CN110941926A - Free-form surface metal reflector and design method thereof - Google Patents
Free-form surface metal reflector and design method thereof Download PDFInfo
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Abstract
The invention discloses a free-form surface metal reflector and a design method thereof. The invention greatly improves the surface shape precision of the reflector, and has simple structure and easy processing. The reflector comprises a cylindrical reflector main body and at least three ear seats uniformly arranged on the excircle of the cylindrical reflector main body along the circumferential direction; the diameter of the excircle of the cylindrical reflector main body is phi D; the front end surface of the cylindrical reflector body is a curved surface; each ear seat is provided with a screw mounting hole, and the screw mounting hole on each ear seat is positioned on a reference circle PhiD taking the center of the cylindrical reflector body as the center of circlemidThe above step (1); the front end face and the rear end face of each ear seat are respectively provided with a flexible groove which is integrally arc-shaped, and the arc center line of the flexible groove on each ear seat is positioned on a reference circle phi D which takes the center of the cylindrical reflector body as the center of circleinThe above.
Description
Technical Field
The invention belongs to the field of optical precision machinery, and particularly relates to a free-form surface metal reflector and a design method thereof.
Background
With the continuous appearance of ultra-precision machine tools, the advantages of the metal reflector on the processing cost and the development period are more and more obvious, and meanwhile, the metal reflector is widely applied to modern optical instruments and scientific research equipment.
The metal reflector is fixed in an optical system, and a reflector flange is mostly adopted to be connected with a mirror frame, and the connection method comprises two methods:
1. bonding: the bonding is characterized in that the reflector flange is not stressed by other compressive stress, the bonding surface can generate a part of stress after the bonding agent is cured, the influence of the proper bonding agent on the shape precision of the reflector surface is small, and the bonding reliability is greatly reduced along with the time for some application occasions such as space radiation, cold and hot impact and the like;
2. pre-tightening the bolts: compared with bonding, the reflector fixed by the bolts is high in reliability and impact resistance in a harsh environment, a certain bolt pretightening force needs to be borne on a metal flange, the pretightening force can cause micro deformation of the mirror surface, the PV value (which is one of indexes for evaluating the surface shape of the mirror surface and is the difference between the maximum peak and the trough of the surface shape of the mirror) of the reflector of a precision optical instrument after being mounted is generally required to be 50-100 nanometers, the RMS value (which is the root mean square value of the surface shape of the mirror) is required to be below 20-16 nanometers, and the structural form of the reflector and the pretightening force of a mounting screw have great influence on the surface shape of the reflector in actual mounting. For example, a metallic reflector of the form shown in FIG. 1, after screw pre-tightening, has a design specification PV 60nm, and a practical installed mirror surface PV value of 300nm, far exceeding the design specification.
Therefore, under the condition of certain pretightening force, the structural form of the reflector has obvious influence on the surface shape of the mirror surface. Therefore, it is very necessary to find a structure form capable of ensuring the surface shape accuracy of the metal reflector after the bolt is pre-tightened.
Disclosure of Invention
The invention designs a free-form surface metal reflector and a design method thereof, aiming at solving the problems that the shape precision of the reflector is seriously reduced and even the optical design requirement cannot be met after the existing metal reflector is pre-tightened by a screw in the installation process.
The technical scheme of the invention is as follows:
the invention provides a free-form surface metal reflector, which comprises a cylindrical reflector main body and at least three lug seats uniformly arranged on the excircle of the cylindrical reflector main body along the circumferential direction; the diameter of the excircle of the cylindrical reflector main body is phi D; the front end surface of the cylindrical reflector body is a curved surface;
each ear seat is provided with a screw mounting hole, and the screw mounting hole on each ear seat is positioned on a reference circle PhiD taking the center of the cylindrical reflector body as the center of circlemidThe above step (1);
the front end face and the rear end face of each ear seat are respectively provided with a flexible groove which is integrally arc-shaped, and the arc center line of the flexible groove on each ear seat is positioned on a reference circle phi D which takes the center of the cylindrical reflector body as the center of circleinThe above step (1);
wherein, Φ Dmid＞ΦDin＞ΦD；1.03φD≤φDin≤1.05φD。
Further, the rear end face of each ear seat is flush with the rear end face of the cylindrical reflector body.
Further, the flexible groove has a circular arc-shaped cross section.
Furthermore, the positions where the left side surface and the right side surface of each ear seat are connected with the outer circle surface of the cylindrical reflector main body are arc-shaped chamfers.
Further, the key design parameters of the cylindrical reflector body and the ear mount respectively satisfy the following conditions:
the central thickness of the cylindrical reflector main body is h, and the value range of h is as follows:
the thickness of the ear seat is h1，h1The value ranges are as follows:
the distance between the rear end face of the ear seat and the arc center of the flexible groove on one side of the rear end face of the ear seat is h2；h2The value ranges are as follows:
the distance between the arc center of the flexible groove on one side of the rear end face of the ear seat and the front end face of the ear seat is h3；h3The following relation is satisfied: h is3＝h1-h2；
The radius of the arc of the cross section of the flexible groove is R1，R1The value ranges are as follows:
the radius of the circular arc chamfer is R2，R2The following relation is satisfied:
the diameter phi D of a reference circle where the screw mounting hole on each ear seat ismidThe value ranges are as follows: phi Din+2(R1+φH)≤φDmid≤φDin+2(R1+1.5φH)；
The maximum outer diameter of the outermost edge of the ear seat from the center of the cylindrical reflector body is phi Dout，φDoutThe value ranges are as follows: phi Dmid+2φH≤φDout≤φDmid+3 φ H, where φ H is the diameter of the screw mounting hole.
Furthermore, the cylindrical reflector body and at least three ear seats are integrally processed and formed.
Based on the description of the free-form surface metal reflector structure, a design method of the free-form surface metal reflector is introduced, and the method is specifically implemented by the following steps:
step 1: taking key design parameters of a cylindrical reflector main body and an ear seat as design variables, and establishing an initial three-dimensional model of a free-form surface metal reflector in finite element software;
the key design parameters comprise the central thickness h and the ear seat thickness h of the cylindrical reflector body1The distance h between the rear end face of the ear seat and the arc center of the flexible groove on one side of the rear end face of the ear seat2The distance h between the arc center of the flexible groove at one side of the rear end face of the ear seat and the front end face of the ear seat3Radius R of section arc of flexible groove1Radius R of circular arc chamfer2The diameter phi D of the reference circle where the screw mounting hole on each ear seat is locatedmidThe maximum outer diameter of the outermost edge of the ear seat from the center of the cylindrical reflector body is phi DoutThe arc center line of the flexible groove on each ear seat is positioned at the reference circle diameter phi D which takes the center of the cylindrical reflector body as the center of a circlein；
Step 2: setting a rational parameter value range of each key design parameter combination, wherein the parameter value range is set to meet the requirement that the appearance of the three-dimensional model of the free-form surface metal reflector is not changed;
1.03φD≤φDin≤1.05φD；
h3＝h1-h2；
φDin+2(R1+φH)≤φDmid≤φDin+2(R1+1.5φH)；
φDmid+2φH≤φDout≤φDmid+3φH；
and step 3: setting a meshing principle, and meshing the initial three-dimensional model of the free-form surface metal reflector;
the mesh division principle comprises:
A. dividing grids in a hexahedron 8-node unit mode;
B. equally dividing the initial three-dimensional model according to a connecting line between the circle center of the screw mounting hole on each ear seat and the center of the cylindrical reflector main body, and ensuring that the grid structure characteristics and the number of each equally divided part are consistent;
C. local grid thinning is carried out around the screw mounting hole on each ear seat, so that the diameter range of the screw mounting hole on each ear seat is equal to the diameter of the bolt head of the coupling reflector;
D. setting boundary conditions for the nodes of the thinned local grids around the screw mounting hole on each lug seat according to bolt connection;
E. applying load to each grid node according to the actual use environment of the free-form surface metal reflector;
and 4, step 4: loading a genetic algorithm into finite element software, and establishing a relation with the initial three-dimensional model of the free-form surface metal reflector after grid division;
and 5: and inputting the PV value and the RMS value of the actually required free-form surface metal reflector and the excircle diameter phi D of the cylindrical reflector body into finite element software so as to obtain the actually required free-form surface metal reflector three-dimensional model.
The invention has the advantages that:
1. compared with the disc type flange connection structure of the traditional reflector, the metal reflector with the ear seat and double-side flexible grooves connection structure can reduce the mirror surface deformation of the reflector during installation from hundreds of nanometers to tens of nanometers, greatly improves the surface shape precision of the reflector, and has simple structure and easy processing.
2. The invention can parameterize the three-dimensional characteristics of the metal reflector by using finite element software, fix the finite element meshing mode, take the reflector surface shape result as a target function, and realize the optimization search of the structural characteristic parameters of the reflector by using a genetic algorithm and finite element analysis, thereby greatly reducing the workload of engineering technicians.
Drawings
Fig. 1 is a structural view of a conventional metal mirror.
Fig. 2 is a view showing a structure of an ear seat type metal reflector.
Fig. 3 is a view showing a structure of a metal mirror in which an ear mount and a single-sided flexible groove are combined.
Fig. 4 is a structural view of a metal reflector in which an ear mount + double-sided flexible slot are combined.
Fig. 5 is a cross-sectional view of a metal reflector structure combining an ear mount + a double-sided flex groove.
FIG. 6 is a cross-sectional view of a metal reflector structure incorporating an ear mount + double-sided flex grooves with key design parameters;
FIG. 7 is a diagram of a metal mirror structure with an ear mount + double sided flex groove combination having key design parameters;
fig. 8 is a model diagram of a metal reflector with a finite element mesh-divided ear mount + double-sided flex grooves combined.
The reference numbers are as follows:
1-cylindrical reflector body, 2-ear seat, 3-screw mounting hole and 4-flexible groove.
Detailed Description
To make the objects, advantages and features of the present invention more apparent, a free-form metallic mirror and a method for designing the same are provided in the following description with reference to the accompanying drawings and specific embodiments. As will be described in further detail. Advantages and features of the present invention will become apparent from the following description and from the claims. It should be noted that: the drawings are in simplified form and are not to precise scale, the intention being solely for the convenience and clarity of illustrating embodiments of the invention; secondly, the structures shown in the drawings are often part of the actual structure; again, the drawings may require different emphasis, sometimes on different proportions.
As shown in fig. 4 and 5, the present embodiment provides a free-form surface metal reflector, which includes a cylindrical reflector body 1 and at least three ear sockets 2 (the number of the ear sockets in the present embodiment is 3, and the cylindrical reflector body and the three ear sockets are integrally formed) uniformly arranged on the outer circle of the cylindrical reflector body 1 along the circumferential direction; the diameter of the excircle of the cylindrical reflector body 1 is phi D; the front end surface of the cylindrical reflector body 1 is a curved surface;
each ear seat 2 is provided with a screw mounting hole 3, and the screw mounting hole 3 on each ear seat 2 is positioned on a reference circle PhiD which takes the center of the cylindrical reflector body 1 as the center of a circlemidThe above step (1);
the front end face and the rear end face of each ear seat 2 are respectively provided with a flexible groove 4 (the cross section of each flexible groove is also arc-shaped), and the arc center line of the flexible groove 4 on each ear seat is positioned on a reference circle phi D which takes the center of the cylindrical reflector body 1 as the center of circleinThe above step (1); wherein, Φ Dmid＞ΦDin＞ΦD；。
In order to further increase the surface shape accuracy of the reflector with the structure, it is necessary to ensure that the rear end surface of each ear seat 2 is flush with the rear end surface of the cylindrical reflector body 1, and the positions where the left and right side surfaces of each ear seat 2 are connected with the outer circular surface of the cylindrical reflector body 1 are arc chamfers.
In addition, the key design parameters of the cylindrical mirror body and the ear mount described above satisfy the following conditions, as shown in figures 6 and 7,
φDinthe value ranges are as follows: 1.03 PhiD is less than or equal to PhiDin≤1.05φD
The central thickness of the cylindrical reflector body is h, and the value range of h is as follows:
the thickness of the ear seat is h1，h1The value ranges are as follows:
the distance between the rear end surface of the ear seat and the arc center of the flexible groove at one side of the rear end surface of the ear seat is h2；h2The value ranges are as follows:
the distance between the rear end surface of the ear seat and the arc center of the flexible groove at one side of the front end surface of the ear seat is h3；h3The following relation is satisfied: h is3＝h1-h2；
The radius of the arc of the cross section of the flexible groove is R1，R1The value ranges are as follows:
the radius of the circular arc chamfer is R2，R2The following relation is satisfied:
the diameter phi D of a reference circle where the screw mounting hole on each ear seat ismidThe value ranges are as follows: phi Din+2(R1+φH)≤φDmid≤φDin+2(R1+1.5φH)；
The maximum outer diameter of the outermost edge of the ear seat from the center of the cylindrical reflector body is phi Dout，φDoutThe value ranges are as follows: phi Dmid+2φH≤φDout≤φDmid+3 φ H, where φ H is the diameter of the screw mounting hole.
In order to verify the accuracy of the surface shape of the reflector structure provided by the embodiment, the invention further provides the following comparative test, wherein the specific comparative test process is as follows:
determining the structural form of a free-form surface metal reflector
Preparing free-form surface metal reflectors with different structural forms; a conventional flange-type free-form surface metal reflector structure as shown in fig. 1; an ear mount type free-form surface metal reflector structure as shown in fig. 2; the ear seat type + single-sided flexible groove type free-form surface metal reflector structure shown in fig. 3; an ear seat + double-sided flexible groove type free-form surface metal reflector structure (structure of the present embodiment) as shown in fig. 4; the points to be explained are: the four reflector structures have the same caliber phi 132 mm; the thickness of the center is equal to 20mm, and the bolt pretightening force is equal;
secondly, performing surface shape analysis on the free-form surface metal reflector screws in various forms after being pre-tightened; the points to be explained are: the four mirror configurations described above need to have the following same characteristics when performing the above steps: the same caliber; the center thickness of the same reflector and the pretightening force of the same bolt are same;
comparing the surface shapes of the 4 metal reflectors after the bolts are pre-tightened through finite element analysis, wherein the results are shown in table 1, and the comparison shows that the conventional metal reflector structure adopts the bolt to fix the reflector surface shapes, the PV and RMS values are the highest, the surface shape precision is very low, and the design requirements can not be met under most conditions;
and adopt ear seat formula + two-sided flexible slot type metal reflector structure, it adopts the PV and RMS value of bolt fastening back face shape to be minimum, and the shape of face precision after the reflector passes through the bolt fastening is higher, therefore, this kind of structural style can effectively improve the shape of face precision after the reflector is fixed.
TABLE 1
In order to make the ear seat and the double-sided flexible groove type free-form surface metal reflector with different specifications and surface shape precision requirements more convenient to process and manufacture, the invention also provides a design method of the reflector, the core of the method is carried out based on finite element software and a genetic algorithm, and the specific implementation steps are as follows:
step 1: taking key design parameters of a cylindrical reflector main body and an ear seat as design variables, and establishing an initial three-dimensional model of a free-form surface metal reflector in finite element software;
the key design parameters comprise the central thickness h and the ear seat thickness h of the cylindrical reflector body1The distance h between the rear end face of the ear seat and the arc center of the flexible groove on one side of the rear end face of the ear seat2The distance h between the arc center of the flexible groove at one side of the rear end face of the ear seat and the front end face of the ear seat3Radius R of section arc of flexible groove1Radius R of circular arc chamfer2The diameter phi D of the reference circle where the screw mounting hole on each ear seat is locatedmidThe maximum outer diameter of the outermost edge of the ear seat from the center of the cylindrical reflector body is phi DoutThe arc center line of the flexible groove on each ear seat is positioned at the reference circle diameter phi D which takes the center of the cylindrical reflector body as the center of a circlein；
Step 2: setting a rational parameter value range of each key design parameter combination, wherein the parameter value range is set to meet the requirement that the appearance of the three-dimensional model of the free-form surface metal reflector is not changed;
1.03φD≤φDin≤1.05φD；
h3＝h1-h2；
φDin+2(R1+φH)≤φDmid≤φDin+2(R1+1.5φH)；
φDmid+2φH≤φDout≤φDmid+3φH；
Φ D is generally given a fixed value by optical design, Φ H is generally slightly larger than the nominal diameter of the mounting screw;
the parameter value range is set to meet the requirement that the three-dimensional characteristics of the reflector are not changed;
and step 3: setting a meshing principle, and meshing the initial three-dimensional model of the free-form surface metal reflector;
the mesh division principle comprises:
A. the mesh is divided in a hexahedral 8-node unit manner, as shown in fig. 8;
B. equally dividing the initial three-dimensional model according to a connecting line between the circle center of the screw mounting hole on each ear seat and the center of the cylindrical reflector main body, and ensuring that the grid structure characteristics and the number of each equally divided part are consistent;
C. local grid thinning is carried out around the screw mounting hole on each ear seat, so that the diameter range of the screw mounting hole on each ear seat is equal to the diameter of the bolt head of the coupling reflector;
D. setting boundary conditions for the nodes of the thinned local grids around the screw mounting hole on each lug seat according to bolt connection;
E. applying load to each grid node according to the actual use environment of the free-form surface metal reflector;
and 4, step 4: loading a genetic algorithm into finite element software, and establishing a relation with the initial three-dimensional model of the free-form surface metal reflector after grid division;
and 5: and inputting the PV value and the RMS value of the actually required free-form surface metal reflector and the excircle diameter phi D of the cylindrical reflector body into finite element software so as to obtain the actually required free-form surface metal reflector three-dimensional model.
The mirror structure manufactured by the above design method is subjected to surface shape accuracy analysis, and compared with the mirror structure not manufactured by the above design method in surface shape accuracy, as shown in table 2, it can be seen that the mirror surface shape accuracy of the mirror structure designed by the above method is further improved.
TABLE 2
| PV/nm | RMS/nm | |
| Without the above design method | 17.7 | 3.9 |
| By adopting the design method | 14.2 | 2.7 |
Claims (7)
1. A free-form surface metal reflector, comprising: the cylindrical reflector comprises a cylindrical reflector body and at least three ear seats which are uniformly arranged on the excircle of the cylindrical reflector body along the circumferential direction; the diameter of the excircle of the cylindrical reflector main body is phi D; the front end surface of the cylindrical reflector body is a curved surface;
each ear seat is provided with a screw mounting hole, and the screw mounting hole on each ear seat is positioned on a reference circle PhiD taking the center of the cylindrical reflector body as the center of circlemidThe above step (1);
the front end face and the rear end face of each ear seat are respectively provided with a flexible groove which is integrally arc-shaped, and the arc center line of the flexible groove on each ear seat is positioned on a reference circle phi D which takes the center of the cylindrical reflector body as the center of circleinThe above step (1);
wherein, Φ Dmid＞ΦDin＞ΦD；1.03φD≤φDin≤1.05φD。
2. The free-form metallic reflector of claim 1, wherein: the rear end face of each ear seat is flush with the rear end face of the cylindrical reflector body.
3. The free-form metallic reflector of claim 2, wherein: the section of the flexible groove is arc-shaped.
4. The free-form metallic mirror of claim 3, wherein: the left side surface and the right side surface of each ear seat are connected with the outer circle surface of the cylindrical reflector body through arc-shaped chamfers.
5. The free-form metallic mirror of claim 4, wherein: the key design parameters of the cylindrical reflector main body and the ear seat respectively meet the following conditions:
the central thickness of the cylindrical reflector main body is h, and the value range of h is as follows:
the thickness of the ear seat is h1，h1The value ranges are as follows:
the distance between the rear end face of the ear seat and the arc center of the flexible groove on one side of the rear end face of the ear seat is h2；h2The value ranges are as follows:
the distance between the arc center of the flexible groove on one side of the rear end face of the ear seat and the front end face of the ear seat is h3；h3The following relation is satisfied: h is3＝h1-h2；
The radius of the arc of the cross section of the flexible groove is R1，R1The value ranges are as follows:
the radius of the circular arc chamfer is R2，R2The following relation is satisfied:
the diameter phi D of a reference circle where the screw mounting hole on each ear seat ismidThe value ranges are as follows: phi Din+2(R1+φH)≤φDmid≤φDin+2(R1+1.5φH)；
The maximum outer diameter of the outermost edge of the ear seat from the center of the cylindrical reflector body is phi Dout，φDoutThe value ranges are as follows: phi Dmid+2φH≤φDout≤φDmid+3 φ H, where φ H is the diameter of the screw mounting hole.
6. The free-form metallic reflector of claim 5, wherein: the method is characterized in that: the cylindrical reflector body and the at least three ear seats are integrally processed and formed.
7. A design method of a free-form surface metal reflector is characterized by comprising the following steps:
step 1: taking key design parameters of a cylindrical reflector main body and an ear seat as design variables, and establishing an initial three-dimensional model of a free-form surface metal reflector in finite element software;
the key design parameters comprise the central thickness h and the ear seat thickness h of the cylindrical reflector body1The distance h between the rear end face of the ear seat and the arc center of the flexible groove on one side of the rear end face of the ear seat2The distance h between the arc center of the flexible groove at one side of the rear end face of the ear seat and the front end face of the ear seat3Radius R of section arc of flexible groove1Radius R of circular arc chamfer2The screw mounting hole on each ear seat is divided intoDiameter of circle of degree phi DmidThe maximum outer diameter of the outermost edge of the ear seat from the center of the cylindrical reflector body is phi DoutThe arc center line of the flexible groove on each ear seat is positioned at the reference circle diameter phi D which takes the center of the cylindrical reflector body as the center of a circlein；
Step 2: setting a rational parameter value range of each key design parameter combination, wherein the parameter value range is set to meet the requirement that the appearance of the three-dimensional model of the free-form surface metal reflector is not changed;
1.03φD≤φDin≤1.05φD；
h3＝h1-h2；
φDin+2(R1+φH)≤φDmid≤φDin+2(R1+1.5φH)；
φDmid+2φH≤φDout≤φDmid+3φH；
and step 3: setting a meshing principle, and meshing the initial three-dimensional model of the free-form surface metal reflector;
the mesh division principle comprises:
A. dividing grids in a hexahedron 8-node unit mode;
B. equally dividing the initial three-dimensional model according to a connecting line between the circle center of the screw mounting hole on each ear seat and the center of the cylindrical reflector main body, and ensuring that the grid structure characteristics and the number of each equally divided part are consistent;
C. local grid thinning is carried out around the screw mounting hole on each ear seat, so that the diameter range of the screw mounting hole on each ear seat is equal to the diameter of the bolt head of the coupling reflector;
D. setting boundary conditions for the nodes of the thinned local grids around the screw mounting hole on each lug seat according to bolt connection;
E. applying load to each grid node according to the actual use environment of the free-form surface metal reflector;
and 4, step 4: loading a genetic algorithm into finite element software, and establishing a relation with the initial three-dimensional model of the free-form surface metal reflector after grid division;
and 5: and inputting the PV value and the RMS value of the actually required free-form surface metal reflector and the excircle diameter phi D of the cylindrical reflector body into finite element software so as to obtain the actually required free-form surface metal reflector three-dimensional model.
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