US 2022/0065746 A1 · Detection method for radial deformation of flexspline of harmonic reducer under installation eccentricity state

Abstract

The invention discloses a detection method for radial deformation of flexspline of harmonic reducer under installation eccentricity state, taking the center of wave generator as the origin, the reference coordinate system is established in the method, and the offset between the center of wave generator and the pivotal center of rotary table is calculated by measuring the standard circle coaxial with the wave generator; the radial deformation function and the offset of wave generator under eccentricity state are taken to the theoretical ellipse eccentricity mathematical model to obtain the parameters of the actual ellipse; the offset and ellipse parameters are taken into the radial runout correction model of the flexspline to obtain the correction model under eccentricity state; the flexspline deformation function is measured and the correction model is taken to obtain the radial deformation function of the flexspline under standard state. This method solves the problem of installation eccentricity in the process of deformation detection of the flexspline, and obtains a more accurate variation function of the flexspline, and provides a more accurate practical basis for the design and optimization of the tooth shape.

A detection method for radial deformation of flexspline of harmonic reducer under installation eccentricity state, comprising the following steps:

W1. establish reference coordinate system;
taking a center of wave generator as an origin, a reference coordinate system O is established;
in this coordinate, an eccentric coordinate of a pivotal center of rotary table is (ex,ey);
W2. establish a function model of standard circle and a function model of ellipse under theoretical eccentricity state;
1) standard circle under eccentricity state
in the reference coordinate system O, r is a radius of standard circle;
ex is an offset of measuring line;
r0 is a radius of eccentric circle;
d0 is distance variation of measuring points;
θ is a rotation angle;
the function model of standard circle under eccentricity state is as follows:
{
b
2
+
d
1
2
-
2
⁢
bd
1
⁢
⁢
cos
⁡
(
w
)
=
r
2
d
1
-
r
-
r
2
-
e
x
2
=
d
0
⁢
⁢
⁢
therein
⁢
:
⁢
⁢
cos
⁢
⁢
δ
=
e
x
r
0
;
cos
⁡
(
w
)
=
e
x
⁢
r
0
⁢
⁢
cos
⁡
(
δ
-
θ
)
r
0
2
-
b
⁢
r
0
2
-
e
x
2
(
1
⁢
-
⁢
1
)
according to formula (1-1), the function model of standard circle under eccentricity state is obtained:
d0=f(θ);
measured parameters of standard circle are respectively taken into formula (1-1) to obtain an offset of actual circle (ex, ey);
2) elliptic curve under eccentricity state;
the coordinate system is established with the ellipse center as the center, θ is the rotation angle, set a focus of a measuring line and an ellipse as (x, y), and the coordinate of the rotation center as (ex,−ey) ;
(
x
,
y
)
=
{
x
2
a
2
+
y
2
b
2
=
1
⁢
cos
⁢
⁢
δ
=
e
x
(
x
-
e
x
)
2
+
(
y
+
e
y
)
2
cos
⁢
⁢
δ
=
-
x
+
e
x
(
x
-
e
x
)
2
+
(
y
+
e
y
)
2
w
+
θ
=
δ
⁢
(
1
⁢
-
⁢
2
)
d
=
(
x
-
e
x
)
2
+
(
y
+
e
y
)
2
-
e
x
2
(
1
⁢
-
⁢
3
)
a wave generator function and offset (ex,ey) are respectively taken into the above formula (1-2) and (1-3), actual ellipse parameters a and b can be obtained;
W3. establish a correction model A of a flexspline deformation function under theoretical eccentricity state;
in the reference coordinate system O, the correction model of flexspline deformation function under eccentricity state is obtained, which includes two parts:
a correction model of wave generator eccentricity error and a correction model of interval eccentricity error;
A=D+τ
the eccentricity error model of wave generator is a differential function D between wave generator B under standard state and wave generator function model C under eccentricity state:
D
=
B
-
C
therein
⁢
:
⁢
⁢
B
=
ab
a
2
⁢
⁢
cos
2
⁢
⁢
θ
+
b
2
⁢
⁢
sin
2
⁢
⁢
θ
C:
measure a wave generator function by laser rangefinder;
the interval eccentricity error correction model refers to an error model of flexible bearing and thickness of flexspline under eccentricity state, which is an interpolation function τ between standard value and eccentric value;
τ=β−β1
β is an interval variation function under theoretical state;
β1 is an interval variation function under eccentricity state;
the interval variation function β under theoretical state:
{
ρ
1
=
ab
a
2
⁢
⁢
cos
2
⁢
⁢
φ
+
b
2
⁢
⁢
sin
2
⁢
⁢
φ
⁢
ρ
2
=
(
a
+
Δ
)
⁢
(
b
+
Δ
)
(
b
+
Δ
)
2
⁢
⁢
cos
2
⁢
⁢
φ
+
(
b
+
Δ
)
2
⁢
⁢
sin
2
⁢
⁢
φ
β
=
ρ
2
-
ρ
1
⁢
(
1
⁢
-
⁢
4
)
therein Δ is the thickness;
W4. measure coaxial standard circle and wave generator parameter C and flexspline deformation parameter E
deformation parameters of coaxial standard circle, wave generator and flexspline are respectively measured by rotary table and laser rangefinder;
the deformation function C of wave generator under eccentric action is obtained;
W5. establish correction model A1 under eccentricity state
the eccentricity (ex,ey) is obtained by measured parameters of standard circle under eccentricity state and then taken to the formula to obtain the correction model A1 of the radial deformation function of the flexspline under eccentricity (ex,ey) state;
W6. corrected radial deformation function of flexspline
the radial deformation correction model A1 of the flexspline under eccentricity (ex,ey) state established in W5 is taken to the flexspline deformation function model E measured under eccentricity state:
Q=E+A1
Q is the radial deformation function model of flexspline under standard state;

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Detection method for radial deformation of flexspline of harmonic reducer under installation eccentricity state

Life of this patent

Detection method for radial deformation of flexspline of harmonic reducer under installation eccentricity state

Life of this patent

Abstract

Claims2