Frequency Response Modeling of Inductive Position Sensor with Finite Element Tools

Transcription

1 Frequency Reone Modeling of Inductive Poition Senor with Finite Element Tool A. K. Palit Lemfoerder Electronic GmbH (ZF-Friedrichhafen AG grou), DE Eelkam, Germany, Abtract: The aer reent here an inductive oition enor which i baed on a horizontally moveable/liding tye of thin rectangular or rhombu-haed coer (activator element) late and a row of lanar coil, rinted directly on the PCB. The frequency domain model of the reented inductive enor ha been develoed uing the Comol multihyic tool to etimate the change in inductance value of lanar coil due to eddy current effect in the coer activator element at different horizontal oition. The rooed inductive enor ha been already imlemented in the automatic gear hifter module of leading German car. framework /model of a lanar inductive oition enor have been decribed in Section 3. Section 4 decribe the batch wee and frequency domain modeling reult from Comol multihyic tool. Section 5 conclude with brief remark. 2. Inductive Poition Senor Figure-1 how below the chematic view of an inductive oition enor, in which the inductive coil are lanar tye and the Rhombu haed activator element i made u of thin coer late. Keyword: Inductive oition enor, Planar coil, Eddy current effect, Activator element, Frequency domain modeling 1. Introduction The oition enor find everal alication in the automotive ector. Automatic gear hifter, eat oition adjutment and accelerator-edal oition module etc. are ome common examle of oition ening in automotive electronic. Becaue of extreme weather condition, uch a dut, humidity, moiture, vibration, reure, fluctuation of day/night temerature and wide oerating temerature range (-40 C to +90 C) confronted by automotive electronic oition ening baed on reitive or caacitive rincile are inaroriate in many occaion. Intead, a noncontact tye of inductive oition enor ha everal advantage in uch alication. With thi objective in mind, a frequency domain model of a lanar inductive coil ha been develoed to etimate the change of coil inductance correonding to the horizontal moving ditance of the coer activator element over the lanar coil. Inductive oition enor ha been reented briefly in the Section 2. Comol Multihyic ha been alied here a Finite Element tool for uch modeling and therefore, the correonding mathematical Figure 1: Inductive Poition Senor Planar coil are fabricated directly on the PCB in the form of a row of flat coil o that three coil inductance (e.g., coil 2, coil 3 and coil 4) are influenced by the eddy current daming effect due to liding activator element a hown in Figure-1. Due to the limited ace on the PCB often uch coil have maller ize and le number of turn, e.g. 8-9 turn. Again, a mall ize of coil and le number of turn will roduce a mall amount of inductance which may be inufficient for a reliable oition ening. Therefore, inductive oition ening method often ue the multi-layer lanar coil with a liding coer, bra or aluminum metal late a an activator element [1] aroximately 0.2 to 0.3 mm over the coil, wherein the tranducer generate a coil voltage/inductance that change along with moving ditance under the eddy current daming effect at higher frequencie. Planar coil of different geometrical hae (quare, rectangular, traezoidal, circular or even ellitical) together with a rectangular or rhombu or even hexagonal haed coer Excert from the Proceeding of the 2014 COMSOL Conference in Cambridge

2 activator form actually the bai of a non-contact tye of inductive oition enor which can be ued in the automatic gear hifter module for ening the P (ark), N (neutral), R (revere), D (drive) and S (ort) mode with M+ (manual ga/acceleration +) and M- (manual ga/acceleration -) etc. for intance. 3. Ue of COMSOL Multihyic The reented non-contact tye of inductive oition enor can be viewed a leaky and looely couled rimary and econdary winding of a tranformer model. Thi i due to the fact that the behavior of the lanar coil of the inductive oition enor i imilar to the rimary coil of the tranformer and the liding coer late reemblance very much with the horted econdary coil of the tranformer. Intead of a high ermeable ferromagnetic core of the tranformer inductive oition enor decribed here ue the air a core material. Owing to the ue of air a core material in the inductive oition enor the couling factor between the rimary coil and horted econdary i very much maller than the normal tranformer and thereby leakage of magnetic flux i very high in thi tye of inductive enor. The chematic circuit model of an ideal tranformer with a loaded (Z L ) econdary coil i hown in Fig. 2 below. V I R L di dt M di dt, (1a) M di dt I and coul R Z L di dt L M K L L... (1b) where R and R (not hown in Fig. 2) rereent reectively the reitance of the rimary coil and econdary coil. Similarly, L and L (not hown in Fig. 2) rereent reectively the inductance of rimary coil and econdary coil of the tranformer and Z L i the load in the econdary ide. M = mutual inductance between rimary and econdary coil and mathematically, M i rereented by the roduct of couling factor (K coul ) and quare root of the roduct of L and L. The mutual inductance term in the rimary circuit rereent the load due to econdary. It ha negative ign becaue it init the AC uly ource (voltage) to roduce more current in reone to increaing load (mall value of Z L ) in the econdary ide. The mutual inductance term in the econdary rereent the couling from the rimary and act a the voltage ource that drive the econdary circuit [2]. The relation given in equation (2) hold further for an ideal tranformer. V and V I L I N N a... (2) L a For an ideal tranformer with horted econdary the load Z L = 0 and rimary coil reitance (R ) and the econdary coil reitance (R ) are alo aroximated a zero Ohm. Therefore, from equation (2) one can find the econdary current in term of rimary current and turn ratio a follow: I L am di dt ai, V. (3) Figure 2: Equivalent tranformer model In Fig. 2, V and I rereent reectively the alied rimary inut voltage and the correonding current flowing into the rimary coil, and in contrat V and I rereent reectively the induced econdary voltage and current flowing through the loaded econdary coil. Referring to Fig. 2 above, the mathematical model of the (non-ideal) tranformer can be written roughly a follow: Furthermore, from equation (1a) and (3) one can derive the following: K L di dt am K L, V 1 (4) coul coul From the equation (4) one can ee that for a moderate couling between the rimary and econdary winding the rimary coil inductance L i reduced by a factor of (1-K coul ). In reality the couling factor i alway le than 1 i.e., Excert from the Proceeding of the 2014 COMSOL Conference in Cambridge

3 K coul < 1. The aforementioned rincile i ued in the inductive oition enor a decribed below. When the coer activator element i brought very cloe to the lanar coil the couling factor (K coul ) increae from 0 to ome moderate value (e.g., 0.5 to 0.6) and thereby, the inductance of lanar coil i reduced aroximately by 40% to 50% of it nominal value. When the activator element move away further from the concerned lanar coil the couling factor i reduced to zero value and therefore, inductance value of the lanar coil goe back to it nominal value. The change of lanar coil inductance value i uitably converted to correonding voltage ignal and location of liding activator element i etimated. The aforementioned hyical henomenon can alo be exlained alternatively a follow. When an alternating current flow into the lanar coil it roduce a varying magnetic flux in the urrounding air core. The varying magnetic field iminging on the horted econdary winding (coer activator element) induce further a varying voltage and current a er Faraday law [2]. The induced current in the coer activator element, termed a eddy current, further ooe the varying magnetic flux generation a er Lenz law and thu alo ooing the current flow into the lanar coil by giving rie to the lower coil inductance value. Higher the frequency of rimary current, larger i the eddy current effect in the liding coer late. Thi, in turn, reduce the coil inductance of the inductive enor. Model of both a ingle-layer/multilayer (Figure-1) lanar coil, along with a liding Cuactivator of Rhombu hae, oerating at 10 MHz frequency ha been develoed to imulate uch effect. The change of coil inductance value with liding activator ditance over the lanar coil form the bai of reented inductive enor. The above henomenon ha been modeled and imulated with the hel of Comol multihyic frequency domain tool. The model building wa erformed with the following te a hown in Figure- 3 under Geometry 1. After the 3D Geometry contruction of lanar coil and Rhombu hae activator element coer material wa aigned to both the lanar coil and activator element and both thee model were laced in an air-filled big here. The diameter of here wa greater than 2 time of Xoff (mm). The move 1 te wa neceary in model building, a the activator element move left and right horizontally above the lanar coil. Figure 3. Geometry building te of lanar coil with activator element in Model Builder. ACDC Magnetic field (mf) wa elected under add Phyic. After the meh generation of Geometry model Batch Swee tudy wa erformed in frequency domain. In the Batch Swee tudy the uer defined Xoff arameter wa et to 7 mm and 9 mm reectively for a ingle layer and double layer lanar coil imulation reectively, wherea uer defined both Yoff and Zoff arameter were et to Reult Figure 4. Cu-activator X-off oition (mm) v. Inductance (nh) grah for a ingle layer lanar coil. Excert from the Proceeding of the 2014 COMSOL Conference in Cambridge

4 Figure 4 and Figure 5 how the frequency domain (batch-wee) imulation reult of a 3D model of an inductive oition enor (both lanar coil and a Rhombu hae coer activator element) obtained from Comol multihyic tool at f = 10 MHz frequency. Figure 4 deict the horizontal ditance (Xoff oition in mm) of the coer activator element veru coil inductance (nh) grah. It can be oberved from Figure 4 that for a ingle layer lanar coil the coil inductance (L-coil) change from 195 nh to 100 nh and then again to 195 nh when the Cu-activator lide from horizontal oition Xoff = -7 mm to Xoff = 0 mm and then further to Xoff = +7 mm reectively maintaining a fixed vertical ditance (Z_dit = 0.3 mm) between the lanar coil and the activator element. Note that for a contant vertical ditance of 0.3 mm, coil inductance change due to liding activator in the reent imulation i aroximately 49%. Figure 6. Screen hot of Flux denity norm (mt) for a double layer lanar coil. Figure 7. Zoomed view of flux denity norm (mt) for a double layer coil. Figure 5. Flux denity norm (mt) for a ingle layer lanar coil. Figure 5 how the magnetic flux denity norm (B norm in mt) at f = 10 MHz frequency which can attain mt when the activator element i at Xoff = +7 mm from the center of the lanar coil. Figure 5 alo how the magnetic flux denity arrow line. Further exerimental imulation were erformed with a double layer lanar coil alo at f = 10 MHz frequency (Figure 6, Figure 7 and Figure 8). Figure 6 how the creen hot of batch wee and frequency domain imulation of double layer lanar coil and Figure 7 how the zoomed view of magnetic flux denity norm for the double layer lanar coil with magnetic flux arrow volume. Figure 8. Cu-activator X-off oition (mm) v. Inductance (nh) curve for a double layer coil. Figure 8 how the inductance (nh) grah of a lanar coil for different horizontal ditance (Xoff oition in mm) of coer activator Excert from the Proceeding of the 2014 COMSOL Conference in Cambridge

5 element from the center of a double layer lanar coil. It can be oberved from Figure 8 that for a double layer lanar coil the coil inductance (Lcoil) change from 720 nh to 340 nh and then again to 720 nh when the Cu-activator lide from horizontal oition Xoff = -9 mm to Xoff = 0 mm and then further to Xoff = +9 mm reectively. The hae of thi curve i imilar to the coer activator element horizontal ditance (Xoff oition in mm) veru coil inductance (nh) curve for a ingle layer lanar coil a hown in Figure 4. Similar to ingle layer lanar coil in thi cae alo a fixed vertical ditance (Z_dit = 0.3 mm) between the double layer lanar coil and the activator element i maintained. Note that for the double layer lanar coil the coil inductance change by aroximately 53%. The Xoff-oition veru coil inductance curve in Figure 8 and Figure 4 both look like an inverted Gauian function. 5. Concluion An inductive oition enor wa modeled uing Comol Multihyic frequency domain (batch-wee) tool, where the lanar coil inductance change due to eddy current formation in the liding Cu-activator element at high frequency. The inductance (nh) curve (X off oition (mm) veru coil inductance grah) look like an inverted Gauian function. The coil inductance will be further reduced at Xoff = 0 mm horizontal oition if the vertical ditance (Z_dit) between the center of activator and center of to layer (for multi-layer coil) of lanar coil i made equal to 0.2 mm or even lower. Thi i due to the fact that with maller vertical ditance (Z_dit) couling factor (K coul ) between the lanar coil (rimary winding) and activator (horted econdary winding) increae further in equation (4). The enitivity of the inductive enor wa alo invetigated at different frequencie with the reented model. It wa oberved that enor efficiency and enitivity are highly deendent on the hae/geometry, ize and hyical dimenion of both lanar-coil and Cu-activator element beide the vertical Z- ditance between the lanar coil and Cu-activator element. All uch fine effect were imulated with Comol multihyic tool for deign otimization of inductive oition enor. The imulation reult were ued in the develoment of an automatic gear hifter module of a leading German car. 6. Reference 1. ZF-Friedrichhafen AG Patent-document: CN B, (2007) 2. htt://en.wikiedia.org/wiki/tranformer 3. COMSOL Multihyic, ACDC Module Uer Guide, (2013) 4. COMSOL Multihyic, ACDC Model Library Manual, (2013) Excert from the Proceeding of the 2014 COMSOL Conference in Cambridge