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VERIFICATION OF OUTPUT PARAMETERS OF MAGNETOELASTIC SENSOR OF PRESSURE FORCE Hodulíková A., Ing., PhD., Technical University in Košice, assistant professor Technical University of Košice, Letná 9, 042 00 Košice, Slovak Republic Address: Park Komenského 3, 042 00 Košice, Slovak Republic E-mail: [email protected] In its first part the article described the utilization of elastomagnetic phenomena in magnetoelastic sensors of pressure force (MES). In the second part the article is focused on verification of the output parameters (output voltage and effective output voltage) of magnetoelastic sensor. The aim was to figure out, if the values of magnetic induction obtained by MES model simulation in COSMOS/EMS environment and used for calculation of output parameters are corresponding to the experimental results. Key words: simulation, magnetoelastic sensor, model, finite element method, ferromagnetic material. INTRODUCTION. In present days the sensors are utilized more and more. In the field of measurement they present the most important part of the measurement chain. The overall accuracy of the measurement is limited by them, therefore, there is a higher requirement on their accuracy. They are used in measurements of the big pressure force, rolling force, measurement of the forces in bridge pylons, as a protiection for mechanical overload or in the rough weighing of the railway wagons [1]. PROBLEM STATEMENT. The advantage of the EMS is their relatively high sensitivity and possibility of utilization of the output quantity without the need of signal amplification. When compared to other sensors, they are more massive, however, their shape and construction gives them better mechanical propertes, resitance to overloading, air humidity, dust, shocks and vibration. The disadvantage lies in higher energy consumption and sensor´s error. Magnetoelastic sensors of force are divided into two groups - sensors of compressive and tensile force. The sensors are of transformer type and have been designed and assembled for the measurement of compressive force from 1,2kN to 12MN. A lot of attention has been given to the improvement of output parameters of the sensors MES 120kN and 6MN. The verification of output parameters and effective output voltage was realised for magnetoelastic sensor of 120kN pressure force (Fig.1). F Magnetoelastic sensors belong to the group of nonlinear systems. They are operates on the Villari’s effect principle, which is based on a change of feromagnetic material permeability proportionally to acting mechanical stress. The permeability increment Δμ proportional to the mechanical stress σ can described by relation [1] Δμ 2λ ms μ 2 .σ 2 Bsef (1) where λ ms is the middle value of magnetostriction coefficient in fed state, is permeability of ferromagnetic material when the affecting force is zero, Bsef is effective value of magnetic induction in fed state, k M is the material coefficient. The equation (1) is valid for case, when the direction of mechanical tension and magnetic field intensity are parallel. From the equation (1) we can see, that for magnetoelastic sensors it is convenient to use the materials with high permeability μ, high value of magnetostriction λs and also low value of magnetic induction Bs . Practical fabrication of magnetoelastic sensor of pressure force 120 kN, which correspond to 100 MPa pressure. The input parameter of the sensor is the external pressure force affecting the sensor and output parameter is the effective value of voltage, which is induced in the secondary winding of the sensor. For the voltage expression we are utilizing the induction law. The voltage will be induced in case when the whole magnetic flux will be encircled by secondary wire. This requirement is fulfilled in case when secondary winding will be winded by the holes of the primary winding. In case when the sensor is not affected by the external pressure force, the induced voltage uv t can be expressed as: Figure 1 – Magnetoelastic force sensor 120kN PREVIOUS RESEARCHES ANALYSIS. uv t N 2 B t dS , t s (2) uvF t N 2 F B t dS , t s (3) where BF t is the magnetic inductance in sensor´s core when external pressure affects the sensor in time t. The magnetic field in sensor´s core is activated by harmonic current i1 t I m1 sin t A , where Im1 is the maximal value of the current i1 t , = 2 f is the angle frequency of time changes of feeding current which passes through the primary winding of the sensor. Magnetic induction and output voltage then have the timely harmonic course. The question is, which value of the time changing course should be measured. The results of the practical measurements point to the value of effective value of output voltage. In order to express the effective value of output voltage it will be convenient to to come out from the simplified assumption, that the course of sensor´s magentic induction is also harmonic and for effective value of voltage U vef a U vef voltage uv (t) is: 1T 2 1T uv dt N 2 B t dS dt T0 T 0 t S 2 U vef (4) U vef 1T 2 uv dt T0 1T F B t B t dS dt T 0 S t affected by external pressure force as well as the case when the sensor is affected by external pressure force. For the needs of magnetostatic analysis, the magnetization curve had to be measured. This curve was for ferromagnetic material (transformator sheet) from which the sensor´s core lamellas are manufactured. The values measurement for these curves was realised by Epstein´s device for frequencies f = 200 and 400 Hz. From the measured and calculated values the graphical representation had been made µ = f (B ), shown on (Fig. 2). magnetic permeability [H/m] 10E-03 where N2 is the amount of the threads of secondary winding, B t is magnetic induction in the sensor´s core without the external pressure force in time t, dS is the surface element, S is the surface of the cross section of sensor´s core. In case, when the external pressure force affects the sensor, the induced voltage uvF t can be expressed as: 4 f = 200Hz 3 2 f = 400Hz 1 0 0 0,2 0,4 0,6 0,8 1 magnetic flux density B [T] Figure 2 – The dependence of the permeability on the magnetic flux density μ = f B From the results it can be seen, that with increasing pressure force the value of magnetic inductance is rapidly decreasing, the magnetic field gets deformed resulting in change in core´s magnetic properties which result in the change of magnetic permeability. The graphs on Fig. 3 and Fig. 4 show not only the abovementiond conclusions, but it can be seen, that the value of magnetic inductance decreases also with increased value of frequency. 2 N2 (5) The output signal of sensor is the effective value of voltage measured by voltmeter. From the equations (4) and (5) we can see, that for the effective value of output signal and output effective signal we need to know the value of magnetic induction, which we can obtain by solving the magnetic field of the magnetoelastic sensor. The output signal of the sensor is directly proportional to the change of permeability and the deformation of magnetic field. The task was solved as a magnetostatic problem for chosen value of current I1max = 1A in nonlinear environment for the case, when the sensor is not Figure 3 - The dependencies of magnetic flux density, in the dependence on pressure force applied to the sensor, F = 0, 80, 100, 120 kN, f = 400Hz Fi gure 7 - Dependency of output voltage value from affecting force for f = 200Hz Figure 4 - The dependencies of magnetic flux density, in the dependence on pressure force applied to the sensor, F = 0, 80, 100, 120 kN, f = 200Hz The effective values of output voltage and effective signal of sensor proportional to affecting force were calculated by equations (4) and (5) and compared to the experimental values. The comparison of the calculated and measured values is shown in graphical way on following figures. (Fig. 5, Fig. 6, Fig. 7 and Figr. 8) . Figure 8 - Dependency of output effective voltage value from affecting force for f = 200Hz Figure 5- Dependency of output voltage value from affecting force for f = 400Hz CONCLUSION. In the article, the relation between the input and output parameter of the elastomagnetic sensor of 120kN had been verified. By the comparison of calculated and experimental values, the results diferences had been obtained. These differences are caused by the utilization of simplified assumption, that the magnetic induction dourse is harmonic and permeability in sensor´s core is constant. In reality however, the permeability is dependent on magnetic induction. Therefre, the sensor´s field had to be solved as a nonstationary magnetic field. ACKNOWLEDGMENT. The paper has been prepared by the support of Slovak grant projects VEGA No. 020069/15. REFERENCES 1. Hodulíková A. Computer simulation model of EMS of force to the PhD Thesis, Košice, 2012. 2. Mayer,D Ulrych,B, Škopek,M. Solution of electromagnetic fields using modern software products, Journal EE, vol 7, no1, 2 , 2001. Figure 6 Dependency of output effective voltage value from affecting force for f = 400Hz