[go: up one dir, main page]
More Web Proxy on the site http://driver.im/

WO2021128844A1 - 一种大口径非球面镜数控铣磨成形抛光方法及装置 - Google Patents

一种大口径非球面镜数控铣磨成形抛光方法及装置 Download PDF

Info

Publication number
WO2021128844A1
WO2021128844A1 PCT/CN2020/105663 CN2020105663W WO2021128844A1 WO 2021128844 A1 WO2021128844 A1 WO 2021128844A1 CN 2020105663 W CN2020105663 W CN 2020105663W WO 2021128844 A1 WO2021128844 A1 WO 2021128844A1
Authority
WO
WIPO (PCT)
Prior art keywords
axis
diameter
ring
aspheric
annular
Prior art date
Application number
PCT/CN2020/105663
Other languages
English (en)
French (fr)
Inventor
郭培基
陈曦
戴卓成
朱永翔
李晨超
Original Assignee
苏州大学
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by 苏州大学 filed Critical 苏州大学
Priority to US17/440,744 priority Critical patent/US12019424B2/en
Publication of WO2021128844A1 publication Critical patent/WO2021128844A1/zh

Links

Images

Classifications

    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B24—GRINDING; POLISHING
    • B24B—MACHINES, DEVICES, OR PROCESSES FOR GRINDING OR POLISHING; DRESSING OR CONDITIONING OF ABRADING SURFACES; FEEDING OF GRINDING, POLISHING, OR LAPPING AGENTS
    • B24B13/00—Machines or devices designed for grinding or polishing optical surfaces on lenses or surfaces of similar shape on other work; Accessories therefor
    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B19/00—Programme-control systems
    • G05B19/02—Programme-control systems electric
    • G05B19/18—Numerical control [NC], i.e. automatically operating machines, in particular machine tools, e.g. in a manufacturing environment, so as to execute positioning, movement or co-ordinated operations by means of programme data in numerical form
    • G05B19/19—Numerical control [NC], i.e. automatically operating machines, in particular machine tools, e.g. in a manufacturing environment, so as to execute positioning, movement or co-ordinated operations by means of programme data in numerical form characterised by positioning or contouring control systems, e.g. to control position from one programmed point to another or to control movement along a programmed continuous path
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B24—GRINDING; POLISHING
    • B24B—MACHINES, DEVICES, OR PROCESSES FOR GRINDING OR POLISHING; DRESSING OR CONDITIONING OF ABRADING SURFACES; FEEDING OF GRINDING, POLISHING, OR LAPPING AGENTS
    • B24B13/00—Machines or devices designed for grinding or polishing optical surfaces on lenses or surfaces of similar shape on other work; Accessories therefor
    • B24B13/01—Specific tools, e.g. bowl-like; Production, dressing or fastening of these tools
    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B15/00—Systems controlled by a computer
    • G05B15/02—Systems controlled by a computer electric
    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B2219/00—Program-control systems
    • G05B2219/30—Nc systems
    • G05B2219/45—Nc applications
    • G05B2219/45145—Milling
    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B2219/00—Program-control systems
    • G05B2219/30—Nc systems
    • G05B2219/45—Nc applications
    • G05B2219/45157—Grind optical lens

Definitions

  • the invention belongs to the field of optical processing, and relates to a numerical control processing method for a large-diameter aspheric optical element.
  • Aspheric optics can well correct a variety of aberrations in the optical system, improve the imaging quality, and improve the system's discrimination ability.
  • the aspheric mirror is a very important optical element in the optical system. It can replace multiple spherical elements with one or several aspheric elements, thereby simplifying the structure of the instrument, simplifying the system structure, shortening the length, and effectively reducing the weight of the instrument.
  • the design of the spherical optical system can greatly simplify the calculation method.
  • the processing methods mainly include: CNC grinding and polishing technology, single-point diamond turning technology, ion beam processing, compression molding, etc.
  • Different processing methods have their own advantages. Disadvantages.
  • CNC grinding and polishing technology usually the side of the aspheric optical element closest to the spherical surface is processed first, then the spherical surface is ground according to this surface, and finally the aspheric surface that meets the requirements is processed by grinding and polishing; but This method takes too long and the production efficiency is low.
  • Single-point diamond turning technology is mainly used for the cutting of typical parts of non-ferrous metal materials such as duralumin, brass, oxygen-free copper, etc.
  • Tool offset is prone to occur during the cutting process, and online inspection equipment is often required to obtain ideal non-ferrous materials. Spherical accuracy. Although ion beam processing can obtain an aspheric surface with better precision, the processing equipment and cost are relatively high, and the processing equipment is not universal, which limits its popularization and use. Molding technology is mainly used to prepare micro and small aspheric lenses in batches, and is not suitable for large-aperture and high-precision aspheric lenses. Therefore, the high-efficiency and low-cost processing technology of large-aperture aspheric mirrors is still under continuous exploration and research.
  • the roughing method is first performed to obtain the closest spherical surface, and then the numerical control machine tool is used to directly mill and finish the aspheric surface in accordance with the aspheric surface equation. Because this method uses the Fan Cheng method to open the rough to quickly remove a large amount of material, usually only a single CNC finishing can be used to change the closest spherical surface to an aspherical surface. It has high processing efficiency and good economics and has gradually been widely used. However, when changing the aspheric surface in finishing machining, the excessively large tool path pitch will lead to obvious undercutting and poor surface roughness.
  • the pitch of the tool path is usually less than 0.2mm.
  • the total length of the tool path will be very large, and the processing time will be longer; especially when the meter-level aspheric surface is processed, it is affected by tool wear. It is difficult for the tool to follow the complete tool path, so the tool has to be changed. After the tool change, the tool will usually leave traces on the aspheric surface. And because the tool parameters of different tools are different, it will inevitably cause the source of the error of the aspheric surface. Complexity brings great difficulty to the later compensation processing and seriously affects the processing accuracy.
  • the present invention proposes a large-diameter aspheric mirror numerically controlled milling and forming method.
  • the aspheric mirror is concave and the generatrix equation is denoted as f1.
  • the diameter of the spherical mirror is D, and the positioning accuracy of the CNC machine tool used for milling is ⁇ .
  • the aspheric surface of the aspheric mirror is discretized into a series of rings with different radii, the rings are equally spaced and the total number is N, and the width of the rings is dx, use a ring grinding tool with a diameter larger than the half diameter of the aspheric surface to machine each ring in turn;
  • the working principle of the above scheme is that according to the positioning accuracy of the machine tool, the aspheric surface is discretized into a series of annular belts of different radii, and each annular belt is formed in turn by the annular grinding wheel tool, and the aspheric surface is enveloped by the numerous annular belts.
  • the number of endless belts is much smaller than the number of traditional machining pitches, and because of this solution, the increment dx in the x-direction of the tool path of the different endless belts is limited by the positioning accuracy of the machine tool, that is, the number of endless belts is minimized, and the The maximum residual error of the different belts does not exceed the machine positioning accuracy ⁇ .
  • the above-mentioned processing method can process concave rotationally symmetric curved surfaces with monotonically increasing properties, including concave quadratic aspheric surfaces and concave high-order aspheric surfaces.
  • the CNC machine tool has at least two translational motions of X axis and Z axis Axis, and the two rotation axes of B axis and C axis.
  • the B axis is the rotation axis around the Y axis
  • the C axis is the rotation axis around the Z axis
  • the rotation axis of the CNC machine tool turntable is located on the C axis
  • the spindle of the CNC machine tool Located on the Z axis;
  • the ring cutter is T D , T D >D/2; the convex round chamfer radius between the outer diameter and the inner diameter of the ring cutter is r 0 ; the ring cutter The thickness between the outer diameter and the inner diameter is 2r 0 ; the origin of the workpiece coordinate system is established at the apex of the starting spherical surface;
  • the annular tool is a hollow grinding wheel tool, including: electroplated diamond grinding wheel, bronze adhesive grinding wheel, and resin grinding wheel;
  • the dx is jointly determined by the Nth annulus, the N-1th annulus, the positioning accuracy is denoted as ⁇ , and the generatrix equation f1 of the aspheric mirror:
  • the generatrix equation of the N-1th ring zone is denoted as f2, the generatrix equation of the Nth ring zone is denoted as f3, the intersection point of f1 and f3 is denoted as (x1, z1), the intersection point of f1 and f2 is denoted as (x2, z2), f2
  • the ring tool on the CNC machine tool is processed sequentially from the first ring to the Nth ring.
  • the C axis rotates continuously and uniformly, and the X axis coordinate of the tool center in the workpiece coordinate system:
  • * is the multiplication calculation symbol
  • sqrt is the open radical calculation symbol
  • sin, cos, and asin are the sine, cosine, and arc sine calculation symbols respectively.
  • the relational expressions of the tool position points X T and Z T are derived based on the basic principle of processing the spherical surface by the Fan Cheng method.
  • a numerical control polishing method for large-diameter aspheric mirrors is also provided.
  • the above-mentioned annular cutter is replaced with a circular polishing disc, and the circular polishing disc is mounted on the spindle of the numerical control machine tool;
  • the outer diameter of the circular polishing disc is T D
  • the convex round chamfer radius between the outer diameter and the inner diameter of the annular polishing disc is r 0 ; T D >D/2; the origin of the workpiece coordinate system is established at the apex of the initial spherical surface;
  • the annular polishing disc includes: Polyurethane polishing pad, ring-shaped flexible polishing skin, ring-shaped airbag;
  • the ring-shaped polishing disk on the CNC machine tool is processed from the first ring belt to the N-th ring belt, and the ring polishing disk and the large-diameter aspheric mirror are sprayed during the processing.
  • polishing powder solution According to the hardness of the material being polished, the polishing powder solution is commonly selected as aluminum oxide, cerium oxide, diamond powder, and white corundum powder. Since the contact trajectory between the polishing disc and the surface of the workpiece is an elliptical arc. After the workpiece is rotated, the envelope of the arc is just a spherical surface, and each ring-shaped spherical surface constitutes an aspherical surface. Therefore, this polishing method can be used for aspherical surfaces. polishing.
  • the aforementioned large-diameter aspheric mirror numerically controlled milling and forming method can be used to manufacture a large-diameter aspheric mirror numerically controlled milling and forming device.
  • the aforementioned large-diameter aspheric mirror numerical control polishing method can be used to manufacture a large-diameter aspheric mirror numerical control milling and forming device.
  • the present invention has the following advantages compared with the prior art:
  • the diameter of the tool used in processing is larger than the half diameter of the aspheric surface.
  • the contact between the tool and the surface of the workpiece is an endless belt, while the contact between the traditional processing tool and the surface of the workpiece is a point. Therefore, the service life of the large ring tool is far greater when processing large-diameter aspheric surfaces. Tool life in traditional machining methods;
  • the processing efficiency is greatly improved compared with traditional processing, because the dx processed by this method is much larger than 0.2mm.
  • Figure 1 Schematic diagram of the radial section of the ring cutter
  • Figure 2 Schematic diagram of an aspherical ring with discrete and equal intervals
  • Figure 3 Schematic diagram of the position of the ring tool knife point
  • Figure 4 Schematic diagram of solving the ring width dx
  • Figure 5 Schematic diagram of a series of spherical annulus enveloped aspheric surfaces
  • Figure 6 Schematic diagram of an example of an ordinal residual relationship of annulus
  • Figure 7a The front view of the principle of enveloping grinding of the trajectory of the rotary aspheric surface
  • Figure 7b An oblique view of the principle of enveloping grinding of the trajectory of the revolving aspheric surface
  • Figure 8 Schematic diagram of the relationship between the rectangular off-axis aspheric mirror and its parent mirror
  • Figure 9 A schematic diagram of the relationship between a circular off-axis aspheric mirror and its parent mirror
  • Figure 10 Schematic diagram of the off-axis aspheric mirror and its mother mirror generatrix
  • R 0 is the aspheric surface
  • k is the quadratic cone coefficient
  • x is the independent variable on the abscissa
  • z is the ordinate corresponding to the x coordinate
  • the positioning accuracy of the CNC machine tool used for milling is ⁇
  • the processing steps of the aspheric mirror are as follows :
  • the CNC machine tool has at least two translational motions of X axis and Z axis Axis, and the two rotation axes of B axis and C axis.
  • the B axis is the rotation axis around the Y axis
  • the C axis is the rotation axis around the Z axis
  • the rotation axis of the CNC machine tool turntable is located on the C axis
  • the spindle of the CNC machine tool Located on the Z axis;
  • the ring cutter is T D
  • the convex chamfer radius between the outer diameter and the inner diameter of the ring cutter is r 0
  • the difference between the outer diameter and the inner diameter of the ring cutter The thickness is 2r 0
  • the origin of the workpiece coordinate system is established at the apex of the starting spherical surface
  • the ring tool is a hollow grinding wheel tool, including: electroplated diamond grinding wheel, bronze adhesive grinding wheel, Resin grinding wheel;
  • N takes an integer
  • the width of any annular band dx D/N
  • the dx is jointly determined by the Nth annulus, the N-1th annulus, the positioning accuracy is denoted as ⁇ , and the generatrix equation f1 of the aspheric mirror:
  • the generatrix equation of the N-1th ring zone is denoted as f2, the generatrix equation of the Nth ring zone is denoted as f3, the intersection point of f1 and f3 is denoted as (x1, z1), the intersection point of f1 and f2 is denoted as (x2, z2), f2
  • the ring tool on the CNC machine tool is processed from the first ring belt to the Nth ring belt in sequence, and when the nth ring belt is processed,
  • the C-axis rotates continuously and uniformly, as shown in Figure 3.
  • the X-axis and Z-axis coordinates of the tool center in the workpiece coordinate system are deduced as follows:
  • the convex round chamfer area of the ring-shaped grinding wheel tool is usually attached with abrasive materials such as emery, which is used as a cutting edge to grind the glass material that comes into contact with it.
  • abrasive materials such as emery, which is used as a cutting edge to grind the glass material that comes into contact with it.
  • the cutting edge of the ring grinding wheel tool is always on the center axis of the workpiece rotation.
  • the entire machining process is from the first ring to the Nth ring.
  • the performance is as follows: the grinding wheel moves up and down along the central axis of rotation, and swings at the corresponding B angle at different positions. Even if the tool center X T is different when processing different belts, the cutting edge of the tool never deviates from the center axis of the workpiece rotation.
  • * is the multiplication calculation symbol
  • sqrt is the open radical calculation symbol
  • sin, cos, and asin are the sine, cosine, and arc sine calculation symbols respectively.
  • the root formula can be used to obtain:
  • the above scheme discretizes the aspheric surface into a series of rings with different radii.
  • the ring-shaped grinding wheel cutter is used to sequentially form R 1 , R 2 , R 3 ... ring belts, which are enveloped by a large number of spherical rings.
  • Aspherical The number of endless belts is much smaller than the number of traditional machining pitches, and because of this solution, the increment dx in the x-direction of the tool path of the different endless belts is limited by the positioning accuracy of the machine tool, that is, the number of endless belts is minimized.
  • the shaded part shows the residual error between the different annulus and the actual aspheric surface. As long as the width of the annulus is reasonably controlled, the maximum residual error of the different annulus can be controlled within the positioning accuracy of the machine tool.
  • H 1 200.2, starting spherical surface with a caliber of 1000;
  • n R n B unit: degree X T Z T 1 3000.14128305847 5.17200629931126 269.349606399328 24.3800543493219 2 3000.56509231960 5.17127257598519 269.349855076213 24.3766502520008 3 3001.27130809688 5.17005039701697 269.350269204175 24.3711157227581 4 3002.25973110051 5.16834080055154 269.350848283963 24.3636590059685 5 3003.53008271821 5.16614523656417 269.351591618667 24.3545712344803 6 3005.08200540723 5.16346556345177 269.352498315739 24.3442260215403 7 3006.91506319597 5.16030404367734 269.353567289577 24.3330789392348 8 3009.02874229390 5.15666333848735 269.354797264659
  • the residual error curve from the first to the Nth belt shown in Figure 6 From the residual error curve from the first to the Nth belt shown in Figure 6, it can be seen that the residual error shows a monotonous increasing trend as N increases, and the maximum residual error does not exceed the positioning accuracy of the machine tool axis.
  • the target aspheric surface can be obtained by processing 17 rings with different radii at 17 different positions. The smaller the belt spacing, the smaller the residual error, but at the same time the lower the processing efficiency.
  • This method defines the residual error as not exceeding the positioning accuracy of the machine tool, which can not only meet the processing accuracy, but also improve the processing efficiency.
  • only 17 spherical ring belts with different radii of curvature can be spliced and enveloped to form an aspheric surface, and the efficiency is greatly improved compared with the prior art with a pitch of 0.2 mm.
  • the aspheric surface shape errors processed in this method all come from the outer diameter T D , and the convex round chamfer radius between the outer diameter and the inner diameter of the ring tool is r 0. During the compensation process, only these two need to be adjusted. Compensation can be achieved with only one tool parameter.
  • the Z-axis movement corresponding to the meridian section curve AB of the spherical surface is at least 41.6725mm.
  • surface quality and machining efficiency are two requirements to be met in the research of tool path planning, but these two requirements are contradictory in the planning process and need to be met at the same time.
  • Wear and machine tool axis positioning errors are the main factors that affect the accuracy of aspheric machining.
  • the solution of the present invention envelops the aspheric surface through a number of spherical belts, and sets the width of the belts reasonably, which not only guarantees the processing efficiency, but also greatly reduces the length of the tool path.
  • the processing machine tool axis of this scheme moves very little, and the positioning of the machine tool causes The error of can be ignored, so the machining accuracy can be improved.
  • R 0 is an aspheric surface
  • k is the quadratic cone coefficient
  • x is the independent variable on the abscissa
  • z is the ordinate corresponding to the x coordinate
  • the diameter is D
  • the positioning accuracy of the CNC machine tool used for milling is ⁇ , which is characterized by:
  • the numerical control machine tool has at least two translational motion axes of X axis and Z axis, and two rotation axes of B axis and C axis, wherein the B axis is a rotation axis around the Y axis, and the C axis is a rotation axis around the Z axis.
  • Rotation axis, and the rotation axis of the turntable of the CNC machine tool is located on the C axis; the spindle of the CNC machine tool is located on the Z axis; the ring tool is mounted on the spindle of the CNC machine tool; the outer diameter of the ring tool is T D , and the outer diameter of the ring tool is convex
  • the ring tool on the CNC machine tool is processed sequentially from the first ring to the Nth ring.
  • the C axis rotates continuously and uniformly.
  • the X axis coordinate of the tool center in the workpiece coordinate system: X T (( (T D -2*r 0 )+2*r 0 *sin(B))/2)*cos(B),
  • * is the multiplication calculation symbol
  • sqrt is the open radical calculation symbol
  • sin, cos, and asin are the sine, cosine, and arc sine calculation symbols respectively.
  • the CNC machine tool has at least two translational motion axes, X-axis and Z-axis, and two rotation axes, B-axis and C-axis.
  • the B axis is the rotation axis around the Y axis
  • the C axis is the rotation axis around the Z axis
  • the rotation axis of the CNC machine tool turntable is located on the C axis
  • the spindle of the CNC machine tool is located on the Z axis; as shown in Figure 8, the proximal end of the mirror body
  • the projection on the turntable of the CNC machine tool connected with the distal axis coincides with the X axis; the distance between the center of the mirror body and the turntable of the CNC machine tool is equal to the off-axis amount ⁇ ;
  • the ring tool is T D , and the convex round chamfer radius between the outer diameter and the inner diameter of the ring tool is r 0 ; T D >D/2; set the workpiece coordinate system
  • the origin of is established at the apex of the starting spherical surface;
  • the annular tool is a hollow grinding wheel tool, including: electroplated diamond grinding wheel, bronze adhesive grinding wheel, resin grinding wheel;
  • the mirror body is regarded as a part of the aspheric mother mirror, using the fan method Directly process the lens body into a spherical surface with a radius of curvature R 0;
  • the dx is jointly determined by the Nth annulus, the N-1th annulus, the positioning accuracy is denoted as ⁇ , and the generatrix equation f1 of the aspheric mirror:
  • the generatrix equation of the N-1th ring zone is denoted as f2, the generatrix equation of the Nth ring zone is denoted as f3, the intersection point of f1 and f3 is denoted as (x1,z1), the intersection point of f1 and f2 is denoted as (x2,z2), f2
  • the point of intersection with f3 is denoted as (x3, z3), and the point on the generatrix equation f1 of the aspheric mirror at x3 on the X axis is denoted as (x3, z4);
  • Figure 8 is a schematic diagram of the relationship between the rectangular off-axis aspheric
  • the ring tool on the CNC machine tool is processed from the N 0th endless belt to the Nth endless belt in sequence.
  • the nth endless belt is processed,
  • the C-axis rotates continuously and uniformly, and it is derived that the X-axis and Z-axis coordinates of the tool center in the workpiece coordinate system are as follows:
  • X T (((T D -2*r 0 )+2*r 0 *sin(B))/2)*cos(B),
  • * is the multiplication calculation symbol
  • sqrt is the open radical calculation symbol
  • sin, cos, and asin are the sine, cosine, and arc sine calculation symbols respectively.
  • Figure 10 is a schematic diagram of the relationship between the two-dimensional curve between the proximal and distal ends of the off-axis aspheric mirror and its mother mirror generatrix. It can be seen from the figure that the off-axis aspheric mirror is a part of the aspheric mother mirror.
  • the off-axis spherical mirror, which is placed in the off-axis CNC machine is equal to the amount of the turntable from the position of the shaft, according to the processing method of processing an aspheric off-axis mirror mother curved mirror; when Generating Cutting R 0, the annular cutter wheel
  • the depth of the upper end of the mirror body processed downward is the sagittal height Hz at the edge of the aspheric surface of the mother mirror with a diameter of D.
  • the invention belongs to the field of optical processing.
  • the aspheric surface is discretized into a series of annular belts with different radii, and the annular grinding wheel cutter is used to form each annular belt in turn;
  • the belts are equally spaced and the total number is N.
  • the width of any belt is determined by the Nth belt, the N-1th belt, the positioning accuracy, and the generatrix equation of the aspheric mirror.
  • the nth belt's curvature radius Rn sqrt(R02- k*(n*dx)2); an aspheric surface is enveloped by numerous rings.
  • the diameter of the tool used for processing is larger than the half diameter of the aspheric surface, and the contact between the tool and the workpiece surface is an endless belt, so when processing large-diameter aspheric surfaces, the service life of the large ring tool is much longer than that of the traditional processing method; the distance between the belts is much larger than the traditional Processing the pitch, so the processing efficiency has been significantly improved.
  • the processing method of this scheme can also be extended to the processing of off-axis aspheric surfaces, so it has strong practicability.

Landscapes

  • Engineering & Computer Science (AREA)
  • Mechanical Engineering (AREA)
  • Physics & Mathematics (AREA)
  • General Physics & Mathematics (AREA)
  • Automation & Control Theory (AREA)
  • Human Computer Interaction (AREA)
  • Manufacturing & Machinery (AREA)
  • General Engineering & Computer Science (AREA)
  • Grinding And Polishing Of Tertiary Curved Surfaces And Surfaces With Complex Shapes (AREA)
  • Polishing Bodies And Polishing Tools (AREA)

Abstract

一种大口径非球面镜数控铣磨成形方法、抛光方法及装置，将非球面离散为一系列不同半径的环带，使用环形砂轮刀具依次范成每个环带；环带等间距且总数为N，任意环带的宽度由第N环带、第N-1环带、定位精度、非球面镜的母线方程共同确定，由众多的环带包络出非球面。加工所用的刀具直径大于非球面半口径，刀具与工件表面的接触为环带，因此提高了环形刀具的使用寿命；环带间距远大于传统加工螺距，因此加工效率得到显著提升。

Description

一种大口径非球面镜数控铣磨成形抛光方法及装置 技术领域
本发明属于光学加工领域，涉及一种大口径非球面光学元件的数控加工方法。
背景技术
非球面光学在光学系统中能够很好地矫正多种像差，改善成像质量，提高系统鉴别能力。非球面镜是光学系统中非常重要的光学元件，能以一个或几个非球面元件代替多个球面元件，从而简化仪器结构，简化系统结构、缩短简长、并有效地减轻仪器的重量，同时非球面光学系统的设计能使计算方法大为简化。
近年来，非球面光学元件的加工技术有了显著的发展，其加工方法主要有：数控研磨抛光技术、单点金刚石车削技术、离子束加工、模压成型等，不同的加工方法都有各自的优缺点。使用数控研磨抛光技术加工非球面镜时，通常会先加工出非球面光学元件最接近球面的一面，然后再按照该面磨削出球面，最后通过研磨和抛光加工出符合要求的非球面；但这种方法耗时太长，生产效率较低。单点金刚石车削技术主要用于有色金属材料如硬铝、黄铜、无氧铜等的典型零件的切削，在切削过程中易发生刀具偏置，往往需要配上在线检测设备才能获得理想的非球面精度。离子束加工虽然可以获得精度较好的非球面，但加工设备和成本较高，且加工设备不具有通用性，因而限制了它的推广使用。模压技术主要用来批量制备微小型的非球面透镜，不适用大口径高精度的非球面镜。因此，大口径非球面镜的高效、低成本加工技术仍然在不断的探索和研究之中。
目前，为了缩短非球面透镜的加工周期，在加工非球面时先范成法开粗加工出最接近球面，然后再用数控机床直接在球面基础上铣磨精加工出符合非球面方程的非球面。该方法因使用范成法开粗快速去除了大量的材料，通常只需一次数控精加工就可将最接近球面改为非球面，加工效率高、经济性好已经逐渐被广泛使用。但在精加工改非球面时，过大的刀具轨迹螺距会导致明显的切除不足，且表面粗糙度较差。为了提高表面质量，刀具轨迹螺距通常小于0.2mm，对于大口径非球面而言，刀具轨迹总长将非常大，加工耗时更长；尤其是加工米级非球面时，受刀具磨损影响，一把刀具难以走完全部刀具轨迹就不得不换刀，换刀会后通常会在非球面表面留下接刀痕迹，且由于不同刀具的刀具参数不同，必然会使得加工的非球面面形误差来源因素复杂，给后期补偿加工带来巨大难度，严重影响加工精度。因此现有技术加工大口径非球面镜，尤其是米级非球面镜，还存在刀具轨迹过长导致刀具磨损严重、加工效率低、难以补偿加工导致的非球面精度低的问题。
发明内容
为解决现有技术加工大口径非球面时存在的刀具轨迹过长导致的一系列问题，本发明提出一种大口径非球面镜数控铣磨成形方法，非球面镜为凹面且母线方程记为f1，非球面镜口径为D，用于铣磨的数控机床定位精度为β，其特征在于：将非球面镜的非球面离散为一系列不同半径的环带，环带等间距且总数为N，环带宽度为dx，使用口径大于非球面半口径的环形砂轮刀具依次范成加工每个环带；该环带宽度dx求解流程：第N-1环带的母线方程记为f2，第N环带母线方程记为f3，f1与f3的交点记为(x1,z1)，f1与f2的交点记为(x2,z2)，f2与f3的交点记为(x3,z3)，x3处非球面镜的母线方程f1上的点记为(x3,z4)；其中x1＝D/2，z4-z3＝β，x2＝x1-dx，从上述几何关系中计算求得dx。
上述方案的工作原理是，根据机床定位精度，将非球面离散为一系列不同半径的环带，使用环形砂轮刀具依次范成每个环带，由众多的环带包络出非球面。环带的个数远小于传统加工螺距个数，且由于该方案的不同环带的刀具轨迹x方向的增量dx由机床定位精度限定，即最大限度的减少了环带的个数，又使的不同环带的最大残余误差不超过机床定位精度β。上述加工方法可以加工凹的具有单调递增性质的旋转对称曲面，包括凹二次非球面，凹高次非球面。
下面以二次凹非球面为例详细描述加工方法：
所述的非球面镜的母线方程f1的方程为：z 2＝2*R 0*x-(1+k)*x 2，其中R 0为非球面的顶点曲率半径，k为二次圆锥系数，x为横坐标上自变量，z为x坐标处对应的纵坐标；该非球面镜的加工步骤依次如下：
1)根据非球面的顶点曲率半径R 0、中心厚H 0、口径D在非球面镜体材料上加工出半径为R 0、中心厚H 1、口径D的起始球面；此处0≤H 1-H 0≤0.5；
2)将步骤1)中的非球面镜体固定在数控机床转台上，且非球面镜体的光轴和数控机床转台的转轴重合；所述的数控机床至少具有X轴、Z轴这两个平移运动轴，以及B轴、C轴这两个旋转轴，其中的B轴为绕Y轴的旋转轴，C轴为绕Z轴的旋转轴，且数控机床转台的转轴位于C轴；数控机床的主轴位于Z轴；
3)将环形刀具安装在数控机床主轴上；所述环形刀具外径为T D，T D>D/2；环形刀具外径与内径之间外凸的圆倒角半径为r 0；环形刀具外径与内径之间厚度为2r 0；将工件坐标系的原点建立在起始球面顶点处；
所述的环形刀具为空心的砂轮刀具，包括：电镀金刚石砂轮、青铜粘合剂砂轮、树 脂砂轮；
4)将非球面离散为N个在X轴方向等间距的环带，N为整数，任意环带的宽度dx＝D/N，第n个环带对应的非球面口径为：n*dx，第n个环带曲率半径R n＝sqrt(R 0 2-k*(n*dx) 2)；其中n为第一个环带至第N个环带中任意环带的序数；
所述dx由第N环带、第N-1环带、定位精度记为β、非球面镜的母线方程f1共同确定：
第N-1环带的母线方程记为f2，第N环带母线方程记为f3，f1与f3的交点记为(x1,z1)，f1与f2的交点记为(x2,z2)，f2与f3的交点记为(x3,z3)，X轴上x3处非球面镜的母线方程f1上的点记为(x3,z4)；其中x1＝D/2，z4-z3＝β，x2＝x1-dx，从上述几何关系中计算求得dx；
5)数控机床上的环形刀具依次从第一个环带加工至第N个环带，其中加工第n环带时，C轴连续均匀旋转，工件坐标系下刀具中心X轴坐标：
X T＝(((T D-2*r 0)+2*r 0*sin(B))/2)*cos(B)，
Z轴坐标：
k≠-1时：
Z T＝R 0/(1+k)+k/(1+k)*sqrt(R 0 2-(1+k)*(n*dx) 2)-sqrt(R 0 2-k*(n*dx) 2)+(((T D-2*r 0)+2*r 0*sin(B))/2)*sin(B)，
k＝-1时：
Z T＝R 0+(n*dx) 2/(2*R 0)–sqrt(R 0 2+(n*dx) 2)+(((T D-2*r 0)+2*r 0*sin(B))/2)*sin(B)，
B轴坐标：B＝asin((T D-2*r 0)/(2*(R n-r 0)))；
其中*为乘法计算符，sqrt为开根号计算符，sin、cos、asin分别为正弦、余弦、反正弦计算符。刀位点X T、Z T的关系式，是基于范成法加工球面的基本原理推导出来的。
基于上述铣磨成形方法还提供一种大口径非球面镜数控抛光方法，将上述环形刀具替换为环形抛光盘，将环形抛光盘安装在数控机床主轴上；所述环形抛光盘外径为T D，环形抛光盘外径与内径之间外凸的圆倒角半径为r 0；T D>D/2；将工件坐标系的原点建立在起始球面顶点处；所述的环形抛光盘包括：环形聚氨酯抛光垫、环形柔性抛光皮、环形气囊；数控机床上的环形抛光盘依次从第一个环带加工至第N个环带，在加工过程中在环形抛光盘与大口径非球面镜之间喷射抛光粉溶液；抛光粉溶液根据被抛光的材料硬度常用的选择有氧化铝、氧化铈、金刚石微粉、白刚玉微粉。由于抛光盘和工件表面的接触轨迹为一段椭圆弧该段工件旋转后该段圆弧的包络刚好是球面，而各个环带球面又组成了非球面，因 此这种抛光方式可以用于非球面抛光。
上述大口径非球面镜数控铣磨成形方法可以用于制作一种大口径非球面镜数控铣磨成形装置。
上述大口径非球面镜数控抛光方法可以用于制作一种大口径非球面镜数控铣磨成形装置。
由于上述技术方案的运用，本发明与现有技术相比具有下列优点：
a.对数控机床的要求大大降低，只需要两个平移轴，两个旋转轴即可实现非球面加工；
b.对数控机床的平移轴以及旋转轴行程范围要求大大降低，因为在加工过程中刀具只需要沿着X轴和Z轴以及B轴做少量的移动；
c.加工所用的刀具直径大于非球面半口径，刀具与工件表面的接触为环带，而传统加工刀具与工件表面的接触为点，因此在加工大口径非球面时大的环形刀具使用寿命远大于传统加工方式的刀具寿命；
d.加工效率较传统加工得到很大提升，因为此方式加工的dx远大于0.2mm。
附图说明
图1：环形刀具径向剖面示意图；
图2：非球面离散等间距的环带示意图；
图3：环形刀具刀位点位置示意图；
图4：环带宽度dx求解示意图；
图5：一系列球面环带包络非球面示意图；
图6：环带序数残差关系实例示意图；
图7a：回转非球面轨迹包络磨削加工原理前视图；
图7b：回转非球面轨迹包络磨削加工原理斜视图；
图8：矩形离轴非球面镜与其母镜关系示意图；
图9：圆形形离轴非球面镜与其母镜关系示意图；
图10：离轴非球面镜与其母镜母线示意图；
具体实施方式
为了更清楚地说明发明的技术方案，下面结合附图及实施例作进一步描述
实施例一：
一种大口径非球面镜数控铣磨成形方法，所述的非球面镜的母线方程f1的方程为： z 2＝2*R 0*x-(1+k)*x 2，其中R 0为非球面的顶点曲率半径，k为二次圆锥系数，x为横坐标上自变量，z为x坐标处对应的纵坐标；用于铣磨的数控机床定位精度为β，该非球面镜的加工步骤依次如下：
1)根据非球面的顶点曲率半径R 0、中心厚H 0、口径D在非球面镜体材料上加工出半径为R 0、中心厚H 1、口径D的起始球面；此处0≤H 1-H 0≤0.5；
2)将步骤1)中的非球面镜体固定在数控机床转台上，且非球面镜体的光轴和数控机床转台的转轴重合；所述的数控机床至少具有X轴、Z轴这两个平移运动轴，以及B轴、C轴这两个旋转轴，其中的B轴为绕Y轴的旋转轴，C轴为绕Z轴的旋转轴，且数控机床转台的转轴位于C轴；数控机床的主轴位于Z轴；
3)将环形刀具安装在数控机床主轴上；如图1，环形刀具外径为T D，环形刀具外径与内径之间外凸的圆倒角半径为r 0；环形刀具外径与内径之间厚度为2r 0；T D>D/2；将工件坐标系的原点建立在起始球面顶点处；所述的环形刀具为空心的砂轮刀具，包括：电镀金刚石砂轮、青铜粘合剂砂轮、树脂砂轮；
4)如图2所示，将非球面离散为N个在X轴方向等间距的环带，N取整数，任意环带的宽度dx＝D/N，第n个环带对应的非球面口径为：n*dx，第n个环带曲率半径R n＝sqrt(R 0 2-k*(n*dx) 2)；其中n为第一个环带至第N个环带中任意环带的序数；
所述dx由第N环带、第N-1环带、定位精度记为β、非球面镜的母线方程f1共同确定：
第N-1环带的母线方程记为f2，第N环带母线方程记为f3，f1与f3的交点记为(x1,z1)，f1与f2的交点记为(x2,z2)，f2与f3的交点记为(x3,z3)，X轴上x3处非球面镜的母线方程f1上的点记为(x3,z4)；其中x1＝D/2，z4-z3＝β，x2＝x1-dx，从上述几何关系中计算求得dx；
5)数控机床上的环形刀具依次从第一个环带加工至第N个环带，其中加工第n环带时，
C轴连续均匀旋转，如图3，根据图3所示的环形刀具与非球面工件之间位置关系推导得出工件坐标系下刀具中心X轴坐标、Z轴坐标分别为：
X T＝(((T D-2*r 0)+2*r 0*sin(B))/2)*cos(B)，
k≠-1时：
Z T＝R 0/(1+k)+k/(1+k)*sqrt(R 0 2-(1+k)*(n*dx) 2)-sqrt(R 0 2-k*(n*dx) 2)+(((T D-2*r 0)+2*r 0*sin(B))/2)*sin(B)，
k＝-1时：
Z T＝R 0+(n*dx) 2/(2*R 0)–sqrt(R 0 2+(n*dx) 2)+(((T D-2*r 0)+2*r 0*sin(B))/2)*sin(B)，
B轴坐标：B＝asin((T D-2*r 0)/(2*(R n-r 0)))；
环形砂轮刀具的外凸的圆倒角区域为通常附着金刚砂等磨料，加工时作为刃口对接触到的玻璃材料进行磨削。将刀具中心的刀位点定位于B，X T，Z T处，加工过程中环形砂轮刀具的刃口始终位于工件旋转中心轴线上，从第一环带加工至第N环带时整个加工过程表现为：砂轮沿着旋转中心轴线上下移动，且在不同的位置摆动相对应的B角度。即使加工不同环带时刀具中心X T不同，但刀具刃口始终未偏离工件旋转中心轴线。
其中*为乘法计算符，sqrt为开根号计算符，sin、cos、asin分别为正弦、余弦、反正弦计算符。
具体的dx求解如下：如图4所示，
二次非球面方程f1:x 2＝2R 0z-(1+k)z 2
f2:
Figure PCTCN2020105663-appb-000001
f3:
Figure PCTCN2020105663-appb-000002
求出两圆之间的交点
令f2-f3，得到
Figure PCTCN2020105663-appb-000003
求出
Figure PCTCN2020105663-appb-000004
由二次曲面方程代得：
Figure PCTCN2020105663-appb-000005
Figure PCTCN2020105663-appb-000006
所以(x3，z3)为
Figure PCTCN2020105663-appb-000007
将x3代入二次曲面母线方程，可以求得z4。
由二次曲面公式f1:x 2＝2R 0z-(1+k)z 2
利用求根公式可求得：
Figure PCTCN2020105663-appb-000008
将x3代入可得z4
Figure PCTCN2020105663-appb-000009
Figure PCTCN2020105663-appb-000010
Figure PCTCN2020105663-appb-000011
Figure PCTCN2020105663-appb-000012
其中
Figure PCTCN2020105663-appb-000013
由此求出了dx与β关系式，当R 0，k，半口径x1，β已知时，就可以求解出符合条件的dx。
上述方案将非球面离散为一系列不同半径的环带，如图5所示，使用环形砂轮刀具依次范成R 1、R 2、R 3……环带，由众多的球面环带包络出非球面。环带的个数远小于传统加工螺距个数，且由于该方案的不同环带的刀具轨迹x方向的增量dx由机床定位精度限定，即最大限度的减少了环带的个数，图中阴影部分为不同环带和实际非球面之间的残差示意，只要合理控制环带宽度，即可将不同环带的最大残余误差控制在机床定位精度内。
实施例二：
以一个具体非球面为例，进一步说明实施例一中的方法。k＝-0.98，R 0＝3000，D＝1000，机床定位精度β＝0.001。
一种大口径非球面镜数控铣磨成形方法，根据非球面的顶点曲率半径R 0＝3000、中心厚H 0＝200、口径D＝1000，在非球面镜体材料上加工出半径为3000、中心厚H 1＝200.2、口径1000起始球面；
环形刀具选用电镀金刚石砂轮，外径为T D＝550，环形刀具外径与内径之间外凸的圆倒角半径为r 0＝5；
由第N环带、第N-1环带、定位精度记为β、非球面镜的母线方程求解出dx
由上述关系计算出的dx＝30.9，取整数后N＝17，重新计算dx＝29.4112；使用实施例一中的方案计算的不同环带序数下的R n，B，X T，Z T见表1。
从表1中可以看出只需要17个宽度为29.4112的圆环带即可包络出1000口径的非曲面，且整个加工过程中机床B轴角度变化范围5.172°～5.103°，变化量0.069°；机床X轴变化范围： 269.3496～269.3728，变化量0.0232；机床Z轴变化范围：24.3800～24.2850，变化量0.095。
表1.不同环带序数对应的环带曲率半径、B，X T，Z T
环带序数n R n B，单位：度 X T Z T
1 3000.14128305847 5.17200629931126 269.349606399328 24.3800543493219
2 3000.56509231960 5.17127257598519 269.349855076213 24.3766502520008
3 3001.27130809688 5.17005039701697 269.350269204175 24.3711157227581
4 3002.25973110051 5.16834080055154 269.350848283963 24.3636590059685
5 3003.53008271821 5.16614523656417 269.351591618667 24.3545712344803
6 3005.08200540723 5.16346556345177 269.352498315739 24.3442260215403
7 3006.91506319597 5.16030404367734 269.353567289577 24.3330789392348
8 3009.02874229390 5.15666333848735 269.354797264659 24.3216668839150
9 3011.42245180749 5.15254650172625 269.356186779202 24.3106073313538
10 3014.09552456008 5.14795697277598 269.357734189330 24.3005974844438
11 3017.04721801292 5.14289856865239 269.359437673738 24.2924133153022
12 3020.27671528443 5.13737547529366 269.361295238809 24.2869085054286
13 3023.78312626461 5.13139223807930 269.363304724182 24.2850132875273
14 3027.56548882090 5.12495375162105 269.365463808719 24.2877331921918
15 3031.62277009187 5.11806524887000 269.367770016859 24.2961477035142
16 3035.95386786479 5.11073228958621 269.370220725314 24.3114088283671
17 3040.55761203275 5.10296074821945 269.372813170093 24.3347395827187
从图6所示的第1环带到第N环带的残留误差曲线中可以看到，残差随着N增大呈现单调递增趋势，且最大残差不超过机床轴定位精度。在加工第n个环带时，只需将刀位点放置于X T，Z T处，并且刀轴线与数控机床转台转轴线夹角为B，C轴旋转大于360度即可完成该环带加工，只需分别在17个不同的位置加工出17个不同半径的环带即可获得目标非球面。环带间距越小残差越小，但同时加工效率越低，本方法将残差定义在不超过机床定位精度，可以既满足加工精度，又提高了加工效率。本实施例中只需要17个不同曲率半径的球环带即可拼接包络出非球面，与现有技术相比螺距0.2mm相比效率得到极大的提高。此外本方法中加工得到的非球面面形误差全部来源于外径为T D，以及环形刀具外径与内径之间外凸的圆倒角半径为r 0，补偿加工中，只需要调整这两个刀具参数即可实现补偿。而传统加工，采用小的刀具，刀具移动行程大，既需要较大的轴行程，对机床的长距离定位精度要求高，本案中的B轴、X轴、Z轴变化范围极小，加工中仅用轴上极小一部分，因此降低了对整个机床轴的直线度的要求。
作为对比，参考文献：周旭光,阎秋生,孔令叶,朱光力.砂轮几何参数对非球面轨迹包络磨削的影响研究[J].工具技术.2015年8期。中提出应用轨迹包络磨削法加工凹凸轴对称回转曲面的精密磨削加工方法，在轨迹包络磨削非球面过程中，盘形砂轮的圆弧截面的形状精度被复制在零件曲面上，因此保持盘形砂轮具有高精度的圆弧形状截面是高精度非球面轨迹包络磨 削加工中的重要内容。其轨迹包络磨削加工原理如图7所示，在轨迹包络磨削轴对称回转非球面过程中，非球面绕其对称轴线旋转，盘形砂轮的圆弧部分沿轴对称回转非球面的子午截面曲线AB运动。在磨削中，砂轮圆弧部分始终与非球面曲面相切，砂轮的磨削点沿着砂轮圆弧截面不断移动。如果用该参考文献的方案加工本实施例中的1000口径非球面，非球面的子午截面曲线AB对应的X轴移动量至少为500mm，非球面镜边缘处的矢高f1(500)＝41.6725，因此非球面的子午截面曲线AB对应的Z轴移动量至少为41.6725mm。目前，表面质量和加工效率是刀具路径规划研究中要打到的两个需求，但是这两个需求是规划过程中相互矛盾的，需要同时满足。刀具路径如果相邻的间距太大，会使得工件表面质量无法满足粗糙度等要求，但如果间距太小，则会大大提高加工所需要的时间，效率必定不会达标。因此，现有技术方案加工大口径非球面时，尤其是米级量级非球面，要求机床的直线轴在行程内均有较高的定位精度，且口径大了以后势必增加加工时常，按照常规螺距0.2mm为例，机床C轴至少转2500圈，其刀具轨迹线长度远远超出本案dx＝29.4112mm，机床C轴17圈的长度；盘形砂轮刀具加工米级大口径非球面时，刀具磨损以及机床轴定位误差是影响非球面加工精度的主要因素。本发明的方案，通过若干个球形环带包络非球面，并且合理设置环带宽度，即保证了加工效率，又大大缩减了刀具轨迹的长度，本方案加工机床轴移动极少，机床定位引起的误差可以忽略，因此可以提高加工精度。
实施例三：
一种大口径非球面镜数控铣磨成形装置，所述的非球面镜的母线方程f1的方程为：z 2＝2*R 0*x-(1+k)*x 2，其中R 0为非球面的顶点曲率半径，k为二次圆锥系数，x为横坐标上自变量，z为x坐标处对应的纵坐标，口径为D；用于铣磨的数控机床定位精度为β，其特征在于：所述的数控机床至少具有X轴、Z轴这两个平移运动轴，以及B轴、C轴这两个旋转轴，其中的B轴为绕Y轴的旋转轴，C轴为绕Z轴的旋转轴，且数控机床转台的转轴位于C轴；数控机床的主轴位于Z轴；环形刀具安装在数控机床主轴上；所述环形刀具外径为T D，环形刀具外径与内径之间外凸的圆倒角半径为r 0；T D>D/2；非球面离散为N个在X轴方向等间距的环带，任意环带的宽度dx＝D/N，第n个环带对应的非球面口径为：n*dx，第n个环带曲率半径R n＝sqrt(R 0 2-k*(n*dx) 2)；其中n为第一个环带至第N个环带中任意环带的序数；
数控机床上的环形刀具依次从第一个环带加工至第N个环带，其中加工第n环带时，C轴连续均匀旋转，工件坐标系下刀具中心X轴坐标：X T＝(((T D-2*r 0)+2*r 0*sin(B))/2)*cos(B)，
Z轴坐标：k≠-1时：
Z T＝R 0/(1+k)+k/(1+k)*sqrt(R 0 2-(1+k)*(n*dx) 2)-sqrt(R 0 2-k*(n*dx) 2)+(((T D-2*r 0)+2*r 0*sin(B))/2) *sin(B)，
k＝-1时：
Z T＝R 0+(n*dx) 2/(2*R 0)–sqrt(R 0 2+(n*dx) 2)+(((T D-2*r 0)+2*r 0*sin(B))/2)*sin(B)，
B轴坐标：B＝asin((T D-2*r 0)/(2*(R n-r 0)))；
其中*为乘法计算符，sqrt为开根号计算符，sin、cos、asin分别为正弦、余弦、反正弦计算符。
实施例四：
一种离轴非球面镜数控铣磨成形方法，所述非球面的母线方程f1的方程为：z 2＝2*R 0*x-(1+k)*x 2，其中R 0为非球面的顶点曲率半径，k为二次圆锥系数，离轴量为γ，x为横坐标上自变量，z为x坐标处对应的纵坐标；包含离轴非球面镜的非球面母镜口径为D，用于铣磨的数控机床定位精度为β，该离轴非球面镜的加工步骤依次如下：
1)根据离轴非球面镜的外形几何参数制备包络该离轴非球面镜的镜体，所述镜体上下两个端面平行；
2)将步骤1)中的镜体固定在数控机床转台上，所述的数控机床至少具有X轴、Z轴这两个平移运动轴，以及B轴、C轴这两个旋转轴，其中的B轴为绕Y轴的旋转轴，C轴为绕Z轴的旋转轴，且数控机床转台的转轴位于C轴；数控机床的主轴位于Z轴；如图8所示，镜体的近轴端与远轴端连线在数控机床转台上的投影与X轴重合；镜体中心距离数控机床转台转轴距离等于离轴量γ；
3)将环形刀具安装在数控机床主轴上；环形刀具外径为T D，环形刀具外径与内径之间外凸的圆倒角半径为r 0；T D>D/2；将工件坐标系的原点建立在起始球面顶点处；所述的环形刀具为空心的砂轮刀具，包括：电镀金刚石砂轮、青铜粘合剂砂轮、树脂砂轮；将镜体视为非球面母镜的一部分，用范成法直接将所述镜体加工为曲率半径为R 0的球面；
4)将非球面母镜离散为N个在X轴方向等间距的环带，N取整数，任意环带的宽度dx＝D/N，第n个环带对应的非球面口径为：n*dx，第n个环带曲率半径R n＝sqrt(R 0 2-k*(n*dx) 2)；其中n为第一个环带至第N个环带中任意环带的序数；
所述dx由第N环带、第N-1环带、定位精度记为β、非球面镜的母线方程f1共同确定：
第N-1环带的母线方程记为f2，第N环带母线方程记为f3，f1与f3的交点记为(x1,z1)，f1与f2的交点记为(x2,z2)，f2与f3的交点记为(x3,z3)，X轴上x3处非球面镜的母线方程f1上的点记为(x3,z4)；其中x1＝D/2，z4-z3＝β，x2＝x1-dx，从上述几何关系中计算求得dx；根据离轴非球面镜的口径求出离轴非球面镜的环带序数范围N 0～N；图8为矩形离轴非球面镜与 其母镜关系示意图；图9为圆形形离轴非球面镜与其母镜关系示意图；从图中可以看出根据离轴镜与母镜的位置关系，可以求出其环带序数范围；
5)数控机床上的环形刀具依次从第N 0个环带加工至第N个环带，其中加工第n环带时，
C轴连续均匀旋转，推导得出工件坐标系下刀具中心X轴坐标、Z轴坐标分别为：
X轴坐标：X T＝(((T D-2*r 0)+2*r 0*sin(B))/2)*cos(B)，
Z轴坐标：k≠-1时：
Z T＝R 0/(1+k)+k/(1+k)*sqrt(R 0 2-(1+k)*(n*dx) 2)-sqrt(R 0 2-k*(n*dx) 2)+(((T D-2*r 0)+2*r 0*sin(B))/2)*sin(B)，
k＝-1时：
Z T＝R 0+(n*dx) 2/(2*R 0)–sqrt(R 0 2+(n*dx) 2)+(((T D-2*r 0)+2*r 0*sin(B))/2)*sin(B)，
B轴坐标：B＝asin((T D-2*r 0)/(2*(R n-r 0)))；
其中*为乘法计算符，sqrt为开根号计算符，sin、cos、asin分别为正弦、余弦、反正弦计算符。
图10为离轴非球面镜近轴端与远轴端之间二维曲线与其母镜母线关系示意图，从图中可以看出，离轴非球面镜为其非球面母镜的一部分，在加工离轴离轴非球面镜时，将其放置于数控机床转台上距离转轴等于离轴量的位置，即可按照非球面母镜的加工方法加工离轴非曲面镜；范成法加工R 0时，环形砂轮刀具从镜体上端面向下加工的深度为口径为D的母镜非球面边缘处的矢高Hz。
本发明属于光学加工领域，为解决米级大口径非球面加工耗时长、刀具磨损严重问题，将非球面离散为一系列不同半径的环带，使用环形砂轮刀具依次范成每个环带；环带等间距且总数为N，任意环带的宽度由第N环带、第N-1环带、定位精度、非球面镜的母线方程共同确定，第n个环带曲率半径Rn＝sqrt(R02-k*(n*dx)2)；由众多的环带包络出非球面。加工所用的刀具直径大于非球面半口径，刀具与工件表面的接触为环带，因此在加工大口径非球面时大的环形刀具使用寿命远大于传统加工方式的刀具寿命；环带间距远大于传统加工螺距，因此加工效率得到显著提升。本方案的加工方法还可以推广到离轴非球面的加工，因此具有很强的实用性。
本方案中所用的字母符号仅仅是为了表示其物理量之间的数值关系而做的简化表述，不应理解为其字母符号对方案构成的特别限定。

Claims (7)

  1. 一种大口径非球面镜数控铣磨成形方法，所述的非球面镜为凹面且母线方程记为f1，非球面镜口径为D，用于铣磨的数控机床定位精度为β，其特征在于：将非球面镜的非球面离散为一系列不同半径的环带，环带等间距且总数为N，环带宽度为dx，使用口径大于非球面半口径的环形砂轮刀具依次范成加工每个环带；该环带宽度dx求解流程：第N-1环带的母线方程记为f2，第N环带母线方程记为f3，f1与f3的交点记为(x1,z1)，f1与f2的交点记为(x2,z2)，f2与f3的交点记为(x3,z3)，x3处非球面镜的母线方程f1上的点记为(x3,z4)；其中x1＝D/2，z4-z3＝β，x2＝x1-dx，从上述几何关系中计算求得dx。
  2. 根据权利要求1所述的一种大口径非球面镜数控铣磨成形方法，所述的非球面镜的母线方程f1的方程为：z 2＝2*R 0*x-(1+k)*x 2，其中R 0为非球面的顶点曲率半径，k为二次圆锥系数，x为横坐标上自变量，z为x坐标处对应的纵坐标；其特征在于该非球面镜的加工步骤依次如下：
    1)根据非球面的顶点曲率半径R 0、中心厚H 0、口径D在非球面镜体材料上加工出半径为R 0、中心厚H 1、口径D的起始球面；此处0≤H 1-H 0≤0.5；
    2)将步骤1)中的非球面镜体固定在数控机床转台上，且非球面镜体的光轴和数控机床转台的转轴重合；所述的数控机床至少具有X轴、Z轴这两个平移运动轴，以及B轴、C轴这两个旋转轴，其中的B轴为绕Y轴的旋转轴，C轴为绕Z轴的旋转轴，且数控机床转台的转轴位于C轴；数控机床的主轴位于Z轴；
    3)将环形刀具安装在数控机床主轴上；所述环形刀具外径为T D，环形刀具外径与内径之间外凸的圆倒角半径为r 0；T D>D/2；将工件坐标系的原点建立在起始球面顶点处；
    4)将非球面离散为N个在X轴方向等间距的环带，N为整数，任意环带的宽度dx＝D/N，第n个环带对应的非球面口径为：n*dx，第n个环带曲率半径R n＝sqrt(R 0 2-k*(n*dx) 2)；其中n为第一个环带至第N个环带中任意环带的序数；
    所述dx由第N环带、第N-1环带、定位精度β、非球面镜的母线方程f1共同确定：
    第N-1环带的母线方程记为f2，第N环带母线方程记为f3，f1与f3的交点记为(x1,z1)，f1与f2的交点记为(x2,z2)，f2与f3的交点记为(x3,z3)，X轴上x3处非球面镜的母线方程f1上的点记为(x3,z4)；其中x1＝D/2，z4-z3＝β，x2＝x1-dx，从上述几何关系中计算求得dx；
    5)数控机床上的环形刀具依次从第一个环带加工至第N个环带，其中加工第n环带时，C轴连续均匀旋转，工件坐标系下刀具中心X轴坐标：
    X T＝(((T D-2*r 0)+2*r 0*sin(B))/2)*cos(B)，
    Z轴坐标：
    k≠-1时：
    Z T＝R 0/(1+k)+k/(1+k)*sqrt(R 0 2-(1+k)*(n*dx) 2)-sqrt(R 0 2-k*(n*dx) 2)+(((T D-2*r 0)+2*r 0*sin(B))/2)*sin(B)，
    k＝-1时：
    Z T＝R 0+(n*dx) 2/(2*R 0)–sqrt(R 0 2+(n*dx) 2)+(((T D-2*r 0)+2*r 0*sin(B))/2)*sin(B)，
    B轴坐标：B＝asin((T D-2*r 0)/(2*(R n-r 0)))；
    其中*为乘法计算符，sqrt为开根号计算符，sin、cos、asin分别为正弦、余弦、反正弦计算符。
  3. 根据权利要求1所述的一种大口径非球面镜数控铣磨成形方法，其特征在于所述的环形刀具为空心的砂轮刀具，包括：电镀金刚石砂轮、青铜粘合剂砂轮、树脂砂轮。
  4. 一种大口径非球面镜数控抛光方法，其特征在于：根据权利要求1所述的一种大口径非球面镜数控铣磨成形方法，将其中的环形刀具替换为环形抛光盘；将环形抛光盘安装在数控机床主轴上；所述环形抛光盘外径为T D，环形抛光盘外径与内径之间外凸的圆倒角半径为r 0；T D>D/2；将工件坐标系的原点建立在起始球面顶点处；数控机床上的环形抛光盘依次从第一个环带加工至第N个环带，在加工过程中在环形抛光盘与大口径非球面镜之间喷射抛光粉溶液；抛光粉溶液根据被抛光的材料硬度常用的选择有氧化铝、氧化铈、金刚石微粉、白刚玉微粉。
  5. 根据权利要求3所述的一种大口径非球面镜数控抛光方法，其特征在于所述的环形抛光盘包括：环形聚氨酯抛光垫、环形柔性抛光皮、环形气囊。
  6. 根据权利要求1所述的大口径非球面镜数控铣磨成形方法的一种大口径非球面镜数控铣磨成形装置。
  7. 根据权利要求3所述的大口径非球面镜数控抛光方法的一种大口径非球面镜数控抛光装置。
PCT/CN2020/105663 2019-12-25 2020-07-30 一种大口径非球面镜数控铣磨成形抛光方法及装置 WO2021128844A1 (zh)

Priority Applications (1)

Application Number Priority Date Filing Date Title
US17/440,744 US12019424B2 (en) 2019-12-25 2020-07-30 Method for numerical control milling, forming and polishing of large-diameter aspheric lens

Applications Claiming Priority (2)

Application Number Priority Date Filing Date Title
CN201911356383.5A CN111376142B (zh) 2019-12-25 2019-12-25 一种大口径非球面镜数控铣磨成形抛光方法及装置
CN201911356383.5 2019-12-25

Publications (1)

Publication Number Publication Date
WO2021128844A1 true WO2021128844A1 (zh) 2021-07-01

Family

ID=71213454

Family Applications (1)

Application Number Title Priority Date Filing Date
PCT/CN2020/105663 WO2021128844A1 (zh) 2019-12-25 2020-07-30 一种大口径非球面镜数控铣磨成形抛光方法及装置

Country Status (3)

Country Link
US (1) US12019424B2 (zh)
CN (2) CN111376142B (zh)
WO (1) WO2021128844A1 (zh)

Families Citing this family (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN111376142B (zh) 2019-12-25 2021-09-10 苏州大学 一种大口径非球面镜数控铣磨成形抛光方法及装置

Citations (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US3492764A (en) * 1967-03-28 1970-02-03 American Optical Corp Lens generating method
US4768308A (en) * 1986-12-17 1988-09-06 University Of Rochester Universal lens polishing tool, polishing apparatus and method of polishing
CN103056731A (zh) * 2012-12-21 2013-04-24 中国科学院长春光学精密机械与物理研究所 大口径离轴非球面反射镜的五轴精密超声铣磨加工方法
CN110076680A (zh) * 2019-05-27 2019-08-02 苏州大学 一种近轴端远轴端等厚离轴非球面加工方法
CN111376142A (zh) * 2019-12-25 2020-07-07 苏州大学 一种大口径非球面镜数控铣磨成形抛光方法及装置

Family Cites Families (24)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JP3598534B2 (ja) * 1994-04-28 2004-12-08 豊田工機株式会社 非球面加工装置
US5861114A (en) * 1994-06-10 1999-01-19 Johnson&Johnson Vision Products, Inc. Method of manufacturing complex optical designs in soft contact lenses
JPH08216007A (ja) * 1995-02-17 1996-08-27 Sigma Corp 非球面加工装置
JPH0929598A (ja) * 1995-07-25 1997-02-04 Hitachi Ltd 非球面形状物体の加工装置
JP3482079B2 (ja) * 1996-10-01 2003-12-22 ペンタックス株式会社 回転対称非球面加工方法
DE19814045A1 (de) * 1998-03-31 1999-10-14 Fraunhofer Ges Forschung Verfahren zur Herstellung von Zylinder-Mikrooptiken mit der Diamantschleiftechnik
US6589102B2 (en) * 2001-01-30 2003-07-08 Larsen Equipment Design, Inc. Surface polishing method and apparatus
JP2003211462A (ja) * 2002-01-18 2003-07-29 Nippon Sheet Glass Co Ltd 非球面構造体の製造方法およびその方法により製造された非球面レンズアレイ用成形型並びに非球面レンズアレイ
DE10207379A1 (de) * 2002-02-21 2003-09-04 Asphericon Gmbh Verfahren zum Schleifen und Polieren von Freiformflächen, insbesondere von rotationssymmetrischen asphärischen optischen Linsen
JP2005001100A (ja) * 2003-02-21 2005-01-06 Seiko Epson Corp 非球面加工方法及び非球面形成方法
WO2005083536A1 (de) * 2004-02-10 2005-09-09 Carl Zeiss Smt Ag Programmgesteuertes nc-datengenerierungsverfahren mit korrekturdaten
CN101244530B (zh) * 2008-04-02 2010-08-11 陈耀龙 一种磨床
JPWO2010058740A1 (ja) * 2008-11-19 2012-04-19 コニカミノルタオプト株式会社 非球面レンズの製造方法
CN203171384U (zh) * 2013-03-19 2013-09-04 西安交通大学苏州研究院 一种非球面光学元件的点接触抛光装置
WO2014146620A1 (zh) * 2013-03-19 2014-09-25 西安交通大学 一种光学元件的磨抛装置及方法
CN103331671A (zh) * 2013-07-25 2013-10-02 长春设备工艺研究所 一种应用于中大口径非球面光学元件的点线包络磨削方法
CN103586753B (zh) * 2013-11-15 2016-03-16 成都精密光学工程研究中心 离轴非球面光学加工装置
CN104175192B (zh) * 2014-08-08 2016-08-24 中国科学院长春光学精密机械与物理研究所 多环形自适应抛光磨头
CN105643396B (zh) * 2016-01-29 2018-05-08 中国科学院上海光学精密机械研究所 大型口径离轴非球面透镜的铣磨加工方法
CN105690187B (zh) * 2016-02-06 2018-03-27 苏州大学 离轴非球面镜的加工方法
CN107932198B (zh) * 2017-12-08 2019-02-15 苏州大学 一种消边缘效应的非球面镜加工方法
CN108051882B (zh) * 2017-12-08 2020-04-14 苏州大学 一种消边缘效应的非球面镜胚
CN108188864B (zh) * 2018-02-14 2019-08-16 浙江大学 一种非球面光学元件自动化抛光系统及方法
CN110340737B (zh) * 2019-06-20 2020-05-22 西安交通大学 基于多轴联动的大离轴量非球面磨削刀具路径规划方法

Patent Citations (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US3492764A (en) * 1967-03-28 1970-02-03 American Optical Corp Lens generating method
US4768308A (en) * 1986-12-17 1988-09-06 University Of Rochester Universal lens polishing tool, polishing apparatus and method of polishing
CN103056731A (zh) * 2012-12-21 2013-04-24 中国科学院长春光学精密机械与物理研究所 大口径离轴非球面反射镜的五轴精密超声铣磨加工方法
CN110076680A (zh) * 2019-05-27 2019-08-02 苏州大学 一种近轴端远轴端等厚离轴非球面加工方法
CN111376142A (zh) * 2019-12-25 2020-07-07 苏州大学 一种大口径非球面镜数控铣磨成形抛光方法及装置

Also Published As

Publication number Publication date
US12019424B2 (en) 2024-06-25
CN111376142B (zh) 2021-09-10
CN113579917A (zh) 2021-11-02
CN113579917B (zh) 2022-05-03
US20220179389A1 (en) 2022-06-09
CN111376142A (zh) 2020-07-07

Similar Documents

Publication Publication Date Title
WO2021179515A1 (zh) 一种拼接法铣磨大口径非球面的方法与装置及抛光方法
US4640595A (en) Aspheric contact lens
CN103056731A (zh) 大口径离轴非球面反射镜的五轴精密超声铣磨加工方法
CN105014503A (zh) 大口径轴对称非球面的精密磨削方法
CN104759964B (zh) 光学非球面元件的变形加工方法
CN105690187A (zh) 离轴非球面镜的加工方法
CN115032945B (zh) 复杂曲面零件慢刀伺服磨削加工刀具轨迹规划方法
US20100280650A1 (en) Machining apparatus and machining method
WO2021128844A1 (zh) 一种大口径非球面镜数控铣磨成形抛光方法及装置
KR100659433B1 (ko) 비구면 가공 방법, 비구면 형성 방법 및 비구면 가공 장치
CN211841341U (zh) 一种拼接法铣磨大口径非球面的装置
CN108466107A (zh) 一种利用离轴三反成像系统的加工装置及加工方法
CN110039406A (zh) 一种单晶硅光学复杂表面的超精密加工工具及加工方法
CN113050538B (zh) 一种映射到柱面上的复杂微特征球冠面车削轨迹生成方法
CN112207291B (zh) 一种慢刀伺服下过渡区刀具轨迹优化超精密车削方法
Wu et al. Study of trajectory and experiment on steel polishing with elastic polishing wheel device
CN100484713C (zh) 光学二次非球面凹面零件仿形加工方法及装置
CN109299514B (zh) 斜轴磨削自由曲面的砂轮路径生成方法
CN211540639U (zh) 一种离轴非球面镜铣磨成形数控机床
JP2859001B2 (ja) 非球面眼用レンズおよびその製造方法
CN108356608B (zh) 一种确定性抛光Wolter-I型光学芯轴的方法
EP0231174A4 (en) CONTACT LENS.
SU865619A1 (ru) Способ обработки асферических поверхностей оптических деталей
Liu et al. Research on processing technology of grinding aspheric workpiece in the five-axis machine tool
JP5404500B2 (ja) レンズ研磨装置

Legal Events

Date Code Title Description
121 Ep: the epo has been informed by wipo that ep was designated in this application

Ref document number: 20905603

Country of ref document: EP

Kind code of ref document: A1

NENP Non-entry into the national phase

Ref country code: DE

122 Ep: pct application non-entry in european phase

Ref document number: 20905603

Country of ref document: EP

Kind code of ref document: A1