US 2026/0310169 A1 · TRAJECTORY OPTIMIZATION METHOD FOR SLOW TOOL SERVO TURNING OF COMPLEX CURVED SURFACES BASED ON CURVATURE GRADIENT CLUSTERING AND TRAJECTORY ERROR CONSTRAINTS

Abstract

The present disclosure discloses a trajectory optimization method for Slow Tool Servo (STS) turning of complex curved surfaces based on curvature gradient clustering and trajectory error constraints, which belongs to the technical fields of ultra-precision cutting machining and Computer Numerical Control (CNC) trajectory optimization. The method comprises the following steps: Step 1, performing trajectory parameterization and initial equal-angle sampling; Step 2, calculating a trajectory curvature and curvature gradient; Step 3, performing automatic region classification based on curvature gradient density; Step 4, performing point deletion in the flat regions based on target error constraints; Step 5, performing global error validation and conducting local encryption of out-of-tolerance feedback; Step 6, outputting a final optimized trajectory point set.

A trajectory optimization method for Slow Tool Servo (STS) turning of complex curved surfaces based on curvature gradient clustering and trajectory error constraints comprises the following steps:

Step 1, performing trajectory parameterization and initial equal-angle sampling;
Step 2, calculating a trajectory curvature c(θ) and curvature gradient G(θ), specific steps are as follows:
Step 2-1, defining a trajectory space vector r(θ) in terms of a trajectory parameter θ, and defining derivative vectors r1(θ) and r2(θ):
r
⁡
(
θ
)
=
[
x
⁡
(
θ
)
y
⁡
(
θ
)
z
⁡
(
θ
)
]
,
r
1
(
θ
)
=
dr
d
⁢
θ
,
r
2
(
θ
)
=
d
2
⁢
r
d
⁢
θ
2
,
Wherein x(θ) and y(θ) are coordinates in a rectangular coordinate system corresponding to a polar angle θ;
then the trajectory curvature c(θ) is:
κ
⁡
(
θ
)
=

r
1
(
θ
)
×
r
2
(
θ
)


r
1
(
θ
)

3
Step 2-2, denoting an arc length differential as ds=∥r1(θ)∥dθ, and integrating with respect to θ over the arc length yields
s
⁡
(
θ
)
=
∫
0
θ

r
1
(
u
)

⁢
du
,
then the curvature gradient G(θ) is:
G
⁡
(
θ
)
=
❘
"\[LeftBracketingBar]"
d
⁢
κ
ds
❘
"\[RightBracketingBar]"
Step 2-3, according to the initial trajectory point set , calculating a curvature gradient set {G(θi)};
Step 3, performing automatic region classification based on curvature gradient density, specific steps are as follows:
Step 3-1, constructing a one-dimensional kernel density estimation for the curvature gradient set {G(θi)}, and calculating a probability density function estimate {circumflex over (p)}G(g);
Step 3-2, using a derivative method to detect local valleys on {circumflex over (p)}G(g) for determining one or more segmentation thresholds {TG,i};
Step 3-3, taking a first significant valley TG as a dividing threshold for complex/flat division:
Region
⁢
catergory
⁢
(
θ
i
)
=
{
complex
⁢
region
,
G
⁢
(
θ
i
)
>
T
G
flat
⁢
region
,
G
⁢
(
θ
i
)
≤
T
G
Step 3-4, merging continuous segments of the obtained category sequence:
for segments shorter than a minimum length threshold Lmin, merging them into a more similar adjacent side based on a median or mean of neighboring segments, thereby eliminating isolated short segments caused by noise;
Step 4, performing point deletion in the flat regions based on target error constraints, specific steps are as follows:
Step 4-1, for each continuous interval [θa, θb] classified as flat, using interval endpoints to construct a linear interpolation reconstruction function {circumflex over (z)}(θ), and defining a local interpolation error function of the interval:
E
[
a
,
b
]
(
θ
)
=
❘
"\[LeftBracketingBar]"
f
⁡
(
ρ
⁡
(
θ
)
⁢
cos
⁢
θ
,
ρ
⁡
(
θ
)
⁢
sin
⁢
θ
)
-
z
^
[
a
,
b
]
(
θ
)
❘
"\[RightBracketingBar]"
Wherein f(ρ(θ)cos θ),ρ(θ)sin θ) is a theoretical sagittal height at the polar angle θ, and {circumflex over (z)}[a, b](θ) is a sagittal height obtained through linear interpolation at polar angle θ;
a basis for point deletion is:
max
θ
∈
(
θ
a
,
θ
b
)
E
[
a
,
b
]
(
θ
)
≤
Δ
⁢
z
tol
Wherein Δztol is the trajectory target error;
Step 4-2, using a following numerical decision logic to efficiently find a maximum internal interval that can be deleted:
starting from a left endpoint θa of the interval, attempt to quickly find a right endpoint θb through exponential expansion such that the local maximum error of the interval [θa, θb] is less than the trajectory target error Δztol;
if an expansion fails, determine a maximum deletable right endpoint via binary search between a last successful position and a failed position;
marking all deletable interior points within this maximum interval as “deletable”;
then, starting from this right endpoint, continue repeating the above steps moving rightward until the end of the interval is reached;
Step 5, performing global error validation and conducting local encryption of out-of-tolerance feedback;
Step 6, outputting a final optimized trajectory point set.

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Trajectory optimization method for slow tool servo turning of complex curved surfaces based on curvature gradient clustering and trajectory error constraints

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Trajectory optimization method for slow tool servo turning of complex curved surfaces based on curvature gradient clustering and trajectory error constraints

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Abstract

Claims6