Technical Information

Machining Accuracy of Machine Tools
Productivity and accuracy of machine tools are important competition aspects. Rapidly changing operating conditions for machine tools,
however, make it difficult to increase productivity and accuracy. In the manufacture of parts, increasingly small batch sizes have to be
produced economically, and yet accurately. In the aerospace industry, maximum cutting capacity is needed for the roughing processes,
whereas the subsequent finishing processes must be executed with maximum precision. For milling high-quality molds, high material
removal rates are required during roughing and excellent surface quality must be obtained after finishing. At the same time, maximum
contouring feed rates are necessary to realize the required minimum distances between the paths within acceptable machining times.
Thermal accuracy of machine tools is becoming increasingly important considering the strongly varying operating conditions in
manufacturing. Especially with small production batches that require constantly changing machining tasks, a thermally stable condition
cannot be reached. At the same time, the accuracy of the first workpiece is becoming very important for the profitability of production
orders. Constant changes between drilling, roughing and finishing operations contribute to the fluctuations in the thermal condition of amachine tool. During the roughing operations, the milling rates increase to values above 80 %, whereas values below 10 % are reachedduring finishing operations. The increasingly high accelerations and feed rates cause heating of the recirculating ball screw in linear feed
drives. Position measurement in the feed drives therefore plays a central role in stabilizing the thermal behavior of machine tools.

Thermal stability of machine tools
Solutions for avoiding thermally induced
dimensional deviations of workpieces havebecome more crucial than ever for themachine tool building industry. Active
cooling, symmetrically designed machine
structures and temperature measurements
are already common practice.
Thermal drift is primarily caused by feed
axes on the basis of recirculating ballscrews. The temperature distribution along
the ball screw can rapidly change as aresult of the feed rates and the moving
forces. On machine tools without linear
encoders, the resulting changes in length(typically: 100 µm/m within 20 min.) cancause significant flaws in the workpiece.

September 2011

Figure 1

Heating of a recirculating ball screw during multipass milling at a mean
feed rate of 10 m/min. This thermographic snapshot shows temperaturesof 25 °C
to 40 °C.

Position Measurement on
Feed Drives
The position of an NC feed axis can bemeasured in principle through the ball screw
in combination with a rotary encoder, or
through a linear encoder.
If the slide position is determined from thepitch of the feed screw and a rotary encoder(Figure 2, top), then the ball screw must
perform two tasks: As the drive system it
must transfer large forces, but as themeasuring device it is expected to provide
highly accurate values and to reproduce
the screw pitch. However, the position
control loop only includes the rotary
encoder.
Because changes in the driving mechanics
due to wear or temperature cannot becompensated, this is called semiclosedloop operation. Positioning errors of thedrives become unavoidable and can have aconsiderable influence on the quality of
workpieces.
If a linear encoder is used for measurementof the slide position (Figure 2, bottom), theposition control loop includes the complete
feed mechanics. This is therefore referred
to as closed-loop operation. Play andinaccuracies in the transfer elements of themachine have no influence on the accuracyof the position measurement. Measurement
accuracy depends almost solely on the
precision and installation location of thelinear encoder.
This basic consideration applies both forlinear axes and rotary axes, where theposition can be measured with a speedreduction mechanism connected to arotary encoder on the motor, or with ahighly accurate angle encoder on themachine axis. Significantly higher accuracy
grades and reproducibility are achieved if
angle encoders are used.
Additional measures for semiclosedloop operation
In order to prevent heating of the ball screw
and the surrounding parts of the machine,some ball screws feature hollow cores forcoolant circulation. In semiclosed-loop
operation the positioning accuracy is affectedby thermal expansion of the ball screw andthus depends on the temperature of thecoolant. A temperature increase of only 1 K
results in positioning errors up to 10 µm
over a traverse range of 1 m. Common
cooling systems, however, are often unable
to restrict the temperature variations tovalues significantly below 1 K.

Measurementof velocity and position

Velocity
measurement
Position measurement

Figure 2

Position feedback control in semiclosed-loop mode (top) and in closed-loop
mode (bottom)

For drives in semiclosed-loop operation,
thermal expansion of the ball screw isoccasionally approximated using a modelin the control. Because the temperature
profile is difficult to measure during
operation and is influenced by numerous
factors – such as the wear of therecirculating ball nut, the feed rate, thecutting forces, the traverse range used,etc. – considerable residual errors up to
50 µm/m can occur when this method isused.
The ball screw is sometimes provided with
fixed bearings at both ends in order toincrease the rigidity of the drive mechanics.
But even very rigidly designed bearings
cannot prevent expansion caused by local
heat generation. The resulting forces are
considerable. They deform the most rigid
bearing configurations and can even cause

structural distortions in the machinegeometry. Mechanical tension also changes
the friction behavior of the drive, thus
adversely affecting the contouring accuracyof the machine.
Due to these restrictions, the drive accuracy
that can be attained by taking the described
additional measures cannot be comparedwith closed-loop operation using linear
encoders. Also, the additional measures
for semiclosed-loop operation cannot
compensate the effects of changes in the
bearing preload due to wear, or elastic
deformations of the drive mechanics.

Effect of Drive Accuracy on the
Manufacture of Parts

1. Drilling and reaming on acold machine

In the machine building industry thedemand for small parts manufactured insmall production runs is increasing
considerably. The accuracy of the first
workpiece is therefore becoming animportant factor for the profitability of
manufacturing companies. Machine tools
for high-accuracy production of small
batches are facing a real challenge.
Constant changes between setting up theworkpiece, drilling, roughing and finishingcause constant changes in the thermal
condition of a machine.
The typical feed rates for roughing aworkpiece range from 3 m/min to 4 m/min,whereas feed rates from 0.5 m/min to
1 m/min are used for finishing. Rapid
traverse movements during tool exchange
also considerably increase the averagevelocities. The medium feed rates during
drilling and reaming are negligible for heatgeneration in recirculating ball screws.
Due to the strongly varying feed rates,
the temperature distribution along the ballscrews changes during the individual
process steps. In semiclosed-loop operation
the varying loads on the recirculating ballscrew may cause the workpiece accuracy
to suffer, even if the workpieces arecompletely machined in just one setup.
Machine tools with linear encoders inclosed-loop mode are therefore absolutely
necessary for high-accuracy production ofsmall parts.
Example of machining several parts
from one blank form
An aluminum blank with a length of
500 mm is first drilled and then reamed ona machine tool. The medium feed rates
during the two machining operations are
low, so the heat generation in therecirculating ball screws is negligible. In thenext production step the contour is milled
and the medium feed rate increases
significantly, resulting in considerable heatgeneration in the ball screws (Figure 3).
If the milling machine is operated insemiclosed-loop mode, thermal expansionof the recirculating ball screws causes
deviations between the drilling pattern andthe milling pattern. The maximum deviationsof 135 µm were measured near the loose
bearings of the ball screw. In closed-loop
operation these errors can be completely
avoided (Figure 4).

2. Contour milling on a
hot machine

0
10

0
50

mm

mm

Z
Z
CAD model

m

m
13
0.0

±
12

Figure 3

Closed loop:
No thermal drift

Effect of drive accuracy on the production of small parts= Fixed bearing of the recirculating ball screw

Semiclosed loop:
Thermal drift

Figure 4

Semiclosed loop:
Thermal drift

Closed loop:
No thermal drift

Effect of drive accuracy on the series production of small parts

The functional dimension between theposition of the hole and the bisecting lineof the individual workpiece is 12 mm andmust meet tolerance grade IT8 in theillustrated example. This results in apermissible deviation of ±13 µm. All of theworkpieces machined in closed-loop modeare significantly within this tolerance.
Deviations up to 135 µm were measured insemiclosed-loop mode. Thus the workpiece
only complies with tolerance grade IT13
instead of meeting the required tolerance
grade IT8.

Integral Components withHigh Degree of Stock Removal
for the Aerospace Industry
Using integral components in theaerospace industry provides the benefitof combining optimum utilization of thematerial characteristics with minimum
weight. Typical integral components featurea degree of stock removal of 95% andmore. Today high-performance HSC
machine tools in conjunction with high feed
rates and high cutting speeds are used in
the manufacturing processes. The highmaterial removal rates made possible by
the remarkable degree of stock removal of
the components are of great economic
significance. But the resulting feed rates
and machining forces also generateconsiderable frictional heat in therecirculating ball screws. Also, friction
losses and the resulting thermal expansionof the ball screws vary during a machining
process, for example because of different
feed rates during roughing and finishing.
If the feed drives are operated insemiclosed-loop mode (without linear
encoders), part dimensions differ for eachsingle component manufactured in small
production runs with short cycle times.
Due to thermal expansion, the specified
manufacturing tolerances might not be
achieved. Such sources of errors can beprevented through the use of linear
encoders, since thermal expansion of theball screws is then fully compensated forin closed-loop operation.

m

m
100

200

m

m
390
450

mm

Twenty repetitions
without tool contact;
then 10 mm infeed in Z

m

m

mm

0
10

Z
20

mm

Z

m

0m

m

0m

39

m

0m

45

10 mm

Constraints:
Machining time: 2 hMax. feed rate: 3.5 m/min.
Medium feed rate: 2.8 m/min.

Figure 5

Example of machining a coupling lever
for an aerofoil
Figure 5 describes the manufacturing of acoupling lever, requiring the machining of
two holes at distance of 350 mm fromeach other with a tolerance grade of IT7.
The integral component is manufactured
twice from the same blank form to permit
evaluation of the accuracy that can beachieved in semiclosed-loop mode. The
second workpiece is simply machined
10 mm below the first. Between the twomachining operations, twenty machining
cycles for the same part are executed
above the blank.
In semiclosed-loop operation, the contourof the second workpiece deviates from thecontour of the first workpiece, as is shownby an edge (Figure 6). The farther the drives
move away from the fixed bearings of therecirculating ball screw during machining,the more obvious the thermal expansion of
the ball screw becomes.

10

Closed loop:
No thermal drift

Manufacturing of the coupling lever= Fixed bearing of the recirculating ball screw

Semiclosed loop:
Thermal drift

Figure 6

Semiclosed loop:
Thermal drift

Closed loop:
No thermal drift

Coupling lever, processed twice from one blank form

The required functional dimension of
350 mm with a tolerance grade of IT7
corresponds to a permissible deviation of± 28 µm. The second workpiece machined
in semiclosed-loop mode is unable to meetthis requirement. The deviation is 44 µm.
With the use of linear encoders in closedloop mode in this test, no edge results.

The residual deviations of 10 µm that occur
in closed-loop operation are due tothermally induced, structural distortions of
the machine geometry. The specified
dimensions for the two bore holes caneven be improved to IT5. A reproducible
accuracy from the very first part is thus
guaranteed.

Effects on Mold and Die Making
The manufacturing of molds or dies forinjection-molded or die-cast components isa time-consuming task because it requires
superior surface finish for sometimes veryfine structures. Today many molds are
directly milled in order to avoid the cost
and time consuming eroding process.
Increasingly small milling cutters withdiameters as small as 0.12 mm are used.
Mold and die making for milling ischaracterized not only by high demands
upon dimensional accuracy. It also requires
high feed rates, including for hardenedmaterials, to reduce the machining times.
Typical machining times for molds and dies
range from 10 minutes to several days.
Dimensional accuracy, however, must not
be sacrificed to fast execution. The first andlast machining paths must be identical inorder to ensure that the time previously
gained is not lost to complex rework.
The heating of the recirculating ball screws
in the feed axes substantially depends onthe velocity profile specified for theindividual axes by the NC program, and cancause changes in length up to 150 µm/m
in the recirculating ball screws. These
conditions make it impossible to guarantee
dimensional accuracy in semiclosed-loop
operation. Typical heating of the recirculatingball screw would cause an edge deviationof more than 20 µm in a mold with a lengthof only 150 mm. The expansion of therecirculating ball screw would result in solarge a half of a die that the flaw can nolonger be corrected by rework.
Example of 3-D milling of freeform
surfaces
The following example illustrates themachining of a mold with the classic profileof the Watzmann – a legendary mountainin the German Alps. A 500-mm long
workpiece is machined with multipass,
climb and upcut milling cycles in the X
direction, using a ball-nose cutter with adiameter of 12 mm and a maximum
feed rate of 4.5 m/min. It takes around60 minutes to machine the contour with aninfeed of 0.2 mm in the Z and Y directions.
The high feed rate of 4.5 m/min together
with the constant accelerations anddecelerations generate heat in therecirculating ball screw and cause thermally

Semiclosed loop:
Thermal drift

Figure 7

Closed loop:
No thermal drift

Watzmann profile with free-formed surfaces

induced linear deviations of 130 µm insemiclosed-loop operation. Because thelinear deviation with this mold component
is difficult to visualize, machining wasdeliberately begun in the middle of theworkpiece. Start and end paths therefore
lie side by side and clearly show thethermal drift. The farther the workpiece
position is away from the fixed bearing,
the higher the thermal drift is.
In order to fulfill the high requirements ofmold and die making, it is necessary tocompensate the expansion of ball screws
by using accurate linear encoders. In
Figure 7 the high-accuracy workpiece withan excellent surface finish manufactured inclosed-loop mode is compared with aworkpiece manufactured in semiclosedloop mode.
Summary
The successful fulfillment of manufacturing
orders requires machine tools with highthermal stability. Machine accuracy must
be maintained even under strongly varying
load conditions. As a consequence, feed
axes must achieve the required accuracy
over the complete traverse range evenwith strongly varying speeds andmachining forces. Thermal expansion in therecirculating ball screws of the linear feed
axes adversely affects accuracy and varies
depending on the velocity and load.
Position errors of 100 µm and more may
result within 20 minutes during amachining operation if the slide position is
only determined from the spindle pitch anda rotary encoder. Because essential drive
errors are not compensated in the control
loop when this method is used, this isreferred to as semiclosed-loop operationof the feed drive. These errors can becompletely eliminated by using linear
encoders. Feed drives with linear encoders
are operated in closed-loop mode because
errors in the recirculating ball screw areconsidered in position measurement andcompensated in the position control loop.
Angle encoders used on rotary axes
provide similar benefits since themechanical drive components are also
subject to thermal expansion. Linear andangle encoders therefore ensure highprecision of the components to be
manufactured even under strongly varying
operating conditions of the machine tools.

Linear Encoders for Machine Tools

Linear encoders for position feedback areindispensable for high positioning accuracyof machine tools. They directly capture theactual position of the feed axis. Mechanicaltransfer elements therefore have noinfluence on position measurement – bothkinematics errors and deviations due tothermal influences or other forces aremeasured by the linear encoder andconsidered in the position control loop.
This can eliminate a number of potential
error sources:• Positioning error due to thermal behaviorof the recirculating ball screw• Reversal error• Errors due to deformation of the drive
mechanics by machining forces• Kinematics error through ball-screw
pitch error
Linear encoders are therefore indispensable
for machines that must fulfill highrequirements for positioning accuracy
and machining speed.

Accuracy grade

SignalperiodMeasuring
lengthInterface

Model

Linear encoders with slimline scale housing
1)

Absolute± 5 µm; ± 3 µm–

to 2 040 mm

EnDat 2.2

LC 415

Incremental± 5 µm; ± 3 µm

4 µm

to 1 220 mm» 1 VPPLF 485± 5 µm; ± 3 µm

20 µm

to 2 040 mm1)

» 1 VPPLS 487

Linear encoders with full-size scale housing
Absolute

Incremental

1)± 5 µm; ± 3 µm–

to 4240 mm

EnDat 2.2

LC 115± 5 µm–to 28 040 mm

EnDat 2.2

LC 211± 3 µm; ± 2 µm

4 µm

to 3040 mm» 1 VPPLF 185± 5 µm; ± 3 µm

20 µm

to 3040 mm» 1 VPPLS 187± 5 µm40 µm

to 30 040 mm» 1 VPPLB 382

Over 1 240 mm measuring length only with mounting spar

Linear encoders from HEIDENHAIN fornumerically controlled machine tools canbe used nearly everywhere. They are ideal
for machines and other equipment whose
feed axes are in a closed loop, such as
milling machines, machining centers,
boring machines, lathes and grinding
machines.

LC 415The beneficial dynamic behavior of thelinear encoders, their highly reliable
traversing speed, and their acceleration in
the direction of measurement predestine
them for use on highly-dynamic conventionalaxes as well as on direct drives.
LC 115

LC 211

DR. JOHANNES HEIDENHAIN GmbH
Dr.-Johannes-Heidenhain-Straße 583301 Traunreut, Germany{ +49 8669 31-0
| +49 8669 5061
E-mail: info@heidenhain.dewww.heidenhain.de635 399-22 · 5 · 9/2011 · F&W · Printed in Germany

For more information:• Linear Encoders for NumericallyControlled Machine Tools catalog• Accuracy of Feed Axes Technical
Information