Structural Dynamic Behavior
of a High-Speed Milling Machine
FEA Vs. EMA Assessment
* J. Rotberg , ** B. Bork
* "Technion" – I.I.T ** Technische Universitat Darmstadt
Faculty of Mechanical Eng. PTW Institut Petersenstr. 30
Haifa 32000, Israel Darmstadt 64287, Germany
ABSTRACT. This work deals with the assessment of the structural dynamic behavior of a
High Speed Milling machine, during the machine development and testing period. The task
was carried out by a combination of Finite Element Analysis (FEA) , and Experimental Modal
Analysis (EMA) techniques. In the paper , the importance of this combination is explained ,
and , on the other hand , its applicability and availability are demonstrated.
The dynamic behavior of the machine structure in any milling condition, may be determined
in terms of its natural frequencies and mode shapes, as obtained from the FEA and EMA
combined application. The significance of the results is explained by specific examples. Thus ,
improving of machine tool performance is achieved by the application of modern means for
engineering analysis and testing.
KEY WORDS: High speed machine, Finite element method (FEM), Modal analysis
This paper deals with the assessment of the dynamic behavior of the structure of a
newly developed Milling Machine for High Speed Machining (HSM), mainly in the
manufacturing of dies and moulds.
.Fig. 1: High Speed linear motor milling machine
The High Speed Milling machine, equipped with linear motor driven axes was
developed and built in the Institute of Production Engineering and Machine Tools
(“PTW”) in Darmstadt University of Technology, Germany [SCH 95]. The work
described in the paper was carried out within the development process [ROT 96].
This work demonstrates the necessity of knowing the machine structural dynamic
features in high speed milling , and on the other hand , the availability of fast,
effective means for the assessment of these required features, applying modern
The machine is a 3-axis vertical , bridge type milling machine, having high speed
(up to 60,000 rpm) spindle, linear motor driven slides, yielding up to 80 m/min
feed rate and 25 m/s2 acceleration.
The machine’ bed and side columns are made of a concrete compound. The head
console and all slides are made of light weight welded steel structures.
While working , the machine structure is submitted to two kinds of exciting
forces: The acceleration and inertia forces of the slides and work-piece are not
negligible in this machine [SCH 96]. In addition, the milling exciting force is a
periodic, sharp signal of high frequency , [SCH 96], [ROT 97], [SCH 94],
resulting also in higher harmonic components (Fig. 2), reaching definitely the
range of natural frequencies of the machine structure.
Fig. 2: Examples of force signals in milling operations
Consequently , the machine response to these exciting forces must be acquired in
order to avoid operating in non-preferred conditions, and yet enable maximal
2. Finite Element and Experimental Modal Analyses
If a linear approximation of the machine structure is made , the machine response
to any dynamic excitation may be estimated based on its Natural Frequencies and
corresponding Mode Shapes.
These , may be acquired either from a theoretical computation of Finite Element
Analysis (FEA) , or from an Experimental Modal Analysis (EMA) [EWI 84].
The FEA, starting with a model which is then used to predict the machine
response (Fig. 3) , is essential at the design phase and provides us with general
information. However , in the FEA model there are several points of uncertainty
(such as contact points stiffness of bearings and guide-ways, internal damping of
structural materials etc.) , which require simplification and assumptions , that may
result in large errors.
The EMA (Experimental Modal Analysis) of the built machine prototype is
therefore required in order to verify the machine real behavior. In this method
the actual machine response is measured , leading to an EMA machine model.
(Fig. 3 ).
Fig. 3: Theoretical (FEA) and Experimental (EMA) modal analysis
Thus , the two inverse methods , as compared in Fig. 3, complete each other, and
only a proper combination of the two enables the design and correct prediction of
the machine behavior.
A detailed FEA model of about 7000 elements was constructed using “IDEAS”
software (Fig. 5a). Naturally, subsystem connecting points were simplified , the
stiffness of the roller guide-ways was taken from the manufacturer information,
internal damping of steel elements was neglected, etc. Yet the FE model is
rather detailed. The first 10 Natural Frequencies and corresponding Mode
Shapes were then computed theoretically. (examples in Figs. 5b , 5c).
The Experimental Modal Analysis was carried out by means of an impulse
hammer excitation technique, which was found to be very convenient, practical
and effective, even for such a large complicated structure.
In Fig. 4 the experimental equipment is shown: A “PCB” impulse hammer
and accelerometer, plus an HP35670A signal analyzer were used. “STAR”
software was used for data analysis.
Fig. 4: Experimental Modal Analysis equipment
The machine structure was modeled by 34 points (Fig. 5a ). About a hundred
transfer functions were measured (three directions at each point).
Analyzing the acquired data, an EMA model of the machine was created, yielding
12 natural frequencies and corresponding mode shapes in the frequency range of
0-2400 Hz. (examples in Figs. 5b , 5c ).
The Transfer Functions at the force-application point (the milling cutter zone),
were measured as well, giving a direct estimation of the tool point response to the
periodic cutting force in any given case of milling .
The EMA model, which was acquired experimentally in less than 3 weeks,
provided a solid, real base for the structure behavior evaluation, the identification
of possible modifications, and most important , machine operating guidelines.
Fig. 5: FE Vs. EMA machine models, mode shapes and natural frequencies.
3. Results and Discussion
Some of the main results of the evaluation process will be brought here, in
order to demonstrate the importance of the combined action in the machine
development process, the way and importance of the result application for
operating the machine, and maybe to point out the method applicability and
availability for other cases.
The FE model , as described above, yields the predicted natural frequencies and
the corresponding mode shapes appearing in Table 1 . The first two are shown in
Figs. 5b and 5c. From this data , general features of the structure may be derived,
i.e. what kind of vibrations would be excited by a given milling operation.
Exact natural frequencies, as well as the Evaluation of the Response Amplitude
depends , however, on accurate definition of damping values and machine parts
contact stiffness. (which must be acquired experimentally ).
During the FEA computations, it was noted that proper modeling of the
interconnections between different machine subsystem , is of great influence on
the computation results.
Table 1 : Natural Frequency values as obtained by FEA and EMA methods
The EMA results start with Fig. 6 showing two typical frequency-response-
functions (F.R.F), as acquired from the impulse test, at the point of the milling
force application (model point no. 41). Response typical values are as follows:
Direction Nat. Freq. Damping ratio Compliance X/F max. Stiffness F/X
[Hz] [%] [um/N] N/um]
Y 220 0.65 0.042 24
X 280 0.90 0.032 30
Table 2: Typical response values at the milling force application point.
Fig. 6: Frequency Response Functions at the cutting force application point.
Comparing the natural frequency values obtained by the two methods, one may
notice the consistent difference showing always higher real frequency values
then predicted. Based on our experience, this is related to inaccurate
approximation of the machine subsystems contact-points (guide-ways, etc.).
Anyway, this demonstrates again the necessity of the Experimental evaluation by
In Figs. 5b , 5c the first two mode shapes are shown , as computed based on the
EMA model. (as constructed from the whole experimental testing data).
The mode shapes are similar to the FE predicted shapes, but now we have real
Frequency Response including exact natural frequencies as well response
It is clear that these two modes of vibrations might be excited by a milling
operation in the X or Y direction at proper rotating spindle speed ( see Fig. 2).
As a practical Example:
In milling with a 2 - teeth end mill, tooth frequencies of 220 Hz and 280 Hz
should be avoided. This results in non recommended spindle speeds of 6600
rpm and 8400 rpm.
A semi-finish milling of an alloy steel , say , AISI 4140, with an 2-teeth 10 mm
diameter end mill, at Cutting Speed of about 210 or 260 m/min. ( realistic
conditions for coated carbide tools) , will require operating the machine in the non
recommended rpm values .
The pulsating cutting force, (see Fig. 2), under realistic cutting conditions (feed
rate 0.05 mm/tooth , depth of cut 5 mm ) will lead to a vibration amplitude which
is now computable , (table 2) and may reach 0.015-0.020 mm.
Operating the machine for cutting at any rpm value, even with an almost
constant cutting force (face milling with a wide, multi-tooth, milling cutter),
necessarily produces some "wide-band" force signal (cutting "noise"), exciting
the structure and translated into amplified vibration in the natural frequencies.
In that case, the machine response (vibration amplitude) can now be computed and
the performance limitations may be well established.
Thus, the detailed data of the structure response is essential for estimating the
machine performance in any operating conditions, while avoiding the dangerous
The structural dynamic behavior of a machine for high speed milling was
investigated during the machine development process. This was done by a
combined application of both FEA and EMA techniques.
The Finite Element computation, essential in the design phase, supplied the
general behavior characteristics, and the basic evaluation of natural frequencies
and mode shapes.
The Experimental Modal Analysis, carried out in the machine prototype has
completed the required knowledge by verifying the basic concept and obtaining
real accurate values for natural frequencies, mode shapes, and structure response
In the article , the definite necessity of proper combination of the two techniques
was explained. On the other hand, the availability of means and procedures for
the task was demonstrated .
The combined application of the two, provides the information for machine design
improvement, and machine operating recommendations leading eventually to
machine performance improvement.
1. [SCH 95] SCHMITT, T. “Linearmotortechnik fur den werkzeug-und formenbau”
PTW – Wissenswert, TH- Darmstadt Nr. 1 1995.
2. [ROT 96] ROTBERG, J., Short report on EMA , and on control response test,
development of high speed machine. A report submitted to the PTW
TH- Darmstadt, 1996.
3. [SCH 96] SCHULZ, H., Hochgeshwindigkeits - bearbeitung (High speed machining),
Carl Hanser Verlag 1996.
4. [ROT 97] ROTBERG J., SHOVAL S., BER A., "Fast evaluation of cutting forces
in milling." J. of Advanced Manufacturing Technology Vol. 13 No. 1 pp.17-26,
5 [SCH 94] SCHULZ, H., HERGET, T., “Simulation and measurement of transient
cutting force signal in high speed milling”, Production Engineering R&D in Germany,
Vol. I/2, pp. 19-22, 1994.
6. [EWI 84] EWINS, D., J. , Modal testing theory and practice, Research Studies Press
3rd print, 1984.