Sensorless Condition Monitoring of Feed Axis Components in

Production Systems by Applying Prony Analysis

Chris Schöberlein, Johannes Quellmalz, Holger Schlegel and Martin Dix

Institute for Machine Tools and Production Processes, Chemnitz University of Technology, Reichenhainer Str. 70,

09126 Chemnitz, Germany

Keywords: Electromechanical Axis, Condition Monitoring, Prony Analysis, Data Acquisition.

Abstract: Condition monitoring of modern production systems has established itself as an independent area of research

in recent years. Main goal is to achieve an increase in machine productivity by reducing downtime and

maintenance costs. In particular, the installed electromechanical axes offer great potential for improvement.

Besides an installation of additional sensors, modern drive systems also provide various signals suitable for

superordinated monitoring systems. The paper presents a novel approach for monitoring of specific

mechanical axis components based solely on internal control loop signals. Fundamental idea is to combine a

parametric approach for vibration analysis, the so-called Prony analysis, with a drive-based setpoint

generation and data aquisition. The method is verified by detecting emulated malfunctions on a single-axis

test stand and a three-axis vertical milling machining center. Experimental investigations prove that the

presented approach is capable of reliably detecting the artificially introduced defects on different axis

components.

1 INTRODUCTION

In modern production systems, electromechanical

feed axes realize the required motion profiles. In the

case of metal-cutting machine tools, they generate the

feed movements, thus maintain chip removal as well

as all other necessary positioning, infeed and tool

change movements. In the field of forming

technology, servo screw presses gain more and more

attention. One ore more electromechanical axes

generate the main process movements for different

forming processes (Sewohl et. al., 2018). In addition,

electromechanical systems are also installed in

production systems for conveying, positioning and

synchronization applications, in printing and textile

machines as well as in packaging, filling and

assembly systems. Altintas states that

electromechanical axes, together with the main drive,

determine the work accuracy and productivity of

modern production systems to a particular extent

(Altintas et al., 2017). Figure 1 illustrates the general

structure of such an axis. It consists of an electrical

part including an industrial control, a drive system

with servomotor and the associated position

https://orcid.org/0000-0002-2344-1656

measuring systems, as well as a mechanical part. In

the case of linear feed axes, the latter is usually

designed as a ball screw drive with comprising

coupling, bearing and gear elements. The main causes

for unplanned malfunctions of feed axes arise from

errors in the mechanical subsystem and frequently

result in downtime of the machine tool itself (Plapper

and Weck, 2001). Therefore, goal of progressive

research efforts is to detect damage on mechanical

axis components prematurely and derive consecutive

maintenance strategies with minimum downtime and

costs. In addition, the utilization of drive-internal

measuring systems makes additional sensors

redundant.

Content of the paper is a novel methodology for

monitoring mechanical components of feed axes

based on characteristic frequency components. In the

context of this paper, the term sensorless denotes that

the approach utilizes only signals available in the

drive internal control loops and therefore does not

require the installation of additional sensors.

Furthermore, it is applicable during regular machine

operation. In contrast to established methods based on

frequency spectra analysis (e.g. Bellini and Tassoni

214

Schöberlein, C., Quellmalz, J., Schlegel, H. and Dix, M.

Sensorless Condition Monitoring of Feed Axis Components in Production Systems by Applying Prony Analysis.

DOI: 10.5220/0011287200003271

In Proceedings of the 19th International Conference on Informatics in Control, Automation and Robotics (ICINCO 2022), pages 214-221

ISBN: 978-989-758-585-2; ISSN: 2184-2809

Figure 1: Schematic structure of a typical electromechanical fedd axis.

2008, Huang et al., 2020) or methods of time-

frequency analysis (e.g. Putz et. al., 2018), a

parametric signal analysis method is used, the so-

called Prony analysis. This approach was already

successfully applied for the assessment of drive

control loops (Neugebauer et al., 2011) or

characterization of mechanical transfer systems

(Schöberlein et al., 2017). Within the scope of this

paper, we extend the analysis method by an

automatic, partially invasive test signal application

combined with simultaneous data recording for

machine tool controls. Functionality is demonstrated

in two exemplary cases: detection of an emulated

damage on a feed-axis coupling as well as

determining preload changes in belt drive systems.

The paper has the following structure. In chapter

2, the basics of prony analysis are explained initially.

Subsequently, the overall methodology including

automatic test signal generation and data recording is

presented. Chapter 3 shows a single-axis test stand for

detecting emulated coupling defects as well as a

machine tool for belt drive monitoring. Core of the

paper is chapter 4 inlcuding experimental

investigations on previously described test scenarios.

The paper closes with a summary and an outlook on

further research topics.

2 METHODOLOGY

2.1 Fundamentals

Similar to Fourier transform, Prony analysis allows

the decomposition of a signal into its spectral

components. Main difference is that Prony analysis is

a parametric method. Due to the low number of

required measurement points, short term signals such

as impulse or step responses can also be evaluated,

which is almost impossible with conventional Fourier

analysis (Neugebauer et al., 2011).

The measured input signal is represented as a sum

of individual, damped sine oscillations. Starting point

is a time signal 𝑥



sampled equidistantly with

sampling time 𝑇



, which is reproduced as sum of

complex functions 𝑥



(Eq. 1).

𝑥





=𝑏



∙𝑧













(1)

𝑏



𝐴



∙𝑒





(2)

𝑧



=𝑒









∙



(3)

Substituting (2) and (3) into (1), applying Euler's

formula results in a sum of 𝑝 damped sinusoidal

signals of magnitude 𝐴



, angular frequency 𝜔



initial phase 𝛷



as well as damping ratio 𝛼



. For

details on mathematical derivation and

implementation, consider (Schönherr et al., 2011.).

By specifying a fixed model order 𝑝 and subsampling

𝑛∙𝑇



of the input signal, the analysis can be adapted

to specific frequency ranges.

Figure 2 shows the result of a Prony analysis for

an exemplary signal curve. The input signal is the

control deviation after a speed setpoint step, recorded

on an exemplary drive test stand. The measured signal

(black) is represented by four damped sinoids

(dashed) whose sum (green) leads to an appropriate

approximation of the input response.

Sensorless Condition Monitoring of Feed Axis Components in Production Systems by Applying Prony Analysis

215

Figure 2: Application of Prony analysis to an exemplary

input signal.

2.2 Overall Concept

Application of the described method for monitoring

mechanical components of feed axes is carried out by

using the overall approach shown in Figure 3. The

electromechanical feed axis is excited during

conventional operation mode with a superimposed

setpoint impulse at level of the speed control loop.

This ensures an excitation over a broad frequency

range. At the same time, speed setpoint and actual

values are recorded utilizing the drive-internal

oscilloscope (trace function). Note that control and

drive systems usually include all necessary functions

for setpoint generation and signal recording.

However, one usually controls them manually during

axis commissioning or for diagnostic purposes. In

order to apply the presented method autonomous

during regular machine operation, an interface

software developed in (Hellmich et al., 2016,

Schöberlein et al., 2018) was utilized. It connects an

external computer to the machine control via Ethernet

connection and grants remote access to all drive

parameters and functions. Data storage via CSV-files

ensures further processing of the logged signals.

Subsequently, the recorded signal is decomposed into

its spectral components using an application-

dependent parameterized Prony analysis. Based on

calculated vibration parameters, one can derive

statements on the condition of specific axis

components. The assignment of the considered

vibration component to a concrete axis component is

based on previously recorded frequency response

analysis. The required data is usually available during

commissioning of the axis.

3 TEST SETUP

Functional verification of the presented approach is

performed on a single-axis test rig and a machine tool

feed axis. Both systems are equipped with Siemens

drive and control systems. These systems already

provide a parameterizable setpoint generator in the

drive control unit, which allows generating specific

test signals (square wave, sine wave, binary noise

signal) at various input points of the control loops.

Furthermore, it provides an internal oscilloscope

(trace function) for recording time signals with

maximum sample frequency of the drive control unit.

Smallest achievable sampling time for both test

stands is 𝑇



= 125 µ𝑠.

3.1 Rotary Axis

In the first experiment, we emulate an exemplary

damage of a feed-axis coupling on a rotary single-

axis. As shown in Figure 4 on the left side the

corresponding test stand consists of a servo motor, a

coupling, a bearing block as well as optional

additional weights. The control is a motion control

type SIMOTION D445 with a SINAMICS S120 drive

system. The artificially introduced defect is simulated

Figure 3: Overall concept of the sensorless monitoring strategy.

0 20 40 60 80

-200

-100

100

200

300

time [ms]

control error [1/min]

measurement

prony estimation

component 1

component 2

component 3

component 4

ICINCO 2022 - 19th International Conference on Informatics in Control, Automation and Robotics

216

Figure 4: Rotary single-axis test stand (left) and machine tool feed axis with belt drive (right).

by loosening a single lamella connection screw of the

coupling (cf. Figure 4). Drive-internal system

excitation and recording of measured values are

controlled manually via an engineering system.

Calculation of Prony method and analysis of the

results follows the finished data aquisition in Matlab.

3.2 Linear Feed Axis

The second functional verification is performed on a

machine axis (x-direction) installed in a DMG Mori

DMC850V three-axis vertical milling machining

center (Figure 4, right). The machine tool is equipped

with Sinumerik 840D sl CNC control as well as

Sinamics S120 drive system. Additional

measurements via reflexion sensor confirm correct

preload setting of the belt drive. A laptop connected

to the controller includes all necessary

communication interface for writing and reading

required drive parameters and signals. Consequently,

test signal generation and recording run fully

automated (cf. Figure 3). Prony method estimates the

corresponding parameters externally on the laptop

after recording is completed. As an exemplary wear

feature, the loss of preload of the toothed belt drive is

simulated.

4 EXPERIMENTAL RESULTS

4.1 Rotary Axis Test Stand

Main objective is to detect malfunctions on axis

couplings represented by an artificially introduced

fault in form of a loosened lamella connection screw.

Measurements are performed with and without

defect. The mechanical configuration corresponds to

Figure 4 without additional mass on output side. First,

we suggest detecting the introduced defect using

conventional spectral analysis in frequency domain.

For this purpose, the system is excited by a pseudo-

binary noise signal at torque level. Simultaneously,

internal trace function records motor torque and

speed. After transforming all time signals into

frequency domain, frequency response function is

plottet in a Bode diagram. Considering Figure 5, one

cannot make a clear distinction between functional

and damaged coupling. Although a horizontal shift of

the mechanical natural frequency is observable in

magnitude and phase response, this could also result

from deviations in repeated measurements of the

frequency responses. Furthermore, the analysis

provides the result only in form of a frequency

response, which is not easy to interpret without expert

knowledge. For direct access, its further processing to

characteristic values (e.g. natural frequency) is

necessary.

Figure 5: Frequency response function of the speed control

plant.

One advantage of Prony method is that all

parameters necessary for an interpretation of the

vibration components are direct result of the analysis.

frequency in Hz

-30

coupling ok

coupling damaged

fre

uenc

in H

-180

-90

180

Sensorless Condition Monitoring of Feed Axis Components in Production Systems by Applying Prony Analysis

217

Therefore, the methodology described in section 2.2

is applied. All specified parameters for setpoint

generator and Prony analysis are listed in Table 1.

The axis is moved at constant speed of 200 min

-1

with

closed control loops for speed and current.

Table 1: Parameters for rotary axis test stand.

Paramete

Value

Spee

offset 200 min

-1

ulse ma

nitude -100 min

-1

ulse duration 500

Sam

le time 125

Recording time 50 ms

Analysis time 15 ms

Model orde

Subsam

lin

facto

Fre

uenc

ran

e 1200

–

1400 Hz

Simultaneously, the signal generator creates a

speed setpoint pulse with absolute magnitude of 100

min

-1

and duration of 500 µs while the drive-internal

trace function simultaneously records signals for

setpoint and actual speed. Subsequently, Prony

method with model order 𝑚=4 and subsampling

time 𝑇

,

= 2∙𝑇



is calculated. Based on

preliminary tests (cf. Figure 5), the model component

with a frequency in the range of 1200 Hz to 1400 Hz

is selected. Figure 6a shows the estimation results

without defect (top) and with loosened connecting

screw (bottom). Comparing the measured time

signals and Prony estimation, one may recognize

slight differences in decay behavior. By repeating the

described procedure five times each with intact and

damaged coupling while plotting all output

parameters (damping, frequency, amplitude) of Prony

analysis individually above test number, one gets the

picture shown in Figure 6b. Note that measurements

one to five represent the undamaged case while six to

ten show results with damaged coupling. Especially

in the damping values, significant differences occur.

Thus, the value is approximately 𝐷 = 0.002 in the

intact case and in damaged case around 𝐷 = 0.011.

Although there occur clear differences regarding the

frequency values (Figure 6b, center), tests with

additional mass have shown that these are

occasionally subject to significant fluctuations.

Investigations for linear feed axis in the following

section confirm this conclusion. Eventually, it can be

stated that clear distinctions are possible between

undamaged and damaged coupling considering the

damping value of Prony estimation.

4.2 Linear Feed Axis

In the next step, the described method is applied on a

linear feed axis of a machine tool. Main objective is

to detect changes in preload of the installed toothed

belt drive (cf. Figure 4, right). The procedure

corresponds to the schematic diagram in Figure 3 and

previous investigations on the single-axis test rig,

respectively. Only difference is the autonomous

setpoint connection and signal recording parallel to

conventional NC operation. Consequently, all control

loops (position, speed and current) are closed. The

axis moves at constant feed rate of 2000 mm/min.

Magnitude of the superimposed reference pulse is set

to 50 min

-1

. Recording duration and sample time

remain unchanged. For model order and subsampling

time, previous experiments showed that the values

listed in Table 2 lead to better results. Frequency

range of the analysis was again determined based on

preliminary tests analogous to the single-axis test

stand. According to the manufacturer, correct belt

tension is present when the manual measurement with

reflexion sensor reaches an oscillation frequency of

approximately 130 Hz. By applying drive based

excitation and calculating the frequency response

Figure 6: Prony estimation (a) and calculated values for intact and damaged axis coupling (b).

rotational speed in rad/s

)

coupling ok

coupling damaged

coupling ok

coupling ok coupling damaged

coupling damaged

ICINCO 2022 - 19th International Conference on Informatics in Control, Automation and Robotics

218

function, this leads to a characteristic natural

frequency of approximately 300 Hz. Therefore, we

suggest to set the observed frequency range for the

Prony analysis as listed in Table 2

Table 2: Parameters for linear feed axis.

Paramete

Value

Speed offse

2000 mm/min

Impulse ma

nitude

50 min

-1

Impulse duration

500 µs

Sample time

125 µs

Recordin

time

50 ms

Anal

sis time

15 ms

Model orde

Subsamplin

facto

Frequenc

ran

250 – 400 Hz

In a first test, the belt tension was significantly

reduced so that manual measurements with reflexion

sensor lead to a frequency drop from 130 Hz to 60 Hz.

Results of the subsequent Prony analysis are shown

in Figure 7a. Again, no significant differences in the

signal curves are visible at first sight. However, there

occur large differences in the calculated damping

values. For correct preloaded belt drive, Prony

analysis estimates a damping value of

𝐷 = 0.100. On the other hand, with reduced tension

the approach calculates the damping value to

𝐷 = 0.329 . If one repeats the measurement at

different points over the whole travel range of the axis

(Figure 7b, blue crosses and orange circles), single

measurements may sometimes lead to unambiguous

results (e.g. measurement No. 3). This can be

countered by a cyclically recurring application and

subsequent averaging of the calculated parameters

(cf. Table 3). In real operation mode, however, there

is no sudden, but rather gradual drop in belt preload.

Consequently, resolution of the analysis is crucial for

practical applicability and therefore the method must

reliably detect slow tension losses. For this reason,

further tests were carried out in which the preload was

changed in smaller steps.

Table 3: Results of the Prony analysis for linear feed axis.

Parameter Average

Standard

deviation

Preload appropriate (130 Hz)

𝛼



(-)

0.10 0.02

𝜔



(Hz)

316.80 9.20

𝐴



(mm/min)

61.58 15.37

Preload not appropriate (87 Hz)

𝛼



(-)

0.20 0.04

𝜔



(Hz)

297.50 14.40

𝐴



(mm/min)

85.22 33.85

Preload not appropriate (80 Hz)

𝛼



(-)

0.23 0.09

𝜔



(Hz)

296.20 10.70

𝐴



(mm/min)

95.43 31.81

Preload not appropriate (60 Hz)

𝛼



(-)

0.29 0.06

𝜔



(Hz)

326.70 22.10

𝐴



(mm/min)

49.22 34.93

Note that a correctly pretensioned belt drive has a

natural frequency of 130 Hz when measured

manually by reflexion sensor. Figure 7b shows the

results for different preloads and several

measurements at different points over the whole

travel range of the axis. Considering the individual

values, it becomes clear that a single measurement

Figure 7: Prony estimation (a) and calculated values for gradually reduced belt drive preload (b).

damping

frequency

in Hz

magnitude

in mm/min

velocity in mm/min

)

preload ok (130 Hz)

preload reduced (60 Hz)

Sensorless Condition Monitoring of Feed Axis Components in Production Systems by Applying Prony Analysis

219

can once again lead to incorrect conclusions

regarding the belt configuration. However, if one

calculates average values of the identified parameters

as well as their standard deviation (cf. Table 3), the

damping values of the associated vibration

component provide a clear result. In case of the

frequency values, which can be considered as an

alternative comparison criterion, a distinction is not

always possible (e.g. between 87 Hz and 80 Hz.

Furthermore, when preload is reduced down to 80 Hz,

a drop in average frequency is obervable, which,

however, increases again in case of 60 Hz. The same

applies in reverse for the magnitude values. Only the

average damping increases proportionally to the

reduction in preload and therefore provides a suitable

feature for superimposed condition monitoring and

diagnosis.

5 SUMMARY AND CONCLUSION

The paper presents a novel approach for sensorless

condition monitoring of mechanical parts of

electromechanical axis by applying Prony analysis.

Main advantages of the approach are the partially

invasive applicability during conventional machine

operation without dismantling any axis components.

Due to the exclusive utilization of drive internal

signals, no additional sensors are required. In contrast

to conventional Fourier analysis, Prony analysis

decomposes a signal into a series of damped

sinusoidal oscillations. In addition, characteristic

oscillation parameters (magnitude, frequency,

damping, phase angle) are directly calculated output

parameters. A communication interface for NC

controls including automated setpoint generation as

well as drive signal acquisition qualifies the method

for application during regular machine operation.

This was proven by extensive experimental

investigations. Initially, fundamental verification was

demonstrated on an exemplary rotational single-axis

test rig. The method was able to detect an artificially

introduced damage (loosening of a lamellaa

connecting screw) by changes in calculated damping

values. The subsequent application on the linear axis

of a conventional three-axis machine tool shows the

capability of the approach. Component damage was

simulated by reducing preload of the installed toothed

belt drive. However, the experiments led to the

conclusion that cyclically recurring analysis is

necessary for reliable results. Nonetheless, the

average damping values are able to display slow

changes in preload.

Future research activities should investigate to

what extent the methodology is able to detect

malfunctions on other axis parts (e.g. bearing

damage). In particular, with regard to the industrial

application of the method, reliable threshold values

must be defined which classify a component as

defective. Suitable reference values can be identified

by determining parameters during machine

commissioning. In addition, suitable times for

connecting the test signal must be specified regarding

practical applicability on machine tools. One possible

solution is to analyze the current machining program

and identify safe motion areas for superimposition

(e.g. rapid movements, tool change movements). By

connecting a data storage with parameter history as

well its combination with an enterprise resource

planning system, an extended diagnosis with a

suitable maintenance strategy and spare parts supply

is possible.

ACKNOWLEDGEMENTS

Funded by the Federal German Ministry for

Economic Affairs and Climate Action.

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