Engineering, 2010, 2, 403-407
doi:10.4236/eng.2010.26053 Published Online June 2010 (http://www.SciRP.org/journal/eng)
Backlash Error Measurement and Compensation on the
Vertical Machining Center
Huanlao Liu*, Xiaoning Xue, Guangyu Tan
Engineering college, Guangdong Ocean University, Zhanjiang, China
Received December 21, 2009; revised February 9, 2010; accepted February 18, 2010
Abstract
The position errors in the axis direction of a vertical machine center have been measured by means of the
VM101 linear encored measurement system. The character of the backlash error is discussed; results show
that the backlash error has great influence on the position error. The position accuracy is enhanced after the
backlash errors are compensated.
Keywords: Position Error, Backlash Error, Error Model, Artificial Neural Network
1. Introduction
The laser interferometer is commonly used in the meas-
urement of various error components. Geometric errors
have many different components like linear displacement
error (positioning accuracy), straightness and flatness of
movement of the axis, spindle inclination angle, square
ness error, backlash error etc. The errors can be reduced
with the structural improvement of the machine tool
through better design and manufacturing practices. How-
ever, in most cases, due to physical limitations production
and design techniques cannot solely improve the machine
tool accuracy. Therefore, identification, characterization
and compensation of these error sources are necessary to
improve machine tool accuracy cost-effectively. Eung-
Suk Lee et al. [1] used the interferometer in measuring 19
of the 21 components on a three-axis CNC milling ma-
chine with the exception of angular roll. Ni et al. [2] de-
veloped an optical system consisting of a laser interfer-
ometer, beam splitters, flat mirrors and dual-axis lateral-
effect photo detectors to facilitate simultaneous on-line
measurement of five errors on each axis, which are linear
and vertical straightness, roll, pitch and yaw errors. Shin
[3], Ertekin et al. [4] also presented the results of accu-
racy characterization of a CNC Machining Center using
laser interferometer. Other techniques such as disc checks
[5] and double ball bar (DBB) [6] measurements are also
used in the position error measurement. Knapp et al. [7]
listed a few tests for assessing the quality of machine
tools on a periodic basis. The diagonal displacement test
was one of the means adopted to estimate the volumetric
accuracy of the machine tool through evaluation of the
positioning accuracy and repeatability along the body
diagonals. The circular test can also be used in assessing
the accuracy of the machine tools and the identification of
backlash error, a software strategy that is able to com-
pensate the backlash error [8].
Backlash error can be obtained through some kinds of
methods, it is either time-costly (laser interferometer) or
only the maximum value obtained (DBB) and the effects
of backlash error on the machine accuracy are not dis-
cussed in detail so far. The aim of the investigation pre-
sented in this paper was to illustrate the effects of the
backlash error on the position accuracy of the machine
tools and attracted more attention about the backlash
error in the machine production process.
VM101 Comparator System, which has the advantages
of easy operation, time-less and also high accuracy, was
used to measure the axis linear displacement and backlash
error in this paper. A simple introduction about the sys-
tem and measurement process was given in the following
section. The third part presents the experimental results.
Two kinds of models including Back Propagation Artifi-
cial Neural Network (BP-ANN) and polynomial function
model that can be used in different occasions were pre-
sented in the fourth part. The results after backlash error
compensated were given in the fifth part. Then some con-
clusions have made in the final part of this paper.
2. Experimental Procedures
2.1. The VM101 Linear Encored Measurement
System
The VM101 Comparator System which has made in

H. L. LIU ET AL. 404
HEIDENHAIN cooperation consists of a precision scan-
ning head, auxiliary carriage, interface electronics and
sturdy storage case. The sturdy scale carrier is a U-shaped
stainless steel extrusion. The material measure―a preci-
sion scale with a phase grating graduation and an 8 μm
grating period―lies in the neutral stress zone of the
U-shaped scale carrier. The scanning head which is usu-
ally connected to the spindle of the machine tools runs
along the scale without making mechanical contact. It is
an exposed incremental linear encoder with high accu-
racy. Its measuring lengths is 720 mm, accuracy grade is
±1 μm at 20℃ (±0.00004 in. at 68°F) [9]. Figure 1
shows the measurement setup on the X-axis.
2.2. Measurement Process
A new vertical machining centre tape DM4600 was cho-
sen for the tests. Its working volume was 600 × 400 ×
420 (mm). After the workspace was defined, accuracy
and repeatability were tested for each axis direction. To
minimize the error that might arise due to the temperature
change during the measurements because of the axis mo-
tions. The machine was put in operation for three hours
with a programmed exercise. This routine activated all the
axis motions simultaneously before any measurements
have been taken so that the machine could pass the ther-
mal transition state to reach its equilibrium state.
In order to keep errors resulting from uneven guide
ways (Abbe error) at a minimum, the comparator system
must be installed as near as possible both to the point of
tool contact as well as to the encoder. The sides of the
scale carrier should be aligned with the axis to be meas-
ured within 0.1 mm.
To eliminate the influence of speeds, the machine was
programmed to move with a lower feed rate of 50 mmpm,
after the warm-up cycle, position displacement meas-
urements were taken in both travel directions. The data
was captured at equal intervals (20 mm) and the meas-
urement cycle CNC part program composes a sequence
of moves beginning at one limit of the axis in forward
direction (f), extending to the opposite limit, and return-
ing to the beginning position in reverse direction(r). The
commanded machine position is nominal axis position,
which is determined by the part program being executed.
A PC reads the absolute machine positions directly into
Figure 1. The X-axis measurement setup.
the database from the VM101. A sample measurement
cycle CNC program for X-axis is given in Table 1.
3. Experimental Results
3.1. Axis Linear Displacement Error
The X-axis linear displacement error plots are shown in
Figure 2. In the legend of the error graphs, Error 1-f and
Error 1-r indicates that errors were measured when the
machine was in the first cycle motion for forward (f) and
reverse (r) directions after about 3 hours warm-up period.
The error plots show that positional errors are generally
lower at the beginning of axis travel (home position) and
have linearly increasing trend with increasing axis no-
minal position. It was found that the position error in
forward direction was bigger than the position error in
the reverse direction at the same point. The maximum
displacement error is about 40 μm at the end of the axis.
The Y-axis linear displacement error (Figure 3) and
the Z-axis linear displacement error (Figure 4) showed
similar linear trends with increasing nominal axis posi-
tion as in X-axis. The Y-axis linear displacement error was
the smallest among the three axes being tested and the
magnitude was approximately 25 μm. Maximum linear
displacement error of the Z-axis was almost the same
value as the end of the X-axis. The slope of the error line
of the Y-axis is the smallest when the machine is moving
in the forward directions. There are obviously two
Table 1. VM101 measurement cycle CNC program.
N001 #1 = 0 N010 X560
N002 G92 X0 Y0 Z0 N011 G04 P10
N003 WHILE #1 LT 28 N012 WHILE #1 LT 20
N004 G91 G01 X20 F50 N013 G91 G01 X-20
N005 G04 P10 N014 G04 P10
N006 #1 = #1 + 1 N015 #1 = #1 + 1
N007 ENDW N016 ENDW
N008 #1 = 0 N017 M30
N009 G90 G01 X562
X-Axis Nominal Position (mm)
Figure 2. X-axis linear displacement error.

H. L. LIU ET AL.405
Y-Axis Nominal Position (mm)
Figure 3. Y-axis linear displacement error.
Z-Axis Nominal Position (mm)
Figure 4. Z-axis linear displacement error.
groups error line on the axis linear displacement error
plot. That means there are two different error values at
the same location in the axis. The main reason of these
results is the backlash error.
3.2. Backlash Error
Backlash error is a position dependent error affecting the
contouring accuracy. When the axis changes direction
from one side to the other, there is a lag before the table
starts moving again, that would cause position error-
backlash error. The backlash error was the major reason
why there are two groups of error lines on the displace-
ment error plot. It has great influence on the accuracy of
the machine and should be compensated. Figure 5 shows
the backlash error of the axes. B
ex means the X-axis
backlash error, Bey is the Y-axis backlash error and the
Z-axis backlash error is Bez.
The backlash error value of the axis was not constant
and has different value at different axis nominal posi-
tions. Maximum backlash error is about 27 μm at the
beginning of travel in X-axis, the backlash error is 18 μm
and 11 μm at the home point of the Y-axis and Z-axis. It
leads to the relatively large error of the axis in the
forward direction. The Z-axis has the smallest average
Axis Nominal Position (mm)
Figure 5. The value of backlash error.
backlash error among the three axes and obtained maxi-
mum Bez at the end of the axis travel with a magnitude of
14 μm.
4. The Models of Backlash Error
4.1. The ANN Models of Backlash Error
The neural net using the back-propagation algorithm has
been used to predict the total positioning error at any
given thermal state and location of the cutting tool from
knowledge of that error at some specified point in the
workspace as measured by the laser ball bar [10]. The
neural network which utilizes the learning ability to pre-
dicate the backlash error value from the knowledge of
the error as measured by the VM101 system was devel-
oped. The neural networks developed in this study have
three layers―one input layer, one hidden layer, and one
output layer. The input layer comprises the units that
represent the nominal position of the axis. The output
layer has three output units that represent the backlash
errors of the three axes. The hidden units of the network
are used to extract the underlying features of relation-
ships between the nominal position and the backlash
errors of the machine tools. The Figure 6 shows the flow
chart of the neural net work.
Training of the networks can proceed only after the
entire experimental data is obtained. The training process
of the net was shown in Figure 7.
During learning, the nominal position value of the axis
was input into the self-learning and prediction unit, the
output of the neural net is the backlash error value. Then
the backlash error compensation can be taken. However
because the training time is relatively long, the ANN
model can only be used in the off-line compensation, the
advantage of the net model was very high-nonlinear
mapping ability.
Figure 6. The flow chart of the neural net.

H. L. LIU ET AL. 406
Figure 7. The training process of the neural network.
4.2. The Polynomial Models of Backlash Error
For on-line compensation, the backlash errors (Bex, Bey, Bez)
can also be modeled as polynomial functions with the
position along each axis. As the Equations (1), (2) and (3)
expressed.
Bex = a0 + a1x + a2x2 + a3x3 (1)
Bex = b0 + b1y + b2y2 + b3y3 (2)
Bex = c0 + c1z + c2z2 + c3z3 (3)
The error models then can identify using the least-
squares criterion method. The calculation process of the
backlash error value was very fast, but the drawback of
the polynomial model was its relatively lower accuracy.
5. Accuracy after Backlash Error
Compensated
After the models have been developed, the backlash error
then can be compensated. The procedure can be divided
into three stages: calibration of the backlash errors (part
2), modeling of the errors (part 4), and compensation
control implementation.
The principle of the error compensation control im-
plementation is as the following steps: the backlash er-
rors on the nominal position of the axis at any given
thermal stage are collected and the errors are estimated
by the models. Then the resultant errors between the
commanded position and the real position are calculated.
Finally, the compensation singles are sent to the CNC
controller to shift the origins of the slide axes to imple-
ment the error compensation. The results of the position
accuracy after the backlash error compensated using the
ANN model were measured using the same procedure as
mentioned above. Figures 8-10 show the X-axis, Y-axis
and Z-axis measurement results.
All three plots show that the backlash errors were well
compensated and the accuracy of these axes was highly
increased. All linear positional errors increasing linearly
with respect to axis nominal position and are the highest at
the end of the axis travel range. These results correspond
with the most previous work and the assumption that the
linear errors components change linearly with position.
Machine home position gave best linear accuracy; maxi-
mum linear displacement error was about 10 μm in the X
and Y-axes, the Z-axis maximum linear displacement was
about 25 μm at the end of the axis position.
The variation of the linear displacement error (position
systematic deviation) was about ±2 μm at the same
position in the axis when the backlash errors were com-
pensated. The repeatability of position of the axes was
obtained with a magnitude of about 4 μm. This is the limits
X-Axis Nominal Position (mm)
Figure 8. X linear displacement error after compensated.
Y-Axis Nominal Position (mm)
Figure 9. Y linear displacement error after compen-
sated.
Z-Axis Nominal Position (mm)
Figure 10． Z linear displacement error after compensated.

H. L. LIU ET AL. 407
accuracy through the off-line software for the software-
compensation.
The experimental results show that the accuracy was
enhanced after the backlash error eliminated. So more
attention should be paid to the backlash error during the
production and assemble processing of the machine tools.
6. Conclusions
From the results of this research, the following conclu-
sions can be drawn:
 All linear position errors increased almost linearly
with respect to axis nominal position and are the highest
at the end of the axis travel range even the backlash error
compensated.
 The backlash errors cause relatively large linear dis-
placement error deviation between different directions at
the same point in the axis. The backlash errors value is
the function of the point in the axis.
 The accuracy of the machine increased after the
backlash error compensated, so more attentions should
be paid to the backlash errors in the machine tool pro-
duction procession.
7. Acknowledgements
This work was financially supported for the research of
geometric error measurement and compensation on CNC
machine tool by National 863 Subject Plan under grant
2002AA423260.
8
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