US 11,467,066 B2 · Method for determining the preload value of the screw based on thermal error and temperature rise weighting

Abstract

A method for determining the preload value of the screw based on thermal error and temperature rise weighting. Firstly, thermal behavior test of the feed shaft under typical working conditions is carried out to obtain the maximum thermal error and the temperature rise at the key measuring points in each preloaded state. Then, a mathematical model of the preload value of the screw and the maximum thermal error is established; meanwhile, another mathematical model of the preload value of the screw and the temperature rise at the key measuring points is also established. Finally, the optimal preload value of the screw is obtained. The thermal error of the feed shaft and the temperature rise of the moving components are comprehensively considered, improving the processing accuracy and accuracy stability of the machine tool, and ensuring the service life of the moving components such as bearings.

A method for determining a preload value of a screw based on thermal error and temperature rise weighting, wherein, firstly, under a different preload states of the screw, a thermal behavior test of a feed shaft under typical working conditions is carried out to obtain a maximum thermal error and a temperature rise at a key measuring points in each preload state;

then, a mathematical model of the preload values of the screw and the maximum thermal error is established and, meanwhile, a mathematical model of the preload value of the screw and the temperature rise at the key measuring points is also established;
finally, a optimal preload value of the screw is obtained by optimizing a weighting function of the maximum thermal error and the temperature rise at each measuring point as an objective function;
specific steps are as follows:
first step is a thermal behavior test of the feed shaft under typical working conditions;
a first temperature sensor is located on a front bearing of a feed system, a second temperature sensor is located on a nut, a third temperature sensor is located on a rear bearing of the feed system, and a fourth temperature sensor is located on a bed near the screw;
a motion trajectory of a machine tool is analyzed when machining workpieces, and a motion information of the feed shaft is extracted, including a travel range, a feed speed and a running frequency;
in a different preload states of the screw, the preload value of the screw is measured by a preload angle of the preload nut, and a thermal behavior test of the feed shaft is performed:
in an initial thermal steady state, a full-range positioning error of the feed shaft is measured by a laser interferometer, and a temperature value of the first temperature sensor, the second temperature sensor, the third temperature sensor and the fourth temperature sensor are recorded;
the feed shaft is heated under a motion process, and the full-range positioning error of the feed shaft and a temperature of each measuring point under the motion process is tested regularly, that is a testing process and it stop until the screw reaches thermal balance;
second step is to calculate the maximum thermal error of the feed shaft and the temperature rise at the key measuring points;
based on the temperature value collected in the first step, the maximum thermal error of the feed shaft is calculated according to equation (1) for each preload condition:
thermal error of the feed shaft is calculated according to equation (1) for each preload condition:
Emax_i=Ei(Mi,N)−Ei(1,N) (1)
where:
Emax_i is the maximum thermal error when an ith preload value is used;
Mi is a number of positioning error tests when the ith preload value is used;
N is a number of points for the positioning error test;
Ei(Mi, N) is a Nth point data of a Mith positioning error test when the ith preload value is used;
Ei(1,N) is the Nth point data of a first positioning error test when the ith preload value is used;
the temperature rise of each measuring point under each preload value is calculated according to equation (2):
ΔTi,j=[Ti,j(Mi)−Ti,j(1)]−[Ti,4(Mi)−Ti,4(1)] (2)
wherein:
ΔTi,j is the temperature rise of a jth temperature sensor when an ith preload value is used;
Ti,j(Mi) is a Mith measurement value of the jth temperature sensor when the ith preload value is used;
Ti,j(1) is a first measurement value of the jth temperature sensor when the ith preload value is used;
Ti, 4(Mi) is the Mith measurement value of the fourth temperature sensor when the ith preload value is used, and Ti,4 (1) is a first measurement value of the fourth temperature sensor when the ith preload value is used;
third step is to establish a mathematical model of the preload values of the screw and the maximum thermal error and another mathematical model of the preload values of the screw and the temperature rise at the key measuring points;
a relationship between the preload value of the screw and the maximum thermal error of the feed shaft is as shown in equation (3):
Emax=a0−a1×A (3)
where:
Emax is the maximum thermal error of the feed shaft, A is the preload value of the screw, that is, a locking angle of the preload nut, and a0 and a1 are coefficients;
a mathematical model of the preload value of the screw and the temperature rise of the jth temperature sensor is shown in equation (4):
Δ
⁢
T
j
=
b
j
,
0
+
b
j
,
1
×
e
(
b
j
,
2
×
A
)
(
4
)
where:
ΔTj is the temperature rise of the jth temperature sensor, and bj,0, bj,1, and bj,2 are coefficients;
according to the maximum thermal error and temperature rise data of the screw under different preload values obtained in the second step, the coefficients a0, a1, bj,0, bj,1, and bj,2 in formula (3) and formula (4) are identified by a least squares method;
fourth step is to calculate the optimal preload value of the screw;
the weighting functions of the maximum thermal error and temperature rise at key measuring points are shown in equation (5):
F
⁡
(
E
max
,
Δ
⁢
⁢
T
j
)
=
λ
0
×
E
max
+
∑
j
=
1
3
⁢
λ
j
⁢
Δ
⁢
⁢
T
j
(
5
)
where:
λ0 is a weight coefficient of the maximum thermal error of the feed shaft, and λj is a weight coefficient of the temperature rise of the jth temperature sensor;
rewriting equation (5) according to equations (3) and (4) gives:
F
⁡
(
A
)
=
λ
0
×
(
a
0
-
a
1
×
A
)
+
∑
j
=
1
3
⁢
λ
j
⁡
(
b
j
,
0
+
b
j
,
1
×
e
(
b
j
,
2
×
A
)
)
(
6
)
through automatic optimization based on equation (7), the optimal preload value of the screw can be obtained;
min
⁡
[
F
⁡
(
A
)
]
=
min
⁡
[
λ
0
×
(
a
0
-
a
1
×
A
)
+
∑
j
=
1
3
⁢
λ
j
⁡
(
b
j
,
0
+
b
j
,
1
×
e
(
b
j
,
2
×
A
)
)
]
(
7
)
A
min
≤
A
≤
A
max
where:
Amin and Amax are a lower and upper limits of the preload value A of the screw respectively in the automatic optimization process.

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Method for determining the preload value of the screw based on thermal error and temperature rise weighting

Life of this patent

Method for determining the preload value of the screw based on thermal error and temperature rise weighting

Life of this patent

Abstract

Claims1