Technical Information

Positioning accuracy of rotary axes: a key factor
in 5-axis machining
The rise of globalization and the resulting internationalization of markets have led to strong diversification in customer demands. The endcustomer market increasingly expects variant diversity and ever greater product individualization. These trends have not gone unnoticed
in the manufacturing technology sector. To compete with global providers, companies must offer innovative products with superior quality
and functionality. This fact, combined with ever smaller lot sizes per variant, places growing demands on geometrical tolerances and thefinish quality of visible and functional surfaces. At the same time, manufacturing companies must adapt to shorter product-to-market
times and product life cycles.
One approach to achieving high variant flexibility in manufacturing is to use a machine tool for 5-axis machining. Universal workholding
systems permit multi-sided, complete machining and enable high-level automation for output flexibility and excellent machine utilization.
Being able to vary the tool orientation along the milling path allows complex geometries to be machined extensively using standard tools.
During 5-axis machining, all five machine axes are moved relative to each other and are synchronously interpolated (three linear axes andtwo rotary axes). When the rotary axes are moved to a fixed position prior to machining and held there throughout, this approach is
known as 3+2-axis machining.

Machine tools ought to be able to maintainthe high required machining accuracy on
the workpiece even under fluctuating
environmental and machining conditions.
Position feedback must therefore be
evaluated based on both the measurement
accuracy and its consistency over time.
During 5-axis machining in particular, errors
in the positioning of rotary axes have asignificant effect on machining accuracy
and translate directly to the workpiece.

02/2020

Figure 1: Example of a part for 5-axis machiningDepending on the cost structure, customer
requirements, and machining scenario of
the machine tool, the power train of a given
rotary axis is based either on a torquemotor or on a servomotor combined with amechanical transmission. The choice of
encoder is particularly important for rotary
axes with a mechanical transmission,
which will be the main focus of this article.
The simplest way to obtain position
feedback for a rotary axis consisting of a
servomotor and gear system is to use a
motor encoder while accounting for thetransmission ratio. This type of position
feedback is referred to as semi-closed loop
control. It does not account for errors
arising in the mechanical transmission
elements. These errors are not part of the
feedback loop. In Semi-Closed Loop
operation, cyclic loads that cause frictioninduced heating of the transmission
components are a particular source ofsignificant positioning error. However,when position feedback is obtained froman angle encoder mounted directly on theaxis of the rotary table, this configuration is
known as closed loop control. In a Closed
Loop system, nearly all of the mechanicaltransmission errors are taken into accountby the position control loop.

Configuration of the tested machine
The following measurement results wereobtained on a high-end 5-axis vertical­machining center featuring one linear axis
and two rotary axes for the workpiece, andtwo linear axes for the tool (similar to­Figure 2). The range of traverse was approximately 600 mm x 600 mm x 500 mm.
The test focused on the “C” rotary axis in
the table, which was driven by a servomotor
and worm gear.

The following discussion will show thathaving a gear system in the measurement
chain has a significant effect on rotary table
positioning and will compare this approachwith that of an angle encoder integrated
directly into the rotary table.
Figure 2: Schematic design of a machine tool for 5-axis machining

Reference encoder
A reference encoder was designed andbuilt for determining the positioning
accuracy of the rotary table. Figure 3
provides a schematic representation of thedesign. The reference encoder consists ofan optical scale drum [1] read by four, noncontact scanning heads [2]. The drum wascentered and mounted to the rotary table
via an adapter [3] so that it would turn withthe rotary table during the measurement.
The scanning heads were arrayed in aholder [4] and connected to the clamped
main spindle of the machine tool by meansof the tool clamping system [5].

Figure 4 shows the reference encoder as
mounted inside a machine tool. During themeasurement, the rotary axes of thefollowing components were in alignment:
the rotary table, the scale drum of thereference encoder, and the main spindle.
The reference encoder was qualified on acalibrated measuring machine and is able
to ensure a high system accuracy of ±0.5”.
This accuracy was attained within the widemounting and operating tolerances of±1.0 mm radially and 0.4 mm for radial
runout. Measurement series performed on
the machine tool verified the reproducibility
and quality of the reference encoder.

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4

2
2

1

3

Figure 3: S chematic representation of thereference encoder

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The benefit of this reference encoderlies in its generous mounting tolerances(especially its permissible eccentricity of±0.2 mm), which greatly facilitate
installation and operation. The encoder’sstated system accuracy refers to thecomplete reference encoder and isunaffected by external environmental
factors. Measurements are also possible
at any rotary axis position and in small
stepping angles. No fixed value for thenumber of measurement positions or theequal distance between them was
specified. It was not necessary to link thereference encoder with the machine
control.

Figure 4: Reference encoder on the rotary table of a machine tool

Position measurement on rotary axes
Although direct drive systems with torquemotors are widespread, a high proportionof machine-tool rotary axes still use a
servomotor combined with a mechanicaltransmission. Reasons for this include therequired level of machining complexity andthe cost structure of the machine. When aservomotor is used, there are two ways todetermine the angular position of the axis.
The two position feedback configurations—
Closed Loop (CL) and Semi-Closed Loop
(SCL)—are schematically depicted in
Figures 5 and 6.

Figure 5: Closed Loop configuration

Figure 6: Semi-Closed Loop configuration

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Compared with the Closed Loop setup, theSemi-Closed Loop configuration contains
more sources of error due to the greaternumber of components located between
the point of position measurement at theencoder and the affected rotary table.
Particularly problematic in this context are
geometric errors, elasticity errors in themechanical transmission elements,
thermal effects, and wear. Position
measurement is also influenced bydynamic effects arising from the machining
forces and vibrations. In a Closed Loopconfiguration, however, the positioning
accuracy remains largely unaffected by themain error sources mentioned above sincethese errors are measured at their point oforigin by the angle encoder and can be
accounted for in the position control loop.

Although the measured rotary table isnormally operated under Closed Loop
control, this machine’s control can be easily
reparameterized to position the table underSemi-Closed Loop control. This allows for a
direct comparison of the position error of
the rotary table for both configurations (seeFigures 7 and 8). For this comparison, 720
measuring positions evenly distributed
along the circumference of the table werefirst approached from two directions:clockwise (CW) and counterclockwise(CCW). This high-resolution characterizationof the position behavior revealed theconstant, position-dependent, and nonsystematic effects that influence rotary
axis positioning. In the Closed Loopconfiguration, high positioning accuracy
was attained across the measured angular

Figure 7: P osition error from measurement of 720 positions under
Closed Loop control

4range of the axis, and the two directions ofapproach were barely distinguishable fromeach other. This measurement curve
primarily reflects the behavior of the angle
encoder used for position control. In the
Semi-Closed Loop configuration, higher
reversal error between the directions wasapparent, as was a much larger variancewithin a single direction. This is primarily
due to position-dependent errors in themechanical transmission elements (i.e.,play, friction, and gear-meshing effects).
The larger amplitude of high-frequency
vibration in the CW measurementcompared with CCW also points toheightened wear in the gear flanks for thisevidently preferred direction.

Figure 8: P osition error from measurement of 720 positions underSemi-Closed Loop control

Determining the positioning accuracy ofrotary tables with the reference encoder
All of the measurements presented here
were performed on the machine tool
described above. Its control enables therotary table to be switched between
Closed Loop and Semi-Closed Loop
operation. In Closed Loop operation,
position feedback was provided by an
RCN 8310 angle encoder. In Semi-Closed
Loop mode, the position of the rotary table
was calculated based on the motor

Static positioning accuracy as per
ISO 230-2
First, the static positioning accuracy of therotary table was determined in accordancewith ISO 230-2. To this end, the 360°
measuring range was subdivided into
twelve, equidistant positions at 30°
intervals. This represents the typicalnumber of measuring points when an
autocollimator with a polygon mirror isused. The measuring points wereapproached sequentially at a feed rate of1000 °/min. The final position was thenmeasured at standstill by the reference
encoder for the rotary table. In order toencoder signal and the transmission ratioof the worm gear. Because these results
were obtained on the same machine andwith the same feed-axis power train, a
direct comparison was possible. The
positioning accuracy of the rotary table
was determined using the standardized
measuring procedures laid out in the
ISO 230-2 and ISO 230-3 standards.

obtain a statistically meaningful result for
the acquired parameters, this procedure
was repeated five times each underclockwise and counterclockwise rotation.
Similar starting conditions for thecomparative measurements were created
not only by using the same machine but
also by initially deactivating the C-axis
compensation tables stored in the control
for both configurations.
Under Closed Loop control (Figure 9), themeasured accuracy remained stable within

Figure 9: Position error as per ISO 230-2 under Closed Loop control(without compensation)a range of ±1.3”, which is to be expected
when an angle encoder is used. By
comparison, the measurement results for
Semi-Closed Loop operation (Figure 10)
exhibited a lower rotary table positioning
accuracy of ±5” in each direction. In
addition, a reversal error of 31” was clearly
detected under varied approach directions.
During a second round of measurements,
the positioning accuracy values determined
for the twelve sampling points in eachconfiguration (CL and SCL) were stored in
a compensation table and activated.

Figure 10: P osition error as per ISO 230-2 under Semi-Closed Loop control(without compensation)5

After parameterization and activation of the
non-linear axis error compensation on themachine’s control, the results from bothcontrol loop configurations were now
available in a good and acceptable accuracy
range (see Figures 11 and 12). The accuracy
under Closed Loop control improved to±0.35”. The Semi-Closed Loop configuration
also performed well in this measurement,
exhibiting a low position error of ±1.4”across the measured range of rotation.
However, a low reversal error of 1.0” wasstill noticeable. At this point, it is importantto remember that the compensation values
represent a discrete machine state, arevalid for only the first measurement, andare stored as static values in a table.
During operation, however, both themachine state and position uncertainty
change in response to thermal andmechanical loads, as well as due to wear in
the mechanical components.

Thus, over time, the use of static tables tocompensate for position error will fail toattain the quality depicted in Figures 11
and 12.
The positioning accuracy behavior between
the sampling points used for compensation
can be seen from a repeatedmeasurement under Semi-Closed Loop
control using twelve sampling points and
60 measuring points. This is the typicalnumber of sampling points generated
during a measurement with anautocollimator and polygon mirror. The
results from this additional measurement
are shown in Figure 13. The plot shows asignificantly higher position error of ±4.5”
and a reversal error of up to 4.0”. In
addition, high-level, non-linear effects areapparent between the selected sampling
points. Like the short-range errors in
Figure 8, these non-linear effects cannot be

Figure 11: Position error as per ISO 230-2 under Closed Loop control(with compensation)modeled by the compensation values from
Figure 10 and are thus unknown to thecontrol. The use of compensation tables in
Semi-Closed Loop operation does not
ensure attainment of the positioning
accuracy between the sampling points,
and the results will deviate considerablyfrom those in Figure 12. Therefore, thismethod of compensation is suitable only
when the rotary table approaches
previously known positions. This may be
the case, for example, in 3+2-axis machining.
In theory, a much greater number ofsampling points could be used in thecontrol’s static compensation table, but
this would require an unreasonable amountof measurement work. Furthermore,during the machining process and evenduring measurement, the thermal state of
the machine tool is subject to change. This
will be discussed in the following.

Figure 12: P osition error as per ISO 230-2 under Semi-Closed Loop control(with compensation)

Figure 13: P osition error as per ISO 230-2 under Semi-Closed Loop control(60 measuring points, with compensation)

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Determining the effects of thermal drift
as per ISO 230-3
A measurement as per ISO 230-3 for eachconfiguration revealed the change inpositioning behavior due to heat build-up in
the power train of the rotary axis and its
other mechanical components. For thismeasurement, compensation was
activated in the machine’s control based on
the sampling points defined in the previous
section. In addition, the effects of thermal
position drift on the positioning accuracy of
the rotary axis were determined inaccordance with ISO 230-3. For thispurpose, two positions were defined(0° and 180°) and likewise approached fromtwo directions (CW and CCW). Between
the individual measurements, a temperature
increase for the measurement range (0° to180°) was achieved through five cyclic
movements at a feed rate of 3000 °/min.
The measured values continued to berecorded until the thermal position drift of
the rotary table stopped changing.

The measurement results in Figure 14
show that, when an angle encoder is usedin Closed Loop control, the positioning
accuracy remains stable even despite
cyclic movement of the rotary table axis
and the resulting temperature increase in
the power-train components. In thisconfiguration, the angle encoder measures
the thermally-dependent position drift andfeeds it back into the position control loop.
The maximum value in this measurement
was 0.5”.
By comparison, the Semi-Closed Loopconfiguration exhibited a considerable
change in positioning accuracy over time
(Figure 15). This change involves two
parameters: the amplitude, with amaximum of 8”, and a very short time
constant of approximately 2 minutes. In
addition, a position drift component wassuperimposed at the 0° measurement
position. This component arose from heatbuild-up in the structural elements of themachining center with a considerably
longer time constant. As a result, thedistance between both measuring points
was also constantly changing.

Figure 14: Position error as per ISO 230-3 under Closed Loop control(with compensation)

In addition, the reversal error between the
two approach directions rose to 3”.
Regardless of the maximum error
acceptable in some applications, the shorttime constant is problematic in many
machining scenarios. Examples include themachining of smaller lot sizes or the cyclic
alternation between positioning of therotary axis with subsequent standstill(machining in opposite orientations) andcontinuous motion of the axis. The
replacement of a broken tool also falls
within this time constant.
In the case of the measured rotary table, it
has already been shown that the use of acompensation table is not helpful. The
seemingly stable state of the position error
reached after approximately 25 minutes
will change every time the machine or feed
axis comes to a standstill, such as during
rechucking or the loading of a newworkpiece. This translates into a high levelof uncertainty for the attainable machining
accuracy and will have a direct impact on
workpiece accuracy during 5-axis
simultaneous machining, and even during
3+2-axis machining.

Figure 15: P osition error as per ISO 230-3 under Semi-Closed Loop control(with compensation)

7

Conclusions
On the standard rotary table of a high-end
machining center, it was shown that
position errors as large as 8” occurred
within 10 minutes under Semi-Closed Loop
control. This is equivalent to a deviation of
20 µm on a radius of 0.5 m. The complex
design of rotary tables consisting of a
servomotor with mechanical transmission,
combined with the difficulties associatedwith measuring the various errors causedby environmental factors, renders practicalonline compensation of rotary axis position
errors largely impossible.
This was illustrated by means of a suitablereference encoder, which performed
comparative measurements of thepositioning accuracy of a machine tool’srotary table in Closed Loop and SemiClosed Loop operation. Both the static
positioning accuracy of the rotary axis andits stability under heating from a cyclic load
were ascertained. Likewise, the effects ofmeasuring point compensation with twelve
sampling points were determined andcompared. In all of these measurements,
the Closed Loop configuration exhibitedstable behavior with high positioning
accuracy and low reversal error. Under
Semi-Closed Loop control, the initially
inaccurate positioning behavior did see
significant improvement fromcompensation, but this could not be
maintained under cyclic loading of thepower-train components. The change inbehavior over time with increasing
temperature in the mechanicaltransmission system was chiefly
characterized by a very short time constantin the measurements shown. In practicalterms, this rules out the possibility ofcompensation through the machine’s
control. It was also shown that, between
the sampling points, high-level, non-linear
effects arose that could not be covered bythis method of compensation.

When the rotary axis is operated under
Closed Loop control with angle encoders
from HEIDENHAIN, the motion of therotary axis is measured directly. This allows
most of the influencing factors and timedependent mechanical changes to betaken into account in the position control
loop. These factors include mechanicaltransmission errors, thermal effects, andwear. The only exceptions are those errorsthat the angle encoders are able tomeasure but whose dynamic behavior
exceed the dynamic performance of theposition control loop. Absolute RCN angle
encoders with an integrated bearing andstator coupling are well suited to highaccuracy rotary axes with mechanicaltransmission elements, as well as to directdrive technology. These angle encoders
combine a high system accuracy with easy
mounting and high contamination
immunity thanks to their enclosed design.
If these encoders cannot be integrated fordesign reasons, then it is still possible touse modular angle encoders with opticalscanning. With an correspondingly highnumber of signal periods, the ERA 4000
and ECA 4000 series likewise offer highpositioning accuracy. In this case, thechoice of rotary table bearing requires
special attention regarding its stiffness andoperating characteristics, because these
traits directly affect the attainablemeasurement accuracy of the angle
encoder and therefore the positioning
accuracy of the rotary table. A rotary axis
designed in this manner delivers the ideal
conditions for 5-axis machining with highprocess reliability and throughput.
This article’s comparison of Closed Loop
control and Semi-Closed Loop control on
rotary axes primarily applies to the rotarytables on machine tools. However, as
mentioned at the outset, 5-axis machining
involves two precisely positionable rotaryaxes. Similar measurements for the tilting
axis of machine tools are currently
underway and will be presented as well.

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02/2020 · H · Printed in Germany• Brochure: Angle Encoders• Brochure: Modular Angle Encoders with Optical Scanning

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