CN107103111A - Electronics function shape region feature point displacement field reconstructing method based on strain transducer - Google Patents
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Abstract
The invention discloses a kind of electronics function shape region feature point displacement field reconstructing method based on strain transducer, including：Determine position and the quantity of structural parameters, material properties and the strain transducer distribution in electronics function shape face, gather the strain value of the lower function shape face strain transducer measurement of military service load effect, set up the structural finite element model in function shape face, the face model analysis of function shape, obtain Mode Shape, the strain mode vibration shape in function shape face, extract the corresponding strain mode vibration shape matrix of strain transducer nodes of locations, calculate generalized Modal coordinate, the corresponding Mode Shape matrix of abstraction function shape region feature point, reconstructs the displacement of function shape region feature point.The present invention is based on Modal Analysis Theory, in the case where structural loads information is unknown, the strain value measured using a small amount of strain transducer reconstructs the displacement field of electronics function shape region feature point, and then instructs the malformation compensation and electrical property compensation in electronics function shape face.
Description
Technical Field
The invention belongs to the technical field of radar antennas, and particularly relates to a method for reconstructing a displacement field of functional surface characteristic points of electronic equipment based on a strain sensor. The method can be used for reconstructing the characteristic point displacement field of the functional surface of the electronic equipment, lays a foundation for the structural deformation compensation and the electrical property compensation of the functional surface of the subsequent electronic equipment, and ensures the service performance of the functional surface.
Background
The most remarkable characteristic of the functional surface of the electronic equipment is electromechanical combination, the electrical performance is used as the main performance of the functional surface of the whole electronic equipment, and the mechanical structure performance serves as the electrical performance and is a carrier and guarantee of the electrical performance. At present, the functional surface of the electronic equipment is widely applied to the fields of astronomical observation, airborne early warning, spaceborne imaging, ground air defense and the like, and becomes the mainstream of the current development.
With the continuous development and change of military requirements, the functional surface of electronic equipment is mainly developed towards multifunction, light weight and high performance. Along with the development of electronic equipment functional surface towards lightweight direction, when it receives external load effect, electronic equipment functional surface produces the structure more easily and warp, and the structure warp also more and more obvious to electronic equipment functional surface influence effect, and then leads to electronic equipment functional surface electromagnetic property extremely to worsen. Therefore, reconstructing the displacement field of the functional surface under the action of the load to perform corresponding structural deformation compensation and electrical performance compensation is the key for ensuring the system performance.
At present, there are two main methods for domestic and foreign scholars to reconstruct displacement field: (1) a response reconstruction method based on transmissibility, such as Li J, Law SS. sub structural response in wavelet domain. journal of Applied Mechanics,2011,78(4):41010 proposes a transmissibility response reconstruction method aiming at a multi-degree-of-freedom system, provides a system generalized transmissibility matrix, and uses the matrix for the reconstruction of structural response. Although the method reconstructs the displacement field of the deformation surface, the position of the excitation load needs to be known, so that the application of the method is limited and the practicability is not strong. (2) Ko displacement theory, Yuan-Ching, Yan Meijia, a stretch-scarf, a method for reconstructing deformations suitable for beam-type airfoils, Nanjing university of aerospace, 2014,46 (6): 825-830, the Ko displacement theory is used to reconstruct the deformation of the beam-type wing structure and verify the feasibility and reliability of the method, but the method requires a large number of sensors with high reconstruction accuracy and can only be used for simpler structures.
Therefore, on the premise of meeting reconstruction accuracy, the number of the sensors needs to be reduced, and the displacement field of the functional surface characteristic point of the electronic equipment is reconstructed under the condition that structural load information is not needed, so that a foundation is laid for the subsequent functional surface structure deformation compensation and electrical property compensation of the electronic equipment, and the development period is further shortened.
Disclosure of Invention
In order to solve the above-mentioned defects in the prior art, an object of the present invention is to provide a displacement field reconstruction method based on modal analysis, which reconstructs a displacement field of a feature point of a functional surface of an electronic device by using strain values measured by a small number of strain sensors under the condition that structural load information is unknown, and further guides structural deformation compensation and electrical performance compensation of the functional surface of the electronic device.
The invention is realized by the following technical scheme.
A method for reconstructing a displacement field of a functional surface characteristic point of electronic equipment based on a strain sensor comprises the following steps:
(1) determining the structural parameters and material properties of the functional surface of the electronic equipment and the distribution positions and the quantity N of the strain sensors;
(2) acquiring a functional surface strain value of the electronic equipment under the action of service load through a strain sensor;
(3) establishing a structural finite element model of the functional surface of the electronic equipment by using ANSYS software according to the structural parameters and the material properties of the functional surface of the electronic equipment;
(4) performing modal analysis on a structural finite element model of the functional surface of the electronic equipment by using ANSYS software, and extracting M-order modes including a modal vibration mode and a strain modal vibration mode in front of the functional surface according to a result of the modal analysis;
(5) extracting a strain mode vibration mode matrix corresponding to a position node of the strain sensor from the strain mode vibration mode of the functional surface;
(6) calculating generalized modal coordinates according to the strain value measured by the strain sensor in the step (2) and a strain modal shape matrix corresponding to the position node of the strain sensor in the step (5);
(7) extracting a modal shape matrix corresponding to the characteristic point of the functional surface from the modal shape of the functional surface;
(8) and (4) reconstructing the displacement of the functional surface characteristic point by combining the generalized modal coordinate calculated in the step (6) and the modal shape matrix corresponding to the functional surface characteristic point extracted in the step (7).
Further, determining structural parameters of a functional surface of the electronic equipment in the step (1), wherein the structural parameters comprise the number of rows and columns of radiation units in the functional surface, unit spacing, unit form, T/R assembly, cold plate, functional surface frame and mounting framework parameters; determining material properties of the radiating element, including density, elastic modulus, and poisson's ratio; the location and number N of strain sensor distributions are determined.
Further, in the step (2), strain sensors are used for collecting strain values measured by the functional shape surface strain sensors under the action of service load { } ═ retaining facess1,s2,…,sN}。
Further, in the step (4), performing modal analysis on the structure finite element model of the functional surface by using ANSYS software, and extracting an M-order mode in front of the functional surface according to a result of the modal analysis, wherein M is N-1; mode shape including functional surfaceStrain mode vibration type psiiWherein i is 1, 2.
Further, the step (5) is carried out according to the following process:
(5a) determining the node number corresponding to the position node of the strain sensor according to the result of the ANSYS software grid division: the corresponding node numbers of the 1 st to N th strain sensor position nodes are s1, s2, … and sN respectively;
(5b) according to the serial numbers s1, s2, … and sN of the position nodes of the strain sensor and the strain mode type psi of the M-order mode in front of the functional shapeiAnd extracting a strain mode shape matrix [ psi ] corresponding to strain sensor position nodes (s1, s2, …, sN)]S：
Wherein,the strain mode of the sj node corresponding to the ith order mode is shown.
Further, the step (6) is carried out according to the following process:
(6a) according to the mode superposition principle, the strain of the functional surface structure under the action of the load can be expressed as the linear combination of strain modes of each order:
wherein { q } - } is1,q2,…,qMDenotes the generalized modal coordinates;
(6a) according to the strain value { } measured by the strain sensor in the step (2) and the strain mode shape matrix [ psi ] corresponding to the position node of the strain sensor in the step (5)]SThe generalized modal coordinates can be found:
{q}＝(([ψ]S)T([ψ]S))-1([ψ]S)T{}；
where T is the matrix transpose symbol.
Further, the step (7) is carried out according to the following process:
(7a) determining the node number corresponding to the functional surface feature point according to the result of ANSYS software grid division: the 1 st to P th characteristic points respectively have the corresponding node numbers of c1, c2, … and cP;
(7b) extracting a modal shape matrix corresponding to functional surface characteristic points (c1, c2, …, cP) from modal shapes of M-order states in front of the functional surface
Wherein,and the displacement mode of the cl node corresponding to the ith order mode is shown.
Further, in step (8), the generalized mode coordinates { q } - { q } calculated in step (6) are combined with each other1,q2,…,qMThe modal shape matrix corresponding to the functional surface characteristic points extracted in the step (7)Reconstructing displacement { } ═ of functional shape surface feature pointsc1,c2,…,cP}：
Compared with the prior art, the invention has the following characteristics:
1. the modal analysis theory is applied to the reconstruction of the displacement field of the functional surface characteristic point of the electronic equipment, and the displacement field of the functional surface characteristic point of the electronic equipment is reconstructed by utilizing strain values measured by a small amount of strain sensors without structural load information. The method effectively solves the problems that the traditional displacement field reconstruction method is not strong in practicability and high in cost and can only be applied to a simpler structure.
2. When the functional surface of the electronic equipment performs modal analysis, M (M is equal to N-1) order modes including modal modes and strain modal modes in front of the functional surface are extracted according to the result of the modal analysis. The dimension of the electronic equipment functional surface structure model can be further reduced by determining the selected modal order M, the later model operation time can be greatly reduced, the calculation efficiency can be improved, a foundation is laid for the structural deformation compensation and the electrical property compensation of the electronic equipment functional surface later, and the development period is shortened.
Drawings
FIG. 1 is a flow chart of a method for reconstructing a displacement field of a functional surface characteristic point of an electronic device based on a strain sensor according to the invention;
FIG. 2 is a schematic view of an arrangement of radiating elements of a functional surface of an electronic equipment;
FIG. 3 is a schematic structural view of a functional surface of the electronic equipment;
FIG. 4 is a functional topographical feature point location diagram of an electronic equipment;
FIG. 5 is a sensor layout;
FIG. 6 is a mesh model of the functional faces of the electronic equipment in ANSYS software;
FIG. 7 is a schematic view of a restraint position of a functional face of the electronic equipment.
Detailed Description
The invention is further described in detail below with reference to the drawings and examples, but the invention is not limited thereto.
Referring to fig. 1, the invention relates to a method for reconstructing a displacement field of a functional surface characteristic point of an electronic device based on a strain sensor, which comprises the following specific steps:
step 1, determining structural parameters of functional surfaces of electronic equipment, and distribution positions and quantity of strain sensors.
1.1. Determining structural parameters of the functional surface of the electronic equipment (selecting typical representative active phased array antenna of the functional surface of the electronic equipment for example analysis in the invention), including the length L in the functional surface (x, y direction)xAnd a width LyThe number of rows and columns of the radiation units in the functional surface, and the distance d between the radiation units in the x and y directionsx,dy(as shown in the figure)2), radiation unit form, T/R assembly, cold plate, functional panel frame, and mounting frame parameters, etc.
1.2. Material properties of the radiating element are determined, including density, elastic modulus, poisson's ratio, etc.
1.3. And determining the position and the number N of the distribution of the strain sensors.
And 2, acquiring a strain value measured by the functional surface strain sensor under the action of service load.
Using a strain sensor to acquire a strain value measured by the functional surface strain sensor under the action of service load { } ═ retainings1,s2,…,sN}。
And 3, establishing a structural finite element model of the functional surface.
And establishing a structural finite element model of the functional surface by using ANSYS software according to the determined material properties of the T/R assembly, the functional surface frame, the mounting framework and the radiation unit in the functional surface, including density, elastic modulus, Poisson ratio and the like.
And 4, performing modal analysis on the functional surface to obtain a modal shape and a strain modal shape of the functional surface.
Performing modal analysis on the structural finite element model of the functional surface by using ANSYS software, and extracting M (M is equal to N-1) order modes in front of the functional surface, including the modal mode of the functional surface, according to the result of the modal analysisStrain mode vibration type psiiWherein i is 1, 2.
And 5, extracting a strain mode vibration mode matrix corresponding to the position node of the strain sensor.
5.1. Determining the node number corresponding to the position node of the strain sensor according to the result of the ANSYS software grid division: the corresponding node numbers of the 1 st to N th strain sensor position nodes are s1, s2, … and sN respectively.
5.2. According to the serial numbers s1, s2, … and sN of the position nodes of the strain sensor and the strain mode psi of the M (M-1) order mode in front of the functional shapeiAnd extracting a strain mode shape matrix [ psi ] corresponding to strain sensor position nodes (s1, s2, …, sN)]S：
Wherein,the strain mode of the sj node corresponding to the ith order mode is shown.
And 6, calculating generalized modal coordinates according to the strain value measured by the strain sensor and a strain modal shape matrix corresponding to the position node of the strain sensor.
6.1. According to the mode superposition principle, the strain of the functional surface structure under the action of the load can be expressed as the linear combination of strain modes of each order:
wherein { q } - } is1,q2,…,qMDenotes the generalized modal coordinates.
6.2. According to the strain value { } measured by the strain sensor in the step (2) and the strain mode shape matrix [ psi ] corresponding to the position node of the strain sensor in the step (5)]SThe generalized modal coordinates can be found:
{q}＝(([ψ]S)T([ψ]S))-1([ψ]S)T{} (3)
where T is the matrix transpose symbol.
And 7, extracting a mode shape matrix corresponding to the functional surface characteristic point.
7.1. Determining the node number corresponding to the functional surface feature point according to the result of ANSYS software grid division: the 1 st to P characteristic points respectively have the corresponding node numbers of c1, c2, … and cP.
7.2. From the mode shape of the M (M ═ N-1) order state in front of the functional surface, the mode shape matrix corresponding to the functional surface characteristic points (c1, c2, …, cP) is extracted
Wherein,and the displacement mode of the cl node corresponding to the ith order mode is shown.
And 8, reconstructing the displacement of the functional surface characteristic point by combining the generalized modal coordinate.
Combining the generalized modal coordinates { q } - { q } calculated in step (6)1,q2,…,qMThe modal shape matrix corresponding to the functional surface characteristic points extracted in the step (7)Reconstructing displacement { } ═ of functional shape surface feature pointsc1,c2,…,cP}：
The advantages of the present invention can be further illustrated by the following simulation experiments:
determining structural parameters of functional surface of electronic equipment, and distribution positions and quantity of strain sensors
1. Determining structural parameters of functional surface of electronic equipment
The invention selects a typical representative active phased array antenna of the functional surface of the electronic equipment for example analysis. The radiating units are arranged in a rectangular grid at equal intervals in the functional surface, and the central working frequency f is 2.5GHz (the wavelength lambda is 120 mm). As shown in FIG. 3 and Table 1, the number of rows of x-direction radiating elements in the functional surface is 6, the number of columns of y-direction radiating elements is 3, and the spacing d of the radiating elements in the x and y directionsx＝dyThe distribution position of the characteristic points in the functional surface of the electronic equipment is shown in fig. 4, wherein the value is 0.5 · λ, 60 mm.
TABLE 1 geometric model parameters of functional surfaces of electronic equipment
TABLE 2 Material Properties of functional surfaces of electronic Equipment
2. Location and number of strain sensor distributions
The functional surface of the electronic equipment is distributed with 10 strain sensors, and the distribution positions of the strain sensors are shown in figure 5.
Secondly, reconstructing the displacement field of the functional surface characteristic point of the electronic equipment
1. Establishing a structural finite element model of the functional surface of the electronic equipment
And establishing a structural finite element model of the functional surface of the electronic equipment in ANSYS software according to the geometric model size and the material attribute parameters of the functional surface of the electronic equipment. According to the engineering practice, the material properties of the functional surface frame, the mounting bracket and other carrier layers are set according to the material parameters of the aluminum alloy in the table 2, and the material properties of the radiation unit are set according to the material parameters of the printed circuit board. The carrier layer unit type is SOLID unit SOLID92, the radiating unit structure unit type is plane unit SHELL63, and the carrier layer and the radiating unit are connected with each other without relative displacement. The mesh division is performed on the geometric structure model of the functional surface of the electronic equipment by adopting the free mesh set by ANSYS software, and the mesh model of the functional surface of the electronic equipment is obtained as shown in FIG. 6.
2. The modal shape and the strain modal shape of the functional surface are obtained by the modal analysis of the functional surface
2.1 according to the mounting position of the bracket in the engineering practice, adopting cantilever beam structure stress analysis, and fixing one end of the functional surface of the electronic equipment as a constraint condition as shown in figure 7;
2.2 using ANSYS software to perform modal analysis on the structural finite element model of the functional surface of the electronic equipment, and extracting the front 9 (M-N-1-10-1) order modes of the functional surface including the modal shape of the functional surface of the electronic equipment according to the result of the modal analysisStrain mode vibration type psiiWherein i is 1, 2.
3. Reconstructing the displacement field of functional surface characteristic points of electronic equipment
3.1 finding out the generalized modal coordinate { q } according to the formulas (1), (2) and the step (2):
{q}＝(([ψ]S)T([ψ]S))-1([ψ]S)T{} (6)
in the formula, [ psi]SAnd the shape matrix is a strain mode shape matrix corresponding to the position node of the strain sensor, and the { } is a strain value measured by the functional surface strain sensor under the action of the service load.
3.2, reconstructing the displacement { } of the feature point of the functional surface according to the formulas (3), (4), (5) and the step (7):
in the formula, [ psi]SA strain mode vibration mode matrix corresponding to a strain sensor position node;a mode shape matrix corresponding to the functional surface characteristic point; the method comprises the following steps of (1) determining a functional surface strain sensor under the action of service load, and obtaining strain values measured by the functional surface strain sensor.
Third, results and analysis
Obtaining a strain mode vibration mode matrix corresponding to a position node of the strain sensor according to the formula (1), and combining the step (2), the step (6) and the formula (6) to obtain a generalized mode coordinate of the strain mode matrix; and (5) obtaining a mode shape matrix corresponding to the functional surface characteristic point through the step (7), and reconstructing the displacement of the functional surface characteristic point by using a formula (7) to obtain a displacement field of the functional surface characteristic point of the electronic equipment.
The method comprises the steps of obtaining a functional surface characteristic point displacement by using a functional surface strain sensor, and obtaining a strain value { } measured by the functional surface strain sensor under the action of service load by using the strain sensor in the table 3, and obtaining a generalized modal coordinate value { q } in the table 4, and obtaining a reconstructed functional surface characteristic point displacement { }inthe table 5.
TABLE 3 strain values measured by the sensor
TABLE 4 generalized Modal coordinate values
Table 5 reconstructed functional surface characteristic point displacement
According to the reconstructed functional surface characteristic point displacement (table 5), the deformation of the functional surface characteristic point in the Z direction under the load action is larger than the deformation of the functional surface characteristic point in the X direction and the Y direction, and the maximum deformation amount in the Z direction reaches 6.4493 mm; the integral deformation of the 8 th characteristic point in the functional surface of the electronic equipment is the largest and reaches 6.4495 mm.
The experiment shows that the strain modal shape matrix corresponding to the position node of the strain sensor and the modal shape matrix corresponding to the characteristic point of the functional surface can be extracted by applying the method, the generalized modal coordinate is calculated, and the method can be used for reconstructing the displacement field of the characteristic point of the functional surface of the electronic equipment so as to guide the structural deformation compensation and the electrical property compensation of the functional surface of the electronic equipment.
Claims (8)
1. A method for reconstructing a displacement field of a functional surface characteristic point of electronic equipment based on a strain sensor is characterized by comprising the following steps:
(1) determining the structural parameters and material properties of the functional surface of the electronic equipment and the distribution positions and the quantity N of the strain sensors;
(2) acquiring a functional surface strain value of the electronic equipment under the action of service load through a strain sensor;
(3) establishing a structural finite element model of the functional surface of the electronic equipment by using ANSYS software according to the structural parameters and the material properties of the functional surface of the electronic equipment;
(4) performing modal analysis on a structural finite element model of the functional surface of the electronic equipment by using ANSYS software, and extracting M-order modes including a modal vibration mode and a strain modal vibration mode in front of the functional surface according to a result of the modal analysis;
(5) extracting a strain mode vibration mode matrix corresponding to a position node of the strain sensor from the strain mode vibration mode of the functional surface;
(6) calculating generalized modal coordinates according to the strain value measured by the strain sensor in the step (2) and a strain modal shape matrix corresponding to the position node of the strain sensor in the step (5);
(7) extracting a modal shape matrix corresponding to the characteristic point of the functional surface from the modal shape of the functional surface;
(8) and (4) reconstructing the displacement of the functional surface characteristic point by combining the generalized modal coordinate calculated in the step (6) and the modal shape matrix corresponding to the functional surface characteristic point extracted in the step (7).
2. The strain sensor-based electronic equipment functional surface feature point displacement field reconstruction method according to claim 1, wherein the step (1) determines the structural parameters of the electronic equipment functional surface, including the number of rows and columns of radiating elements in the functional surface, the unit spacing, the unit form, the parameters of the T/R assembly, the cold plate, the functional surface frame and the mounting framework; determining material properties of the radiating element, including density, elastic modulus, and poisson's ratio; the location and number N of strain sensor distributions are determined.
3. The method for reconstructing a displacement field of a functional surface feature point of an electronic device based on a strain sensor as claimed in claim 1, wherein in the step (2), the strain sensor is used to collect the strain value { } ═ f measured by the functional surface strain sensor under the action of the service loads1,s2,…,sN}。
4. The strain sensor-based electronic equipment functional form of claim 1The method for reconstructing the surface feature point displacement field is characterized in that in the step (4), the ANSYS software is used for carrying out modal analysis on a structural finite element model of the functional surface, and M-order modes in front of the functional surface, including the modal mode of the functional surface, are extracted according to the result of the modal analysisStrain mode vibration type psiiWherein i is 1, 2.. M, M is N-1.
5. The method for reconstructing the displacement field of the functional surface feature point of the electronic equipment based on the strain sensor as claimed in claim 1, wherein the step (5) is performed as follows:
(5a) determining the node number corresponding to the position node of the strain sensor according to the result of the ANSYS software grid division: the corresponding node numbers of the 1 st to N th strain sensor position nodes are s1, s2, … and sN respectively;
(5b) according to the serial numbers s1, s2, … and sN of the position nodes of the strain sensor and the strain mode type psi of the M-order mode in front of the functional shapeiAnd extracting a strain mode shape matrix [ psi ] corresponding to strain sensor position nodes (s1, s2, …, sN)]S：
Wherein,the strain mode of the sj node corresponding to the ith order mode is shown.
6. The method for reconstructing the displacement field of the functional surface feature point of the electronic equipment based on the strain sensor as claimed in claim 1, wherein the step (6) is performed according to the following process:
(6a) according to the mode superposition principle, the strain of the functional surface structure under the action of the load can be expressed as the linear combination of strain modes of each order:
wherein { q } - } is1,q2,…,qMDenotes the generalized modal coordinates;
(6a) according to the strain value { } measured by the strain sensor in the step (2) and the strain mode shape matrix [ psi ] corresponding to the position node of the strain sensor in the step (5)]SThe generalized modal coordinates can be found:
{q}＝(([ψ]S)T([ψ]S))-1([ψ]S)T{}；
where T is the matrix transpose symbol.
7. The method for reconstructing the displacement field of the functional surface feature point of the electronic equipment based on the strain sensor as claimed in claim 6, wherein the step (7) is performed according to the following process:
(7a) determining the node number corresponding to the functional surface feature point according to the result of ANSYS software grid division: the 1 st to P th characteristic points respectively have the corresponding node numbers of c1, c2, … and cP;
(7b) extracting modal shape matrix corresponding to functional surface characteristic points (c1, c2, …, cP) from modal shape of M-order mode in front of functional surface
Wherein,and the displacement mode of the cl node corresponding to the ith order mode is shown.
8. The strain-based strain transfer of claim 7The method for reconstructing the displacement field of the functional surface feature point of the electronic equipment of the sensor is characterized in that in the step (8), the generalized modal coordinate { q } - { q } calculated in the step (6) is combined with1,q2,…,qMThe modal shape matrix corresponding to the functional surface characteristic points extracted in the step (7)Reconstructing displacement { } ═ of functional shape surface feature pointsc1,c2,…,cP}：
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