensating mass, so that the compensating mass can be installed in the first object.
In one possible implementation, the determined gravitational effect value without neglecting the second object volume is specifically:
wherein a is x ，a y A) z Acceleration in the x-axis, y-axis and z-axis directions, respectively; Γ -shaped structure xx ，Γ xy ，Γ xz ，Γ yy ，Γ yz And gamma-ray zz Is the gravitational gradient between different axes; g is the constant of universal gravitation, M is the mass of the point mass obtained after the first object is meshed, V TM The volume of the second object, (X, Y, Z) is the coordinates of any point on the second object, and (X, Y, Z) is the coordinates of the point mass.
In one possible implementation, the attractive multipole field is calculated by the formula:
wherein, in the formula, Q lm Representing the gravitational multipole field of the point mass at the center of the second object, l representing the number of times the gravitational multipole field (preferably: 1,2,3, … …), m representing the order of the gravitational multipole field (preferably: 0, ±1, ±2, …, ±l), m s The mass representing the mass of the point,the coordinates (R, theta, phi) of the representative point mass in a spherical coordinate system taking the second object as the center, m respectively takes-1, 0 and 1 when l=1, m respectively takes-2, -1, 0, 1 and 2 when l=2, and other possible values of l and m can be obtained by analogy; y is Y lm (θ, φ) represents spherical harmonics, the formula of which is:
in the method, in the process of the invention,P lm and (θ) represents a Bullebrand polynomial, e is a natural constant, and i is an imaginary unit.
In one possible implementation, the comparison relationship is:
wherein a is x0 、a y0 、a z0 、Γ xx0 、Γ xy0 、Γ xz0 、Γ yy0 、Γ yz0 、Γ zz0 To ignore the attractive force effect value when the second object volume,and->Respectively represent Q 11 Real and imaginary parts of>And->Respectively represent Q 22 Is used for the real and imaginary parts of (a),and->Respectively represent Q 21 Real and imaginary parts of (a) are provided.
In one possible implementation manner, at least one compensation mass block is designed at a proper position in the first object according to the spatial symmetry distribution corresponding to the spherical harmonic function and the spatial distribution condition of the object in the first object, and the mass of each compensation mass block is designed according to the comparison relation, so that the third attractive force multipole fields corresponding to all the compensation mass blocks counteract the second attractive force multipole field under the condition of neglecting the volume of the second object, specifically:
and designing the positions of a certain number of compensation mass blocks according to the spatial symmetric distribution characteristics corresponding to each second gravitational multipole field and the spatial distribution condition of the objects in the first object so that the sum of the gravitational multipole fields corresponding to the compensation mass blocks can be cancelled by the second gravitational multipole fields.
In one possible implementation, the first object is a spacecraft and the second object is a proof mass.
In a second aspect, the present invention provides an attraction effect compensation system comprising:
the gravitation effect value determining unit is used for determining a first gravitation effect value of the first object to the second object under the condition that the volume of the second object is not ignored, comparing the first gravitation effect value with a preset gravitation effect threshold value and determining a second gravitation effect value exceeding the preset gravitation effect threshold value; wherein the second object is located inside the first object; the gravitational effect value includes gravitational acceleration and gravitational gradient;
an attractive force multipole field determining unit for meshing the first object to obtain a plurality of point masses, and determining a first attractive force multipole field of the first object to the second object based on attractive force multipole fields of each point mass to the second object under the condition of neglecting the volume of the second object; the gravitational multipole field is related to the mass of the point mass, the distance between the point mass and the second object and spherical harmonics, and the spatial distribution corresponding to different orders of the spherical harmonics is different;
a comparison relation determining unit, configured to determine a comparison relation between the first attractive force multipole field and a third attractive force effect value of the first object on the second object under the condition that the second object volume is ignored;
the gravitational multipole field determining unit is further used for determining a second gravitational multipole field corresponding to the second gravitational effect value based on the second gravitational effect value and the comparison relation and neglecting the second object volume corresponding to the second gravitational effect value;
the compensation mass block design unit is used for designing at least one compensation mass block at a proper position in the first object according to the spatial symmetry distribution corresponding to the spherical harmonic function and the spatial distribution condition of the objects in the first object, and designing the mass of each compensation mass block according to the comparison relation so as to enable the third gravitation multipole fields corresponding to all the compensation mass blocks to counteract the second gravitation multipole field under the condition of neglecting the volume of the second object; and adjusting the mass of each compensation mass block under the condition that the volume of the second object is not ignored, so that the fourth gravitation effect value of all the compensation mass blocks on the second object and the second gravitation effect value are mutually counteracted to compensate the gravitation effect of the first object on the second object.
In one possible implementation, the compensation mass design unit is configured to design the shape and size of the compensation mass according to the available space in the first object and the mass of the compensation mass, so that the compensation mass can be installed in the first object.
In general, the above technical solutions conceived by the present invention have the following beneficial effects compared with the prior art:
according to the compensation method, translational acceleration and translational gradient effect components in different directions caused by the gravitational effect are decoupled from each other by utilizing the space symmetry differences of different orders of the gravitational multipole field, so that the purpose of respective compensation is realized. According to the steps of the compensation method, the distance from the compensation mass block to the center of the checking mass can be flexibly set according to the space where the compensation mass block can be added by reserving the mass of the compensation mass block and the distance from the center of the checking mass block. According to the compensation method, the actual compensation mass block meeting the compensation space constraint can be designed in a flow manner, and the residual gravitation effect value is reduced.
Drawings
FIG. 1 is a flow chart of a method for compensating for gravitational effects provided by an embodiment of the present invention;
FIG. 2 is a flow chart of another spacecraft attraction effect compensation method based on spherical harmonic multipole expansion provided by an embodiment of the invention;
FIG. 3 is a rectangular coordinate system and a corresponding spherical coordinate system provided by an embodiment of the present invention, wherein the rectangular coordinate system is provided with a center of a test mass as an origin, and three mutually orthogonal edge lengths parallel to the test mass are used as coordinate axes;
FIG. 4 is a graph of the spatial distribution characteristics of the first two spherical harmonics provided by an embodiment of the present invention;
FIG. 5 is a schematic diagram of a spacecraft model provided by an embodiment of the invention;
FIG. 6 is a schematic diagram of compensation space for an inertial sensor model provided by an embodiment of the present invention;
FIG. 7 is a diagram of ideal compensation mass azimuth calculated from multipole expansion provided by an embodiment of the present invention;
FIG. 8 is a detailed shape diagram of a proof mass actual proof mass provided by an embodiment of the present invention;
FIG. 9 is a diagram of an embodiment of an attraction effect compensation system according to the present invention.
Detailed Description
For convenience of understanding, the following description will explain and describe related technical terms related to the embodiments of the present invention.
The terms "first" and "second" and the like in the description and in the claims are used for distinguishing between different objects and not for describing a particular sequential order of objects. For example, the first and second gravitational effects values, etc. are used to distinguish between different gravitational effects values, and are not used to describe a particular order of gravitational effects values.
In embodiments of the invention, words such as "exemplary" or "such as" are used to mean serving as an example, instance, or illustration. Any embodiment or design described herein as "exemplary" or "e.g." in an embodiment should not be taken as preferred or advantageous over other embodiments or designs. Rather, the use of words such as "exemplary" or "such as" is intended to present related concepts in a concrete fashion.
In the description of the embodiments of the present invention, unless otherwise indicated, the meaning of "at least one" means one or more, the meaning of "a plurality" means two or more, for example, at least one compensation mass means one or more compensation masses or the like.
Embodiments of the present invention will be described below with reference to the accompanying drawings in the embodiments of the present invention.
FIG. 1 is a flow chart of a method for compensating for gravitational effects provided by an embodiment of the present invention; as shown in fig. 1, the method comprises the following steps:
s101, under the condition that the volume of the second object is not ignored, determining a first gravitation effect value of the first object to the second object, comparing the first gravitation effect value with a preset gravitation effect threshold, and determining a second gravitation effect value exceeding the preset gravitation effect threshold; wherein the second object is located inside the first object; the gravitational effect value includes gravitational acceleration and gravitational gradient;
s102, carrying out grid division on a first object to obtain a plurality of point masses, and determining a first attractive multipole field of the first object to the second object based on attractive multipole fields of the second object of each point mass under the condition of neglecting the volume of the second object; the gravitational multipole field is related to the mass of the point mass, the distance between the point mass and the second object and spherical harmonics, and the spatial distribution corresponding to different orders of the spherical harmonics is different;
s103, determining a comparison relation between the first gravitation multipole field and a third gravitation effect value of the first object to the second object under the condition of neglecting the volume of the second object;
s104, based on the second gravitation effect value and the comparison relation, neglecting the volume of a second object corresponding to the second gravitation effect value, determining a second gravitation multipole field corresponding to the second gravitation effect value, and designing at least one compensation mass block at a proper position in the first object according to the spatial symmetry distribution corresponding to the spherical harmonic function and the spatial distribution condition of the object in the first object;
s105, designing the mass of each compensation mass block according to the comparison relation so as to enable third attractive force multipole fields corresponding to all the compensation mass blocks to counteract the second attractive force multipole fields under the condition of neglecting the volume of the second object;
and S106, under the condition that the volume of the second object is not ignored, adjusting the mass of each compensation mass block so that the fourth gravitation effect value of all the compensation mass blocks on the second object and the second gravitation effect value are mutually counteracted to compensate the gravitation effect of the first object on the second object.
It should be noted that the gravitational effect compensation method provided by the present invention is theoretically applicable to any two objects, and should not be limited to specific types, structures or materials of the objects.
Further, in a specific application scenario, the gravitation effect compensation method provided by the invention is suitable for compensating the gravitation effect of the spacecraft on the inspection quality, and at this time, the first object is the spacecraft, and the second object is the inspection quality.
In a specific embodiment, the invention discloses a spacecraft gravitation effect compensation method based on spherical harmonic multipole expansion, and belongs to the field of space gravitation wave detection. The method comprises the steps of obtaining the mass distribution of a spacecraft, calculating the gravitation effect of the spacecraft on the internal inspection mass serving as an inertial sensor probe, and determining the gravitation effect quantity exceeding the gravitation effect requirement; calculating the gravitation multipole field of the spacecraft, and designing a compensation mass block of each check mass according to the spatial distribution characteristics of different orders of spherical harmonics; calculating the gravitation effect value of the compensation mass block on the checking mass and adjusting the mass of the compensation mass block to enable the gravitation effect value to meet the requirement; the shape and the size of the compensation mass are designed according to the space which can be compensated in the spacecraft, so that the compensation mass block can be installed on the spacecraft. The invention can utilize the orthogonality of the sphere multipole expansion basis function to mutually decouple the translational acceleration in different directions and each component of the gravitational gradient effect caused by the gravitational effect, thereby realizing the purpose of respectively compensating.
The invention provides a spacecraft gravitation effect compensation method based on spherical harmonic multipole expansion, which aims to decouple a plurality of gravitation effect values of a spacecraft on inspection quality and conveniently and independently compensate each gravitation effect value.
Specifically, the spacecraft gravitation effect compensation method based on spherical harmonic multipole expansion provided by the invention, as shown in fig. 2, comprises the following steps:
step S1), an initial mass distribution model of the spacecraft is obtained.
Further, the initial mass distribution model is specifically a position distribution and a density distribution of each structural model in the spacecraft.
Step S2), calculating the gravitation effect value of the spacecraft on the inspection quality, and determining the gravitation effect value exceeding the gravitation requirement of the spacecraft.
Further, the step S2) calculates an gravitational effect value of the spacecraft on the inspection mass, specifically, calculates gravitational acceleration and gravitational gradient of the spacecraft on the inspection mass, and the specific steps include:
step S21), meshing the spacecraft, and equivalent each unit as a point mass with mass concentrated on the mass center, wherein the coordinates of the point mass under the inspection mass coordinate system are (X, Y, Z).
Step S22), gravitational acceleration and gravitational gradient of each point mass to the proof mass are calculated and summed. The three gravitational acceleration components and six gravitational gradient components of each point mass versus proof mass are:
wherein G is the constant of universal gravitation, M is the mass of the point mass, V TM For the volume of the proof mass, (X, Y, Z) is the coordinates of any point on the proof mass under the proof mass coordinate system and (X, Y, Z) is the coordinates of the point mass under the proof mass coordinate system.
Step S3), calculating the attractive force multipole field of the spacecraft.
Further, the step S3) of calculating the gravitational multipole field of the spacecraft specifically includes calculating the gravitational multipole field of the spacecraft at the center of inspection mass, specifically including:
step S31), meshing the spacecraft, and equivalent each unit as a point mass with mass concentrated on the mass center, wherein the coordinates of the point mass under the inspection mass coordinate system are (X, Y, Z).
Step S32), the attractive multipole field of each point mass versus proof mass is calculated and summed. The attractive force multipole field formula is:
q in lm Gravitational multipole field representing point mass at center of proof mass, where l represents the number of times the gravitational multipole field, m represents the order of the gravitational multipole field, m s The mass representing the mass of the point,the coordinates (R, θ, Φ) representing the point mass in a spherical coordinate system centered on the proof mass are shown in fig. 3. The calculated order is l=1, m takes-1, 0, 1, respectively, and l=2, m takes-2, -1, 0, 1,2, respectively. Y is Y lm (θ, φ) represents spherical harmonics, the formula of which is:
wherein P is lm (θ) represents a continuous Legendre polynomial, e is a natural constantI is an imaginary unit.
Furthermore, the compensation mass block of the inspection mass is designed according to different symmetrical distribution represented by spherical harmonics, particularly, the gravitational multipole field has a comparison relation with gravitational acceleration and gravitational gradient at the center position of the inspection mass, and different spherical harmonics of different orders have different spatial symmetries, and decoupling of the gravitational acceleration and gravitational gradient is realized by utilizing the different spatial symmetries, so that the compensation mass block can be respectively added for compensating different gravitational acceleration and gravitational gradient components.
Step S4), determining the corresponding relation between the gravitation effect value and the gravitation multipole field.
Further, the comparison relation between the gravitational multipole field and gravitational acceleration is:
wherein a is x0 、a y0 、a z0 To approximate the proof mass to the gravitational acceleration of the spacecraft to the X, Y, Z direction of the proof mass when the proof mass is centered at the point mass,is Q 11 Real part of->Is Q 11 Is a virtual part of (c).
Further, the contrast relationship between the gravitational multipole field and the gradient is:
wherein Γ is xx0 、Γ xy0 、Γ xz0 、Γ yy0 、Γ yz0 、Γ zz0 For the gravitational gradient of the spacecraft at the inspection center of mass location,and->Respectively represent Q 22 Real and imaginary parts of>And->Respectively represent Q 21 Real and imaginary parts of (a) are provided.
And S5), designing the center position and the mass of the ideal compensation mass block by utilizing different symmetrical distributions characterized by spherical harmonics.
Further, compensating masses are added for compensating for different gravitational acceleration and gravitational gradient components, specifically, the mass m of each compensating mass needs to be determined c And its position in the proof mass spherical coordinate system is (r, θ, φ). Wherein the value of (theta, phi) is designed according to the spatial distribution characteristics of the spherical harmonics of the previous two times. As shown in fig. 4, the middle one of each line is an image when m=0, m>0 time represents the image of the real part of the spherical harmonic function, m<The 0 th order represents the image of the imaginary part of the spherical harmonic, the gray part represents the positive value, and the black part represents the negative value. According to the spatial distribution characteristics, the angular component (theta, phi) of the compensation mass block coordinates required to be added in the compensation of each multi-pole field can be determined, so that the compensation mass block only compensates the multi-pole field and the compensation quantity of the rest multi-pole fields is 0.
Further, for each Q lm Of the compensation mass of (c), m c The value of r should ensure that the following formula is satisfied:
wherein m is ci Is Q lm The i-th compensation mass of (r) i ,θ i ,φ i ) The coordinates of the ith compensating mass in the proof mass spherical coordinate system.
Step S6), translational acceleration and gravitational gradient of the compensation mass block to the checking mass are calculated.
Further, the compensation mass to proof mass gravitational effect values are calculated by first calculating the gravitational effect value of each compensation mass to proof mass and then summing.
Step S7), the mass of the compensation mass block is adjusted, so that the translational acceleration and the gravitational gradient of the spacecraft meet the required values.
Further, the step S7) specifically includes adjusting the mass of the compensating mass according to the ratio of the gravitation effect value of the compensating mass of the proof mass to the gravitation effect value of the spacecraft to the proof mass, so that the compensating mass of the proof mass completely compensates the gravitation effect value of the spacecraft to the proof mass;
step S8), selecting the material of the compensation mass block, and designing the size and shape of the compensation mass block according to the available compensation space of the spacecraft.
Furthermore, the material of the compensation mass block is selected, and the size and shape of the compensation mass block are designed according to the available compensation space of the spacecraft, specifically, the material of the compensation mass block is selected by taking two factors into consideration, namely, the density is larger, so that the occupied space is smaller; secondly, the influence of other physical effects is avoided, and meanwhile, the compensation mass block which can be fixed on the spacecraft is designed by combining the compensatory space position constraint of the spacecraft.
Step S9), confirming that the gravitation effect value of the spacecraft after the compensation mass block is added meets the requirement value.
Taking the initial established Tianqin spacecraft model shown in fig. 5 as an example, analyzing and calculating the gravitation of the spacecraft to the inspection mass, and compensating the gravitation effect by utilizing spherical harmonic multipole expansion and adding a compensation mass block. The example steps are as follows:
as shown in fig. 5: implementing the step (1): acquiring an initial mass distribution model of the spacecraft, and implementing the step (2): and calculating the gravitation effect value of the spacecraft on the inspection quality, and determining the gravitation effect value exceeding the requirement. The mass distribution model of the spacecraft is obtained through fine three-dimensional modeling of the spacecraft, tetrahedral mesh subdivision is carried out on the spacecraft, a mesh position file of the spacecraft is obtained, the mass center position of each mesh is calculated according to the mesh position file, and the meshes are equivalent to point masses with mass concentrated on the mass center. And calculating and summing the gravitation effect of the mass of each point on the inspection mass to obtain the gravitation effect of the whole spacecraft on the inspection mass. Wherein the excess is the gravitational acceleration of the spacecraft in the direction X, Y for each proof mass and a gravitational stiffness Γ xx 。
As shown in fig. 5: implementing the step (3): calculating the attractive multipole field of the spacecraft:
according to the obtained spacecraftCalculating gravitational multipole field of each point mass to the center of the inspection mass according to the corresponding relation between gravitational acceleration and gravitational gradient, wherein the compensation is performed by adding a compensation mass
As shown in fig. 6 and 7: implementing the step (5): the compensation mass for each proof mass is designed with a different symmetry distribution of spherical harmonic characterizations:
the basis for designing the compensating mass is two:
firstly, according to the different symmetries represented by spherical harmonics, the orientation of the compensation mass block can be determined;
according to the space schematic diagram of the additional compensation mass block of the inertial sensor shown in fig. 6, the cylinder is a vacuum cavity shell of the inertial sensor, the cuboid is the installation position of the sensitive probe and the auxiliary structural component thereof, and the compensation space is the middle position of the cylinder and the cuboid.
The ideal compensating mass is designed as a point mass, the position of which is shown in fig. 7 for the compensation of the proof mass 1.
Implementing the step (6): and calculating the gravitation effect value of the compensation mass block on the checking mass.
Implementing the step (7): the mass of the compensation mass block is adjusted, so that the corresponding gravitation effect value of the inspection mass meets the requirements:
and adjusting the mass of the compensation mass block: since the gravitational multipole field corresponds in fact to gravitational acceleration and gravitational gradient at the center of the proof mass, which has a certain mass distribution in space, the compensation mass cannot just compensate for the gravitational effect of the proof mass, but rather requires an adjustment of the mass of the compensation mass. The adjustment mode is to adjust the mass of the compensation mass block according to the ratio of the gravitation effect value of the compensation mass block of each inspection mass to the gravitation effect value of the spacecraft to the inspection mass, so that the compensation mass block of each inspection mass completely compensates the gravitation effect value of the spacecraft to the inspection mass.
As shown in fig. 8: implementing the step (8): the actual size of the compensation mass block is designed according to the compensation space of the inertial sensor.
Because of the limitation of the internal compensation space of the inertial sensor, the compensation mass block needs to be designed, so that the compensation mass block can be compatible with the internal space of the inertial sensor; while considering that the compensating mass should be easy to install and should therefore be designed to be flat. The final design of the compensating mass is shown in fig. 8, the middle is a cubic mass for detection, and the periphery is a strip compensating mass.
The beneficial effects of the invention are as follows: decoupling translational acceleration and gravitational gradient effects in different directions caused by gravitational effects by utilizing the spatial symmetry differences of different orders of the gravitational multipole field, so as to realize the purpose of respective compensation; the distance from the compensation mass block to the center of the checking mass can be flexibly set according to the space where the compensation mass block can be added by reserving two parameters of the compensation mass block and the distance from the compensation mass block to the center of the checking mass block; the actual compensation mass block meeting the compensation space constraint can be designed in a flow manner, and the residual gravitation effect value is reduced.
FIG. 9 is a diagram of an embodiment of an gravitation effect compensation system; as shown in fig. 9, includes:
a gravitation effect value determining unit 910, configured to determine a first gravitation effect value of the first object to the second object without ignoring the volume of the second object, and compare the first gravitation effect value with a preset gravitation effect threshold, and determine a second gravitation effect value exceeding the preset gravitation effect threshold; wherein the second object is located inside the first object; the gravitational effect value includes gravitational acceleration and gravitational gradient;
an attractive force multipole field determining unit 920, configured to grid-divide the first object to obtain a plurality of point masses, and determine a first attractive force multipole field of the first object to the second object based on the attractive force multipole field of each point mass to the second object when the second object volume is ignored; the gravity multipole field is related to the mass of the point mass, the distance between the point mass and the second object and spherical harmonics, and the spatial symmetry distribution corresponding to different orders of the spherical harmonics is different;
a comparison determining unit 930, configured to determine a comparison between the gravitational multipole field and a third gravitational effect value of the first object on the second object when the volume of the second object is ignored;
the gravitational multipole field determining unit 920 is further configured to determine a second gravitational multipole field corresponding to a second gravitational effect value based on the second gravitational effect value and the comparison relationship, and neglecting a second object volume corresponding to the second gravitational effect value;
a compensation mass block design unit 940, configured to design at least one compensation mass block at a suitable position in the first object according to the spatial symmetry distribution corresponding to the spherical harmonics and the spatial distribution of the objects in the first object, and design the mass of each compensation mass block according to the comparison relationship, so that the third gravitational multipole field corresponding to all the compensation mass blocks counteracts the second gravitational multipole field under the condition of neglecting the volume of the second object; and adjusting the mass of each compensation mass block under the condition that the volume of the second object is not ignored, so that the fourth gravitation effect value of all the compensation mass blocks on the second object and the second gravitation effect value are mutually counteracted to compensate the gravitation effect of the first object on the second object.
The specific functional implementation of each unit may be referred to the description in the foregoing method embodiment, and will not be repeated herein.
It will be appreciated that the various numerical numbers referred to in the embodiments of the present invention are merely for ease of description and are not intended to limit the scope of the embodiments of the present invention.
It will be readily appreciated by those skilled in the art that the foregoing description is merely a preferred embodiment of the invention and is not intended to limit the invention, but any modifications, equivalents, improvements or alternatives falling within the spirit and principles of the invention are intended to be included within the scope of the invention.
Claims (9)
1. A method of compensating for gravitational effects comprising the steps of:
under the condition that the volume of the second object is not ignored, determining a first gravitation effect value of the first object to the second object, comparing the first gravitation effect value with a preset gravitation effect threshold, and determining a second gravitation effect value exceeding the preset gravitation effect threshold; wherein the second object is located inside the first object; the gravitational effect value includes gravitational acceleration and gravitational gradient;
grid dividing the first object to obtain a plurality of point masses, and determining a first attractive multipole field of the first object to the second object based on attractive multipole fields of the second object by each point mass under the condition of neglecting the volume of the second object; the gravity multipole field is related to the mass of the point mass, the distance between the point mass and the second object and spherical harmonics, and the spatial distribution corresponding to different orders of the spherical harmonics is different;
determining a comparison relationship between the first attractive multipole field and a third attractive force effect value of the first object on the second object under the condition of neglecting the volume of the second object; determining a second gravitation multipole field corresponding to a second gravitation effect value based on the second gravitation effect value and the comparison relation and neglecting the second object volume corresponding to the second gravitation effect value, designing at least one compensation mass block at a proper position in the first object according to the spatial symmetry distribution corresponding to the spherical harmonic function and the spatial distribution condition of the object in the first object, and designing the mass of each compensation mass block according to the comparison relation so as to enable the third gravitation multipole field corresponding to all the compensation mass blocks to counteract the second gravitation multipole field under the condition of neglecting the second object volume;
and under the condition that the volume of the second object is not ignored, adjusting the mass of each compensation mass block so that the fourth gravitation effect value of all the compensation mass blocks on the second object and the second gravitation effect value are mutually counteracted to compensate the gravitation effect of the first object on the second object.
2. The method of claim 1, further comprising the step of:
the shape and size of the compensating mass are designed according to the available space in the first object and the mass of the compensating mass, so that the compensating mass can be installed in the first object.
3. The method of claim 1, wherein the attractive force effect value comprises: gravitational acceleration and gravitational gradient.
4. A method according to claim 3, characterized in that the determined gravitational effect value without neglecting the second object volume is in particular:
wherein a is x ，a y A) z Acceleration in the x-axis, y-axis and z-axis directions, respectively; Γ -shaped structure xx ，Γ xy ，Γ xz ，Γ yy ，Γ yz And gamma-ray zz Is the gravitational gradient between different axes; g is the constant of universal gravitation, M is the mass of the point mass obtained after the first object is meshed, V TM The volume of the second object, (X, Y, Z) is the coordinates of any point on the second object, and (X, Y, Z) is the coordinates of the point mass.
5. The method of claim 1, wherein the attractive multipole field is calculated by the formula:
in which Q lm Gravitational multipole field representing point mass at the center of the second object, l representing the number of times the gravitational multipole field, m representing the order of the gravitational multipole field, m s The mass representing the mass of the point,representing the coordinates (R, theta, phi), Y of the point mass in a spherical coordinate system centered on the second object lm (θ, φ) represents spherical harmonics, the formula of which is:
wherein P is lm And (θ) represents a Bullebrand polynomial, e is a natural constant, and i is an imaginary unit.
6. The method of claim 5, wherein the comparison is:
wherein a is x0 、a y0 、a z0 、Γ xx0 、Γ xy0 、Γ xz0 、Γ yy0 、Γ yz0 、Γ zz0 To ignore the attractive force effect value when the second object volume,and->Respectively represent Q 11 Real and imaginary parts of>And->Respectively represent Q 22 Real and imaginary parts of>And->Respectively represent Q 21 Real and imaginary parts of (a) are provided.
7. The method according to claim 6, wherein at least one compensation mass is designed at a suitable position in the first object according to the spatial symmetry distribution corresponding to the spherical harmonics and the spatial distribution of the objects in the first object, and the mass of each compensation mass is designed according to the comparison relation, so that the third gravitational multipole field corresponding to all compensation masses counteracts the second gravitational multipole field under the condition of neglecting the volume of the second object, in particular:
and designing the positions of a certain number of compensation mass blocks according to the spatial symmetric distribution characteristics corresponding to each second gravitational multipole field and the spatial distribution condition of the objects in the first object so that the sum of the gravitational multipole fields corresponding to the compensation mass blocks can be cancelled by the second gravitational multipole fields.
8. An attraction effect compensation system, comprising:
the gravitation effect value determining unit is used for determining a first gravitation effect value of the first object to the second object under the condition that the volume of the second object is not ignored, comparing the first gravitation effect value with a preset gravitation effect threshold value and determining a second gravitation effect value exceeding the preset gravitation effect threshold value; wherein the second object is located inside the first object; the gravitational effect value includes gravitational acceleration and gravitational gradient;
an attractive force multipole field determining unit for meshing the first object to obtain a plurality of point masses, and determining a first attractive force multipole field of the first object to the second object based on attractive force multipole fields of each point mass to the second object under the condition of neglecting the volume of the second object; the gravitational multipole field is related to the mass of the point mass, the distance between the point mass and the second object and spherical harmonics, and the spatial distribution corresponding to different orders of the spherical harmonics is different;
a comparison relation determining unit, configured to determine a comparison relation between the first attractive force multipole field and a third attractive force effect value of the first object on the second object under the condition that the second object volume is ignored;
the gravitational multipole field determining unit is further used for determining a second gravitational multipole field corresponding to the second gravitational effect value based on the second gravitational effect value and the comparison relation and neglecting the second object volume corresponding to the second gravitational effect value;
the compensation mass block design unit is used for designing at least one compensation mass block at a proper position in the first object according to the spatial symmetry distribution corresponding to the spherical harmonic function and the spatial distribution condition of the objects in the first object, and designing the mass of each compensation mass block according to the comparison relation so as to enable the third gravitation multipole fields corresponding to all the compensation mass blocks to counteract the second gravitation multipole field under the condition of neglecting the volume of the second object; and adjusting the mass of each compensation mass block under the condition that the volume of the second object is not ignored, so that the fourth gravitation effect value of all the compensation mass blocks on the second object and the second gravitation effect value are mutually counteracted to compensate the gravitation effect of the first object on the second object.
9. The system of claim 8, wherein the compensation mass design unit is configured to design the shape and size of the compensation mass based on the space available in the first object and the mass of the compensation mass such that the compensation mass is mountable in the first object.
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