ENERGETICAL ASPECTS IN TRANSDUCERS OPERATION AND CLASSIFICATION, WITH EMPHASIS ON ELECTRICAL MEASUREMENT

OF MECHANICAL QUANTITIES

Dan Mihai �tef�nescu

Romanian Measurement Society, stefidanro@yahoo.com

Abstract: Several ways in which the energy transfer is involved in the operation of electromechanical transducers are examined. Among the SI quantities, classes of intensive and extensive quantities may be distinguished, pairs of them forming together parameters having the dimension of an energy. Another interesting classification is in terms of the degree with which they appear in the fundamental equations of Physics, characterizing active and passive systems. Such systems are frequently found in the structure of force transducers. As a representative category of electromechanical devices, force transducers are deeply analyzed, their classification is commented and a few significant examples based on strain gauges are presented. Keywords: energetical aspects, transducers classification, electrical measurement, mechanical quantities, strain gauges

1. INTRODUCTION The key component in any measurement system for mechanical quantities is the transducer, which can use various measurement principles or methods.

The most convenient description of the transducer field is offered by the physics-oriented approach [1]. There are generally accepted six signal domains following the main physical parameters: mechanical (acoustic included), thermal, electrical, magnetic, radiant (optical), and chemical. These domains are tightly related to certain groups of quantities and their measurement units; the globally accepted and widely utilized is the International System of quantities and units (SI).

In a “planetary” representation of SI units (Fig. 1) there are seven “planets” along the border of an elliptic field, corresponding to the seven basic units (meter, kilogram, second, ampere, kelvin, mol and candela), and a lot of “satellites”, as derived units, “navigating” inside the ellipse.

An interesting feature of this representation is that mechanical units are located in the left side of the figure, while the electromagnetic units are situated in the center and others in the right side. Also, the “energetic” quantities (with their units: joule J for energy, work or quantity of heat, watt W for power or radiant flux, etc.) are mostly grouped around the center of the ellipse, irrespective of their nature (mechanical, electrical, thermal). One may consider that they constitute the “energetical core” of the International System.

moment of force

density

volume

volume flow rate pressure/

stress

work / energy /quantity of heat

electric field strength

area

illuminanceluminous

fluxplane angle

solid angle

luminance

magnetic flux density

concentrationof substance

permeability

heat flux density/irradiance/

power density

Celsius temperature

force

voltage/ electric potential difference

inductance

magnetic flux

specific heat capacity/specific entropy

capacitance

electric charge

Ifrequency

permittivity

exposure x and rays�

power/radiant flux

molar energy

molar heat capacityheat capacity

/entropy

electric resistance

conductance

seconds

ampereA

kelvinK

molemol

candelacd

meterm

N·m

Im3/s

N

kg/m3

m3

m2

cd/m2

H/m

oC

mol/m3

V/m

V

Wb

H

J/K

J/mol

J/(mol·K)

W/m2

SC

m/s2

kg/s

acceleration

mass flow rate

rad/s

m/s

W/(m·sr)

Pa

J

Iangular velocity

radiance

velocity

lxlm

rad

srT

F

F/m

C/kg

W

J/(kg·K)

Hz

kilogramkg

SI base units

SI derived unitsdivision

multiplication

mass

length

time

amount ofsubstance

electriccurrent

thermodynamic temperature

luminousintensity

Figure 1. The “planetary system” representation for SI quantities and units

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2. INTENSIVE OR EXTENSIVE QUANTITIES AND THE “ENERGY” DIMENSION

An intensive property is a of a system that does not depend on the system size or the amount of material in the system. Intensive quantities are independent of the extension of the system and determine a “quality” of the system. Examples of intensive properties include: force, , , velocity, acceleration, , , flow, or

), temperature.

physical property

hardness pressureelasticity viscosity density specific

gravityBy contrast, an extensive property of a system is

directly proportional to the system size or the amount of material in the system. Such a property is additive: it can be expressed as the sum of the properties for the separate subsystems that compose the entire system and determine a “quantitative property” of the system. Examples of extensive properties: , charge, , volume,

, , length. Note that route, movement, displacement and other synonyms are variants of the physical quantity length.

energy massentropy enthalpy

Extensive and intensive quantities are charac-terized in that together they can form parameter couples having the dimension of energy:

Quantity Type of energy

Intensive Extensive

Force × Route Mechanical energy

Pressure × Volume

Electrical energy Potential × Charge

Thermal energy Temperature × Entropy

O

R

K

PO

It = Power

X

Inspired byNaszlady - 1998

Figure 2. Energy sources and their power transformation

It is worthwhile to compare them with those of the

global vision of Dr. Attila Naszlady, defining the energy, work and power from four different angles (Fig. 2) [2].

ra me th el ma chra

meth

el

ma

ch

Y-axis

X-axis

Z-axis

Radiation (ra)

Mechanical (me)

Thermal (th)

Electrical (el)

Magnetic (ma)

Chemical (ch)Modulating energy

Outputenergy

Inputenergy

AfterA.F.P. Van PuttenUniversity of TechnologyEindhoven, NL

Measurands:

Y-axis

> Preferred output is electrical > > > >

> > > > > > > > > > > > > > >

Ia)

Ib)

FORCE

Figure 3. a) 3D representation of the energetical transduction process (Transducers’ cube). b) Example of mechanical force input “transduced” into a digital signal output.

3. TRANSDUCTION POSSIBILITIES – TRANSDUCER CUBE

A suggestive way of describing the different transduction possibilities is by applying a 3D energy space diagram, as presented in Figure 3,a [3], in which:

– X-axis represents the input energy domain. It contains the required auxiliary energy only, if a modulating transducer is involved. In the case of a self-generating transducer it represents the energy and information bound to it.

– Y-axis represents the output energy domain in which the outcoming information content is available.

– Z-axis represents the modulating energy domain in which the incoming information is available, if an auxiliary energy source is required.

In the X-Y plane (so-called input-output plane), all 36 possible self-generating transducers can be found. In the transducers placed on the main diagonal, i.e. modifiers (shown by dots), no energy conversion is involved, but an energy shape conversion is executed.

If somebody represents the entire transducer cube, as it was imagined by Middelhoek, in each elemental box within this cube a complete transduction system could be defined [4]. A wide range of physical and/or chemical phenomena can be used to perform the transduction process represented by that box. In practice, only devices offering an electric output are called transducers, because most measurement systems use electric signals. The digital Force One Indicator is an example of electric output transducer (Fig. 3,b).

4. ENERGY DOMAINS AND ENERGETICAL TRANSFORMATIONS

There exist complex interactions between the six usually defined energy domains (Fig. 4) [5], with some specific connections identified by Isihara et al. [6]. Specific examples of energetical transformation are given in [7] and their names are written on the connection arrows in the above-mentioned figure: – Friction stir welding (FSW) is an autogenous solid-

state technique that uses a nonconsumable tool to generate frictional heat [8].

– Electromagnetic force compensation (shortly EMFC) principle is illustrated by two applications: a) A force feedback weighing machine – a complete

measuring system, which combines sensing with actuating [9]: the applied force is directly proportional to the current through the actuator coil, and calibration is possible by finding the

current required to balance a body with known mass m (or force m·g), as presented in Figure 5.

0Current

Force

Im gWeighing

EMFC

Figure 5. Weighing by electromagnetic force compensation (EMFC)

b) A PTB force standard machine (FSM), based on

an electromagnetically compensated balance and combining a variety of measurement principles (resistive, capacitive, piezoelectric and electro-magnetic) and computerized signal processing [10].

– Chemical (embedded piezoresistive) cantilevers can react volumetrically when exposed to various analyte molecules; the mechano-chemical reactions might be absorption, diffusion or adsorption [11].

– The light pressure has been calculated by James Clerk Maxwell [12].

– Our focus is on the transduction from mechanical input to electrical output (so-called electromechanical transducer), and it is “localized” in the lower right corner of Figure 4. In this reversible process, a bidirectional force transducer can be seen as a sensor (from the mechanical input to its electrical output) or as an actuator (referring to the opposite direction).

Force is one of the most complex measurands, being strongly connected with other mechanical quantities by their definition formulas, and employing practically the same measurement methods.

Chemical

Electrical

Magnetic

Thermal Mechanical

Optical

Force

Friction force

EMFC

Chemical cantilever Lightpressure

ACTUATOR

SENSOR

FORCE TRANSDUCER

Figure 4. A suggestive positioning of the six energy domains in order to represent their complex interactions and transformations between basic energies

5. CLASSES OF QUANTITIES ACCORDING TO THEIR “DEGREE” – “ACTIVE” AND “PASSIVE”

SYSTEMS Another classification of physical quantities (somehow parallel to the previous one) is based on the degree with which those quantities appear in the equations of Physics [13]. This criterion best applies to the electromagnetic quantities; from this point of view, they may be divided into three groups: – A first group is that of the “first degree” quantities,

like electric charge, current, voltage, field strength, electric and magnetic flux, etc. They are of the type of “intensity” or “strength” and enter as first degree terms in the general equations of Electromagnetism.

– A second group constitutes the “second degree” quantities, as for example power and energy densities, the Poynting vector, electric power and energy in circuits, etc. All of these quantities are of the “power” or “energy” type and are defined as products of two “first degree” quantities, e.g. power (U × I) as well as energy (U × I × t).

– The third group includes quantities that are ratios of two “first degree” or “second degree” quantities; they may be called “zero degree” quantities, such as electrical parameters: resistance R or impedance Z (U/I), inductance L (�/I), capacitance C (Q/U) or

dimensionless quantities like the Q factor (�L/R), transformer ratio (U1/U2) and so on.

In practice, classification in terms of “degrees” reveals some general properties of quantities: – First degree quantities (a) are characteristic for

“active” systems, (b) have a polarity (positive or negative), (c) may be easily converted directly into quantities of different nature (mechanical, thermal, optical, etc.), and so (d) are well suited for various methods of direct measurement.

– On the contrary, second degree quantities (a) are typical for “passive” systems, (b) are normally only positive, and (c) may be measured only by yielding a certain energy to the measuring device.

Concerning the force transducers, both active and passive systems can be found in their structure; this property is more visible in the next sections of this paper, for example: piezoelectric FT (active) versus piezo-resistive FT (passive).

6. ELECTROMECHANICAL TRANSDUCTION The most useful effects in the mechanical energy domain are summarized in Table 1, including their Miller indices of transduction (the conventional abbreviations for input, output and modulating energies) and short explanations, particularized when applying mechanical forces [3].

Table 1. Some effects in mechanical force domain and their summary description

Effect Notation Macroscopic description

Piezoresistance [el, el, me]Change in semiconductors conductivity due to a mechanical force

Piezoelectric [me, el, 00] Generation of a surface charge due to a mechanical force

Triboelectric [me, el, 00] Positive or negative charges generation due to the surface rubbing of materials

Magnetoelastic [me, ma, 00] Change in magnetization by a mechanical force

Acoustoelectric [me, el, 00] Generation of an electric current by a traveling acoustic wave (SAW)

Thermoelastic [th, el, me]Voltage generation in two regions of a metal due to a mechanical strain and a temperature difference in those regions

Piezooptic [ra, ra, me]Change in refractive index due to a mechanical force

Photoelastic [ra, ra, me]Generation of double refraction by a mechanical force

7. FORCE TRANSDUCERS’ CLASSIFICATION Twelve measurement principles and their typical ranges for force transducers (FTs) are presented in Table 2 [14]. The most common method to measure force F relies on resistive sensing, and the usual sensors are strain gauges (SGs). Within the same reference, the force ranges for twelve types of strain gauged elastic elements are shown, among them cantilever beam being the most widespread.

8. APPLICATIONS WITH STRAIN GAUGED FORCE TRANSDUCERS (SGFTs)

A “trampoline”-shaped elastic body, equipped with four piezoresistive elements connected in Wheatstone bridge and loaded in bending mode, is presented in Figure 6.

The next example (Fig. 7) is a good illustration for a complex six-component force transducer, as compared to the simple one-component arrangement.

Table 2. Classification of electrical measurement principles for force transducers

Type Name Range [N]: 10 10 10 10 10 10 10 10 -12 -9 -6 0 63 9

I IpN nN N mN k MN GN N N

-3

1 RESISTIVE

2 INDUCTIVE

3 CAPACITIVE

4 PIEZOELECTRIC

5 ELECTROMAGNETIC

6 ELECTRODYNAMIC (EMFC)

7 MAGNETOELASTIC

8 GALVANOMAGNETIC (HALL)

9 VIBRATING WIRE

10 RESONATOR

11 ACOUSTIC (SAW)

12 GYROSCOPIC

(MICRO)

Type Name Range [ N ] :

<

<

KRISS “scale” of ranges: Optical Electrostatic Deadweight Hydraulic

Radioactive Capacitive F = m g

Applied force

Resulteddeflection

Piezoresistive bridge circuit

Max. stress region

I

Connection dots

CANTILEVER BEAM (E-3)

Support

Current supply source

Output voltage

SIGNAL CONDITIONING

MEASURING AMPLIFIER

Figure 6. Piezoresistive cantilever beam with symbolization of associated circuitry (signal conditioning and bridge amplifier). Other useful details on force transducers’ principles and components are given in [14].

An original balance for aircraft models tested in a

supersonic wind tunnel [15] is shown in Figure 7. The axial aerodynamic force (X = 2.85 kN) is measured by four short lateral arms close to the middle of the balance interior. The other five components (Y = 9.65 kN, Z = 14.7 kN, L = 320 N·m, M = 820 N·m and N = 760 N·m) are measured in two symmetrical sections, each consisting of a casing with three beams. This complicated structure has been developed by means of finite element analysis (FEA); the loads from 722 isoparametric elements and the displacements for 1536 nodes were calculated by computer. The elastic tail of the balance was manufactured to the highest possible accuracy by electroerosion from a single piece of Armco 17-4 PH stainless steel, and metallurgically treated to ensure

a permissible tensile strength in excess of 400 MPa (N/mm

This integral solution offers the best relation between its capacity (complex loading) and volume, since the interaction between forces and/or moments is accurately specified by calibration.

2). It is 353 mm long and 50.8 mm in diameter. The six components (three forces and three

torques) are measured by six Wheatstone bridges with four or eight active strain gauges. In order to resolve two conflicting requirements, the choice went to HBM’s Y series foil SGs with standard resistances as follows: – 120 � – strain gauges of smaller dimensions better

satisfy the space restrictions; – 350 � – strain gauges having higher resistance

dissipate less power.

A

A’

A – A’Y, Z, M, N X, L

3/120 XY 21I

Front central bar

– Z

– XY

Source: DMSHotline Hottinger – 2 / 2001

1.5/120 LY 11I

3/350 LY 11I

Rear central bar

L

N

M

Figure 7. Six-component strain gauged balance for aircraft models tested in wind tunnel

9. CONCLUSION

Certain energetical aspects in transducers operation and classification have been analyzed and interpreted, underlining the important role of energy transfer in any kind of transducers, with particular emphasis on electrical measurement of mechanical quantities. The result is a better understanding of the principles and operating conditions of all types of transducers, active or passive, simple or complex. As a next step in this approach, some useful hints will be brought forward in connection with presenting and teaching the general theory of transducers.

ACKNOWLEDGEMENTS

The author thanks his mentor and promoter, Prof. Dr. Aurel Millea, former General Director of the National Institute of Metrology in Bucharest, for the fruitful discussions on concepts and terminology, as well as for the final revision of this text.

REFERENCES [1] S. Middelhoek, and S.A. Audet, Silicon Sensors, Academic Press Ltd (Harcourt Brace Jovanovich Publishers), London, UK, 1989. [2] A. Naszlady, “Universality of measurement in medical sciences”, in Proc. XVIIIth IMEKO World Congress, Rio de Janeiro, Brazil, 17–22 Sept. 2006, paper 654. [3] A.F.P. van Putten, Electronic Measurement Systems, Prentice Hall, New York – London – Toronto – Sydney – Tokyo, 1988. [4] B. Culsaw, Smart Structures and Materials, Artech House, Boston – London, 1996. [5] I.J. Busch-Vishniac, Electromechanical Sensors and Actuators, Springer-Verlag, New York – Berlin – Heidelberg, 1999.

[6] H. Isihara, F. Arai, and T. Fukuda, “Micro mecha-tronics and micro actuators,” IEEE/ASME Transactions on Mechatronics, vol. 1, no. 1, pp. 68-79, 1996. [7] W. Brenner, F. Svemecz, and A. Vujanic, “Principles of micro torque measurement – An overview,” in Proc. XVIIth IMEKO World Congress, Dubrovnik, Croatia, 23-27 June 2003, pp. 277-281. [8] C. Blignault, D.G. Hattingh, G.H. Kruger, T.I. van Niekerk, and M.N. James, “Friction stir weld process evaluation by multi-axial transducer,” Measurement, vol. 41, pp. 32–43, 2008. [9] M.J. Usher, and D.A. Keating, Sensors and Transducers – Characteristics, Applications, Instrumen-tation, Interfacing, MacMillan, Houndmills, Basingstoke, Hampshire, 1996. [10] J. Illemann, and R. Kumme, “Research for a national force standard machine in the range from micro Newton to Newton, relying on force compensation,” in Proc. XVIIIth IMEKO World Congress, Rio de Janeiro, Brazil, 17–22 Sept. 2006, paper 180. [11] T.L. Porter, and W. Delinger, “Electronics for LabVIEW based piezoresistive microcantilever sensor system,” Sensors & Transducers Magazine, vol. 68, no. 6, pp. 568-574, June 2006. [12] R. Carson, Blavatsky's foreknowledge of the wave / particle duality of light, www.seekerbooks.com, © 1996-2004. [13] A. Millea, and D.M. �tef�nescu, “Thoughts about the International System of Quantities and Units (SI): properties, classifications, graphical representations,” International Conference of Metrology, I.N.M. Bucharest, 17-18 Nov. 2011. [14] D.M. �tef�nescu, Handbook of Force Transducers – Principles and Components, Springer-Verlag, Berlin – Heidelberg, 2011. [15] D.M. �tef�nescu, “DMS in Windkanal – Rumänische Windkanalwaage mit Dehnungsmeßstreifen vom HBM,” Hotline Hottinger – Informationen aus der industriellen Messtechnik, no. 2, pp. 12-13, 2001.