US 12,194,657 B2 · Variable-step-distance micro-milling repair cutter path generating method for damage points on surface of optical crystal

Abstract

A variable-step-distance micro-milling repair cutter path generating method for damage points on a surface of an optical crystal related to a field of optical material and optical element surface repair and includes steps of establishing a mathematical model of a repair profile; determining discrete contact points between a cutter and the repair profile to obtain a cutter contact control point set by a GPR path generating method to control a movement trend of a pseudo-random path; interpolating the cutter position control point set into a spatial curve by a NURBS modeling method; creating a UG curve in a UG software according to the mathematical model, and using the UG curve as the repair path to perform a machining process simulation. The method has good elimination effects on cutter marks with constant period and improves the ability of the KDP crystal to resist strong laser damage.

A variable-step-distance micro-milling repair cutter path generating method for damage points on a surface of an optical crystal, comprising:

step 1:
designing a damage repair profile with suitable depth and width according to a laser damage degree of a surface of a potassium dihydrogen phosphate (KDP) crystal and morphological characteristics of damage points;
establishing a mathematical model of the damage repair profile;
determining a conical repair profile as a laser-friendly repair profile;
establishing a mathematical model of the conical repair profile, and a control equation is as follows:
z
=
f
⁡
(
x
,
y
)
=
-
D
2
⁢
h
⁢
x
2
+
y
2
+
h
(
1
)
wherein x, y, and z respectively represent a Cartesian coordinate value of any point on the conical repair profile;
D is a width of the conical repair profile;
h is a depth of the conical repair profile;
since the mathematical model of the conical repair profile is a revolving model, if ρ2=x2+y2, coordinates of any point P on the conical repair profile is P=(x,y,z);
the point P is expressed in polar coordinates as P=(ρ, θ) and satisfies:
{
x
=
ρ
⁢
cos
⁢
θ
y
=
ρ
⁢
sin
⁢
θ
z
=
f
⁡
(
x
,
y
)
(
2
)
step 2:
determining Gaussian pseudo-random (GPR) path generation parameters according to a processing requirement;
determining discrete contact points between a cutter and the conical repair profile when the cutter is milling the conical repair profile to obtain a cutter contact control point set by a GPR path generating method;
wherein the cutter contact control point set is configured to control a movement trend of a pseudo-random path;
a process is as follow:
adopting a spiral repair path with a cutting depth and a step distance;
generating pseudo-random cutter contact control points by adjusting polar angles and polar diameters under a GPR strategy;
when establishing a GPR path, a first cutter contact control point is initialized, and the first cutter contact control point is initialized to a point on an edge of the conical repair profile where a polar angle is 0, wherein
PCC0=(D/2,0) (3)
other cutter contact control points are generated by a polar diameter and polar angle control equation as follow:
{
θ
i
⁢
=
θ
i
-
1
+
K
lg
⁡
(
ρ
i
-
1
)
+
b
ρ
i
⁢
=
D
2
-
θ
i
2
⁢
π
⁢
μ
-
δ
i
,
⁢
i
=
1
,
2
,
3
,
⋯
(
4
)
a formula (4) gives a distribution law of an ith cutter contact control point PiCC=(ρi, θi);
in a circumferential direction of the conical repair profile, a polar angle θi gives a stepped size
K
lg
⁡
(
ρ
i
-
1
)
+
b
related to ρi−1 on a basis of θi−1:
K and b are polar angle adjustment parameters;
by adjusting values of K and b, a sparseness of the cutter contact control points in the conical repair profile under different polar diameters is adjusted;
a pseudo-random processing is performed on the polar diameters in a radial direction of the conical repair profile;
where
D
2
-
θ
i
2
⁢
π
⁢
μ
is a pole diameter of the cutter contact control points on the spiral repair path, and δi is an offset of the cutter contact control points to the spiral repair path;
when θi∈[0, 2π), δi=0;
when θi∈[2π, +∞), δi is a pseudo-random number that satisfies a Gaussian distribution δi˜N(μ,σ2);
μ represents a mean;
σ represents a standard deviation and is a pseudo-random adjustment parameter configured to adjust a change degree of the step distance;
bandwidth constraint and adjacent constraint are performed on a generation range of the pseudo-random number;
in (5), ε is a half-bandwidth of the pseudo-random number, and n is an adjacent constraint parameter of the cutter contact control points,
{
|
δ
i
|
<
E
|
δ
i
-
δ
i
-
1
|
<
η
(
5
)
a spiral-like distribution of cutter contact control points is continuously introduced by performing formulas (4)-(5) until the cutter contact control points tangent to a bottom of the revolving model to form the cutter contact control point set;
step 3:
calculating central positions of a ball-end cutter one-to-one corresponding to the cutter contact control points to form a cutter position control point set by the established mathematical model of the repair profile and a size of a selected KDP crystal micro-milling cutter;
wherein the central positions are defined as the cutter position control points;
wherein the KDP crystal micro-milling cutter is a ball-end micro-milling cutter made of cubic boron nitride (CBN);
the cutter position control points PCL are obtained to form the cutter position control point set according to a direction of a curved surface at each of the cutter position control points and a radius Rc of the ball-end micro-milling cutter, where a calculation equation is as follows:
{
P
C
⁢
L
(
j
)
=
P
C
⁢
C
(
j
)
+
R
c
⁢
v
(
j
)
→
|
v
(
j
)
→
|
v
(
j
)
→
=
(
∂
f
∂
x
,
∂
f
∂
y
,
⁢
-
1
)
⁢
|
x
=
x
i
,
y
=
y
i
(
6
)
step 4:
interpolating the cutter position control point set into a spatial curve by a non-uniform rational B-splines (NURBS) modeling method;
a mathematical model of the spatial curve is multiple cubic equation sets controlled by a unique parameter;
wherein in the GPR strategy, the cutter position control points are the discrete contact points on the spiral repair path and are treated as value points;
there are n+1 points in the cutter position control point set, the n+1 points are discrete value points of a kth NURBS curve;
the kth NURBS curve is interpolated as the spiral repair path;
a rational polynomial vector function of the NURBS curve is as follows:
p
⁡
(
u
)
=
∑
i
=
0
n
⁢
ω
i
⁢
d
i
⁢
N
i
,
k
⁡
(
u
)
∑
i
=
0
n
⁢
ω
i
⁢
N
i
,
k
⁡
(
u
)
(
7
)
wherein dii is a curve control vertex and is obtained by an inverse calculation of a cutter position control points PCL;
ωi is defined as a weight factor and is configured to assign weights to the curve control vertex;
in a KDP crystal repair model, each curve control vertex di has a same weight when generating the NURBS curve, so each weight factor ωi=1 (i=0,1, . . . ,n);
Ni,k(u) is a kth standard B-spline basis function defined by a node vector U=[u0,u1, . . . , un+k+1] according to a Cox-De Boor recurrence formula;
wherein
{
N
i
,
0
⁡
(
u
)
=
{
1
,
u
i
≤
u
≤
u
i
+
1
0
,
other
N
i
,
k
⁡
(
u
)
=
u
-
u
i
u
i
+
k
-
u
i
⁢
N
i
,
k
-
1
⁡
(
u
)
+
u
i
+
k
+
1
-
u
u
i
+
k
+
1
-
u
i
+
1
⁢
N
i
+
1
,
k
-
1
⁡
(
u
)
define
⁢
⁢
0
0
=
0
(
8
)
in the GPR strategy, the n+1 cutter position control points PCL have a node vector U=[u0,u1, . . . , un+6], in order to determine a ui+3 corresponding to PiCL (i=0,1, . . . , n), the value points are parameterized, ui+3 represent a chord length;
considering a large change in distances between the cutter position control points, a cumulative chord length parameterization method of a formula (9) is applied to reflect a distribution of data points according to a chord length:
{
u
0
=
u
1
=
u
2
=
u
3
=
0
u
i
+
3
=
u
i
+
2
+
|
P
C
⁢
L
i
-
P
C
⁢
L
i
-
1
|
/
∑
i
=
1
n
⁢
|
P
C
⁢
L
i
-
P
C
⁢
L
i
-
1
|
⁢
i
=
1
,
2
,
⋯
⁢
,
⁢
n
-
1
,
⁢
u
n
+
3
=
u
n
+
4
=
u
n
+
5
=
u
n
+
6
=
1
(
9
)
as long as there are control vertices di, a NURBS repair path of the ball-end micro-milling cutters is calculated;
then weighted control vertices of the NURBS curve are inversely calculated;
for a cubic NURBS curve generated by n+1 PCL, there are n+3 control vertices, and the cubic NURBS curve is defined as a formula (10), where u∈[ui,ui+1]⊂[u3,un+3];
p
i
⁡
(
u
)
=
∑
j
=
i
-
3
i
⁢
d
j
⁢
N
j
,
k
⁡
(
u
)
(
10
)
p
⁢
(
u
i
+
3
)
=
∑
j
=
i
i
+
3
⁢
d
j
⁢
N
j
,
3
⁡
(
u
i
+
3
)
=
P
C
⁢
L
i
,
i
=
0
,
1
,
⋯
⁢
,
n
(
11
)
substituting nodal values in a definition domain of the cubic NURBS curve into the equations in turn, and the cubic NURBS curve of different segments are continuous at the value points, which is defined as a formula (11);
n+1 equations in the formula (10) and formula (11) are not enough to determine n+3 unknown weighted control vertices, so two additional equations (12) are given by boundary conditions:
p
0
′
⁡
(
0
)
=
3
⁢
⁢
ω
1
ω
0
⁢
(
d
1
-
d
0
)
u
4
-
u
3
.
p
n
′
⁡
(
1
)
=
3
⁢
ω
n
+
1
ω
n
+
2
⁢
(
d
n
+
2
-
d
n
+
1
)
u
n
+
3
-
u
n
+
2
(
12
)
[
1
a
2
b
2
c
2
⋱
⋱
⋱
a
n
b
n
c
n
1
]
·
[
d
1
d
2
⋮
d
n
d
n
+
1
]
=
[
e
1
e
2
⋮
e
n
e
n
+
1
]
(
13
)
linear equation sets in the equation (13) are obtained by the two additional equations (12);
and all weighted control vertices are obtained;
then the weighted control vertices are substituted into the equation (10) to obtain a NURBS curve equations set after interpolation of cutter position control point PCL;
there are n sets of the linear equation sets, and each of the linear equation sets has three equations;
the three equations are the equations of u on x, y, and z components of a curve between adjacent cutter position control points PCL:
the three equations are second-order continuous at the cutter position control points PCL;
parameter equation is used as the repair path of the KDP crystal to realize digitization of the repair path, and only related parameter is the chord length u;
step 5:
creating a graphical curve in a computer aided design software according to the mathematical model of the spatial curve, and using the graphical curve as the repair path to performed a machining process simulation;
if a simulation result meets safety and manufacturability requirements of a machining cutter path, a step 6 is performed;
if not, the step 2 is repeated to check the processing requirement and adjust the GPR path generation parameters;
wherein in the step 5, a calculated NURBS curve equation is imported into a CAM module of the computer aided design software;
the machining process simulation is performed in a curve-driven manner, then whether the simulation result meets the safety and manufacturability requirements of the machining cutter path is checked;
if the simulation result meets the safety and manufacturability requirements of the machining cutter path, step 6 is performed;
if not, the step 2 is repeated to check the process and modify the GPR path generation parameters;
the step 6, converting the machining process simulation of the step 5 into general numerical control (NC) codes, and performing precision micro-milling repair on the KDP crystal on a KDP crystal repair machine;
wherein in the step 6, a conventional repair process simulation and a GPR variable-step-distance repair process simulation are converted into the NC codes through a post-processor of the computer aided design software, and the precision micro-milling repair of the KDP crystal is performed on the KDP crystal repair machine.

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Variable-step-distance micro-milling repair cutter path generating method for damage points on surface of optical crystal

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Variable-step-distance micro-milling repair cutter path generating method for damage points on surface of optical crystal

Life of this patent

Abstract

Claims4