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

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:

• z2=2*R0*x−(1+k)*x2, wherein R0 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 r0;
• 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 nth ring is:
• xn:
• xn=n*dx;
• and the nth ring has a curvature radius of Rn=sqrt(R02−k*xn2);
• wherein n is the ordinal number of any one of the first ring to the Nth ring;
• the annular tool on the numerical control machine tool is used to sequentially machine the N0th ring to the Nth ring, wherein when the nth 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:
• xn=n*dx;
• BB=a sin((TD−2*r0)/(2*(Rn−r0)));
• a B-axis coordinate is:
• B=a sin(xn/Rn)+BB;
• the X-axis coordinate of the tool center in the workpiece coordinate system is:
• XT=xn+(((TD−2*r0)+2*r0*sin(BB))/2)*cos(B);
• and
• the Z-axis coordinate is:
• when k≠−1:
• ZT=(((TD−2*r0)+2*r0*sin(BB))/2)*sin(B)+(R0−sqrt(R02−(1+k)*xn2))/(1+k), or
• when k=−1:
• ZT=(((TD−2*r0)+2*r0*sin(BB))/2)*sin(B)+xn2/(2*R0);
• 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.

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:

• z2=2*R0*x−(1+k)*x2, wherein R0 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 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 polishing disk is installed on the spindle of the numerical control machine tool;
• the annular polishing disk has an outer diameter of TD;
• a convex round chamfer between the outer diameter and an inner diameter of the annular polishing disk has a radius of r0;
• 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 nth ring is:
• xn:
• xn=n*dx;
• and the nth ring has a curvature radius of Rn=sqrt(R02−k*xn2);
• wherein n is the ordinal number of any one of the first ring to the Nth ring;
• the annular polishing disk on the numerical control machine tool is used to sequentially machine the first ring to the Nth ring, wherein when the nth ring is machined, the C-axis rotates continuously and uniformly, and a polishing powder solution is sprayed between the annular polishing disk and the large-diameter aspheric lens during the machining process;
• the polishing powder solution is selected based on a hardness of a material to be polished, and polishing powder comprises aluminum oxide, cerium oxide, diamond micro powder and white corundum micro powder;
• an X-axis coordinate and a Z-axis coordinate of the tool center in a workpiece coordinate system are respectively:
• xn=n*dx;
• BB=a sin((TD−2*r0)/(2*(Rn−r0)));
• a B-axis coordinate is:
• B=a sin(xn/Rn)+BB;
• the X-axis coordinate of the tool center in the workpiece coordinate system is:
• XT=xn+(((TD−2*r0)+2*r0*sin(BB))/2)*cos(B);
• and
• the Z-axis coordinate is:
• when k≠−1:
• ZT=(((TD−2*r0)+2*r0*sin(BB))/2)*sin(B)+(R0−sqrt(R02−(1+k)*xn2))/(1+k), or
• when k=−1:
• ZT=(((TD−2*r0)+2*r0*sin(BB))/2)*sin(B)+xn2/(2*R0);
• 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.