Technical Information

Resulting Linear Error after Multipoint Linear Error
Compensation with the LIDA 400
The measuring accuracy specified for incremental linear encoders from HEIDENHAIN typically applies for a range of one meter.
Many applications, such as on measuring machines, require shorter distances, for example 50 mm or 100 mm.
By calibrating the machine and compensating the error in the subsequent electronics it is possible to significantly increase the machineaccuracy. This process is particularly well established in coordinate measurement technology and plays a key role in ensuring highmachining accuracy over large measuring lengths. Modern controls allow ten and more compensation values per meter traverse.
To calculate the expected measuring uncertainty of the machine, the machine manufacturer needs data on the maximum error to be
expected between the compensation points. Because nonlinear error components occur in incremental encoders and cause relevant
error even over short ranges, the usual specification of measuring accuracy is insufficient.
HEIDENHAIN therefore determines the expected residual error after sectional (multipoint) linear compensation for the encoders of theLIDA 400 series. Here the high accuracy and good signal quality of this encoder becames apparent.

September 2008

Multipoint Linear Error Compensation

Finding the residual error
HEIDENHAIN ascertains the position error
after multipoint linear error compensation(residual error) at compensation pointintervals A of 50 mm and 100 mm. The
following example uses the distance A of50 mm (see Figure 2). The compensation
values are determined at n x 50, i.e. at 0,50, 100, 150 etc. The values between
these points are then interpolated. The
following multipoint linear compensation
eliminates the error at the respective
compensation points. The curve in Figure 3
shows the residual error after multipoint
linear compensation.
The maximum residual error
Of course, the residual error determined inthis way greatly depends on the position of
the compensation points. To find the actual
maximum residual error, the compensation
points are each shifted by one millimeterand the compensation values for thepositions 1, 51, 101, etc. to 49, 99, 149 etc.
are recorded. As in the above example, forthese points as well the residual error isrecorded and the maximum residual error
is calculated from the large number of error
curves. This method ensures that thespecified maximum error after multipoint
linear error compensation is independentof the position of the compensation points.

Position error [µm]

0.600
0.400
0.200
0
0.2000.4000.6000.800050100150200

250

300

350

400

450

Position [mm]Figure 1: Typical position error over measuring length
0.800

Position error [µm]With the LIDA 400, the position error
over the measuring length is measured
in a comparative measurement with acalibrated reference measuring device.
The measurement is recorded with ameasuring interval of one millimeter. An
example of the position error over themeasuring length is shown in Figure 1.

0.800

0.600
0.400
0.200
0
0.2000.400A

0.6000.800050

100

150200

250

300

350

400

450

Position [mm]Figure 2: Compensation points for multipoint linear error compensation
0.800

Position error [µm]The accuracy of incremental linear encoders
is comprised mainly of the position error
over larger distance intervals and theposition error within one signal period.

0.600
0.400
0.20000.200
0.4000.6000.800050100150200250300

350

400

Position [mm]Figure 3: Residual error after multipoint linear error compensation

450

Position error u within one signal period
Accuracy evaluation of the entire encoder
must also include the position error within
one signal period.
This error is determined by the quality ofthe measuring standard and the scanning
as well as the signal period of the encoder.
On the LIDA 400, when mounted according
to the Mounting Instructions, it is typically±1% of the signal period. For a signal
period of 20 µm the position error within
one signal period is calculated at ± 0.2 µm.
The range of error, here 0.4 µm, is used forfurther calculation.

Position error

Position error u within one signal period

Signal level

Resulting position error
The resulting error Ftotal after multipoint
linear compensation therefore consists of• the maximum residual error over large
length intervals Fresidual (depending on
the compensation point interval)and• the position errors u within one signal
periodSignal period
360 °elec.

Ftotal = Fresidual + u

Figure 4: Position error u within one signal period
For the LIDA 400 in this example, thefollowing typical values were calculated:• At a compensation point interval A of50 mm:
Ftotal = 0.8 µm + 0.4 µm
Ftotal = 1.2 µm

Conclusion
With its specification of the resulting
length error after multipoint linear error
compensation, HEIDENHAIN provides themachine tool builder with an importantindex.
It allows him to prepare a good assessmentof the measuring uncertainty to beexpected, and at the same time indicatesthe high accuracy of the linear encoderfrom the LIDA 400 series.

Position error [µm]• At a compensation point interval A of
100 mm:Ftotal = 1 µm + 0.4 µm
Ftotal = 1.4 µm

Position [mm]Figure 5: Total error after multipoint linear error compensation under consideration of theposition error u within one signal period

Measuring the Machine

Modern subsequent electronics arecapable not only of linear error compensation
over the entire measuring range, they canalso compensate error at specified points.
This makes it possible to provide goodcompensation down to a relatively small
residual error even for nonlinear error
curves. For both methods, the actual error
curve of the complete axis must be exactly
measured over the path whose error is tobe compensated. Mechanical influences of
the axis, such as guideway error, sag at theend positions, tolerances of the bearing
surface and similar factors, but also lessthan-optimal mounting (Abbe error) always
have an effect. It is therefore not enough toevaluate encoder error solely on the basisof the deviations documented in acalibration chart.
To measure the resulting deviations,
HEIDENHAIN offers the VM 182
comparator system for measuring lengths
up to 1 520 mm. Measuring machines withcorrespondingly high accuracy or laserinterferometers are also suitable.

DR. JOHANNES HEIDENHAIN GmbH
Dr.-Johannes-Heidenhain-Straße 583301 Traunreut, Germany{ +49 8669 31-0
| +49 8669 5061
E-mail: info@heidenhain.dewww.heidenhain.de392 095 · 02 · A · 02 · 8/2008 · PDF

VM 182 comparator system
The VM 182 comparator system serves foracceptance testing, inspection and calibrationof linear axes on machine tools andmeasuring equipment with traverse ranges
up to 1 520 mm. The VM 182 makes it
possible to measure the linear and nonlinear
error curves as well as the reversal error ofmachine axes according to DIN ISO 230-2.
At the same time as it finds the position
error, it also measures the guideway error

orthogonal to the traverse direction of themachine axis. The compensation values
can be used in the subsequent electronics
for electronic error compensation.
The VM 182 is connected through an IK 220
counter card to a PC with the ACCOM
software, which evaluates the measured
values according to DIN ISO 230-2,
ISO 230-3 or the VDI/DQO directive 3441.

For more information• Brochure: Exposed Linear Encoders• Brochure: Measuring Systems
for Machine Tool Inspection andAcceptance Testing