. The difference of RP0
and RP1
is the diagonal
error . With the sequential step diagonal measurement
method, first, collect the diagonal displacement RP0
of point
P0, and then move Dx along the X-axis direction to the
middle measurement point M1 and acquire the diagonal
displacement RM1
, and next move Dy along the Y-axis
direction to the second middle measurement point M2 and
also acquire the diagonal displacement RM2
, finally move
Dz along the Z-axis direction to the point P1 and also
acquire the diagonal displacement RP1
. As there are four
displacement values, three sets of diagonal errors can be
calculated with the differences of the values one and
another, which means three times more data are obtained
than in the conventional diagonal measurement.
For a machine working volume, there are four body
diagonals directions shown in Fig. 4.Here, p means
positive direction while n means negative direction and
the sequence of the three letters is ordered by X-, Y-, and Z-
axis. Thus, 12 sets of measurement results can be identified
if these four diagonals are measured; the same variable
number in Eq. 2 given in the above section. With the
analysis, the relationship between the variables or the nine 4 Measurement of volumetric positioning error
4.1 Measurement setup
The measurements were performed on a vertical machining
center [19]. The machine configuration is shown in Fig. 2.
The machine is equipped with linear motor drives, a cross
bed with two driven axes X, Y and a vertically oriented
spindle (Z-axis) form the structure of the machine. The
measurements were performed on the machining center
over a working volume of X=500 mm, Y=400 mm, and
Z=320 mm. All measurements were performed using
Optodyne laser system and there were four setups, one on
each of the four body diagonal directions. To reduce the
alignment time, two laser systems were aligned in the
directions ppp and nnp as shown in Fig. 5.
In addition, 12 thermocouple temperature sensors were
placed at different locations within the machine frame to
measure the thermal variation of the machine tool. Table 1
gives the number of temperature sensors and their locations.
As the temperature of the machine changes slowly in a
normal condition, some operations were done to warm the
machine warm. The duty cycle consists of a continuous
spindle ran at maximal speed at 15,000 rpm and X-, Y-, and
Z-axes motion at maximum stroke in the ppp diagonal
direction at 50% maximum rapid feed rate. The 12
temperature sensors readings were recorded at 2-min
interval starting before the measurement and ending after
the measurement during the day, shown in Fig. 6.
4.2 Measurement results
During a measurement day, measurement was performed six
times and then six sets of positioning error data are obtained.
For X-axis, the linear displacement errors Ex(x), vertical
straightness errors Ey(x), and horizontal straightness errors
Ez(x) are plotted in Fig. 7a–c, respectively. For the linear displacement errors Ex(x), the maximal error increased from
6.5 to 12 μmat X=500 mm with 3 μm variation due to the
thermal effect; for Ey(x), the maximal error increased from
6.5 to 12 μmat X=100 mm with 3 μm variation; for Ez(x),
the maximal error increased from 9 to 10 μmat X=150 mm
with only 1-μm variation. For the X-axis positioning errors,the change of straightness errors were relatively small over
the temperature range compared with the linear displace-
ment errors.
For Y-axis, as shown in Fig. 8a–c, the maximal error of
linear displacement errors Ey(y), increased from 4 to 8.5 μm摘要：几何定位误差的测量与补偿常常应用于显著提高机床的精度。本文中,一种分布对角线测量介绍了短时间内测量9个立体定位误差。在各种热条件下的测量预制成理解立体定位误差和机械温度场及变化之间的关系。基于径向基函数的神经网络被用于预测在所有位置基于机器分布温度的立体定位误差。补偿实验得到实现以此来验证测量的性能和预测方法。测试结果显示机床的立体误差精度通过误差补偿得到了显著的提高。 计算机数控机床英文文献和中文翻译(2):http://www.751com.cn/fanyi/lunwen_11903.html