CN106649922B - Optical-mechanical integration analysis method of pretreatment interface program and mirror surface shape optimization method - Google Patents
Optical-mechanical integration analysis method of pretreatment interface program and mirror surface shape optimization method Download PDFInfo
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Abstract
The application discloses a light-machine integration analysis method and a mirror surface shape optimization method of a pretreatment interface program, which comprise the following steps: establishing a mirror finite element model; numbering all finite element mesh nodes in the mirror finite element model, and extracting coordinate information of the finite element mesh nodes according to the node numbers; calculating mirror surface node area weighting factors of finite element grid nodes, and fitting by taking a Zernike polynomial as a fitting basis function according to the mirror surface node area weighting factors and coordinate information to obtain mirror surface rigid body displacement and a linear relation between the Zernike polynomial and displacement of mirror surface finite element grid nodes; and (3) carrying out optical-mechanical interface pretreatment on the linear relation, generating a finite element analysis pretreatment file, and importing the finite element analysis pretreatment file into a finite element model to carry out optical-mechanical system dynamics integration analysis and mirror surface shape optimization treatment. The problems of large calculated amount and fitting failure caused by a large amount of fitting data in the optical machine program post-processing mode are solved.
Description
Technical Field
The invention relates to the technical field of optical-mechanical thermal integration analysis, in particular to an optical-mechanical integration analysis method and a mirror surface shape optimization method of a pretreatment interface program.
Background
The high-precision optical imaging system is difficult to avoid various dynamic disturbances in the use process, for example, a space optical remote sensor is subjected to micro-vibration of a reaction flywheel, and a ground-based telescope is subjected to dynamic disturbances such as wind-borne earthquake and the like. After the optical-mechanical system is disturbed by power, the optical elements deform themselves, and the relative distance between the optical elements also changes, so that the optical axis jitter of the optical imaging system caused by the disturbance of power is one of the main factors for reducing the imaging quality of the system.
When the statics integration analysis of the optical-mechanical system is carried out, the method generally adopts the mode that the structural deformation file is subjected to post-processing, the rigid body displacement of the mirror surface and the Zernike polynomial coefficient with the physical significance are separated, and then the rigid body displacement and the Zernike polynomial coefficient are introduced into optical analysis software through format conversion to carry out the influence analysis of mechanics and temperature loads on the optical system.
However, if the optical-mechanical system dynamics analysis is processed by adopting the optical-mechanical interface program post-processing mode, such as instantaneous analysis, the mirror surface node deformation amount needs to be derived after each step interval is calculated, and then the optical-mechanical interface processing is carried out, so that the calculated data amount is obviously increased; when the stochastic response analysis of the optical-mechanical system is carried out, the stochastic response analysis process is carried out in finite element analysis software, and a post-processing program cannot intervene, so that the optical-mechanical interface processing fails, and therefore the conventional optical-mechanical interface post-processing mode cannot effectively meet the requirement of the dynamics analysis of the optical-mechanical system. Because the optical-mechanical interface processing process occurs after finite element solution in the post-processing mode, the process of mirror surface shape optimization cannot be independently completed in finite element analysis software, and other software such as Matlab or Isight is needed to provide an integrated optimization environment, so that the complexity of mirror surface shape optimization design is increased.
Therefore, how to reduce the problems of large calculation amount and fitting failure caused by a large amount of fitting data in the optical-mechanical program post-processing mode is a technical problem which needs to be solved urgently by the technical personnel in the field.
Disclosure of Invention
In order to solve the technical problems, the invention provides an optical machine integration analysis method based on a pre-processing interface program, which solves the problems of large calculation amount and fitting failure caused by a large amount of fitting data in an optical machine program post-processing mode.
In order to achieve the purpose, the invention provides the following technical scheme:
an optical-mechanical integration analysis method and a mirror surface shape optimization method of a pretreatment interface program comprise the following steps:
establishing a mirror finite element model;
numbering all finite element mesh nodes in the mirror surface finite element model, and extracting coordinate information of the finite element mesh nodes according to the node numbers;
calculating mirror surface node area weighting factors of the finite element grid nodes, and fitting by taking a Zernike polynomial as a fitting basis function according to the mirror surface node area weighting factors and the coordinate information to obtain mirror surface rigid body displacement and a linear relation between the Zernike polynomial and displacement of mirror surface finite element grid nodes;
and carrying out optical-mechanical interface pretreatment on the linear relation to generate a finite element analysis pretreatment file, and importing the finite element analysis pretreatment file into the finite element model to carry out optical-mechanical system dynamics integration analysis and mirror surface shape optimization treatment.
Preferably, in the above method, the calculating a node area weighting factor of the finite element mesh node specifically includes:
applying a uniform pressure field at the mirror surface along the optical axis direction, and simultaneously constraining the translational freedom degree of finite element grid nodes on the mirror surface;
carrying out finite element analysis by taking the uniform pressure field and the translation freedom degree as boundary conditions to obtain the support reaction force of the finite element grid nodes along the optical axis direction, and taking the support reaction force as the node area weighting factor wiAnd i is the node number of the finite element grid.
Preferably, in the above method, the fitting with Zernike polynomials as fitting basis functions according to the mirror surface node area weighting factors and the coordinate information to obtain the mirror surface rigid body displacement and the linear relation between the Zernike polynomials and the displacement of the mirror surface finite element mesh nodes specifically includes:
calculating the residual error value of the finite element mesh node with the node number i:
Ei＝ui-zi
wherein u isiFor the deformation value of the finite element mesh node with node number i, ZiRigid body displacement or ring domain Zernike polynomial fitting quantity of finite element grid node with node number i,
cjin order to be a coefficient of fit,
representing the rigid displacement of finite element grid node or the Zernike polynomial of the ring domain with node index i;
according to the node area weighting factor wiAnd the residual error value E of the finite element mesh node with the number iiCalculating the total residual error value of all the mirror surface finite element mesh nodes:
obtaining the fitting coefficient c of the rigid body displacement or the ring domain Zernike polynomial by adopting a least square methodkWherein k is 1 to m,
fitting the minimum total residual error E to obtain the mirror rigid body displacement and a ring domain Zernike polynomial coefficient ckLinear relation with displacement of the metagrid node:
wherein A is a coefficient matrix,
is a vector of displacement amounts of the mirror surface nodes,
fitting coefficient vectors for rigid body displacements and Zernike deformations.
Preferably, in the method, the importing the file before finite element analysis into the finite element model to perform mirror surface shape optimization includes:
taking the target function of the mirror surface shape as the finite element analysis preprocessing file, and calculating the mirror surface shape root mean square value RMS and the peak-to-valley value PV of the target function of the mirror surface shape:
the mirror surface shape root mean square value RMS and the peak-to-valley value PV are:
and establishing a nonlinear relation between the RMS value and the PV value and residual aberration displacement values of all nodes of the mirror surface, thereby establishing a nonlinear relation between the RMS value and the peak-valley value PV and position quantities of all nodes of the mirror surface.
Preferably, in the method, the finite element analysis preprocessing file is imported into the finite element model in a multipoint constraint mode for optical-mechanical integration analysis.
It can be seen from the above technical solutions that the optical-mechanical integrated analysis method and the mirror surface shape optimization method of the pretreatment interface program provided by the present invention include: establishing a mirror finite element model; numbering all finite element mesh nodes in the mirror surface finite element model, and extracting coordinate information of the finite element mesh nodes according to the node numbers; calculating mirror surface node area weighting factors of the finite element grid nodes, and fitting by taking a Zernike polynomial as a fitting basis function according to the mirror surface node area weighting factors and the coordinate information to obtain mirror surface rigid body displacement and a linear relation between the Zernike polynomial and displacement of mirror surface finite element grid nodes; and carrying out optical-mechanical interface pretreatment on the linear relation to generate a finite element analysis pretreatment file, and importing the finite element analysis pretreatment file into the finite element model to carry out optical-mechanical system dynamics integration analysis and mirror surface shape optimization treatment.
The mirror surface node area weighting factor of the finite element grid node is calculated, the mirror surface node area weighting factor represents the weight of the mirror surface finite element node participating in surface shape fitting, the node weighting factor of grid density is small, the node weighting factor of grid sparseness is large, the weighting factor distribution is carried out on the mirror surface nodes with different grid sparseness degrees in the mirror surface fitting process, the problem of reduction of fitting precision caused by non-uniform grid of the mirror surface finite element is solved, meanwhile, the problem of large fitting data volume or fitting failure caused by a post-processing mode in the dynamic analysis of an optical-mechanical system is effectively solved by adopting an optical-mechanical interface program pre-processing mode, and the mirror surface shape optimization process is effectively simplified by adopting the optical-mechanical interface program pre-processing mode.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to the provided drawings without creative efforts.
Fig. 1 is a schematic flow chart of an optical-mechanical integration analysis method and a mirror surface shape optimization method of a preprocessing interface program according to an embodiment of the present invention.
FIG. 2 is a mirror finite element grid diagram provided by an embodiment of the present invention;
FIG. 3 is a contour plot of mirror node area weighting factors provided by an embodiment of the present invention;
fig. 4 is a random response power density spectrum of the first 11 th-order loop domain Zernike polynomial coefficient obtained by fitting the mirror surface provided by the embodiment of the present invention under the unsteady wind load.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
Referring to fig. 1 and 2, fig. 1 is a schematic flow chart of an optical-mechanical integration analysis method and a mirror surface shape optimization method of a preprocessing interface program according to an embodiment of the present invention, and fig. 2 is a finite element mirror grid diagram according to an embodiment of the present invention.
In a specific embodiment, an optical-mechanical integrated analysis method and a mirror surface shape optimization method of a pre-processing interface program are provided, which specifically include the following steps:
step S1: establishing a mirror finite element model;
the mirror surface can be a mirror with a diameter of 1200mm and a central hole of 400mm to establish a mirror surface finite element model, and the type of the mirror surface can be selected according to requirements. FIG. 2 is a schematic diagram of a mirror finite element grid according to an embodiment of the present invention, as shown in FIG. 2.
Step S2: and numbering all finite element mesh nodes in the mirror surface finite element model, and extracting the coordinate information of the finite element mesh nodes according to the node numbers.
And establishing a three-dimensional coordinate system on the mirror surface, wherein the coordinate information comprises three-dimensional coordinates of the nodes. For example, in a reflector with a central hole of 400mm, the diameter of which is 1200mm, the vertex coordinates (x, y, z) of the reflector are set to (0,0,0), the radius of the reflector is set to R3600, the reference wavelength λ is set to 6.8e-4mm, the radial wave number n of the annular Zernike substrate is set to 4, and the annular wave number m is set to 0.
Step S3: and calculating mirror surface node area weighting factors of the finite element grid nodes, and fitting by taking a Zernike polynomial as a fitting basis function according to the mirror surface node area weighting factors and the coordinate information to obtain mirror surface rigid body displacement and a linear relation between the Zernike polynomial and displacement of the mirror surface finite element grid nodes.
In the specific process of calculating the mirror surface node area weighting factor of the finite element grid nodes, total pressure such as uniform pressure of 1N is applied to the mirror surface along the optical axis direction, the translation freedom degree of all the nodes is restrained, and the support of each node on the mirror surface along the optical axis direction is solved through a finite element analysis software Nastran reactionCounter-force, i.e. the node area weighting factor w for this pointi. As shown in fig. 3, fig. 3 is a contour diagram of mirror surface node area weighting factors according to an embodiment of the present invention.
And (3) extracting the node number of the mirror surface, coordinate value information corresponding to the node number and a node area weighting factor through Matlab, and fitting by taking a Zernike polynomial as a fitting basis function, wherein the basis function can be a standard circular domain Zernike polynomial or a ring domain Zernike polynomial. In the Cassegrain optical system, the primary mirror is usually designed to be a circular ring due to the central obscuration of the secondary mirror, while the standard circular domain Zernike polynomials usually adopted in the optical-mechanical integration analysis are only orthogonal in a continuous unit circular domain, so that the orthogonality is lost in an annular discrete sampling point domain, and the non-orthogonality is aggravated by an uneven mirror surface finite element grid, so that the fitting precision is reduced. Therefore, in the embodiment, the circular domain Zernike polynomial is optimized, the non-orthogonality of the standard circular domain Zernike polynomial in the circular domain is solved, and the fitting precision is improved. Table 1 shows a comparison of Zernike polynomials in the standard circle domain and polynomials in the ring domain. Table 1 lists the first 11-term loop-domain Zernike polynomials derived by the scholars v.n.mahajan and the first 11-term standard round-domain Zernike polynomials where the loop factor epsilon is the ratio of the center-hole radius to the mirror radius, and in particular, the round-domain Zernike polynomials are the special forms of the loop-domain Zernike polynomials where the loop factor epsilon is 0.
Table 1 shows a comparison of Zernike polynomials in the standard circle domain and Zernike polynomials in the ring domain
Step S4: and carrying out optical-mechanical interface pretreatment on the linear relation to generate a finite element analysis pretreatment file, and importing the finite element analysis pretreatment file into the finite element model to carry out optical-mechanical system dynamics integration analysis and mirror surface shape optimization treatment.
Specifically, the integration analysis and optimization mainly aims at the interface pretreatment of the optical-mechanical interface part, and the conventional finite element analysis is carried out after the pretreatment to obtain the Zernike term, wherein the RMS value and the PV value of the mirror surface shape are the optimization results of the mirror surface shape.
Taking the wind load analysis of the primary mirror of the foundation telescope as an example, establishing a linear relation between the Zernike deformation quantity and the position quantity of the mirror surface node according to the method, introducing the linear relation into a finite element model in a multi-point constraint mode as pretreatment, taking a power spectrum density curve of unsteady wind load as input, performing the random response dynamics analysis of the system, and solving the front 11-term Zernike polynomial random response power spectrum density. And (3) taking the power spectral density curve of the unsteady wind load as an input, performing dynamic analysis on the system, and solving the power spectral density of the front 11 Zernike polynomial random response. As shown in fig. 4, fig. 4 is a random response power density spectrum of the first 11 order loop domain Zernike polynomial coefficients obtained by fitting the mirror provided in the embodiment of the present invention under the unsteady wind load.
The invention provides an optical-mechanical integration analysis method and a mirror surface shape optimization method, which utilize optical-mechanical interface preprocessing software compiled by Matlab, firstly input an f06 file containing a node area weighting factor and an bdf file containing mirror surface node coordinate information which are obtained by solving by Natran, then set mirror surface vertex coordinate values, working wavelength values, initial node numbers and ring domain Zernike fitting terms used for fitting, and finally import a finite element analysis preprocessing file generated by the preprocessing interface software into a finite element model for optical-mechanical integration analysis and mirror surface shape optimization.
The mirror surface node area weighting factor of the finite element grid node is calculated, the mirror surface node area weighting factor represents the weight of the mirror surface finite element node participating in surface shape fitting, the node weighting factor of grid density is small, the node weighting factor of grid sparseness is large, the weighting factor distribution is carried out on the mirror surface nodes with different grid sparseness degrees in the mirror surface fitting process, the problem of reduction of fitting precision caused by non-uniform grid of the mirror surface finite element is solved, meanwhile, the problem of large fitting data volume or fitting failure caused by a post-processing mode in the dynamic analysis of an optical-mechanical system is effectively solved by adopting an optical-mechanical interface program pre-processing mode, and the mirror surface shape optimization process is effectively simplified by adopting the optical-mechanical interface program pre-processing mode.
Further, the calculating of the node area weighting factor of the finite element mesh node specifically includes:
applying a uniform pressure field at the mirror surface along the optical axis direction, and simultaneously constraining the translational freedom degree of finite element grid nodes on the mirror surface;
carrying out finite element analysis by taking the uniform pressure field and the translation freedom degree as boundary conditions to obtain the support reaction force of the finite element grid nodes along the optical axis direction, and taking the support reaction force as the node area weighting factor wiAnd i is the node number of the finite element grid.
Further, fitting the mirror surface by using a Zernike polynomial as a fitting basis function according to the mirror surface node area weighting factor and the coordinate information to obtain a mirror surface rigid body displacement and a linear relation between the Zernike polynomial and displacement of the mirror surface finite element mesh nodes, specifically comprising:
calculating the residual error value of the finite element mesh node with the node number i:
Ei＝ui-zi
wherein u isiFor the deformation value of the finite element mesh node with node number i, ZiRigid body displacement or ring domain Zernike polynomial fitting quantity of finite element grid node with node number i,
cjin order to be a coefficient of fit,
representing the rigid displacement of finite element grid node or the Zernike polynomial of the ring domain with node index i;
according to the node area weighting factor wiAnd the residual error value E of the finite element mesh node with the number iiCalculating the total residual error value of all the mirror surface finite element mesh nodes:
obtaining the fitting coefficient c of the rigid body displacement or the ring domain Zernike polynomial by adopting a least square methodkWherein k is 1 to m,
fitting the minimum total residual error E to obtain the mirror rigid body displacement and a ring domain Zernike polynomial coefficient ckLinear relation with displacement of the metagrid node:
wherein A is a coefficient matrix,
is a vector of displacement amounts of the mirror surface nodes,
fitting coefficient vectors for rigid body displacement and ring domain Zernike deformation.
Specifically, by
And solving to obtain m equations, and fitting the m equations to obtain a linear relation between the rigid body displacement of the mirror surface and the Zernike polynomial coefficients of the ring domain and the position quantities of all nodes on the mirror surface.
Further, the importing the finite element analysis preprocessing file into the finite element model to perform mirror surface shape optimization processing specifically includes:
taking the target function of the mirror surface shape as the finite element analysis preprocessing file, and calculating the target function of the mirror surface shape, namely the mirror surface shape root mean square value RMS and the peak-to-valley value PV as follows:
and establishing a nonlinear relation between the RMS value and the PV value and the residual aberration displacement value of all nodes of the mirror surface, thereby establishing a nonlinear relation between the position quantity of all nodes of the mirror surface.
The obtained mirror surface root mean square value RMS and the peak-valley value PV are the result of the surface shape analysis and are also the target of the mirror surface shape optimization, the two nonlinear relations are imported into a finite element model as pretreatment, and the optimization analysis can be carried out by utilizing the optimization function of finite element analysis software.
And further, importing the finite element analysis pre-processing file into the finite element model in a multi-point constraint mode for optical-mechanical integration analysis.
The embodiments in the present description are described in a progressive manner, each embodiment focuses on differences from other embodiments, and the same and similar parts among the embodiments are referred to each other.
The previous description of the disclosed embodiments is provided to enable any person skilled in the art to make or use the present invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the generic principles defined herein may be applied to other embodiments without departing from the spirit or scope of the invention. Thus, the present invention is not intended to be limited to the embodiments shown herein but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.
Claims (4)
1. An optical-mechanical integrated analysis method and a mirror surface shape optimization method of a pretreatment interface program are characterized by comprising the following steps:
establishing a mirror finite element model;
numbering all finite element mesh nodes in the mirror surface finite element model, and extracting coordinate information of the finite element mesh nodes according to the node numbers;
calculating mirror surface node area weighting factors of the finite element grid nodes, and fitting by taking a Zernike polynomial as a fitting basis function according to the mirror surface node area weighting factors and the coordinate information to obtain mirror surface rigid body displacement and a linear relation between the Zernike polynomial and displacement of mirror surface finite element grid nodes;
the calculating of the node area weighting factor of the finite element mesh node specifically comprises the following steps:
applying a uniform pressure field at the mirror surface along the optical axis direction, and simultaneously constraining the translational freedom degree of finite element grid nodes on the mirror surface;
carrying out finite element analysis by taking the uniform pressure field and the translation freedom degree as boundary conditions to obtain the support reaction force of the finite element grid nodes along the optical axis direction, and taking the support reaction force as the node area weighting factor wiI is the finite element mesh node number;
and carrying out optical-mechanical interface pretreatment on the linear relation to generate a finite element analysis pretreatment file, and importing the finite element analysis pretreatment file into the finite element model to carry out optical-mechanical system dynamics integration analysis and mirror surface shape optimization treatment.
2. The method according to claim 1, wherein the fitting with Zernike polynomials as fitting basis functions according to the mirror node area weighting factors and the coordinate information to obtain the mirror rigid body displacement and the linear relation between the Zernike polynomials and the displacement of the mirror finite element mesh nodes comprises:
calculating the residual error value of the finite element mesh node with the node number i:
Ei＝ui-zi
wherein u isiFor the deformation value of the finite element mesh node with node number i, ZiRigid body displacement or ring domain Zernike polynomial fitting quantity of finite element grid node with node number i,
cjin order to be a coefficient of fit,
representing the rigid displacement of finite element grid node or the Zernike polynomial of the ring domain with node index i;
the parameter m is the term number of the polynomial adopted in fitting, and comprises the rigid body displacement of the mirror surface and the Zernike polynomial; the parameter j is a jth polynomial;
according to the node area weighting factor wiAnd the residual error value E of the finite element mesh node with the number iiCalculating the total residual error value of all the mirror surface finite element mesh nodes:
obtaining the fitting coefficient c of the rigid body displacement or the ring domain Zernike polynomial by adopting a least square methodkWherein k is 1 to m,
fitting the minimum total residual error E to obtain the mirror rigid body displacement and a ring domain Zernike polynomial coefficient ckLinear relation with displacement of the metagrid node:
wherein A is a coefficient matrix,
is a vector of displacement amounts of the mirror surface nodes,
is a rigid bodyAnd fitting coefficient vectors of the displacement and the loop Zernike deformation.
3. The method of claim 2, wherein importing the pre-finite element analysis processing file into the finite element model for specular surface optimization comprises:
taking the target function of the mirror surface shape as the finite element analysis preprocessing file, and calculating the mirror surface shape root mean square value RMS and the peak-to-valley value PV of the target function of the mirror surface shape:
and establishing a nonlinear relation between the RMS value and the PV value and residual aberration displacement values of all nodes of the mirror surface, thereby establishing a nonlinear relation between the RMS value and the peak-valley value PV and position quantities of all nodes of the mirror surface.
4. The method of claim 3, wherein the pre-processing file for finite element analysis is imported into the finite element model for opto-mechanical integration analysis by a multi-point constraint.
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