Technical Information

Perfect Surfaces with HEIDENHAIN Encoders
It takes much time and effort to manufacture perfect surfaces. The sculpture “Cloud Gate,” for example—a sculpture by the artist Anish
Kapoor in Chicago’s Millennium Park— was polished by 24 specialists for several months as the final step. The stainless steel sculpture,with over 99 metric tons and the gigantic dimensions of 10 m x 20 m x 13 m features a perfect, seamless surface that mirrors the Chicago skyline.
In the same way, flawless surfaces are likewise a frequent goal in the machine tool industry, and particularly in mold making. Here, however, economic aspects play an important role. Manufacturing parts with tight tolerances and high surface quality in a short time presents
a special challenge. The manufacture of high-quality workpieces in mold making demands large cutting volumes during roughing on theone hand while requiring a perfect surface after finishing on the other. Only if surface quality is optimal is it possible to avoid subsequentcost, e.g. through manual polishing. Besides the quality of the machine’s mechanics and the corresponding performance of the control,
the third column responsible for an optimal milling result is the measuring technology.
To achieve high part surface quality, the encoders that provide signals with extraordinarily small deviations within one signal period (interpolation error) are of crucial importance. Interpolation errors are responsible, for example, for periodically recurring irregularities in form on
the workpiece surface, which are particularly disturbing in mold making.

Surface defects stand out
The human eye is very sensitive to structural changes or even the smallest defects
on a surface. A pixel error on the monitor,
for example, with a display comprising up
to five million pixels, is immediately visible.
The human eye is even more sensitive toperiodic surface faults. Test workpieces
show that periodic form errors of as small
as 0.2 µm can be clearly visible. Particularly
in mold making, these form deviations—although they have no influence on accuracy—are disturbing and require expensive
rework.

Cloud Gate—an example of a perfect surface

September 2013

Prerequisites for high surface quality

Possible reasons for periodic surfaceerrors
Surface errors are visible on part surfaces
as shadows or fluctuations in contrast.
From the usual vision distances, the human eye perceives them as disturbing.
They can be attributed to fundamentallydifferent causes:• Vibrations of the machine that disturb themachining process (see the Technical Information document Dynamic Precision)• Short-period errors of the axis encoder(position errors within one signal period,
i.e. interpolation error)
This Technical Information describes surface errors caused by position error within
one signal period.
Position errors within one signal period
The resolution provided directly by an encoder is usually insufficient for modern machine tools. Interpolation processes are
therefore applied that subdivide the periodic analog—typically sinusoidal—scanningsignals A and B. Interpolation factors of
4 096 (12 bits) and more are quite usual.
This makes it possible to start from measuring standards with relatively large graduation periods and attain the measuring
steps of 0.1 µm and less that are needed
for controlling machine tools. The HEIDENHAIN encoders LC 100 and LC 400 achievemeasuring steps of 0.001 µm.

The interpolation processes operate faultlessly as long as the two sinusoidal output
signals are ideal, i.e. have the exactly thesame shape, amplitude, on-off ratio, andare phase-shifted to each other by exactly
90°. Deviations generate errors that repeat
themselves with each period of the scanning signals. One therefore speaks of errors within one signal period or interpolation error.

Effects of position errors within one
signal period
The mold making industry is demanding
workpieces with increasingly complex geometries. In five-axis machining, all combinations of axis movements are common. If
an inclined or curved machining surface ismanufactured through the interpolation ofmultiple NC axes, the interpolation error
can be seen directly on the workpiece.

The size of position errors within one signal
period are determined by the following:• The size of the signal period• The homogeneity and period definitionof the graduation• The quality of scanning filter structures• The characteristics of the sensors• The stability and dynamics of further processing of the analog signals

This becomes particularly apparent when
an inclined surface with a small angle ismachined. The interpolation error of the encoder in Z direction can become visible byprojection on the inclined workpiece surface. Because of the inclination, an n-foldenlargement of the signal period appears in
the tool path. While the axis in Z direction
moves by only one signal period, the X axis
moves n times more. A wave appears on
the inclined workpiece surface with awavelength that corresponds to the n-foldsignal period of the Z-axis encoder.

Signal period Position error 

Position error u within one signal period

Ideal path
Milled path

Signal period
Amplitude
Amplification
Wavelength

Signal period
360° elec.

Figure 1: Position errors within one signal period (interpolation error)

2

Because all sorts of inclined surfaces are
manufactured during the machining of freeform surfaces, there will always be the corresponding amplification of the signal period. A wavelength of 0.5 mm to 5 mm is
especially easy for the human eye to detect.

Figure 2: Illustration of interpolation error on a workpiece inclineWith an interpolation error amplitude ofless than 100 nm, the workpiece surface
has a flawless appearance. Starting froman interpolation error amplitude of approx.
200 nm, the effects on the milling results
becomes visible. Greater interpolation error
results in optically disturbing form deviations.
Machining example
The example workpiece (Figure 4) is
manufactured in multipass milling with aball-nose cutter, ¬ 12 mm. Different sizesof interpolation error exist for each of thethree machined surfaces.
An encoder with very small interpolation
error was used for the top workpiece inFigure 4, for example a HEIDENHAIN linear
encoder of the LC 100 series. In this case,the typical interpolation error is significantly
less than 100 nm. The workpiece surface
appears perfect.

Encoders with larger interpolation error
present a different picture: because thefeed axes follow the high interpolation error, a conspicuous wave pattern appears on
the workpiece surface.
The middle picture in Figure 4 shows theresult of milling if the encoder has an interpolation error of 200 nm. A wave shape isclearly visible. With 500 nm interpolation
error, the workpiece surface has a very
prominent wave shape (Figure 4, below).
Conclusion
Encoders with very small interpolation
error, such as the HEIDENHAIN linear
encoders LC 100, LC 400 or LF, arenecessary in order to mill workpiecesurfaces without a visible wave pattern.

Z axis200 nmSignal period

Figure 4: Machined surfaces from use of encoders with interpolation error less than 100 nm(above), 200 nm (middle) and 500 nm (below)

200 nmn x signal period

X axisFigure 3: Effect of interpolation error (e.g. 200 nm) on an inclined plane3Linear encoders from HEIDENHAIN

Linear encoders from HEIDENHAIN are
distinguished by very high accuracy anddurability. Their high signal quality isachieved through an extremely precise
DIADUR measuring standard and the highly accurate single-field scanning method.
This is the basis for encoders with very
high precision and very small position error
within one signal period.

SignalperiodMax. position
error per signal
periodMeasuring
lengthInterfaceModel

Linear encoders with slimline scale housingAbsolute–± 100 nm

Up to 2 040 mm

1)

EnDat 2.2

LC 415

Incremental

4 µm± 40 nm

Up to 1 220 mm

 1 VPPLF 485The maximum interpolation error of the LC
family of HEIDENHAIN linear encoders, forexample, lies significantly below 100 nm.

Linear encoders with full-size scale housing
Absolute–± 100 nm

Up to 4 240 mm

EnDat 2.2

LC 115Figure 5 shows the RMS values of interpolation errors in a series of measurementsof 1,000 LC 183 model encoders. The RMS
value of the interpolation error for 85 % ofthe tested encoders was less than 12 nm.
As the successor model, the LC 115 features lower RMS deviations.

Incremental4 µm± 40 nm

Up to 3 040 mm

 1 VPPLF 1851)

Over 1 240 mm measuring length with mounting sparFrequency [%]LC 415

LF 485

RMS value of theinterpolation error [nm] LC 115

Figure 5: Distribution of the interpolation error(RMS value) of the LC 183 from HEIDENHAIN

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For more information:• Catalog: Linear Encoders for
Numerically Controlled Machine Tools• Technical Information: Machining
Accuracy of Machine Tools• Technical Information: Linear Encoders
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1081199-20 · 10 · 9/2013 · F&W · Printed in Germany