US 11,287,795 B2 · Self-adaptive compensation method for feed axis thermal error

Abstract

A self-adaptive compensation method for feed axis thermal error, which belongs to the field of error compensation in NC machine tools. First, based on laser interferometer and temperature sensor, the feed axis thermal error test is carried out; following, the thermal error prediction model, based on the feed axis thermal error mechanism, is established and the thermal characteristic parameters in the model are identified, based on the thermal error test data; next, the parameter identification test is carried out, under the preload state of the nut; next, the adaptive prediction model is established, based on the thermal error prediction model, while the parameters in the measurement model are identified; finally, adaptive compensation of thermal errors is performed, based on the adaptive error prediction model, according to the generated feed axis heat.

A self-adaptive compensation method for feed axis thermal error, wherein, first, based on laser interferometer and temperature sensor, a feed axis thermal error test is carried out;

following, a thermal error prediction model, based on a feed axis thermal error mechanism, is established and the thermal characteristic parameters in the model are identified, based on the thermal error test data;
next, a parameter identification test is carried out, under a preload state of a nut;
next, an adaptive prediction model is established, based on the thermal error prediction model, while the parameters in the measurement model are identified;
finally, self-adaptive compensation of thermal errors is performed, based on the adaptive error prediction model, according to a generated feed axis heat;
the steps are as follows:
step one:
feed axis thermal error test
the temperature sensor (11) is placed on a machine tool bed (9), near a screw;
a laser head (1) of the laser interferometer is placed on the ground, through a tripod, while a magnetic stand is used to fix an interference mirror (6), on a main shaft and a reflector (10) on a work table (7);
the process of the thermal test is as follows:
first, a full stroke positioning error of the feed axis is tested, under an initial thermal steady state, while the temperature sensor (11) value is recorded;
then, the feed axis performs a heat engine movement, within a certain range at a certain feed rate, until the heat balance is established;
finally, the feed axis stops at any position to cool down, until it reaches the heat balance state, again;
during this process, the feed axis full stroke positioning error is tested at regular intervals, while the value of the temperature sensor (11) is recorded;
step two:
the feed axis thermal error prediction model is established
the screw, between a front bearing (3) and a rear bearing (12), is subdivided into N segments, each length is L;
the prediction model of the real-time temperature field of the screw is:
T
i
⁡
(
t
)
=
Q
-
{
h
×
S
×
[
T
i
⁡
(
t
-
Δ
⁢
⁢
t
)
-
T
f
⁡
(
t
-
Δ
⁢
⁢
t
)
]
+
λ
×
A
⁢
[
2
×
T
i
⁡
(
t
-
Δ
⁢
⁢
t
)
-
T
i
-
1
⁡
(
t
-
Δ
⁢
⁢
t
)
-
T
i
+
1
⁡
(
t
-
Δ
⁢
⁢
t
)
]
L
}
c
×
m
+
T
i
⁡
(
t
-
Δ
⁢
⁢
t
)
(
1
)
where, Ti(t) is the temperature of the ith segment of the screw at the current moment;
Q is the heat generated by the nut, when passing through each segment of the screw;
Ti(t−Δt) is the temperature of the ith segment of the screw, at the previous moment;
λ is the heat transfer coefficient;
A is the cross-sectional area of the lead screw;
Ti−1(t−Δt) is the temperature of the (i−1)th segment of the screw, at the previous moment;
Ti+1(t−Δt) is the temperature of the (i+1)th segment of the screw, at the previous moment;
h is the convective heat dissipation coefficient;
S is the heat exchange area, between each segment of the screw and the air;
Tf(t−Δt) is the air temperature, in contact with the surface of the lead screw, at the previous moment;
c is the specific heat capacity of the lead screw material;
m is the mass of each segment of the lead screw;
the formula for calculating the predicted value EsI(t) of the thermal error, at the ith segment of the screw is:
E
s
I
⁡
(
t
)
=
∑
i
=
1
I
⁢
(
T
i
⁡
(
t
)
-
T
0
)
×
L
×
k
coff
(
2
)
where, T0 is the initial screw temperature and kcoff is the thermal expansion coefficient of the screw;
based on the automated parameter optimization method and the data obtained in the first step, the Q, h and λ thermal characteristic parameters in Eq. (1) are identified, under the constraint condition described in Eq. (3);
min
⁡
[
F
⁡
(
Q
,
h
,
λ
)
]
=
min
⁡
[
∑
u
=
1
U
⁢
∑
v
=
1
V
⁢

E
t
⁡
(
u
,
v
)
-
E
s
⁡
(
u
,
v
)

]
(
3
)
Q
min
≤
Q
≤
Q
max
⁢
⁢
h
min
≤
h
≤
h
max
⁢
⁢
λ
min
≤
λ
≤
λ
max
where, Et(u, v) represents the thermal expansion error of the vth test point, in the uth thermal error test, Es(u, v) represents the expected thermal expansion error of the vth test point, in the uth thermal error test, U is the total number of thermal error tests, V is the number of test points of each test;
Qmin, hmin and λmin are the lower limit of the parameters Q, h and λ, respectively;
Qmax, hmax and λmax are the upper limit of the parameters Q, h and λ, respectively;
step three:
the parameter identification test and data processing in the thermal error adaptive compensation model
five nut preload states:
state 1—normal preload;
state 2—preload amount reduced by 10%;
state 3—preload amount reduced by 20%;
state 4—preload amount increased by 10%;
the state 5—preload amount increased by 20%;
the following test and data processing is performed under the five states:
the test is carried out, under the condition that the M kinds of nuts are preloaded, while the normal preload state is state 1;
(1) under the initial thermal steady state, the feed axis performs a full-stroke fast-moving motion;
while the position and the torque of the servo motor is recorded synchronously, during a period of constant motion;
based on the position and torque data, the average torque is calculated, during fast-moving motion according to Eq. (4):
M
_
j
=
1
K
j
⁢
∑
k
=
1
K
j
⁢
M
j
⁡
(
k
)
⁢
⁢
j
=
1
,
2
,
…
⁢
,
M
(
4
)
where, Mj is the average torque of the pre-tightening state of the jth nut;
Kj is the number of data collected, under the pre-tightening state of the jth nut;
Mj(k) is the kth torque value, collected under the pre-tightening state of the jth nut;
the difference ΔMj between the average torque of state 2 to state 5 and the average torque of state 1 is calculated as:
ΔMj=Mj−M1 j=2,3, . . . M (5)
(2) the thermal error and machine tool bed temperature of the feed shaft heat engine is tested, for a certain period of time;
based on the thermal error prediction model and the identified h and λ values, in the second step, the thermal error and bed temperature data are identified, based on the set of thermal error and bed temperature data;
according to this group of thermal errors and bed temperature data, the Qj, j=2,3,4,5 as corresponding to the pre-tightening state of the second to the fifth lead screw, are identified;
next, the difference between Qj and the Q, identified in the second step, is calculated as:
ΔQj=Qj−Q j=2,3, . . . , M (6)
step four:
an self-adaptive prediction model for the feed axis thermal error is established
the relationship between the variation of ΔQ and the mean torque difference ΔM is:
ΔQ=α×ΔM+β (7)
where, α and β are coefficients that, based on the least squares method, are identified, according to the data {ΔQj,Mj} (j=2,3, . . . , M), obtained in the third step;
step five:
the implementation of the feed axis thermal error adaptive compensation
during the operation of the feed axis, the position of the feed axis, the feed speed and the servo motor torque data are collected and recorded in real time;
if there is a continuous R sampling period of uniform velocity motion, according to the feed rate, the following calculations are performed:
(1) the average torque, during the R cycles, is calculated, according as:
M
_
s
=
1
R
⁢
∑
k
=
1
R
⁢
M
s
⁡
(
k
)
(
8
)
where, Ms is the average torque for the R cycles and is the value of the kth torque for the R cycles;
(2) it is assumed that, the position interval range of feed axis operation in current R cycles is [P0,P1];
the torque value in the position interval [P0, P1] is extracted from the torque data, acquired in the state 1 of the third step;
the average value is calculated, as:
M
_
1
p
=
1
K
1
p
⁢
∑
k
=
1
k
1
p
⁢
M
1
p
⁡
(
k
)
(
9
)
(3) the average torque difference of the current R cycles is calculated, as:
ΔMs=Ms−M1p (10)
(4) according to ΔMs, the current ΔQs is calculated, based on Eq. (7), while adaptively the heat, generated by the nut passing through each segment of the screw, is corrected, according to:
Qnew=Q+ΔQs (11)
after applying the correction, the thermal error of the feed axis is predicted adaptively, based on Eqs. (1) and (2), while the numerical control system will adaptively compensate the feed axis, according to the predicted value.

378 more elements

Self-adaptive compensation method for feed axis thermal error

Life of this patent

Self-adaptive compensation method for feed axis thermal error

Life of this patent

Abstract

Claims1