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Abstract The measurement and compensation of volumetric positioning errors can be used to significantly improve the accuracy of machine tools. In this paper, a sequential step diagonal measurement is introduced to measure nine volumetric positioning errors in a short time. Measurements under various thermal conditions are preformed to under-stand the relationship between the volumetric positioning errors and the machine temperature field and variations. A radial basis function neural network is used to predict the volumetric positioning errors at all positions based on the temperature distribution of the machine. Compensation experiment is carried out to validate the performance of the measurement and the prediction method. The experi-mental results show that the volumetric accuracy of the machine tool is significantly improved by the error compensation.20215
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Keywords Machine tools .Volumetric positioning errors .Diagonal measurement .Neural network .Error compensation
1 Introduction
Computer numerical controlled (CNC) machine tools with
high volumetric positioning accuracy are required, because
of the growing demand of precision components in
manufacturing. In recent years, many researches have been
carried out on the compensation for volumetric positioning
errors of machine tools [1–3]. To implement the error
compensation scheme, it is necessary to measure the
machining errors first. A laser interferometer system is
most widely used for machine tool calibration even though
many other measurement techniques are also used, such as
the double ball bar [4, 5] or the cross-grid encoder method
[6].
There are two ways to obtain the volumetric positioning
errors, direct error measurement, and indirect error mea-
surement. For direct error measurement, only one compo-
nent of volumetric positioning errors can be measured at
one time. This makes the measurement a tedious and time-
consuming task. For this reason, many measurement
methods have been proposed to improve the measurement
efficiency. With these methods, the volumetric error
components are identified with the combination of the
measurement results and the volumetric error model
derived with the rigid body kinematics [2, 7]. Zhang et al.
[8] developed a displacement method to obtain the error
components by measuring the errors along 22 lines. Some
lines were constrained along specific paths, which made the
method difficult to implement. Chen et al. [9] proposed an
auto-alignment laser interferometer system which can
quickly measure the 21 error components along 22 lines.
Chen et al. [10] further improved Zhang’s approach by
measuring the positioning errors along only 15 lines.3 Sequential step diagonal measurement method
The body diagonal displacement test defined in the ASME
B5.54 [18] or ISO 230-6 standard is a good and quick way
to check the volumetric errors. Although it has been proved
to be useful and successful, it is not clear what is the
relationship between the body diagonal displacement errors
and the 3D positioning errors because of the lack of enough
data to identify these errors.
Compared with the conventional diagonal measurement,
the data in the sequential step diagonal measurement
method are collected after each axis moved an increment,
while the data are collected only along the diagonal
direction in the conventional diagonal measurement. As is
shown in the Fig. 3, P0 and P1 are two measurement points
respectively along the diagonal. With the conventional
diagonal measurement method, first, acquire the diagonal
displacement RP0
of point P0, and then move the measure-
ment point to the P1 by moving the X-, Y-, and Z-axis
simultaneously, the data collected is the diagonal displace-
ment RP1