Hydrodynamic response time of magnetorheological fluid in valve mode: an initial study

Content from this work may be used under the terms of theCreativeCommonsAttribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. Published under licence by IOP Publishing Ltd World Symposium on Smart Materials and Applications (WSSMA 2021) IOP Conf. Series: Materials Science and Engineering 1186 (2021) 012002 IOP Publishing doi:10.1088/1757-899X/1186/1/012002 1 Hydrodynamic response time of magnetorheological fluid in valve mode: an initial study Michal Kubík1, a * and Karel Šebesta 1Brno University of Technology, Faculty of Mechanical Engineering, Brno, Czechia [email protected] Abstract. The transient behaviour of magnetorheological (MR) damper is a very important parameter affecting the performance of this technology in modern semi-actively controlled suspension systems. Currently, the transient behaviour of the MR damper is limited by dynamics of the MR fluid (MRF) itself. The significant part of MRF response time is a hydrodynamic response time which is connected with transient rheology and development of velocity profile in the slit gap. In this paper, the method for measuring the hydrodynamic response time of MRF operating in valve mode is presented. The hydrodynamic response time of MRF-132DG achieved value of τ90 = 0.78 ms for H = 17.5 kA/m a value of τ90 = 0.65 ms for H = 34 kA/m for given geometry of gap. The difference between model and experiment is lower in higher yield stresses of MRF. 1. Introduction Magnetorheological (MR) fluid is a smart material that exhibits a reversible and fast transition from a liquid state to a solid-state (increase of yield stress) under an external magnetic field. This phenomenon is usually called a magnetorheological effect. MR fluid is a two-phase fluid consisting of micron-sized highly magnetizable particles, usually carbonyl iron particles, in a non-magnetizable carrier fluid, such as mineral or silicone oil. When the MR fluid is energized by the magnetic field, the ferromagnetic particles are magnetized and form chain-like structures in the direction of the magnetic field. The fluid then exhibits a significant increase in yield stress. These properties allow the use of MR fluid in electromechanical systems such as dampers. Magnetorheological (MR) dampers are currently used in automotive, railway, aviation, etc. The transient (dynamic) behavior of the MR damper is a fundamental property affecting the performance of this technology in modern semi-actively controlled suspension systems. Two sources of the time delay between the control signal and damping force are as follow: (i) dynamics of MR damper hardware and (ii) the magnetorheological fluid dynamics. 2. Dynamics of MR damper hardware The response time of MR damper hardware was listed in several publications [1,2] and the main sources of the delay were identified as (i) eddy currents in coil core, (ii) inductance of MR damper coil, or (iii) compressibility of the hydraulic system of MR damper. When the magnetic field changes rapidly in the magnetic circuit of the damper, eddy currents are generated, which produce a magnetic field in the opposite direction than the initializing magnetic field [3]. Eddy currents can be eliminated by either a World Symposium on Smart Materials and Applications (WSSMA 2021) IOP Conf. Series: Materials Science and Engineering 1186 (2021) 012002 IOP Publishing doi:10.1088/1757-899X/1186/1/012002 2 material (SMC, ferrite, etc.) or shape approach. The shaped approach is based on the use of a magnetic circuit with thin sheets or with suitably located grooves. This issue is currently being under development. The relatively slow increase and decrease of electric current on control voltage signal due to the inductance of the coil can be solved by the current controller with the over-voltage method. The compressibility of the magnetorheological fluid also affects the transient behaviour of the MR damper [4]. The issue of MR damper hardware dynamics is relatively intensively described. Currently published MR dampers achieve response time (1.2 ms) comparable with a response time of MR fluid itself [5]. 3. Dynamics of MR fluid itself The transient (dynamic) behavior of MR fluid was described just in a few papers. The best-known paper in connection with the MR fluid response time is the paper of Goncalves et al. [6]. This team published a measurement of MR fluid response time on a slit-flow rheometer. The author introduces the fluid dwell time. This is the time that ferromagnetic particles of MR fluid spend in the presence of a magnetic field. The author considered that if the dwell time is short enough, the ferromagnetic particles in the MR fluid will not be sufficient to create chains and the yield stress of the MR fluid will not be created. This can be connected with MR fluid particle chain dynamics. The yield stress decrease was observed in Goncalves experiments. However, the papers of Sherman [7] or Goldasz et. al. [8] show that this pressure drop decrease is due to transient rheology connected with the development of velocity profile. This statement is based on CFD simulations. It is assumed that the yield stress of MR fluid flow will decrease/increase much faster than energy dissipation (pressure drop) due to flow transient. This phenomenon is often referred to as the hydrodynamic fluid response time. Sherman [7] published a model for the hydrodynamic response of MR fluids. This model is based on an analytical solution of the start-up flow of Bingham plastic fluid between parallel plates [9]. The Sherman [7] construct fit of data Darpa et al. [9] (dimensionless response time Tr) as follows: Tr= 0.235/(1+0.2Bi) where Biis Bingham number. For a Newtonian fluid, the dimensionless response time can be calculated as follows: Tr= τrη/ρh2 where τrresponse time, ηis plastic viscosity, ρis the density of the fluid, his gap size. It is important to note that this is the time τrto reach 90% of the final steady-state velocity. The main aim of this paper is to present a method for measuring the hydrodynamic response time of MR fluid operating in valve mode and preliminary results. The measured data will be compared with the model published by Sherman [7]. 4. Materials and methods 4.1. Measurement method idea This method is based on the measurement of pressure drop of the MR valve caused by an external magnetic field acting on the MR fluid Δpτdepending on dwell time tdwell. This method significantly extend the paper of Goncalves et al. [6]. The challenge is to separate the effect of viscosity on pressure drop from measured data and it change with temperature. Therefore, the measurement procedure consists of two blocks. The first measurement block is with zero magnetic fields (H = 0 kA/m) and Newtonian behavior of the magnetorheological fluid is considered in area I to III, see Figure. 1. The pressure drop Δpoff (H = 0 kA/m) for the first section (I) can be described as follows: pIpIII = Δpoff = Δpη + Δpχ World Symposium on Smart Materials and Applications (WSSMA 2021) IOP Conf. Series: Materials Science and Engineering 1186 (2021) 012002 IOP Publishing doi:10.1088/1757-899X/1186/1/012002 3 where Δpη is the viscous pressure drop and Δpχis the pressure drop of entrance and exit losses to the gap. In the second section II of measurement, the test MR valve (gap) is divided into two areas: (I-II) without a magnetic field and (II-III) with a magnetic field, see Figure. 1. It is assumed that the velocity profile on interface (II) is fully developed (Newtonian). Figure. 1 MR fluid flow in slit gap The second measurement of the pressure loss Δpon is already in the presence of a magnetic field (H ≠ 0 kA/m) at a given length (LM). The pressure drop Δpon is then: pIpIII = Δpon = Δpη + Δpχ + Δpτ = Δpoff + Δpτ where Δpτ is pressure drop due to yield stress of MR fluid on the length LM. From the measured pressure drops Δpoff and Δpon, the pressure drop caused by the MR fluid yield stress Δpτis determined as follows: Δpτ = Δpon - Δpoff These two sections must be measured as quickly as possible to keep the temperature difference as small as possible. However, there is always some change in temperature, which is reflected in the change in viscosity and is compensated in data post processing. Next, the dwell time tdwell was defined. This is the time that the MR fluid spends in the presence of a magnetic field. The dwell time tdwell was calculated by the mean flow velocity in the gap vmand the length LMas follows: tdwell = vm / LM It is necessary to note that the length LMis not connected with magnetic pole geometry but has to be calculated by magnetic model. In our case LMachieved a value of 8.8 mm. It is assumed that the MR fluid needs a certain time ttor length Ltto transform the Newtonian velocity profile to a velocity profile with a plug (Bingham plastic) to exhibits dissipation energy due to MR fluid yield stress. This time ttor length Ltis probably the result of MR fluid deceleration/ acceleration in the gap. In the case of Lt>> LM and at given mean velocity in the gap vm, the velocity profile was not developed from Newtonian to Bingham, and dissipation energy due to MR yield stress is not observed Δpτ= 0 although the yield stress is not zero (H ≠ 0 kA/m). Otherwise (Lt<< LM) the velocity profile was developed very quickly and there is no significant effect of MR fluid deceleration/acceleration. 4.2. Experimental device The functional layout of the apparatus is shown in Figure. 2. The experimental device (slit-flow rheometer) is energized by the Inova hydraulic dynamometer which imposes the motion of the floating piston (dp= 32 mm). The motion of the floating piston forces the test MR fluid through the slit gap of the rheometer (MR valve). The slit gap geometry (gap size tg= 0.6 mm, width wg= 32 mm and length L = 50 mm) is made of two grind blocks (position 4 a 5 in Figure. 3). Each block consists of a part made of non-magnetic stainless steel (position 5.1) and a part made of pure iron (5.2). Therefore, the magnetic flux can flow just through part 5.2. World Symposium on Smart Materials and Applications (WSSMA 2021) IOP Conf. Series: Materials Science and Engineering 1186 (2021) 012002 IOP Publishing doi:10.1088/1757-899X/1186/1/012002 4 Figure. 2 Functional layout of the rheometer, rheometer during tests on a hydraulic dynamometer The magnetic circuit is composed of the electromagnetic coil (1), pole pieces (2), and non-magnetic washer (3). The magnetic pole pieces are manufactured from pure iron. The electromagnetic coil is wound with 160 turns of copper wire with a diameter of 0.5 mm. The important dimensions are shown in Figure. 3. Figure. 3 Important dimension of magnetic circuit (left, middle), manufactured magnetic circuit (right) 4.3. Measurement methodology The pressure drop across the slit gap is acquired with pressure sensors HBM P8AP. The MR fluid temperature was acquired by resistance temperature sensor PT100 which was located near the entrance to the slit gap. The motion of the floating piston was measured using the LVDT transducer/position sensor accommodated in a hydraulic dynamometer. These signals were recorded and conditioned with a sampling frequency of 1 kHz by analyzer Dewe-800. The measurement procedure was as follow: (i) 8 sinusoidal cycles at given frequency fwere measured; (ii) pause of 10 sec to switch on the power supply current I; (iii) 8 sinusoidal cycles at given frequency fand given electric current Iwere measured; (iv) demagnetization of the magnetic circuit using a sinusoidal cycle with decreasing amplitude. The rise and fall of the frequency were always with a transition time of 2 s. Measurements were performed for different frequencies at a stroke amplitude of 48 mm. This corresponds to a maximum piston velocity of 0.48 m/s and a mean flow velocity in the slit gap of 22 m/s. The piston velocity vmwas determined by derivation of piston position. The data of pressure drop from the center of stroke (± 2 mm) were selected for the next evaluation. The measured data which achieved at least 99 % of maximum piston velocity was taken also for the next evaluation to eliminate transition to given frequency f. Selected points of pressure drop Δpoff and pressure drop Δpon were averaged and presented in the chapter results. The results were normalized ψ due to the quantitative comparison. The normalized data ψ were then fitted by a least-squares method in Matlab software by the following function:  (   ) =  1 −  1 .   2 . (   −  4 )  .  ℎ (  3 . (   −  4 ) World Symposium on Smart Materials and Applications (WSSMA 2021) IOP Conf. Series: Materials Science and Engineering 1186 (2021) 012002 IOP Publishing doi:10.1088/1757-899X/1186/1/012002 5 where c1, c2, c3, and c4are constants that were obtained by the fitting. From this equation, the primary (τ63) and secondary (τ90) hydrodynamic responses of the MR fluid were determined. MR fluid MRF132DG from Lord Corporation was used for testing. The volume concentration of ferromagnetic particles in the tested sample was experimentally determined to be 32.6 % and the density to be 3106 kg/m3. 5. Results and discussion The graphs below (Figure. 4) show the dependences of the pressure drop Δpon and Δpoff on the mean flow velocity in the slit gap vmfor an electric current of 0.4 A and 0.6 A applied to the electromagnetic coil. It can be seen that with increasing gap velocity vm, the differences in pressure drop decrease. This also corresponds to the data published by [10]. Figure. 4 Pressure drop Δpon and Δpoff for electric current 0.4A (left), and electric current 0.6 A (right). The pressure drop Δpτwas then calculated as a function of dwell time tdwell, and the data were normalized, see Figure. 5. The measured data were fitting functions presented above. Figure. 5 Normalize pressure drop Δpτfor electric current 0.4 A (left), and for electric current 0.6 A (right) The table below (Table 1) shows the fitting coefficients c1to c4, primary and secondary response time from the experiments for the two magnetic fields. The magnetic flux intensity Hwas estimated based on data from the MR fluid manufacturer and measured yield stress. The results of the experiment were compared with the model. Table 1. Result of the experiments I [A] c1[-] c2[-] c3[-] c4[-] τ63 [ms] τ90 [ms] τr m[ms] Y. stress [kPa] H [k A /m] 0.4 0.38 - 2.98 0.332 14.75 0.43 0.78 1.15 5.9 17.5 0.6 - 0.15 - 2.31 0.09 2.28 0.4 0.65 0.9 12.8 34 World Symposium on Smart Materials and Applications (WSSMA 2021) IOP Conf. Series: Materials Science and Engineering 1186 (2021) 012002 IOP Publishing doi:10.1088/1757-899X/1186/1/012002 6 For the MR fluid yield stress of 5.9 kPa (17.5 kA/m), the secondary response time was τ90 = 0.78 ms which is lower than predicted by model (τr model = 1.15 ms). In 5this case, the difference between model ad experiemnt is 34 %. At a higher value of yield stress (12.8 kPa), the difference between model and expeiemnt is slightly lower (28 %). Nevertheless, it can be stated that the measured data corresponding to the model. The differences can be explained by slightly different temperature for each measured point (each dwell time) and simplification of the model. In the following research, it is necessary to focus on determining the effect of the magnetic field, density, or temperature on measured hydrodynamic response time. 6. Conclusion In this paper, the measurement method of the hydrodynamic response time of magnetorheological fluid was presented. The measured data of hydrodynamic response time of MRF-132DG for two levels of the magnetic field was compared with the model. The difference between model and experiment is lower in higher yield stresses of MRF. The measured hydrodynamic response time for yield stress of 12.8 kPa (H = 34 kA/m) was 28 % lower than predicted by the model and achieved a value of 0.65 ms. It can be stated that the model published Sherman correlate with our initial experiment for given geometry and MR fluid rheology. The model is simplified and therefore a difference of about 30% is acceptable. Acknowledgments This paper and experiments have been made possible thanks to the Czech Science Foundation (GAČR) No. 20-23261Y. References [1] Koo, J.H.; Goncalves, F.D.; Ahmadian, M. A comprehensive analysis of the response time of MR dampers. Smart Mater. Struct. 2006,15, 351–358. [2] Kubík, M.; Macháček, O.; Strecker, Z.; Roupec, J.; Mazůrek, I. Design and testing of magnetorheological valve with fast force response time and great dynamic force range. Smart Mater. Struct. 2017,26, 1–9. [3] Strecker, Z.; Mazůrek, I.; Roupec, J.; Klapka, M. Influence of MR damper response time on semiactive suspension control efficiency. Meccanica 2015,50, 1949–1959. [4] Kubík, M.; Goldasz, J. Multiphysics Model of an MR Damper including Magnetic Hysteresis. Shock Vib. 2019,2019. [5] Strecker, Z.; Roupec, J.; Mazurek, I.; Machacek, O.; Kubik, M.; Klapka, M. Design of magnetorheological damper with short time response. J. Intell. Mater. Syst. Struct. 2015,26, 1951– 1958. [6] Goncalves, F.D.; Ahmadian, M.; Carlson, J.D. Investigating the magnetorheological effect at high flow velocities. Smart Mater. Struct. 2005,15, 75–85. [7] Sherman, S.G. MAGNETORHEOLOGICAL FLUID DYNAMICS FOR HIGH SPEED ENERGY ABSORBERS, 2017. [8] Gołdasz, J.; Sapiński, B. Insight into magnetorheological shock absorbers; 2015; ISBN 978-3-31913232-7. [9] Dapri, I.; Scarpi, G. Start-up Flow of a Bingham Fluid in a Pipe. Meccanica 2005,40, 49–63. [10] Mao, M.; Hu, W.; Choi, Y.T.; Wereley, N.; Browne, A.L.; Ulicny, J. Experimental validation of a magnetorheological energy absorber design analysis. J. Intell. Mater. Syst. Struct. 2014,25, 352–363.