CN112611511A - Method for acquiring inertia parameters of complex component based on acceleration frequency response function - Google Patents

Method for acquiring inertia parameters of complex component based on acceleration frequency response function Download PDF

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CN112611511A
CN112611511A CN202011380948.6A CN202011380948A CN112611511A CN 112611511 A CN112611511 A CN 112611511A CN 202011380948 A CN202011380948 A CN 202011380948A CN 112611511 A CN112611511 A CN 112611511A
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rigid body
sensor
acceleration
mass
point
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CN112611511B (en
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孙永厚
杜中刚
刘夫云
邓聚才
叶明松
黄骞
祝家好
陈浩东
汤金帅
蔡珍珍
张旭
王越
徐云展
马雪峰
彭雪梅
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Guilin University of Electronic Technology
Dongfeng Liuzhou Motor Co Ltd
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Guilin University of Electronic Technology
Dongfeng Liuzhou Motor Co Ltd
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01M—TESTING STATIC OR DYNAMIC BALANCE OF MACHINES OR STRUCTURES; TESTING OF STRUCTURES OR APPARATUS, NOT OTHERWISE PROVIDED FOR
    • G01M1/00—Testing static or dynamic balance of machines or structures
    • G01M1/10—Determining the moment of inertia

Abstract

The invention discloses a complex component inertia parameter acquisition method based on an acceleration frequency response function, which comprises the steps of firstly establishing a reference coordinate system and a mass center coordinate system on a rigid body to be tested through mass and mass center positions determined by specification parameters of a sensor, arranging the sensor at a reference point of the rigid body to be tested and a response point determined according to geometric parameters of a test device, determining a coordinate conversion matrix, determining the angular acceleration of the whole rigid body under an excitation force through a base point method, determining mass center coordinates of other sensors by adopting a base point iteration method, and further determining reference point acceleration relative to the response point and mass center acceleration relative to the reference point; secondly, determining a mass center coordinate and the whole rigid body mass by forced translation and a mass center theorem, and calculating the mass of the rigid body to be measured by considering the additional mass of the sensor; and finally, determining the rotational inertia of the whole rigid body around the axis of the center of mass by adopting the force translation along the action line, the momentum moment theory, the fixed-axis rotational inertia and the rotational inertia translation theorem, and calculating the rotational inertia of the rigid body to be measured by considering the additional rotational inertia of the sensor.

Description

Method for acquiring inertia parameters of complex component based on acceleration frequency response function
Technical Field
The invention relates to the technical field of identification of rigid body inertia parameters of complex components, in particular to a complex component inertia parameter acquisition method based on an acceleration frequency response function.
Background
The efficient, convenient and accurate acquisition of rigid body inertia parameters of complex components such as automobiles, aviation, aerospace and the like is always a hotspot and difficulty of research in the field of mechanical manufacturing. The inertia parameters of the complex component comprise mass, mass center, rotational inertia and inertia product, and the current identification method of the inertia parameters of the complex component mainly comprises a falling body test method, a torsion pendulum test method, a numerical calculation method based on a CAD/CAE model and a test modal parameter identification method; the falling body test method is only suitable for an axisymmetric rigid body, needs the movement of an object to be tested, is greatly influenced by air resistance and has low identification precision; the torsional pendulum test method is used for testing different postures, is complex and time-consuming to operate, is difficult to test large parts, and is reliable in identification precision; complicated parts are difficult to solve based on a CAD/CAE model numerical calculation method, and time consumption and precision are poor; the test modal parameter identification method comprises a modal model method, a direct parameter identification method and a quality line method; the mode model method needs multiple excitations to obtain six-order modes of the rigid body to be tested; the direct parameter identification method needs a large number of response points and excitation points and is greatly influenced by noise; the mass line method ignores the influence of system damping and rigidity, assumes that the system moves in a single free mode, and can calculate inertia parameters through excitation and response functions, thereby greatly simplifying experiment operation, cost and calculation.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provides a complex component inertia parameter acquisition method based on an acceleration frequency response function, which can fully utilize specification parameters such as mass, mass center and the like and acceleration response of a three-axis sensor under the condition of not using a three-dimensional coordinate tester to measure points for multiple times, arrange the measuring points of the sensor once and carry out data acquisition processing, thus finishing all identification of the inertia parameters of the complex component.
The technical scheme for realizing the purpose of the invention is as follows:
a complex component inertia parameter obtaining method based on an acceleration frequency response function comprises the following steps:
1) the mass to be measured is m0The rigid body is placed on an elastic support with small rigidity or suspended by a flexible rope with small rigidity and is arranged on the surface of the rigid body to be measuredArrangement mass msThe three-axis acceleration sensor takes the sensor and the rigid body to be measured as a whole, and F is excited when the whole rigid body is stressed by a force hammeriWhen acting, the whole rigid body does approximate unconstrained movement, and simultaneously the sensor measures the instantaneous acceleration response of the arrangement point of the whole rigid body as
Figure BDA0002808449030000021
2) Establishing a reference coordinate system OXYZ by using a certain point on the rigid body to be detected, and simultaneously establishing a centroid coordinate system CXYZ relative to a reference coordinate origin, wherein the coordinate of any point on the rigid body to be detected relative to a reference coordinate origin O is
Figure BDA0002808449030000022
The three-axis sensor 1 is arranged at the origin of a reference coordinate, namely a response point 1, and the coordinates of the mass center relative to the self reference coordinate system are
Figure BDA0002808449030000023
The response is
Figure BDA0002808449030000024
Mass ms；
The three-axis sensor 2 is placed at the response point of the known coordinates of the whole rigid body
Figure BDA0002808449030000025
The coordinates of the mass center relative to the self-reference coordinate system are
Figure BDA0002808449030000026
Acceleration response of
Figure BDA0002808449030000027
Mass ms；
3) Measuring the acceleration of the three-axis sensor 1 placed on the origin of coordinates as
Figure BDA0002808449030000028
On the rigid bodyThree-axis sensor acceleration at response point 2 is
Figure BDA0002808449030000029
Determining the instantaneous acceleration at any response point on the rigid body by a base point method as follows:
Figure BDA00028084490300000210
Figure BDA00028084490300000213
for exciting force FiAngular acceleration (alpha)k βk γk) R is the distance from the coordinate of any response point on the rigid body to the coordinate of the base point,
the matrix form is:
Figure BDA00028084490300000211
according to formula (1) and a known parameter a1 sp、ai rpR at an excitation force Fi(fi ipx fi ipy fi ipz) When the whole rigid body is acted, the acceleration response of the corresponding point measured by the sensor on the rigid body to be measured, and the angular acceleration of the whole rigid body is calculated as follows:
Figure BDA00028084490300000212
G1＝(D1 TD1)-1D1 TA1 (3)
A1is a matrix of accelerations, D1As a coordinate transformation matrix, G1Is an angular acceleration matrix;
4) knowing the translational acceleration measured by each sensor and the angular acceleration under the same excitation force, sequentially calculating the coordinates of the centroid of the sensor arranged at any point of the rigid body to be measured relative to the coordinates of the whole rigid body reference coordinate system by a formula (2) as follows:
Figure BDA0002808449030000031
Figure BDA0002808449030000032
D2＝(G2 TG2)-1G2 TA2 (4)
D2coordinates of the sensor centroid at any point of the rigid body surface to be measured relative to the whole reference coordinate system, A2Is a linear acceleration matrix, G2Is an angular acceleration matrix;
5) and calculating the coordinates of the points on the rigid body to be measured corresponding to the sensor as follows:
Figure BDA0002808449030000033
6) known as FiAnd (3) calculating the acceleration of the reference coordinate origin by the equations (2), (4) and (5) under the excitation force as follows:
Figure BDA0002808449030000034
the reference coordinate origin acceleration is calculated by adopting a least square method fitting method as follows:
Figure BDA0002808449030000035
7) the acceleration of the translational acceleration at the centroid relative to the origin of the overall reference coordinate under the action of the exciting force is expressed as follows according to the formulas (2), (3) and (6):
Figure BDA0002808449030000041
8) according to the translation theorem of force, the action extension line of the exciting force passes through any boundary point of the triaxial sensor and is parallel to any boundary line, and the equivalent effect of translating the exciting force to the centroid of the rigid body to be detected is as follows:
Figure BDA0002808449030000042
will excite force Fi(fi ipx fi ipy fi ipz) Total rigid body mass maAcceleration of the center of mass relative to the origin of the reference system
Figure BDA0002808449030000043
Substituting the equation by the centroid motion theorem:
Figure BDA0002808449030000044
M4＝(A4A4 T)-1A4 TFi (9)
Fias a matrix of excitation forces, A4To convert the matrix, M4A matrix composed of the mass to be solved and the mass center;
the equation requires at least two excitations or at least two excitation points, and the total mass m is calculated by the least square methodaAnd the centroid (x) of the rigid body to be measuredcp ycp zcp) (ii) a The rigid body quality to be measured is:
mo＝ma-∑ms (10)
9) the moment of momentum of the mass point system, the moment of momentum theorem of force translation, medium-efficiency couple and rigid moment of fixed-axis rotation are obtained as follows:
Figure BDA0002808449030000045
in formula (11), LOiIs the moment of momentum of the mass point system to the i-axis of the rigid body,
Figure BDA0002808449030000046
is the vector sum of the moments of all external forces acting on the mass point system with respect to the point of the origin coordinate system O, JoiFor a rigid body inertial parameter matrix to be measured, JoiThe expression is as follows:
Figure BDA0002808449030000051
setting the excitation force FiActing on the rigid body to be measured in the direction along the boundary line of the sensor, FiCan move freely in the action line direction, and the excitation force is as follows:
Figure BDA0002808449030000052
wherein
Figure BDA0002808449030000053
For exciting force FkA vertical distance to the centroid;
obtained by the formulas (11) and (13):
Figure BDA0002808449030000054
after the arrangement, calculating the moment of inertia of a certain axis at the position of the mass center of the relative sensor as follows:
Figure BDA0002808449030000055
the least squares method yields:
Jsc＝(T1T1 T)-1T1 TF1 (16)
the moment of inertia and the inertia product can be solved through at least two excitation points; j. the design is a square1For exciting force FkMoment of a certain axis of a sensor centroid coordinate system; j. the design is a square1Middle (J)xx Jyy Jzz) Is the principal moment of inertia, (J)yz Jxz Jxy) Is the product of inertia;
the coordinates of the rigid body to be measured relative to the whole rigid body reference coordinate system and the coordinates of the sensor centroid relative to the whole rigid body reference coordinate system are known by formulas (4) and (9), and the coordinates of the sensor centroid relative to the coordinates of the rigid body centroid to be measured are obtained as follows:
Figure BDA0002808449030000056
calculating the moment of inertia of a certain axis at the position of the mass center of the rigid body to be measured by inertia axis-shifting theorem as follows:
Figure BDA0002808449030000061
Figure BDA0002808449030000062
Joc＝Jrigid body to be measured+JSensor with a sensor element (18)。
In step 6), the reference coordinate origin acceleration is a point which is determined to be measured integrally relative to the integral reference coordinate system according to the geometric parameters, and an equation is established:
Figure BDA0002808449030000063
determining angular acceleration under the same excitation force, determining the mass center of any sensor on the rigid body to be detected through iteration, and further determining the acceleration of the reference point of the rigid body to be detected with high precision as follows:
Figure BDA0002808449030000064
compared with the traditional mass line calculation method, the method for acquiring the inertia parameters of the complex component based on the acceleration frequency response function considers the influence of the additional mass of the sensor on the identification of the inertia parameters, omits a complicated process of measuring a large number of coordinates of response points by adopting a base point iteration method, adopts a method that an excitation force action extension line passes through any boundary point of a three-axis sensor and is parallel to any boundary line, does not need to measure the coordinates of the excitation points, can calculate the rotational inertia of the rigid body to be detected by the translation theorem and the rotational inertia movement theorem of the binding force, removes the influence of the additional rotational inertia of the sensor and improves the identification precision.
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FIG. 1 is a flow chart of a complex component inertia parameter acquisition method based on an acceleration frequency response function;
FIG. 2 is a schematic diagram of a test system reference coordinate system.
Detailed Description
The invention will be further elucidated with reference to the drawings and examples, without however being limited thereto.
Example (b):
the known mechanical parameters, mass parameters, inertia parameters, coordinate parameter symbols, meanings and units of the test system of the embodiment are shown in the following table 1:
TABLE 1
Figure BDA0002808449030000071
The unknown mechanical parameters, the quality parameters, the inertia parameters, the coordinate parameter symbols, the meanings and the units of the test system are shown in the following table 2:
TABLE 2
Figure BDA0002808449030000072
Figure BDA0002808449030000081
As shown in fig. 1, a method for obtaining an inertia parameter of a complex component based on an acceleration frequency response function includes the following steps:
1) the mass to be measured is m0The rigid body is placed on an elastic support with small rigidity or suspended by a flexible rope with small rigidity, and the mass m is arranged on the surface of the rigid body to be measuredsThe three-axis acceleration sensor takes the sensor and the rigid body to be measured as a whole, and F is excited when the whole rigid body is stressed by a force hammeriWhen acting, the whole rigid body does approximate unconstrained movement, and simultaneously the sensor measures the instantaneous acceleration response of the arrangement point of the whole rigid body as
Figure BDA0002808449030000082
2) Establishing a reference coordinate system OXYZ at a certain point on the rigid body to be measured, and simultaneously establishing a centroid coordinate system CXYZ relative to a reference coordinate origin, as shown in FIG. 2, the coordinate of any point on the rigid body to be measured relative to a reference coordinate origin O is
Figure BDA0002808449030000083
The three-axis sensor 1 is arranged at the origin of a reference coordinate, namely a response point 1, and the coordinates of the mass center relative to the self reference coordinate system are
Figure BDA0002808449030000084
The response is
Figure BDA0002808449030000085
Mass ms；
The three-axis sensor 2 is placed at the response point of the known coordinates of the whole rigid body
Figure BDA0002808449030000086
The coordinates of the mass center relative to the self-reference coordinate system are
Figure BDA0002808449030000087
Acceleration response of
Figure BDA0002808449030000088
Mass ms；
3) Measuring the acceleration of the three-axis sensor 1 placed on the origin of coordinates as
Figure BDA0002808449030000089
Acceleration of the three-axis sensor at response point 2 on the rigid body is
Figure BDA00028084490300000810
Determining the instantaneous acceleration at any response point on the rigid body by a base point method as follows:
Figure BDA00028084490300000811
Figure BDA00028084490300000812
for exciting force FiAngular acceleration (alpha)k βk γk) R is the distance from the coordinate of any response point on the rigid body to the coordinate of the base point,
the matrix form is:
Figure BDA0002808449030000091
according to formula (1) and a known parameter a1 sp、ai rpR at an excitation force Fi(fi ipx fi ipy fi ipz) When the whole rigid body is acted, the acceleration response of the corresponding point measured by the sensor on the rigid body to be measured, and the angular acceleration of the whole rigid body is calculated as follows:
Figure BDA0002808449030000092
G1＝(D1 TD1)-1D1 TA1 (3)
A1is a matrix of accelerations, D1As a coordinate transformation matrix, G1Is an angular acceleration matrix;
4) knowing the translational acceleration measured by each sensor and the angular acceleration under the same excitation force, sequentially calculating the coordinates of the centroid of the sensor arranged at any point of the rigid body to be measured relative to the coordinates of the whole rigid body reference coordinate system by a formula (2) as follows:
Figure BDA0002808449030000093
Figure BDA0002808449030000094
D2＝(G2 TG2)-1G2 TA2 (4)
D2coordinates of the sensor centroid at any point of the rigid body surface to be measured relative to the whole reference coordinate system, A2Is a linear acceleration matrix, G2Is an angular acceleration matrix;
5) and calculating the coordinates of the points on the rigid body to be measured corresponding to the sensor as follows:
Figure BDA0002808449030000095
6) known as FiAnd (3) calculating the acceleration of the reference coordinate origin by the equations (2), (4) and (5) under the excitation force as follows:
Figure BDA0002808449030000101
the reference coordinate origin acceleration is calculated by adopting a least square method fitting method as follows:
AO＝(TSTTS)-1TSTAs (6)
7) the acceleration of the translational acceleration at the centroid relative to the origin of the overall reference coordinate under the action of the exciting force is expressed as follows according to the formulas (2), (3) and (6):
Figure BDA0002808449030000102
8) according to the translation theorem of force, the action extension line of the exciting force passes through any boundary point of the triaxial sensor and is parallel to any boundary line, and the equivalent effect of translating the exciting force to the centroid of the rigid body to be detected is as follows:
Figure BDA0002808449030000103
will excite force Fi(fi ipx fi ipy fi ipz) Total rigid body mass maAcceleration of the center of mass relative to the origin of the reference system
Figure BDA0002808449030000104
Substituting the equation by the centroid motion theorem:
Figure BDA0002808449030000105
M4＝(A4A4 T)-1A4 TFi (9)
Fias a matrix of excitation forces, A4To convert the matrix, M4A matrix composed of the mass to be solved and the mass center;
the equation requires at least two excitations or at least two excitation points, and the total mass m is calculated by the least square methodaAnd the centroid (x) of the rigid body to be measuredcp ycp zcp) (ii) a Then stand byThe rigid body mass is measured as follows:
mo＝ma-∑ms (10)
9) the moment of momentum of the mass point system, the moment of momentum theorem of force translation, medium-efficiency couple and rigid moment of fixed-axis rotation are obtained as follows:
Figure BDA0002808449030000111
in formula (11), LOiIs the moment of momentum of the mass point system to the i-axis of the rigid body,
Figure BDA0002808449030000112
is the vector sum of the moments of all external forces acting on the mass point system with respect to the point of the origin coordinate system O, JoiFor a rigid body inertial parameter matrix to be measured, JoiThe expression is as follows:
Figure BDA0002808449030000113
setting the excitation force FiActing on the rigid body to be measured in the direction along the boundary line of the sensor, FiCan move freely in the action line direction, and the excitation force is as follows:
Figure BDA0002808449030000114
wherein
Figure BDA0002808449030000115
For exciting force FkA vertical distance to the centroid;
obtained by the formulas (11) and (13):
Figure BDA0002808449030000116
after the arrangement, calculating the moment of inertia of a certain axis at the position of the mass center of the relative sensor as follows:
Figure BDA0002808449030000117
the least squares method yields:
Jsc＝(T1T1 T)-1T1 TF1 (16)
the moment of inertia and the inertia product can be solved through at least two excitation points; j. the design is a square1For exciting force FkMoment of a certain axis of a sensor centroid coordinate system; j. the design is a square1Middle (J)xx Jyy Jzz) Is the principal moment of inertia, (J)yz Jxz Jxy) Is the product of inertia;
the coordinates of the rigid body to be measured relative to the whole rigid body reference coordinate system and the coordinates of the sensor centroid relative to the whole rigid body reference coordinate system are known by formulas (4) and (9), and the coordinates of the sensor centroid relative to the coordinates of the rigid body centroid to be measured are obtained as follows:
Figure BDA0002808449030000121
calculating the moment of inertia of a certain axis at the position of the mass center of the rigid body to be measured by inertia axis-shifting theorem as follows:
Figure BDA0002808449030000122
Figure BDA0002808449030000123
Joc＝Jrigid body to be measured+JSensor with a sensor element (18)。
In step 6), the reference coordinate origin acceleration is a point which is determined to be measured integrally relative to the integral reference coordinate system according to the geometric parameters, and an equation is established:
Figure BDA0002808449030000124
determining angular acceleration under the same excitation force, determining the mass center of any sensor on the rigid body to be detected through iteration, and further determining the acceleration of the reference point of the rigid body to be detected with high precision as follows:
Figure BDA0002808449030000125

Claims (2)

1. a complex component inertia parameter obtaining method based on an acceleration frequency response function is characterized by comprising the following steps:
1) the mass to be measured is m0The rigid body is arranged on an elastic support or suspended by a flexible rope, and the mass of the rigid body to be measured is msThe three-axis acceleration sensor takes the sensor and the rigid body to be measured as a whole, and F is excited when the whole rigid body is stressed by a force hammeriWhen acting, the whole rigid body does approximate unconstrained movement, and simultaneously the sensor measures the instantaneous acceleration response of the arrangement point of the whole rigid body as
Figure FDA0002808449020000011
2) Establishing a reference coordinate system OXYZ by using a certain point on the rigid body to be detected, and simultaneously establishing a centroid coordinate system CXYZ relative to a reference coordinate origin, wherein the coordinate of any point on the rigid body to be detected relative to a reference coordinate origin O is
Figure FDA0002808449020000012
The three-axis sensor 1 is arranged at the origin of a reference coordinate, namely a response point 1, and the coordinates of the mass center relative to the self reference coordinate system are
Figure FDA0002808449020000013
The response is
Figure FDA0002808449020000014
Mass ms；
The three-axis sensor 2 is placed at the response point of the known coordinates of the whole rigid body
Figure FDA0002808449020000015
The coordinates of the mass center relative to the self-reference coordinate system are
Figure FDA0002808449020000016
Acceleration response of
Figure FDA0002808449020000017
Mass ms；
3) Measuring the acceleration of the three-axis sensor 1 placed on the origin of coordinates as
Figure FDA0002808449020000018
Acceleration of the three-axis sensor at response point 2 on the rigid body is
Figure FDA0002808449020000019
Determining the instantaneous acceleration at any response point on the rigid body by a base point method as follows:
Figure FDA00028084490200000110
Figure FDA00028084490200000111
for exciting force FiAngular acceleration (alpha)k βk γk) R is the distance from the coordinate of any response point on the rigid body to the coordinate of the base point,
the matrix form is:
Figure FDA00028084490200000112
according to formula (1) and a known parameter a1 sp、ai rpR at an excitation force Fi(fi ipx fi ipy fi ipz) When the whole rigid body is acted, the acceleration response of the corresponding point measured by the sensor on the rigid body to be measured, and the angular acceleration of the whole rigid body is calculated as follows:
Figure FDA0002808449020000021
G1＝(D1 TD1)-1D1 TA1 (3)
A1is a matrix of accelerations, D1As a coordinate transformation matrix, G1Is an angular acceleration matrix;
4) knowing the translational acceleration measured by each sensor and the angular acceleration under the same excitation force, sequentially calculating the coordinates of the centroid of the sensor arranged at any point of the rigid body to be measured relative to the coordinates of the whole rigid body reference coordinate system by a formula (2) as follows:
Figure FDA0002808449020000022
Figure FDA0002808449020000023
D2＝(G2 TG2)-1G2 TA2 (4)
D2coordinates of the sensor centroid at any point of the rigid body surface to be measured relative to the whole reference coordinate system, A2Is a linear acceleration matrix, G2Is an angular acceleration matrix;
5) and calculating the coordinates of the points on the rigid body to be measured corresponding to the sensor as follows:
Figure FDA0002808449020000024
6) known as FiAnd (3) calculating the acceleration of the reference coordinate origin by the equations (2), (4) and (5) under the excitation force as follows:
Figure FDA0002808449020000031
the reference coordinate origin acceleration is calculated by adopting a least square method fitting method as follows:
Figure FDA0002808449020000036
7) the acceleration of the translational acceleration at the centroid relative to the origin of the overall reference coordinate under the action of the exciting force is expressed as follows according to the formulas (2), (3) and (6):
Figure FDA0002808449020000032
8) according to the translation theorem of force, the action extension line of the exciting force passes through any boundary point of the triaxial sensor and is parallel to any boundary line, and the equivalent effect of translating the exciting force to the centroid of the rigid body to be detected is as follows:
Figure FDA0002808449020000033
will excite force Fi(fi ipx fi ipy fi ipz) Total rigid body mass maAcceleration of the center of mass relative to the origin of the reference system
Figure FDA0002808449020000034
Substituted intoEquation of the centroid motion theorem:
Figure FDA0002808449020000035
M4＝(A4A4 T)-1A4 TFi (9)
Fias a matrix of excitation forces, A4To convert the matrix, M4A matrix composed of the mass to be solved and the mass center;
the equation requires at least two excitations or at least two excitation points, and the total mass m is calculated by the least square methodaAnd the centroid (x) of the rigid body to be measuredcp ycp zcp) (ii) a The rigid body quality to be measured is:
mo＝ma-∑ms (10)
9) the moment of momentum of the mass point system, the moment of momentum theorem of force translation, medium-efficiency couple and rigid moment of fixed-axis rotation are obtained as follows:
Figure FDA0002808449020000041
in formula (11), LOiIs the moment of momentum of the mass point system to the i-axis of the rigid body,
Figure FDA0002808449020000042
is the vector sum of the moments of all external forces acting on the mass point system with respect to the point of the origin coordinate system O, JoiFor a rigid body inertial parameter matrix to be measured, JoiThe expression is as follows:
Figure FDA0002808449020000043
setting the excitation force FiActing on the rigid body to be measured in the direction along the boundary line of the sensor, FiCan be moved at will in the direction of the action line,the excitation force is as follows:
Figure FDA0002808449020000044
wherein
Figure FDA0002808449020000045
For exciting force FkA vertical distance to the centroid;
obtained by the formulas (11) and (13):
Figure FDA0002808449020000046
after the arrangement, calculating the moment of inertia of a certain axis at the position of the mass center of the relative sensor as follows:
Figure FDA0002808449020000047
the least squares method yields:
Jsc＝(T1T1 T)-1T1 TF1 (16)
the moment of inertia and the inertia product can be solved through at least two excitation points; j. the design is a square1For exciting force FkMoment of a certain axis of a sensor centroid coordinate system; j. the design is a square1Middle (J)xx Jyy Jzz) Is the principal moment of inertia, (J)yz Jxz Jxy) Is the product of inertia;
the coordinates of the rigid body to be measured relative to the whole rigid body reference coordinate system and the coordinates of the sensor centroid relative to the whole rigid body reference coordinate system are known by formulas (4) and (9), and the coordinates of the sensor centroid relative to the coordinates of the rigid body centroid to be measured are obtained as follows:
Figure FDA0002808449020000051
calculating the moment of inertia of a certain axis at the position of the mass center of the rigid body to be measured by inertia axis-shifting theorem as follows:
Figure FDA0002808449020000052
Figure FDA0002808449020000053
Joc＝Jrigid body to be measured+JSensor with a sensor element (18)。
2. The method for obtaining the inertia parameters of the complex component based on the acceleration frequency response function of claim 1, wherein in the step 6), the acceleration of the origin of the reference coordinate is determined by the geometric parameters at any point relative to the whole reference coordinate system to be measured, and an equation is established:
Figure FDA0002808449020000054
determining angular acceleration under the same excitation force, determining the mass center of any sensor on the rigid body to be detected through iteration, and further determining the acceleration of the reference point of the rigid body to be detected with high precision as follows:
Figure FDA0002808449020000055
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CN113280975A (en) * 2021-05-24 2021-08-20 桂林电子科技大学 Large-scale component quality measurement method based on frequency response function quality line
CN113280975B (en) * 2021-05-24 2022-08-09 桂林电子科技大学 Large-scale component quality measurement method based on frequency response function quality line
CN114646440A (en) * 2022-03-16 2022-06-21 北京卫星环境工程研究所 Three-axis six-degree-of-freedom vibration control input and output coordinate transformation matrix construction method
CN114646440B (en) * 2022-03-16 2023-06-20 北京卫星环境工程研究所 Three-axis six-degree-of-freedom vibration control input/output coordinate transformation matrix construction method
CN114659709A (en) * 2022-03-23 2022-06-24 哈尔滨工业大学 Three-dimensional mass center measuring method for large winged spacecraft
CN114659709B (en) * 2022-03-23 2024-04-19 哈尔滨工业大学 Three-dimensional centroid measurement method for large winged aerospace vehicle

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