Method and device for milling large-diameter aspheric surface by using splicing method and polishing method

Patent metadata

Field	Value
Publication number	US-11969805-B2
Application number	US-202017440739-A
Country	US
Kind code	B2
Filing date	Jul 30, 2020
Priority date	Mar 11, 2020
Publication date	Apr 30, 2024
Grant date	Apr 30, 2024

Abstract

A method and device for milling a large-diameter aspheric surface by using a splicing method and a polishing method to solve the problems of large time consumption and serious tool wear in the machining of a meter-scale large-diameter aspheric surface are disclosed. where an aspheric surface is discretized into a series of rings with different radii, and the rings are sequentially machined via generating cutting by using an annular grinding wheel tool with an outer diameter less than ¼ of a diameter of the aspheric surface; the rings are equally spaced, there are a total of N rings, and a width of any ring is jointly determined by the Nth ring, the (N−1)th ring, positioning accuracy and a generatrix equation of the aspheric surface; and the aspheric surface is enveloped by a large number of rings. A contact area between the tool and a workpiece surface is rings.

First claim

What is claimed is:

1. A method for milling a large-diameter aspheric surface by using a splicing method, the aspheric surface being a concave surface, with a generatrix equation denoted as f1, the aspheric surface having a diameter of D, and a numerical control machine tool for milling having positioning accuracy of β, wherein the aspheric surface is discretized into N rings equally spaced in an X-axis direction, Nis an integer, any ring has a width of dx=D/(2N), and a semi-diameter of the aspheric surface corresponding to the n th ring is denoted as x n ; the rings are sequentially machined via generating cutting by using an annular grinding wheel tool with an outer diameter less than ¼ of the diameter of the aspheric surface; wherein n is the ordinal number of any one of the first ring to the N th ring, and constraint conditions of the dx solution are as follows: the generatrix equation of the (N−1) th ring is denoted as f2, and the generatrix equation of the N th ring is denoted as f3; a point at x1 on f3 is denoted as (x1, z1), a point with a vector height being z1 on f2 is denoted as (x2, z1), and a point at x2 on f1 is denoted as (x2, z2), wherein x n =n*dx, x1=D/2, z1−z2=β, and x2=x1−dx.

2. The method for milling a large-diameter aspheric surface by using a splicing method according to claim 1 , wherein an equation of the generatrix equation f1 of the aspheric surface is: z 2 =2*R 0 *x−(1+k)*x 2 , wherein R 0 is a curvature radius of a vertex of the aspheric surface, the n th ring has a curvature radius of R n =sqrt(R 0 2 −k*x n 2 ), k is a quadratic conic coefficient, x is a horizontal coordinate independent variable, and z is a vertical coordinate corresponding to the x coordinate; steps for machining the aspheric surface are as follows:
(1) machining an aspheric lens body based on the curvature radius of R 0 of the vertex and the diameter of D of the aspheric surface, and machining an original spherical surface with a radius of R 0 and a diameter of D from the aspheric lens body material;
(2) fixing the aspheric lens body in step (1) on a turntable of the numerical control machine tool, and making an optical axis of the aspheric lens body coincide with a rotation axis of the turntable of the numerical control machine tool; wherein the numerical control machine tool has at least two translation motion axes: an X-axis and a Z-axis, and two rotation axes: a B-axis and a C-axis, wherein the B-axis is a rotation axis around a Y-axis, the C-axis is a rotation axis around the Z-axis, and a rotation axis of the turntable of the numerical control machine tool is located at the C-axis; and a spindle of the numerical control machine tool is located at the Z-axis;
(3) installing an annular tool on the spindle of the numerical control machine tool, wherein the annular tool has an outer diameter of TD, and a convex round chamfer between the outer diameter and an inner diameter of the annular tool has a radius of r 0 ; and TD<D/4; and establishing an origin of a workpiece coordinate system at a vertex of the original spherical surface;
(4) solving the width dx of any ring based on the N th ring, the (N−1) th ring, the positioning accuracy, and the generatrix equation of the aspheric surface; and
(5) using the annular tool on the numerical control machine tool to sequentially machine the first ring to the N th ring, wherein when the n th ring is machined,
the C-axis rotates continuously and uniformly,
x n =n*dx;
BB=a sin(( TD− 2* r 0 )/(2*( R n −r 0 )));

a B-axis coordinate is: B=a sin(x n /R n )+BB;
an X-axis coordinate of the tool center in the workpiece coordinate system is:
X T =x n +((( TD− 2* r 0 )+2* r 0 *sin( BB ))/2)*cos( B ); and

a Z-axis coordinate is:
when k=−1:
Z T =((( TD− 2* r 0 )+2* r 0 *sin( BB ))/2)*sin( B )+( R 0 −sqrt( R 0 2 −(1+ k )* x n 2 ))/(1+ k ), or

when k=−1:
Z T =((( TD− 2* r 0 )+2* r 0 *sin( BB ))/2)*sin( B )+ x n 2 /(2* R 0 );

wherein * is the multiplication operator, sqrt is the square root calculation operator, and sin, cos and a sin are the sine, cosine and arc sine operators respectively.

3. The method for milling a large-diameter aspheric surface by using a splicing method according to claim 1 , wherein the annular tool is a hollow grinding wheel tool, comprising: an electroplated diamond grinding wheel, a bronze adhesive grinding wheel and a resin grinding wheel.

4. A device for milling a large-diameter aspheric surface by using a splicing method, wherein an equation of a generatrix equation f1 of the aspheric surface is: z 2 =2*R 0 *x−(1+k)*x 2 , wherein R 0 is a curvature radius of a vertex of the aspheric surface, k is a quadratic conic coefficient, x is a horizontal coordinate independent variable, z is the vertical coordinate corresponding to the x coordinate, and a diameter is D; a numerical control machine tool for milling has positioning accuracy of β, wherein the numerical control machine tool has at least two translation motion axes: an X-axis and a Z-axis, and two rotation axes: a B-axis and a C-axis, wherein the B-axis is a rotation axis around a Y-axis, the C-axis is a rotation axis around the Z-axis, and a rotation axis of a turntable of the numerical control machine tool is located at the C-axis; a spindle of the numerical control machine tool is located at the Z-axis; an annular tool is installed on the spindle of the numerical control machine tool; the annular tool has an outer diameter of TD; a convex round chamfer between the outer diameter and an inner diameter of the annular tool has a radius of r 0 ; and TD<D/4;
the aspheric surface is discretized into N rings equally spaced in an X-axis direction, N is an integer, any ring has a width of dx=D/(2N), a corresponding aspheric semi-diameter of the n th ring is: x n : x n =n*dx; and the n th ring has a curvature radius of R n =sqrt(R 0 2 −k*x n 2 ); wherein n is the ordinal number of any one of the first ring to the N th ring;
the annular tool on the numerical control machine tool is used to sequentially machine the N 0 th ring to the N th ring, wherein when the n th ring is machined, the C-axis rotates continuously and uniformly, and an X-axis coordinate and a Z-axis coordinate of the tool center in a workpiece coordinate system are as follows:
x n =n*dx;
BB=a sin(( TD− 2* r 0 )/(2*( R n −r 0 )));

a B-axis coordinate is: B=a sin(x n /R n )+BB;
the X-axis coordinate of the tool center in the workpiece coordinate system is:
X T =x n +((( TD− 2* r 0 )+2* r 0 *sin( BB ))/2)*cos( B ); and

the Z-axis coordinate is:
when k≠−1:
Z T =((( TD− 2* r 0 )+2* r 0 *sin( BB ))/2)*sin( B )+( R 0 −sqrt( R 0 2 −(1+ k )* x n 2 ))/(1+ k ), or

when k=−1:
Z T =((( TD− 2* r 0 )+2* r 0 *sin( BB ))/2)*sin( B )+ x n 2 /(2* R 0 );

wherein * is the multiplication operator, sqrt is the square root calculation operator, and sin, cos and a sin are the sine, cosine and arc sine operators respectively.

5. A method for polishing a large-diameter aspheric surface by using a splicing method, wherein an equation of a generatrix equation f1 of the aspheric surface is: z 2 =2*R 0 *x−(1+k)*x 2 , wherein R 0 is a curvature radius of a vertex of the aspheric surface, k is a quadratic conic coefficient, x is a horizontal coordinate independent variable, z is a vertical coordinate corresponding to the x coordinate, and a diameter is D; a numerical control machine tool for milling has positioning accuracy of f1, wherein the numerical control machine tool has at least two translation motion axes: an X-axis and a Z-axis, and two rotation axes: a B-axis and a C-axis, wherein the B-axis is a rotation axis around a Y-axis, the C-axis is a rotation axis around t

Assignees

• Univ Soochow

Inventors

• Chen Xi
• Dai Zhuocheng
• Guo Peiji
• Zhu Yongxiang
• Li Chenchao

Classifications

• B23C3/023 Primary

  Milling spherical surfaces · CPC title

• B24B13/00 Primary

  Machines or devices designed for grinding or polishing optical surfaces on lenses or surfaces of similar shape on other work; Accessories therefor (edging optical work, e.g. lenses, prisms B24B9/14) · CPC title

• B24B13/06 Primary

  grinding of lenses, the tool or work being controlled by information-carrying means, e.g. patterns, punched tapes, magnetic tapes · CPC title

• B24B51/00

  Arrangements for automatic control of a series of individual steps in grinding a workpiece (if applicable to other machine tools, G05B takes precedence) · CPC title

• B24B57/02

  for feeding of fluid, sprayed, pulverised, or liquefied grinding, polishing or lapping agents · CPC title