Shock Trasducer with Hall Sesig Elemet Ioa Gavril Tarova, Bogda Tebrea, Titus Eduard Crisa Departamet of Electrical Measuremet, Faculty of Electrical Egieerig, Techical Uiversity of Cluj-Napoca, Str.C.Daicoviciu r.5, 40000 Cluj-Napoca, Romaia, E-mail: ioa.tarova@mas.utcluj.ro Abstract - The aim of this paper is to show a determiatio method for mechaical shocks, usig as sesig elemet a aalogical Hall effect trasducer. I the first part of the paper there will be euciated the used physical priciple, metioig the coservatio laws of mechaical eergy ad i followig part we will describe the experimetal setups ad the behavior of the implemeted captors. We will also aalyze the factors that ca geerate errors or they ca disturb the measuremet process. There will be preseted the sesors as well as a implemetatio method of the sesor i complex itegrated parts which cotai the sigal processig circuits ad the sesig elemet. We ca cosider this trasducers ot a replacemet to the preset methods (piezoresistive, tesometric, optical, etc), but a viable alterative which is easy to implemet. I. Theoretical Approach The measuremet of the aperiodical vibratio or of the mechaical shocks is made i preset techical applicatios with the help of the piezoresistive, tesometric, optical trasducers. The aalogical Hall effect trasducers, used i differet mechaical cofiguratios, ca help us to distiguish a vast area of shocks ad vibratios parameters. It is very well kow the fact that whe a probe, which is i free fall coditio, meets o it s trajectory a obstacle, for example a catilever beam, a eergetic trasfer will be made betwee this two parts of the system. Figure. The trasformatio of the gravitatioal potetial eergy i elastic potetial eergy Practicaly, the potetial eergy stored, durig the time of the displacemet, will be trasferred to the beam accordig with followig formula: mg( h + y) = k y () - where: - m the probe s mass [Kg] - h the throwig height [m] - y the displacemet of the beam [m] - k the elastic costat [N/m] - g the gravitatioal acceleratio [m/s ] We have cosidered for the beam s potetial eergy calculatio the behavior of a classic elastic sprig due to the fact that the relative displacemet is small ad the load is ed cocetrated type. Accordig with the physical pheomea metioed previously ad cosiderig that over the actio of the weight G there are t ay effects or aother exterior force, we ca calculate the weight, respectively the mass of the probe with is i free fall coditio, kowig the value of the elastic costat k, of the the throwig height h ad of the the displacemet of the beam h (which is measured with the aid of the Hall effect trasducer). k y k y G = () m = (3) ( h + y) g ( h + y)
II.Experimetal Setup Startig from the theoretical priciple preseted previously, were desiged a few shock detectors which used the aalogical Hall effect trasducer. I figure ad 3 are preseted two detectores which are based o a sistem made from a catilever beam with a permaet maget ad a aalogical Hall effect trasducer. Figure. Shock detector usig the priciple of simple catilevered beam Figure 3. Shock detector usig the priciple of duble catilevered beam As show i figures above, the devices cosists of: - detectig elemet - sprig - elastic beam - permaet maget - Hall effect trasducer - the detector s capsule. Kowig the theoretical priciple preseted o the course of this paper, but cosiderig the experimetal resuts from the built sesors, we wat to desig a mechaical shock detector o a very small scale. The experimetal setup is show i figure below: Figure 4. The mai parts of the shock detector As show i figure 4, the detector had two distict parts: - mobile assembly, - fix assembly. The mobile assembly is made from materials with good elastic properties, which ca allow a relative costat deformatio uder the iflueces of exteral forces ad to cofer good measuremet process repeatability. The material used i the mobile assembly must be: - o-coductig - to avoid the errors that ca itervee because of the electric cotacts betwee various compoets of the system,
- o-magetic to avoid the ifluece over the electric respose of the trasducer placed o the fixed assembly. Whe implemetig the mobile assembly, ad takig ito accout the eeded dimesios of the elemets foud i the sesig device, it is ecessary to apply the imposed coditios used i the captors havig elastic catilever beams. The most importat part of the mobile assembly is the excitatio coil, this havig the role of geeratig the magetic field required for the correct fuctio of the sesig elemet, i.e. the Hall trasducers. The excitatio coil characteristics are importat because the differet cofiguratios ca modify the respose of the trasducer to mechaical shocks geerated by similar forces. For the preset case, due to practical reasos, we have chose a special coil, i a plaar cofiguratio, the coil beig apart of the mobile elemet. The desig of this captor has preferred the coil solutio to the similar oe with permaet maget. The reaso of this choice was the iappropriate/ukow behavior of ultra thi permaet maget. The costructive solutio usig a regular permaet maget (the smallest we foud beig xx mm) was disregarded because it still is too large for our cofiguratio. The fix assembly has to be made from the same materials as the mobile oe, o-coductig ad o-magetic, but this time it is importat that the trasducer s support to iclude materials that ca absorb the parasite exteral vibratio. The mai part of the detector is the aalogical Hall effect trasducer. It ca be made i differet methods, either due the classical method of impurifyig, if the trasducer s support it is made from a semicoductor material, or i thi film techology, if the trasducer will be attached after the buildig process. This approachig allows us to itegrate, o the same chip or o the same film with the trasducer, the sigal processig circuits. The trasducer must be placed i such maer that the iteractio with the magetic field, give by the excitatio coil, to geerate a Hall voltage which must be: measurable, repetitive ad with a characteristic easy to process. I figure 5 we have a sectio view of the detector: Figure 5. Sectio view of the detector As show i the figure above, the sesig elemet ad the coil must be mechaically separated i order to isure a adequate distace eeded for a proper operatio. This distace is chose as a fuctio of the elasticity modulus of the mobile elemet ad of the measurig rage. The limit case which must be avoided at all costs is the situatio whe, due to a high impact force, the mobile elemet touches the sesig elemet causig irreversible modificatios. I order to determie the accuracy of the detector a series of measuremets were performed usig the experimetal setup show i figure 6. This experimetal setup cosists of :. the shock detector. graded beam 3. trasducer support The experimetal procedure is : two probes of 4 ad 6 g respectively are throw from a well kow height. Cosiderig the elastic elemet costat as k=390 N/m ad the trasducer fuctio y=f(u Hall ), by the meas of equatio (3) we compute the mass of the each elemet for a series o 50 measuremets for each elemet.
Figure 6. The experimetal stad The obtaied values ad the absolute error are preseted i the followig tables for each elemet respectively. The absolute error was computed usig : ε i = x i x (4) Where i= 50 is the measuremet cout. i 3 4 5 6 7 8 9 0 3 4 5 x i 4 4. 4 4 3.9 4 3.95 4 4 4 3.8 4 4 4 4. ε i 0 0. 0 0 0. 0 0.05 0 0 0 0. 0 0 0 0. i 6 7 8 9 0 3 4 5 6 7 8 9 30 x i 4 4 3.8 4 4 3.95 4 4 3.9 4 3.95 4 4. 4 4 ε i 0 0 0. 0 0 0.05 0 0 0. 0 0.05 0 0. 0 0 i 3 3 33 34 35 36 37 38 39 40 4 4 43 44 45 x i 3.7 4 4 3.9 4 4 4 3.95 4 4. 4 4 4 4 4 ε i 0.3 0 0 0. 0 0 0 0.05 0 0. 0 0 0 0 0 i 46 47 48 49 50 x i 4. 4 4 3.9 3.95 ε i 0. 0 0 0. 0.05 Table : Values for the 4g elemet i 3 4 5 6 7 8 9 0 3 4 5 x i 6 6 6 5.8 6 6 6. 6 5.95 6 6 6. 6 6 5.9 ε i 0 0 0 0. 0 0 0. 0 0.05 0 0 0. 0 0 0. i 6 7 8 9 0 3 4 5 6 7 8 9 30 x i 6 6. 6 5.95 6 6 5.7 6 6 6 5.9 6 6. 6 6 ε i 0 0. 0 0.05 0 0 0.3 0 0 0 0. 0 0. 0 0 i 3 3 33 34 35 36 37 38 39 40 4 4 43 44 45 x i 5.9 6 6. 6 6 6 6 5.8 5.95 6 6 6. 6 6 6 ε i 0. 0 0. 0 0 0 0 0. 0.05 0 0 0. 0 0 0 i 46 47 48 49 50 x i 5.95 6 6. 5.95 6 ε i 0.05 0 0. 0.05 0 Table : Values for the 6g elemet
The expected value M[x] is computed usig equatio (5), ad the dispersio σ with equatio (6): M[ x] = x i (5) The r.m.s. deviatio is give by: i= σ = [ xi ( x i ) ] (6) i= i= σ = σ (7) X 4g elemet 6g elemet M[x] 3.988 5.997 σ 7.39. 0-3 8.. 0-3 σ 8.53. 0-9.05. 0 - Table 3 M[x], σ ad σ for both elemets I order to asses the repartitio law of our results we have chose to determie ad plot the empiric repartitio fuctio. I order to do this we first determied the groupig iterval d accordig to the Sturges law: xmax xmi d = (8) + 3.3lg The obtaied values is d = 0.0743 for both elemets for 7 groupig itervals. The iterval limits as well as the occurrece absolute frequecies (OAF) ad the occurrece relative frequecies (ORF) for each elemet respectively are give i Table 4 ad 5. ( ) Groupig itervals i - OAF f i - ORF Σf i 3.70000 3.7743 0.0 0.0 3.7743 3.8486 0.04 0.06 3 3.8486 3.949 4 0.08 0.4 4 3.949 3.9857 5 0. 0.4 5 3.9857 4.0575 33 0.66 0.9 6 4.0575 4.858 0.04 0.94 7 4.858 4.000 3 0.06 Table 4 : Values computed for the 4g elemet Groupig itervals i - OAF f i - ORF Σf i 5.70000 5.7743 0.0 0.0 5.7743 5.8486 0.04 0.06 3 5.8486 5.949 3 0.06 0. 4 5.949 5.9857 5 0. 0. 5 5.9857 6.0575 3 0.64 0.86 6 6.0575 6.858 3 0.06 0.9 7 6.858 6.000 4 0.08 Table 5 : Values computed for the 6g elemet Usig these data we ca ow plot, for both elemets, the repartitio empiric fuctio (figures 7 ad 8). These fuctios allow us to aticipate a ormal repartitio law for our measuremet data. Also the data as preseted above offer a sufficiet view of the accuracy of the measurig system allowig us to pass to the ext stage of implemetatio.
Repartitio empiric fuctio (the 4 g elemet) 0.9 Relative occurece frequecies 0.8 0.7 0.6 0.5 0.4 0.3 0. 0. 0 0.66 0.08 0. 0.0 0.04 0.04 0.06 6 3 4 5 7 Groupig itervals Figure 7 Repartitio empiric fuctio for the 4 g elemet measuremets Repartitio empiric fuctio (the 6 g elemet) 0.9 0.8 Relative occurece frequecies 0.7 0.6 0.5 0.4 0.3 0. 0.64 0. 0. 0.06 0.06 0.04 0.08 0.0 0 3 4 5 6 7 Groupig itervals Figure 8 : Repartitio empiric fuctio for the 6 g elemet measuremets III. Coclusio This approach is a first step toward the o chip implemetatio of this method. We ca cosider this trasducers ot as a replacemet to the preset methods (piezoresistive, tesometric, optical, etc), but a viable alterative which is easy to implemet i MEMS techology. However this is ot the oly structure witch ca be used, the mechaical cofiguratio ca be chaged i order to match specific requiremets. Refereces [] Dragomir N.D., et. al. Măsurarea electrică a mărimilor eelectrice. Vol.3: Măsurarea mărimilor mecaice. Ed. Mediamira Cluj-Napoca, 005 [] Davidescu A., et. al. Maualul igierului. Vol.: Mecaica, Rezisteta materialelor, Materiale- Metale, Masuratori, Topometrie. Ed. Tehica Bucuresti 955. [3] Harris M.C., Crede C.E. Shock ad Vibratio Hadbook.Vol.: Basic Theory ad Measuremet. McGraw-Hill Book Compay. New-York Toroto Lodo 96 [4] Ioa Gavril Tarova, Bogda Tebrea, ad Titus Eduard Crisa Hall Effect Trasducers Used i the Parameter Extractio of Captors Havig Elastic Catilever Beams - Proceedigs of the 007 IEEE Sesors Applicatios Symposium, IEEE Catalog Number 07EX546, ISBN -444-0678-. [5] Ioa Gavril Tarova Metrologie electrică şi istrumetaţie. Ed. Mediamira Cluj-Napoca, 003 [6] Radu Muteau, Gheorghe Todora Teoria si practica prelucrarii datelor de masurare. Ed. Mediamira Cluj-Napoca, 997