Vibration Measurement with Piezoelectric Transducer
`Bozhidar Dzhudzhev1, Veselka Ivancheva2, Silviya Kachulkova3 and Ekaterina
`Gospodinova4
`
`Abstract – This article discusses piezoelectric transducers and
`their application for vibration measurement. The functions of
`conversion are experimentally defined and investigated.
`
`electrical measurement,
`no
`– Vibrations,
`Keywords
`piezoelectric transducer, amplitude, frequency.
`
`I.VIBRATION – BASICS
`
`A. Definition
`
`Vibration is the motion of a particle or a device or system
`of connected devices scattered around the balanced position.
`Most vibrations are undesirable in machines and equipment
`because they lead to increased loads, fatigue and energy loss,
`increased bearing loads, creating discomfort for passengers in
`vehicles and absorbing energy from the system. The rotating
`parts in machines must be carefully balanced to prevent
`vibration damage. [1]
`Vibrations can be obtained from natural forces, such as
`earthquake [2]. There are vibrations created by the people
`who influence the environment. Such vibrations can be caused
`by industry, transport [3], construction [2] and other activities.
`Vibration is a response of the system to internal or external
`impact, which causes it to fluctuate or pulsate.
`Although it
`is commonly believed that vibrations do
`damage to the equipment and the machinery, they do not.
`Instead, the damage is done by dynamic loads, which lead to
`fatigue and dynamic loads are caused by vibration. [4]
`If a vibrating object can be seen in slow motion, it will be
`found running in different directions. Each vibration has two
`measurable variables that help to determine the vibration
`characteristics, how far (magnitude or intensity) and how fast
`(frequency) the subject is moving. The parameters used to
`describe
`this movement
`are
`displacement,
`frequency,
`amplitude and acceleration. (Figure .1)
`
`1 Bozhidar Dzhudzhev is with the Faculty of Automatics at
`Technical University of Sofia, 8 Kl. Ohridski Blvd, Sofia 1000 ,
`Bulgaria, E-mail: bojidar.djudjev@abv.bg
`2Veselka Ivancheva is with the Faculty of Automatics at Technical
`University of Sofia, 8 Kl. Ohridski Blvd, Sofia 1000, Bulgaria.
`3Silvyia Kachulkova is with the Faculty of Automatics of Sofia, 8
`Kl. Ohridski Blvd, Sofia 1000, Bulgaria.
`4Ekaterina Gospodinova is with the Faculty of Automatics at
`Technical University of Sofia, 8 Kl. Ohridski Blvd, Sofia 1000,
`Bulgaria.
`
`Fig.1 Parameters of vibration
`
`B. Amplitude
`
`this how big is the
`The generally accepted term for
`vibration is amplitude, A. The definition of amplitude depends
`on the systems. One can work in units of distance from the
`vibrating subject from extreme left to extreme right (double
`amplitude) but in physics more often is used the distance from
`the center to one of the extremes.
`
`C.Frequency
`
`Frequency f is the number of cycles that occur per unit of
`time. [4]. Unit rate is usually 1 cycle/second, which is defined
`as a special unit 1 Hertz (1Hz). The term frequency is
`common in determining the vibration.
`If one cycle takes time T, then the number of cycles that
`occur per unit time is:
`
`f
`
`
`
`1
`
`cycle
`T
`
` (1)
`
`from the
`
`D. Units for vibration measurement
`Vibration displacement " s "
`This is a deviation of
`the measured point
`equilibrium position. The unit is usually mµ . [5]
`Vibration velocity " v "
`This is the rate at which the measured point moves around
`smm . [5]
`its equilibrium position. The unit is
`Vibration acceleration " a "
`This is the acceleration with which the measured point
`moves about
`the equilibrium position. The unit
`is either
`1
`81,9
`2sm
`sm
`g 
`2
`or g (
`). [5]
`
`Page 1 of 4
`
`HAPTIC EX2014
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`

`

`=
`
`zS
`q
`
`
`
`
`
`
`
`(1)
`
`q
`
`qS
`the sensitivity of Piezoelectric vibration
`where
`transducer for amount of electricity.
`The equivalent replacement scheme of the structure from
`TC is marked the
`Fig. 2 is shown in Fig. 3, in which with
`capacity of the converter with C - the additional capacity with
`LR - the output load resistance of Piezoelectric vibration
`d
`a=
`transducer. The current is
`. The output voltage of the
`i
`dt
`vibration transducer in harmonic mode is:
`
`
`zSj
`w
`&
`q
`+
`Cj
`w
`
`1
`R
`
`L
`
`SS »
`
`CS
`
`q
`
`
`
`=
`
`U
`&
`
`n
`
`
`
`z
`&
`
` (
`
`2)
`
`
`
`Here
`
`
`
`=S
`T +
`C
`C
`C
`The approximate equation is valid when
`
`1
`RL
`SC
`w
`Sometimes this condition is achieved with the given shunt of
`the transducer with additional capacitor with significant
`capacity. This, however, reduces the voltage sensitivity of the
`scheme:
`
`
`ff
`
`.
`
`
`
`U
`&
`
`n
`
`S
`q
`+
`
`C
`T
`
`=
`
`z
`&
`
`zS
`&
`U
`
`
`
`(3)
`
`C
`
`Construction of the piezoelectric transducer is such that any
`additional resonant frequencies are much higher than the
`primary. It is assumed that there is only the main resonance. It
`m , the
`is determined by the equivalent vibrating mass
`equivalent elastic counteraction with constant W and without
`P . The parameters own
`hysteresis friction with constant
`1
`w
`=
`0
`2
`2
`p
`p
`v =
`
` (
`
`4)
`
`
`
`j
`
`b2
`
`v
`
`2 +
`
`v
`)
`
`2
`
`v
`
`CS
`
`q
`
`-» S
`(
`x
`&
`1
`
`U
`&
`
`n
`
`
`To one of the two working ends of the vibrator is attached
`piezoelectric transducer (Fig. 2).
`1ffv
`When
`, amplitude-frequency response and phase-
`frequency response of the piezoelectric transducer tend to:
`
`
`, decay
`
`0f
`
` are
`
`mW
`
`f
`
`frequency of oscillation
`
`=
`
`f
`
`0
`
`=b
`
` and relative frequency
`
`P
`mW
`2
`obtained.
`The condition for the use of piezoelectric transducer as a
`vibrator for measuring the amplitude of the vibration is given
`by:
`
`
`
`
`
`II. PIEZOELECTRIC TRANSDUCER
`
`Piezoelectric effect occurs in some crystalline substances -
`natural quartz, Rochelle salt, lithium sulphate, some ceramics
`and more. When such a crystal is placed in an electric field it
`changes its size synchronously with the changes of the field –
`opposite Piezoelectric effect (used to generate audible and
`ultrasonic signals). When the crystal is deformed in an
`appropriate direction an electric charge is generated (straight
`Piezoelectric effect). [6]
`One of the commonly used structures for vibration
`measurement while controlling the state of the machine is
`shown in Figure 2. The Piezoelectric transducer is glued
`strong at the one end of the bending under the forces of inertia
`plate and the free end is soldered seismic mass. Attenuation is
`achieved through the oil drops placed in the gap between the
`seismic mass and the attenuator. When the base is moving
`downside-up the inertia opposes and deforms the Piezoelectric
`transducer. This generates an electrical charge that is
`proportional to the acceleration. Typical values of the
`2/m in the
`sensitivity of these sensors are 0,5-50 mVs
`frequency range 0,1 Hz to 200 kHz.
`
`Transducer
`
`Plate
`(Base)
`
`Seismic
`Mass
`
`Displace
`ment X
`
`Displace
`ment Y
`
`Vibration
`Exciter
`
`Attenuator
`
`
`
`Fig.2 Stand for vibration measurements
`
`x , absolute
`Between the vibrational displacement
`y and its relative
`displacement of the seismic mass
`movement z exist dependence (
`).
`z
`y
`
`
`-=
`x
`
`i
`
`CT
`
`C
`
`RL
`
`UL
`
`Transducer
`
`
`
`Fig.3 Equivalent replacement scheme
`
`Piezoelectric vibration transducer generates an electrical
`charge that is proportional to the deflection of the
`piezoelectric transducer.
`
`
`Page 2 of 4
`
`»
`

`

`powered externally. It produces a signal proportional to
`ground acceleration g. The signal from the transducer passes
`through the amplifier - Hottinger Baldwin messtechnic Type
`spider 8, where it is transformed in appropriate form and is
`fed to the computer. The results are displayed using the
`program Catman Professional. The program is dedicated
`measurement software that provides great opportunities for
`visualization and analysis of signals. The program allows to
`measure frequencies and amplitudes.
`
`
`Vibration
`Exciter
`
`Generator
`
`Amplifier
`
`Amplifier
`
`Computer
`
`Transducer
`
`Power
`Supply
`
`
`Fig.4 Block diagram of the stand for measuring vibration
`
`IV. RESULTS FROM THE MEASUREMENT
`
`1. Testing the transducer on measuring frequency. The
`amplitude of the signal coming from the piezoelectric
`transducer is maintained constant with the amplifier - Bruel &
`Kjaer power amplifier Type 2712 with values - 5g and 10g.
`The results are presented in Table I. There are very small
`differences (from 0 to 1.2%) between the one from the
`generator and the measured from the transducer.
`
`
`TABLE I
`DEPENDING ON THE FREQUENCY OF THE PIEZO TRANSDUCER FROM
`FREQUENCY GENERATOR
`
`Frequency from the
`piezoelectric
`transducer, Hz
`
`Frequency from
`the generator,
`Hz
`20 20
`30 30,303
`40 40
`50 50
`60 60,606
`70 71,428
`80 80
`90 90,909
`100 100
`
`
`
`2. Study on the dependence of the amplitude of the
`vibration frequency against the frequency signal from the
`(
`)f
`A =
`. The measurements were made at
`generator,
`f
`frequencies from 20 Hz to 500 Hz over 10 Hz (Table II). The
`
` (
`
`5)
`
`x
`
`
`
`CS
`
`q
`
`
`
`U(
`
`)
`vn
`
`=1
`
`ff
`
`
`
`
`
`2
`b
`v
`
`=
`
`xU
`&&
`
`n
`
`
`
`)(
`j
`
`v
`
`1
`ff
`
`=
`
`arg
`
`arctg
`
`Therefore in the above resonant area it is received a signal
`for the amplitude of the vibration.
`
`0
`
`
`
`(6)
`
`x
`)(
`&
`
` it is obtained:
`
`d
`dt
`
`22
`
`1
`2
`w
`
`If X& in Eq. (1) is replaced by
`
`
`
`x)(
`&
`
`(
`1
`
`1
`)
`+
`
`2
`
`v
`
`
`
`(7)
`
`j
`
`2
`
`b
`
`v
`
`CS
`
`q
`
`
`
`=
`
`U
`&
`
`n
`
`1
`2
`
`f
`
`4
`p
`
`2
`0
`
`
`1ppv
`, amplitude-frequency response and phase-
` For
`frequency response tend to:
`and the frequency response FCHH tend to express:
`
`
`
`
` (
`
`0
`
`
`
` (
`
`8)
`
`9)
`
`n
`
`
`Therefore in the under resonant area it is received a signal
`for the amplitude of the vibration acceleration.
`
`III. DESCRIPTION OF THE EXPERIMENTAL SETUP
`
`The setup for vibration measurement and processing of
`results is shown in Figure 4. It includes the following blocks:
`
`• Frequency Generator - Philips GM 2315. Frequency range
`of 20Hz to 20kHz. Range from 0 to 10V.
`• Digital Multimeter - Fluke 83 Multimeter
`• Amplifier - Bruel & Kjaer power amplifier type 2712
`• Vibration exciter - Bruel & Kjaer, permanent magnetic
`vibration exciter type 4808. Maximum acceleration 71g.
`• Sensors for measuring vibration acceleration - Piezoelectric
`- Kistler K-Shear accelerometer Type 8704B500M1.
`Frequency range of 1Hz to 10kHz. Measuring range ±
`500g.
`• Power supply for the piezoelectric sensor - Kistler power
`supply/coupler, type 5134.
`• Amplifier - Hottinger Baldwin messtechnic, type spider 8
`• Computer
`• Software - Catman Professional 5.0
`
`From the frequency generator we are setting the frequency
`and the amplitude of the signal. We are monitoring these
`values with a multimeter. The signal from the generator
`passes through the amplifier 2712 and is succumbed to the
`vibration exciter. It produces in turn a vibration that is
`measured by the transducer. The piezoelectric transducer is
`
`CS
`
`q
`
`xU
`
`
`
`
`
`
`&
`
`U(
`
`)
`vn
`
`1
`pp
`
`)(
`ppj
`v
`1
`
`¢¢fi S
`x
`&
`=
`fi¢¢
`arg
`
`Page 3 of 4
`
`S
`fi
`-
`S
`

`

`function A=f(f) of Piezoelectric tranduser
`
`12
`
`10
`
`02468
`
`amplitude from the
`
`tranduser [g]
`
`0100200300400500600
`frequency from the generator [Hz]
`
`
`
`Fig.5 Function of the converting of the piezoelectric transducer from
`frequency of the generator
`
`V. CONCLUSIONS
`
`The piezoelectric transducer measures frequency very
`accurate. There are differences in some of the results between
`the transducer and the report of the assigned frequency of the
`generator, the biggest difference is 1,4 Hz. This difference is
`caused by the rounding made when reporting the actual data
`from the transducer. The transducer has a large frequency
`range.
`Piezoelectric transducer measures better signals with larger
`amplitudes and around the resonant area. For signals with
`very small amplitudes, the sensor may not report them.
`
`ACKNOWLEDGEMENTS
`
`The researches, the results of which are presented in this
`publication are funded by internal competition TU-2012
`contract to support PhD student № 122 RP 0074-08 "Study
`and optimization of processes for measuring vibration".
`
`REFERENCES
`
`[1] http://www.newagepublishers.com/samplechapter/001413.pdf “
`[2] http://www.acousticassociates.co.uk/environmental-
`vibration.htm
`[3] Department of Environment and Conservation, “Assessing
`Vibration: a technical guideline”, 2006
`[4] Torex sensors, “Vibration”
`[5] Brüel & Kjær Vibro “Basic Vibration – Measurement &
`Assessment”
`[6] James Kark, “Signal Conditioning Piezoelectric Sensors”, 2003
`
`
`measurement was conducted in the same gain.
`The change of amplitude against frequency is shown in Fig.
`5. The figure shows that the vibration exciter has resonance at
`100 Hz.
`
`TABLE II
`AMPLITUDE OF THE TRANSDUCER AS A FUNCTION OF FREQUENCY
`
`Amplitude
`from the
`transducer, g
`
`Frequency
`from the
`generator,
`Hz
`
`Amplitude
`from the
`transducer, g
`
`Frequency
`from the
`generator,
`Hz
`20 3,5
`30 4,4 270 3,2
`40 6,0 280 2,85
`50 7,3 290 2,85
`60 8,5 300 2,45
`70 9,0 310 2,45
`80 9,75 320 2,05
`90 9,75 330 2,05
`100 9,75 340 1,6
`110 9,2 350 1,6
`120 8,9 360 1,6
`130 8,5 370 1,2
`140 8,0 380 1,2
`150 7,7 390 1,2
`160 7,3 400 1,0
`170 6,9 410 1,0
`180 6,5 420 0,8
`190 6,5 430 0,8
`200 6,0 440 0,8
`210 5,6 450 0,8
`220 5,2 460 0,8
`230 4,8 470 0,4
`240 4,4 480 0,4
`250 4,0 490 0,4
`260 3,6 500 0,4
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`Page 4 of 4
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