US 12,162,112 B2 · Mid-frequency error-free machining method under magneto-rheological polishing magic angle-step

Abstract

A mid-frequency error-free machining method under a magneto-rheological polishing magic angle-step includes the following steps: measuring a magneto-rheological removal function, and determining a control accuracy of a machine tool; performing two-dimensional Fourier transform on the removal function, performing compensating filtering on a frequency spectrum based on the control accuracy of the machine tool, and analyzing a corresponding step at the lowest point of an amplitude of the two-dimensional frequency spectrum that undergoes filtering in a direction of a magic angle; planning a grid path under the given step on the basis of adjusting a direction of a machining path or a posture of a magneto-rheological polishing wheel to allow an included angle between the polishing wheel and the path kept to be at the magic angle; and finally, controlling the machining of the machine tool.

A mid-frequency error-free machining method under a magneto-rheological polishing angle-step, comprising:

(1) determining a removal function R(x, y) by performing a removal function test by a polishing process to extract the removal function R(x, y) or using a known removal function directly;
(2) acquiring a control accuracy δ of a machine tool by reading a parameter list of the machine tool or measuring a positioning accuracy δ of the magneto-rheological machine tool;
(3) performing frequency spectrum filtering analysis by performing two-dimensional Fourier transform on the removal function R(x, y) to obtain a frequency spectrum function F(fx, fy), and filtering the frequency spectrum function by a filtering method as follows:
F
⁡
(
f
x
,
f
y
)
=
F
⁡
(
R
⁡
(
x
,
y
)
)
F
m
⁡
(
f
x
,
f
y
)
=
2
⁢
⁢
δ
⁢
⁢
f
2
1
-
δ
2
⁢
f
2
·
∫
1
1
+
δ
⁢
⁢
f
1
1
-
δ
⁢
⁢
f
⁢
F
⁡
(
η
⁢
⁢
f
x
,
η
⁢
⁢
f
y
)
⁢
d
⁢
⁢
η
Wherein
⁢
⁢
f
=
f
x
2
+
f
y
2
;
(4) determining a step d by analyzing a lowest amplitude position of a frequency spectrum Fm(fx, fy) that undergoes filtering at an angle θ, and when a formula as follows is met, determining that a corresponding included angle and a path step are optimal machining parameters:
min
⁢
⁢
E
⁡
(
d
)
=
F
m
⁡
(
f
x
,
f
y
)
=
F
m
⁡
(
1
d
·
cos
⁢
⁢
θ
,
1
d
·
sin
⁢
⁢
θ
)
s
.
t
⁢
⁢
d
≥
d
min
,
θ
=
60
⁢
°
±
10
⁢
°
,
wherein dmin is a minimum step permissible for the machine tool;
(5) generating an angle-step path by according to the step d obtained in step (4), keeping a line feed distance of the path at d, and keeping an included angle between a path direction and a rotary direction of a magneto-rheological polishing wheel always at an angle of θ, at a moment a path equation being expressed as:
{
x
i
⁡
(
t
)
=
g
⁡
(
i
⁢
⁢
mod
⁢
⁢
2
)
·
t
·
sin
⁢
⁢
θ
+
i
·
d
·
cos
⁢
⁢
θ
-
R
y
i
⁡
(
t
)
=
g
⁡
(
i
⁢
⁢
mod
⁢
⁢
2
)
·
t
·
cos
⁢
⁢
θ
+
i
·
d
·
sin
⁢
⁢
θ
-
R
⁢
0
≤
t
≤
2
⁢
R
⁢
⁢
g
⁡
(
x
)
=
{
-
1
x
=
0
1
x
=
1
;
⁢
wherein
⁢
⁢
i
=
0
,
1
,
…
⁢
⁢
2
⁢
R
d
with each i corresponds to a grid line in the path;
and R is a radius of a travel area of the path;
(6) detecting surface-shape error distribution by performing surface-shape error measurement on elements to be machined by using surface-shape detection equipment to obtain the surface-shape error distribution E(x, y);
(7) calculating distribution of residence time by sampling a path of the elements to be machined at intervals of d distance to obtain coordinates of a discrete point that serve as sampling points, and calculating the distribution of the residence time T(x, y) at a position of each sampling point based on the surface-shape error distribution E(x, y);
(8) calculating a distribution of a feed rate for machining V(x, y) by a formula as follows:
V
⁡
(
x
,
y
)
=
d
T
⁡
(
x
,
y
)
;
and
(9) generating a numerical control code according to an optimal path obtained in step (4) and the distribution of the feed rate for machining V(x, y) obtained in step (8), and planning a grid path under the given step on the basis of adjusting a direction of a machining path or a posture of a magneto-rheological polishing wheel to allow an included angle between the polishing wheel and the path to be at the angle;
and controlling the machine tool to implement magneto-rheological polishing on the elements to be machined.

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Mid-frequency error-free machining method under magneto-rheological polishing magic angle-step

Life of this patent

Mid-frequency error-free machining method under magneto-rheological polishing magic angle-step

Life of this patent

Abstract

Claims2