New piezoelectric transducers for internal strain measurement

406

Sensors and Actuators, A21-A23

(1990) 40-409

New Piezoelectric Transducers for Internal Strain Measurement C CAVALLONI and P ENGELER Ksstler Instrmente

AG, Eulachstrmse

22, CH-8408

Wtnterthur (Swmeriand)

Abstract The new stram transducers presented m this paper consist of one or more piezoelectnc elements, preferably quartz crystals, mslde a cyhndncal metal housmg The sensors are easily mounted into a small borehole of the desired depth by prestressmg them Hrlth a nut This allows lon(ptudmal or transverse strains mslde machme structures or tools to be measured Examples are presented where the measured strain m the sensor 1s related to an external force or pressure acting on the structure The sensors can be used at temperatures up to 400 “C 1. Introduction The most widely employed transducers for strain measurement are conventional strain gauges, which have been optmnzed durmg the last decades However, for a number of special apphcations they have some defimte shortcommgs Especially when extremely small strains have to be detected m large heavy structures or a large measuring span 1s required, piezoelectnc transducers offer essential advantages over other measunng principles for stram (a) high sensltlvlty, (b) threshold below 10d3 p (nucrostram, 1 C(E= 10e6 m/m, (c) high span to threshold ratio of up to about 107, (d) temperature range up to 400 “C, (e) virtually overload-proof The only hmltatlon of the plezoelectnc prmclple concerns long-term static measurements, which are not possible In many applications strain 1s not the physical quantity of prmclpal interest, but measurement of strain 1s used to determine a force, pressure, temperature or other physlcal quantities mducmg deformation of a body It 1s much more economical to measure forces or pressures via the strain induced m a machine part or tool Since surface strains are in many cases not very reliable and are difficult to dlstm-

0924-4247/90/%350

gmsh from bendmg strains, new transducers have been developed for internal strain measurement By mstalhng the strain sensor mslde a borehole mto a machme structure or tool, the stram can be measured at the optimum position, 1e , directly m the force path or m the neutral axis to ehmmate bending strains Furthermore, the sensor 1s well protected against external influences, which 1s unportant m mdustnal apphcatlons 2. !hsor

Ikign

2 I Longltudmal Straw Sensor The basic design of the new longtudmal strain sensor 1s shown m Fig 1 The sensor consists of one or more piezoelectnc &am-sensitive elements, preferably quartz crystals, clamped mslde a cyhndncal metal housing With this special design of the sensing element there IS no need for thm diaphragms, because the measured lon@tudmal strain deforms the whole sensor homogeneously The sensor is easily mounted into a structure inside a small borehole (mmlmum 9 mm &ameter) of the desired depth by prestressmg it wth a nut A longtudmal deformation of the borehole is

Sensor

contact

body

sprhlg

Rg 1 SchematIc cross sectson of a longtudmal stram sensor

0 Elsevler Sequola/Prmted m The Netherlands

407

transmitted to the plezoelectnc sensing elements through a rmg-shaped contact surface normal to the sensor axls A stable and well-defined contact area IS achieved by prestressmg the sensor mslde the borehole This allows tensile and compressive strams to be measured as well To calculate the senslhvlty of a longtudmal stram sensor mounted mslde a test object, as shown m Fig 2, the following assumptions are made (a) the hameter D of the cylmdncal test body IS much larger than the diameter d of the sensor, (b) the walls of the sensor housing are much thmner than the diameter and length of the quartz crystal, (c) the sensor IS ngdly tightened and prestressed mslde the borehole By applymg an external pressure p, equivalent to a force per unit area (F/A m Fig 2), the cyhndncal body IS subjected to an axial strain E, Hrlth 8, = PIEI, (1) where Eb denotes the modulus of elastlclty of the body The same amount of stram E,ISmeasured by the sensor and by the plezoelectnc element itself The axial stress u, mslde the plezoelectnc element 1s given by a, = EP&,

(2) Here EP ISthe modulus of elasticity of the plezoelectnc element The charge output Q due to the plezoelectnc effect IS gven by [ I,21

Q =44p,

(3)

where A, IS the electrode area of the plezoelement and $ IS the correspondmg piezoelectnc coefficient with the dlrechon 1normal to the electrode surface

Fmally, the charge Q 1s related to the pressure p according to eqns (1) to (3) as

Q =4+

From eqns (1) and (2) the axial stress oj mslde the plezoelement IS gven by

(5) where ob corresponds to the axial stress in the cyhndncal body Usually, the body (or structure) mto which the stram sensor 1s mounted consists of stainless steel (Ebx 2 1 x 10” Nme2) and the plezoelement IS made of quartz crystal (E, x 7 x 10” N m-‘) because of its excellent stablhty From eqn (5) it follows that the stress mslde the quartz element IS always smaller (by about l/3) than m the surroundmg structure Tins gives the desired overload protection of the sensor Thanks to the advantages of the plezoelectnc measunng pnnaple, the measunng range and the threshold are independent of the amount of prestressmg of the sensor A typlcal strain sensltlvlty of a quartz stram sensor of 9 mm diameter amounts to about 17 pC/p With a charge amphfier set on the most sensltlve range, outputs of 1 V/PC and therefore 17 V/p are obtamed In most practical apphcatlons the sensltlvlty of the stram sensor to an external mechamcal quantlty 1s determmed by a cahbratlon with the sensor installed m the machme structure or m a test body This need for an znsztu cahbration IS mamly due to the unknown comphance of the bolted Joint and the sensor housmg, resulting m a dlfferent strain E,measured mslde the plezoelement than m the surrounding structure Tlus changes the value of the calculated sensltlnty, compared to the slmphfied denvatlon of eqns (1) to (4), by about 10% to 20% 22

Fig 2 Lcmgltudmal &ram sensor mounted msrde a cyhndncal test body

(4) b

Transverse Strain Sensor For certain apphcatlons of Indirect force mea surement it IS desirable to measure the stram m a dlrectlon normal to the axis of the borehole For this reason a transverse measunng strain sensor was developed The basic design IS illustrated m Fig 3 The front part of the sensor contains a mmlature plezoelectnc force transducer mslde a sleeve with the senslhve axis m the transverse direction of the borehole A transverse deformation of the borehole IS transnutti as a strain to the plezoelement through a pnr of dlametncally opposite bermspherical surfaces An mtegrated clampmg system usmg a tlun sleeve, which IS comcally shaped

408 Force

transducer

Quartz

Champing sleeve Rg

3 Schematic cross se&on of a transverse strain sensor

at its sensmg end, 1s used to prestress the sensor m the borehole, enabling it to detect tensile and compressive transverse strains inside a structure The sensitive strain axis of the sensor can easdy be rotated around the axis of the borehole or moved along this axis This allows transverse strain to be measured m different dlrectlons and posltlons and the optimum posltlon of the sensor m the borehole to be found For precise measurements the sensor again needs to be calibrated by comparative measurement inside the structure This yields directly the sensltlMty to an externally applied force or pressure The basic strain sensltlvlty of this sensor (10 mm diameter) mounted inside a test ObJect IS about 7 pC/p~ Here, the plezoelement consists of two quartz discs having a nominal mtrmslc strain sensltlvlty of 6 3 PC/~& m the axial dlrectlon The increased strain senslhvlty of the full sensor 1s due to the higher stiffness of the calotte elements and the sensor housing compared to quartz

serted mto the tube walls One strain sensor, mounted inside a radml borehole, detects the pressure-induced change AL, of the sensitive sensor length L m the radial direction From the basic theory of elasticity, the relative length change ALJL m a thick-walled tube can be expressed as

[31

AL, L

1 - -Er,2

r,

C

-(l-Q4

AP (6) 1 where E denotes the modulus of elastlclty, ~1 the Poisson’s ratio, r, and r, the inner and outer radu of the tube, respectively and r, the distance between the inner end of the sensor and the axis of the tube

3. Applications A typical apphcatlon of the longltudmal strain sensor 1s an indirect pressure measurement m thick-walled tubes Such tubes are used, for example, as inJection nozzles for inJection mouldmg or for mJectlon pumps m diesel engines In these apphcatlons hot gases or hqulds, wluch may even be highly corrosive, flow through the tubes Measurement of the internal pressure m such tubes often represents a difficult measurmg problem Since the new strain sensors are not m direct contact unth the pressunzed medium and are therefore well protected, the pressure can be measured indirectly through the internal strains m the tube walls Figure 4 shows a cross section of a thick-walled tube in which the internal pressure change Ap has to be measured For this purpose, two longtudmal plezoelectnc strain sensors are in-

Fig 4 Cross se&on of a t&k-walled tube arlth two lon@ttinal stram sensors for mtemal pressure measurement

409

The second stram sensor, mounted mslde a tangential borehole, measures the tangential strain In this case the relative change ALJL of the senatlve length L can be calculated m an analogous way as for eqn (6) and results m

AL,_ 1 -----2r, r,

L - E ra2- r,

+(1-2p)lntg

$+: (

)I

Ap

with I#J= arc tg(L/2r,), r, being the distance between the centre of the sensor and the axls of the tube An increasing internal pressure m the tube produces a compressive strain m the radial stram sensor, whereas a tensile stram 1smeasured by the tangential strain sensor On the other hand, temperature-induced strains have the same dnectlon m both sensors, either compressive or tensrle However, such temperature-mduced strams can be eliminated by takmg the difference between the

Transversa

Force

&ah

sanscw

I2I

~lens~r (1)

Stamped

outputs of two identical longtudmal stram sensors, as shown m Fig 4, measnrmg the radial and tangential stram m the tube walls TIN d&l&ence 1s directly proportional to the difference ALJL - ALJL and propotional to the tube pressure change Ap, smce ALJL c 0 and AL,/L > 0 if Ap > 0, as follows from eqns (6) and (7) This difference 1s obtamed m a very easy way, thanks to the plezoelectnc measurmg prmclple The piezoelectnc elements m one sensor are rotated to gve an output agnal of equal magnitude but opposite sign Then, the outputs of the two sensors are directly connected m parallel Another application of mdlrect force sensmg m a stampmg machme 1s shown m Fig 5 Here, a transverse stram sensor IS used to measure the force acting on the stampmg tool The agreement wth the force signal measured urlth a force transducer 1s excellent In the above apphcatlons the stram sensors are calibrated mslde the machme part or structure agamst a reference sensor, which measures dlrectly the physical quantity of interest (pressure, force, etc ) The measurmg range 1snot affected by prestressmg and the operatmg temperature range can be extended up to 400 “C

metal part

(4

4. Conclusions New types of strain sensors based on the plezoelectnc measurmg prmcrple have been presented Since these sensors are easdy mounted and prestressed inside a small borehole, Internal strains in machme structures or tools can be measured and the sensors are well protected However, in most apphcations reqmrmg a good accuracy it has proved useful to cahbrate the sensors after installation agamst an external force or pressure acting on the structure The companson of expenmental results showed that Internal stram measurement 1s a practical and easy apphcable method for measurmg forces or pressures m large machme structures Herem, the structure Itself maybe regarded as a transducer

References Time(s) (‘4

Rg 5 (a) Stampmg machme with a transverse stram sensor for stampmg force measurement (b) Companson of the measured force curve 1 was obtamed with a washer-type cahbratmg force sensor and curve 2 wth the transverse stram sensor

I J F Nye, Physrcul Properlws of Crystals, Oxford Uxuverslty Press, London, 1969, Ch VII, p 110 2 J T~chy and G Gautschl, Aezoelektmche Messtechnrk, Sprmger, Lterlm, 1980, p 68 3 R J Roark and W C Young, Formulas for Stress und Sfram, McGraw-H111, London, 1976, p 504