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Department of physics

Seminar 1B – 1.st year, Nuclear engineering

Calibration procedure for vibration sensors in

nuclear power plants

Author: Bor Kos

Mentor: mag. Matjaž Lindič

Co-Mentor: Miha Kokalj

Co-Mentor: prof. dr. Iztok Tiselj

Ljubljana, December 2014

Abstract In this paper I will give an overview on the concepts of metrology where we will concentrate on the

need for precision measurements and the three basic activities of metrology which are the definition of

internationally accepted units of measurement, realization of these units of measurement in practice

and the application of chains of traceability linking measurements made in practice to reference

standards. In the second part of this seminar practical applications of the described metrology

activities are presented. A presentation of a calibration procedure of vibration sensors used in the

Krško Nuclear power plant made by SIQ Ljubljana (Slovenian institute of Quality and Metrology) will

be given.

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Table of contents

Abstract ................................................................................................................................................... 1

Introduction ............................................................................................................................................. 2

Basic concepts of metrology ................................................................................................................... 3

International system of units SI ........................................................................................................... 4

Basic terminology of metrology .......................................................................................................... 4

Traceability ...................................................................................................................................... 4

Measurement standards ................................................................................................................... 5

Calibration ....................................................................................................................................... 5

Uncertainty ...................................................................................................................................... 5

Vibration sensors in Nuclear power plants .............................................................................................. 5

Vibration transducers .............................................................................................................................. 7

Methods for the calibration of vibration transducers............................................................................... 8

Calibrating procedure of vibration sensors used in Krško Nuclear power plant made by SIQ ............. 10

Conclusion ............................................................................................................................................. 12

References ............................................................................................................................................. 12

Introduction

Nuclear power plants utilizing vibration monitoring ensure continuous power generation and

increased safety for personnel and equipment, while also helping to prevent radiation leaks into the

environment. Vibration sensors are used for many applications, including start-up and hot functional

tests, loose parts monitoring, reactor internals vibration monitoring, fuel pin flow induced vibration,

steam generator, and in-core fuel flow induced vibration programs. [1] To ensure the proper operation

of the vibration sensors, calibration procedures have been developed in accordance to ISO

(International Organization for Standardization) standards. The Slovenian institute of Quality and

Metrology (SIQ) has developed and put in to use procedures for calibrating vibration sensors form the

Krško Nuclear power plant in accordance to the ISO standards on the highest metrological level.

Before we jump into the heart of this calibration procedure we will look at some basic

concepts of metrology including SI (International System of Units) units and metrology terminology.

After this introduction the basic mathematical and physical concepts behind vibration transducers will

be described. Finally we will look at an actual calibrating procedure of vibration sensors including

Excel documents and all the equipment used to perform the calibration at the Metrology laboratory at

SIQ.

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Basic concepts of metrology

Let us start with a short anecdote. The death penalty faced those who forgot or neglected their

duty to calibrate the standard unit of length at each full moon. That was the sentence for architects

responsible for building the temples and pyramids of the Pharaohs in ancient Egypt. The standard unit

used in those times was the length of the forearm from elbow to top of the extended middle finger of

the ruling Pharaoh, plus the width of his hand. The original measurement was transferred to and

carved in black granite. Closer to our time, in 1799 in Paris, the Metric System was created by the

deposition of two platinum standards representing the meter and the kilogram. These were the

predecessors of the present International System of Units – the SI system.

The science of measurement – metrology – is probably the oldest science in the world and

knowledge on how it is applied is a fundamental necessity in practically all science – based

professions. Not only science but also commerce and almost everything in our normal day to day lives

is impossible to describe without using references to weights and measures. From buying the desired

length of wood, checking tire pressure, room temperature, blood pressure, vehicle speed, to weighing

yourself in the morning on a bathroom scale. Accurate measures are essential for a fair, productive and

happy modern life style. In most modern industries the costs bound up in taking measurements

constitute 10 - 15 % of production cost. [2] On the other hand good measurements can significantly

increase the value, effectiveness and quality of a product.

Metrology consists of three main activities:

1. The definition of internationally accepted units of measurements (For example the unit

of a meter).

2. The realization of units of measurement by scientific methods (the realization of a

meter through the use of lasers).

3. The establishment of traceability chains by determining and documenting the value

and accuracy of a measurement and disseminating that knowledge (the documented

relationship between the micrometer screw in a precision engineering workshop and a

primary laboratory for optical length metrology) [2].

Furthermore metrology can be separated into three categories with different levels of

complexity and accuracy:

1. Scientific metrology deals with the organization and development of measurement

standards and with their maintenance (highest level).

2. Industrial metrology has to ensure the adequate functioning of measurement

instruments used in industry, in production and testing processes, for ensuring quality

of life for citizens and for academic research

3. Legal metrology is concerned with measurements, which influence the transparency

of economic transactions, particularly where there is a requirement for legal

verification of the measuring instrument [2]

On top of these three categories there is a Fundamental metrology, which has no international

definition, but it generally signifies the highest level of accuracy within a given field – it is the top

level branch of scientific metrology. As science develops so must metrology. Scientific research forms

the basis of the development of metrology itself. Science pushes forward the frontiers of the possible

all the time and fundamental metrology follows the metrological aspects of these new discoveries. So

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with these new basic discoveries scientific, industrial and legal metrology must also develop to remain

relevant and useful with the needs of industry and society.

International system of units SI

When measuring physical quantities an internationally agreed upon system of units is used.

Basic units are determined in such a way, that scientific experiments can be repeated. Repeatability is

one of the basic principles of the scientific experiment. Furthermore an internationally acclaimed

system of units helps us with the comparison and understanding of data from different worldwide

institutions. The most widely used system of units is the International system of units or the SI system,

which was proposed at the 11th General Conference on Weights and Measures CGPM in 1960. The SI

system introduces 7 base units and all of the other units are derived from them.

Basic terminology of metrology

As we said in on our previous chapters, metrology is the science of measurement. If we look at

a more scientific definition, metrology ensures traceability to the SI units. In this chapter we will look

at some of basic terminology of metrology which ensures an internationally unified understanding of

the concepts in metrology.

Traceability

An unbroken chain of comparisons, in other words a traceability chain, consist of

measurements all having stated uncertainties. This ensures that a measurement result of a value of a

standard is related to references at the higher levels, ending at the primary standard. See Figure 1. [2]

Figure 1: Traceability chain

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Measurement standards

An etalon or measurement standard is a measuring instrument, reference material or measuring

system intended to define, realize, conserve or reproduce a unit or one or more values of a quantity to

serve as a reference. For example the meter is realized at the primary level the wavelengths of an

iodine-stabilized helium-neon laser [2] .

Calibration

When ensuing traceability of a measurement, calibration is one of the basic tools. We can

calibrate measuring instruments, measuring system or reference material. When calibrating an

instrument, system or reference material we determine its performance characteristics. The calibration

process is usually conducted by comparing the device under calibration against measurement

standards or certified reference materials. At the end of the calibration a certificate is issued and

usually a sticker with the date and number of the certificate is given.

Uncertainty

We have covered all aspect of uncertainty from our first semester in college, but let us just

quickly renew our knowledge through the eyes of metrology. Uncertainty is a parameter, closely

connected to the measurement and signifies the dispersion of the measured value. Without giving

uncertainty next to the measured value our result is useless. In metrology uncertainty is also used to

present the quality of the measurement. As we know we can calculate and determine the uncertainty in

many different ways, but in metrology we often use a guide to calculating uncertainty called GUM

(Guide to the expression of uncertainty in measurement).

Vibration sensors in Nuclear power plants

Prevention of problems is critical with nuclear systems because of the inherent risk. There are

numerous examples where vibrations can cause problems of the operation of nuclear power plant. In

the last cycle the Krško NPP had problems with fuel rod vibrations inside the reactor vessel. On the

first startups in the 1980’s it had problems with vibrations of the U-tubes in the steam generators. On

top of that vibrations can cause material fatigue. To prevent this kind of incidents and accidents

predictive maintenance, which is based on the determination of a machine’s condition before

something goes wrong, is used. Most machine components show signs of failure before something

goes wrong. To identify these symptoms several different techniques are used. We will of course be

looking at vibration analysis which is in most cases applied to rotating machinery.

Vibration measurements are one of the primary quantities that govern the commissioning

period of a nuclear power plant. Vibrations during the startup period are usually collected by the

manufacturer of the power plant. Accelerometers are mounted during this startup period and left

installed, so that the vibrations modes and Eigen frequencies of the main components are monitored.

Typical sensor locations on the primary loop of a 4-loop PWR are shown in Figure 2. In recent times

these signals are monitored on-line.

For individual reactors and reactor types databases of resonance frequencies have been

established. Accelerometer mounted on certain main components of the primary loop, i.e. main

coolant pumps, have characteristic frequency spectra. Peaks in these spectra can be identified by

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different methods on the basis of monitoring experience, design information, model calculation or in

recent times using automated vibration diagnostic systems. The system measures and stores baseline

vibration spectra for each machine type, representing normal operating conditions. During the test

period the system continually compares the actual spectrum with the baseline vibration spectrum,

providing an assessment of the machines condition. The baseline spectrum is acquired under normal

operation of the NPP. Anomalies are presented in a report and depending on the level of their severity

they are checked by human experts with conventional frequency analysis methods.

Different methods for vibration monitoring are used in nuclear power plants. For example

optical displacement sensors, strain gauges, acoustic measuring, neutron noise analysis, but mostly

radiation resistant piezoelectric sensors resistant to high temperature variations (-196 ˚C to 650 ˚C) are

used. An example is the Vibro-Meter Piezoelectric accelerometer type CA 962 that is used to monitor

core vibrations at the neutron detector location in the middle of the fuel assemblies inside the reactor

vessel. It is fitted with an integral mineral insulated cable for transmitting data to a collection point,

data logger or wireless transmitter. Wireless technology is finding its way to nuclear systems. Wi-Fi

based on IEEE 802.11g standard, communicating at 2.4 GHz, with WPA2 security and AES

encryption transmitters are used. [14]

Figure 2: Typical arrangement of vibration sensors on a primary loop of a PWR [9]

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Vibration transducers

A transducer is a device for converting the mechanical motion to be measured, for example

acceleration in a given direction, into a quantity which may be conveniently measured or recorded. In

our case the transducer is a piezoelectric accelerometer with a side connector (Figure 3). The most

important thing to remember about piezoelectrics is that the change of polarization when applying

mechanical stress is the cause of surface charge density. In other words mechanical stress causes a

reorientation of molecular dipol moments. We can describe this phenomenon using the following

equation.

(1)

Where P is the polarization and T the mechanical stress tensor and d the piezoelectric module.

An output current proportional to acceleration is thus provided. This particular transducer can

be used for measuring continuous sinusoidal vibration in the range from 0,2 Hz to 3750 Hz with

sensitivity deviation 1 % and from 0,2 Hz to 5300 Hz with sensitivity deviation 2 %. By sensitivity

deviation we mean a deviation from reference sensitivity. A resonance frequency with a 20 gram

stainless steel load is around 38 kHz.

Figure 3: Reference standard transducer (left), schematic of a piezoelectric transducer (right) [8]

Sensitivity of a linear transducer is defined as the ratio of the output to input during sinusoidal

excitation parallel to a specified axis of sensitivity at the mounting surface. Sensitivity includes both

amplitude and phase information and is a complex quantity dependent on frequency. The sinusoidal

input motion may be represented by the following equations:

(2)

(3)

(4)

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s – complex quantity of the displacement

v – complex quantity of the velocity

a – complex quantity of acceleration

u – complex quantity of the output

^ – represents the peak amplitude of each sinusoidal quantity

ω – angular frequency

φ – phase angles

t – time

i – imaginary unit

Three different types of sensitivity can be written with the equations above. We shall consider

only one, acceleration sensitivity Sa, which can be expressed in the units of the output signal per meter

per second squared:

(5)

– magnitude of the acceleration sensitivity

(6)

– phase lag

(7)

Methods for the calibration of vibration transducers

The primary object of the calibration of a transducer is to determine its calibration factor or as

we have named it, sensitivity, over the amplitude and frequency range for which the transducer is to be

used, by measuring the motion or input signal applied by the exciter and measuring the output of the

transducer. This is the basic quantity that can be checked but other things can be calibrated such as:

damping, phase lag, non-linearity, effect of temperature and pressure changes, sensitivity to rotational

motion, strain sensitivity, transverse sensitivity ratio, magnetic sensitivity, mounting torque sensitivity,

etc.

We can divide calibration methods in two basic groups. These are primary and comparison

calibration methods. Let us quickly review some of the primary methods before we shall shift our

attention to the comparison calibration method which we actually use at SIQ.

First of all there is the calibration by measuring displacement amplitude and frequency. This

method is based on laser interferometry to accurately determine the displacement of vibration to which

the transducer is subjected. This is the most accurate and widely used method of calibration. The

reference transducer which is used at SIQ is calibrated with this method in Poland.

The experimental setup for laser interferometry is shown in Figure 4.

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Figure 4: Experimental setup: S – HeNe laser source, E – beam expander, L – collimating lens, BS –beam splitter, M1 –

reference mirror, M2 – measuring mirror, D – photo detector, shaker, signal generator, power amplifier and computer [13]

If the mirror M2 is subjected to vibrations, the Fourier expression of the photo detector output

can be written as:

{ } { } (8)

Where t is time, V denotes the voltage amplitude, ϕ0 is the initial phase of the signal, ω is the

angular frequency (ω = 2πf, where f is the vibration frequency), ϕm is the modulation phase amplitude

(ϕm = 2πd/λ, d being the amplitude of the measuring mirror M2 and λ the wavelength of light) and Jn

are the values of the Bessel function. It follows that the value of the displacement can be written as:

(9)

Where is the nth zero value of the Bessel function and the wavelength of light used in the

interferometer. The acceleration can be expressed as:

(10)

Where f is the frequency of the vibration.

We shall be looking at the comparison calibration method, where the sensor under test is

rigidly fixed in the so called back-to-back configuration with a reference transducer. If both of the

sensors are subjected to the same motion we can compare their sensitivities. The reference transducer

is calibrated by using one of the primary methods, preferably by the calibration by measuring

displacement amplitude and frequency. The down side of this method is that the calibration is limited

to the range of frequencies, time duration of pulses, and amplitudes for which the reference transducer

has been calibrated.

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Calibrating procedure of vibration sensors used in Krško Nuclear power

plant made by SIQ

A comparison method was used for calibration of the vibration sensors for Krško Nuclear

power plant. Comparison methods are usually performed by back-to-back measurements against a

reference standard. Sensitivity, linearity, frequency and phase response are calibrated. The sensor

under test is mounted directly to the reference standard accelerometer. The motion of the reference

accelerometer is practically identical (there are some discrepancies due to the mounting surface of the

two accelerometers) to the DUT sensor. If this is true, the ratio of reference and DUT sensors outputs

correlates to the ratios of their charge sensitivities. The quantity that we need at the end of the

calibration is the sensitivity of the DUT. Sensitivity of the DUT sensor can be expressed using the

Equation 8.

(11)

– sensitivity of the DUT sensor [pC/(m/s2)]

– sensitivity of reference sensor [pC/(m/s2)]

–DUT output voltage from charge amplifier [V]

– reference output voltage from charge amplifier [V]

– gain of reference charge amplifier [V/g]

– gain of DUT charge amplifier [V/g]

– sensitivity of reference charge amplifier [pC/g]

– sensitivity of DUT charge amplifier [pC/g]

The DUT and reference standard are mounted on a vibration exciter. In our case it is an

electro-dynamic type of mini-shaker with a permanent field magnet. It is designed to produce only

small forces up to a frequency of 18 kHz. The suspension system consists of radial flexure springs that

restrict the moving element to almost perfectly rectilinear motion. Laminated flexure springs provide a

high degree of damping to minimize distortion due to flexure resonances. A signal generator provides

a desired frequency and amplitude for the vibration exciter. An amplifier is used between to provide an

appropriate signal.

The calibration equipment is connected as shown in Figure 5. A function generator is

connected through an amplifier to the vibration exciter. The reference accelerometer is connected to

Figure 5: Calibration setup

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the pad and the DUT directly to the reference accelerometer. Each of the accelerometers is connected

to a charge amplifier. The charge amplifier has two settings. The sensitivity setting is directly

connected with the sensitivity of each of the accelerometers. I will investigate the operation of these

charge amplifiers in my master thesis where I plan to develop a method for pulse calibration of the

amplifiers. The second setting is gain. Gain is set in such a way that the output of the amplifier is in

the most accurate range of the digital multi meter. The reference charge amplifier output is connected

to the rear side of the digital multi meter - DMM. The DUT charge amplifier is connected to the front

of the DMM. All connections between the instruments are made with coaxial cables. Cables are

connected in such a way not to interfere with the motion of the vibration exciter and transducers.

We now have everything we need for the calibration, except for one thing, uncertainty

calculation. The uncertainty depends on many different factors. To name just a few: sensitivity of the

reference accelerometer, output voltages form the DUT and reference charge amplifiers, corrections

because of the specification of the DMM and the amplifiers, etc. Because of the complexity of the

uncertainty calculation and because laboratories are graded on their calibration and measurement

capabilities this is a trade secret.

The end product of the calibration is a table which states the charge sensitivity of DUT sensor

and its uncertainty at different frequencies. I should add that usually the manufacturer or user provides

some sort of minimal or maximal allowed value of the measured quantity and metrology laboratories

can check if the calibration values comply or do not comply with these values. An example of a final

calibration table is given bellow (Table 1).

Table 1: End product of calibration. Frequency, DUT sensitivity, uncertainty, reference sensitivity, reference and DUT

voltages on DMM are shown

f Ss N

[Hz] [pC/m/s2] [pC/m/s

2]

20 0,280 0,007

31,5 0,277 0,007

40 0,277 0,007

80 0,276 0,006

160 0,275 0,006

315 0,273 0,005

630 0,274 0,005

1000 0,275 0,005

2000 0,274 0,008

3150 0,277 0,008

4000 0,279 0,008

5000 0,270 0,008

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Conclusion

In this paper a brief overview was given on the principals of metrology and how they are used

on a practical example. In the first part we concentrated on the terminology of metrology including, at

first glance simple things, like base SI units. We must not forget that metrology is a very precise

branch of science and at its foundation are primary measurements of base units. After we gained the

basic knowledge and terminology of metrology we shifted to the main theme of the paper which is

calibration of vibration transducers. We described the problematics which we face in nuclear power

plants and how vibration transducers can help us find a long term solution for the problem. In the last

part of the paper, vibration transducers were physically and mathematically described and calibration

procedures were presented. To sum up the whole paper, a practical example on how a vibration

transducer from Krško Nuclear power plant is calibrated at SIQ. Calibration setup, mathematical

model and results were shown.

References

1. http://www.modernpumpingtoday.com/sensors-for-a-unique-environment/

2. http://www.euramet.org/index.php?id=homepage, 3.1.2015

3. http://en.wikipedia.org/wiki/Metrology, 3.1.2015

4. http://en.wikipedia.org/wiki/International_System_of_Units, 3.1.2015

5. International standard ISO 16036-1 (Methods for the calibration of vibration and shock

transducers, Part 1: Basic concepts), 1998

6. International standard ISO 16036-1 (Methods for the calibration of vibration and shock

transducers, Part 21: Vibration calibration by comparison to a reference transducer), 1998

7. International standard ISO 5348 (Mechanical vibration and shock – Mechanical mounting of

accelerometers), 1998

8. http://www.stiweb.com/appnotes/Comparing-Vibration-Readings-on-Rotating-

Machinery.html, 3.1.2015

9. On-line monitoring for improving performance of nuclear power plants part 2: Process and

component condition monitoring and diagnostic, IAEA (2008)

10. Kalibracija etalonov kapacitivnosti na najvišjem meroslovnem nivoju, Miha Kokalj, Univerza

v Ljubljani Fakulteta za elektrotehniko (2011)

11. http://en.wikipedia.org/wiki/Piezoelectricity, 10.1.2015

12. https://www.pcb.com/TechSupport/Tech_Accel.aspx, 10.1.2015

13. Interferometric vibration displacement measurement, F.Garoi, National Institute for Laser,

Plasma and Radiation Physic, 2010

14. http://www.vibro-meter.com/index.cfm/energy/nuclear_monitoring/accelerometers, 17.1.2015

15. What you need to know about sensor reliability before and after an accident – Wireless, H. M.

Hashemian, IAEA