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Error Estimate at Magnetorheological Transformer Calculation Tests by Flooding Methods
Available online at www.sciencedirect.com
ScienceDirect Procedia Technology 24 (2016) 394 – 398
International Conference on Emerging Trends in Engineering, Science and Technology (ICETEST - 2015)
Error estimate at magnetorheological transformer calculation tests by flooding methods Gordeev B.Ⱥ.a,*, Okhulkov S.N.a, Plekhov Ⱥ.S.a a
Institute of Electric Power Engineering, NNSTU n.a. R.E. Alekseev, Nizhny Novgorod 603950, Russia
Abstract The article reviews the issues of error estimate at measuring deformations in magnetorheological transformers in which the choking channels are replaced by a cylindrical gaping between the two coaxial cylinders. The cylindrical gaping as well as the main and compensation chambers volumes are filled with magnetorheological fluid. Such construction of magnetorheological transformers is preferable for impact loads damping. At impact loads the measurement of flooding methods displacements is connected to a number of features, reviewed in this article. 2016The TheAuthors. Authors.Published PublishedbybyElsevier Elsevier Ltd. ©©2016 Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the organizing committee of ICETEST – 2015. Peer-review under responsibility of the organizing committee of ICETEST – 2015 Keywords: magnetorheological transformer; flooding method
1. Introduction The article analyses the reasons for phase measurement error, caused by sounding signal speeds and the researched object deformations ratio – damper with a magnetorheological transformer (MRT). The actions of shock loads on MRT cavitation processes are significantly increased. Therefore, improving the accuracy of measurements of deformations MRT by wave method becomes relevant.
* Corresponding author. Tel.: +0-000-000-0000 . E-mail address: [email protected]
2212-0173 © 2016 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the organizing committee of ICETEST – 2015 doi:10.1016/j.protcy.2016.05.054
B.А. Gordeev et al. / Procedia Technology 24 (2016) 394 – 398
2. Main Results The process of the damper deformations (displacements) measurement with a magnetorheological transformer by flooding methods is the following (Fig. 1) [1, 7, 8]. Longitudinal displacements radiated by an ultrasonic wave source Utt of a sounding signal are determined by the following equation U tt c 2U xx
0,
wherɟ Uxx – is the initial sounding signal displacement, ɫ
E U - the speed of sound in a rheological
environment which could be represented by gases and liquids, E – the environment elasticity module, ȡ – the environment relative density. The boundary line between the media is supposed to be influenced by ultrasonics from the radiating source and, being reflected by the surface of the researched object they are caught by the correspondent receiver. Thus the condition of continuity at the boundary line between the media is the following Z 0U t (0, t ) EU x (0, t )
P (t ) ,
EU - flood medium resistance, μ(t) – the given functional displacement. where Z 0 Considering the moving boundary impenetrable for a sounding signal, the second boundary condition at x = L + l(t) is U [ L l (ty)] l (t ) , where L – the distance from the source to a fixed boundary, l(t) – boundary displacement law.
Fig. 1. Experimental unit schematic diagram to identify MRT vibration displacements.
395
396
B.А. Gordeev et al. / Procedia Technology 24 (2016) 394 – 398
For example let’s consider the case of a boundary displacement at a steady speed V. In this case l(t) = L1 + Vt, where L1 – is the initial distance from the radiation source to the media boundary and thus the boundary displacement law is represented in the form of [7, 8] 2 L1 1V /c ], f (t ) h[ 1 V / c c(1 V / c) Thus for a harmonic source h(t )
A sin Z 0 t ,
f (t )
A sin(Z1t M ) ,
where A - amplitude, Ȧ0, Ȧ1 frequency of radiated h and reflected f(t) acoustic signals, M - constant phase advance. The constant phase advance is determined as
M
2ZL1 . c(1 V / c)
Between the frequencies of reflected and radiated acoustic signals there exists the following dependency, corresponding to a double Doppler’s effect
Z1
Z0
1V /c . 1V /c
It should be taken into consideration that the falling and reflected signals amplitudes in the environment with rheological features are not equal. However in such a case the informative features will be frequency deviations with Doppler’s effect and the phase corrugation [7, 8]. Generally at voluntary media boundary displacements, if the source is of harmonic nature, the signal received can be expressed as f (t )
A sin Z (t 2
l (t ) R (t ) ), c
(1)
where R(t) – is the function representing the phase error estimate at a given moment. At R(t) = 0 the reflected signal phase respective to the falling (input) one is a constant i.e. the expression being
f (t )
A sin Zt ,
where Ȧ – is the frequency of a reflected acoustic signal. At R(t) < 0 or R(t) > 0 the phase error estimate at a given moment is pre-conditioned by the acoustic signal travel time from the object to the receiver. So, at vibration speeds of 1 m/s rms value it corresponds to 0.3 % at 1 m distances from the researched object. To obtain the information of the law of the researched object boundary displacement the reflected signal is multiplied by the input A0 sin(Ȧt + ij), following this a low-frequency spectrum part is identified, i.e. the spectrum component is examined
f n (t )
AA0 cos(2Zl (t ) R(t ) / c M ) , 2
from which the displacement law l(t) is deducted, being calculated at a quasi-static approximation R(t) = 0. In this micro motion measurement method, the informative parameter is an index m - of frequency modulation of
B.А. Gordeev et al. / Procedia Technology 24 (2016) 394 – 398
the reflected acoustic sounding signal m
Zd :0
,
where Ȧd - the reflected acoustic signal frequency deviation, ȍ0 - the vibration frequency. Fig. 1 shows an experimental unit schematic diagram with an ultrasonic phasing tester of micro motions 1 to identify vibration displacements, determined by the sounding signal speed and the researched magnetorheological damper deformations ratio 5-6-9 [1, 7, 8]. Piezoelectric transformers – radiating unit 2 and the acoustic oscillations receiver 4 are mounted on the console 8 and customized to mechanical and electrical resonance oscillations with a frequency of 30 kHz [1, 7, 8]. As shown in Fig. 1 the magnetorheological damper 5-6-9 with a cylindrical gaping comprises: coax internal surface of a brass wall tube, piston rod external surface 5, field magnet (FM) 6, the main and compensatory chambers volume of a piston type hydromount 9 with magnetorheological fluid (MF) [3]. With the help of an ultrasonic phasing tester the micro motions of the piston rod 5 at the load of 3 have been measured. In article [1] the linear dependence between the brass piston rod speed in the cylindrical gaping with magnetorheological fluid and the magnetic induction value has been identified (Fig. 2). Fig. 2 shown on the Y-axis the relaxation speed of the magnetic fluid in m/s, on X-axis - magnetic induction in T. The brass piston rod speed decreases after being removed from the magnetic field effect in the orthogonal magnetic field of the field magnet has not been recorded.
Fig. 2. The magnetorheological fluid relaxation speed from the orthogonal magnetic field initial induction.
In article [1] the ferrite and steel piston rod speed decreases has been identified after the magnetic field effect removal in the orthogonal magnetic field of the field magnet before and after transmission through their extremes. This result is explained by a magnetorheological effect and magnetorheological fluid relaxation after the magnetic field removal and the remanent magnetic induction of the field magnet leg [4, 5]. Increase speed of the steel piston rod is determined by the magnetorheological liquid rise of temperature (over 40°ɋ) in the cylindrical gaping [1, 2]. Fig. 2 shows relaxation rates of magnetorheological fluids in a transverse (1, 2, 3) and longitudinal (4) magnetic fields, depending on the magnetic field initial induction and the piston rod material. At impact loads the piston-rods speed is rapidly changed [6], and, when it becomes coordinate to the sounding signal propagation velocity, the reflected signal spectral structure is filled with high frequency harmonics, which are absent in the real process [1, 7, 8]. The method of the reflected signal processing should comprise the absolute error of measuring the boundary
397
398
B.А. Gordeev et al. / Procedia Technology 24 (2016) 394 – 398
displacement l(t) which equals '
[l (t ) R (t ) l (t )] l (t )
R (t ) 1 .
(2)
From (2), with a relative error
G
'l (t ) , l (t )
where ǻl(t) – measurement error. So, we get the following condition of quasi-static equation applicability '
R (t ) 1 d G ,
and for the second approximation l (t ) d cG .
As a result, for į = 10-2 we get that the vibrating boundary speed should not exceed the degree of 3 m/s when measured in the air. 3. Conclusion
The results of the work show that the phase measurement error and thus of the vibration displacement are determined by the sounding signal speeds ratio of and researched object deformations ratio – magnetorheological damper. In such cases when at impact loads the rod piston displacement speed exceeds 3 m/s, the reflected signal phase identification, as the informative parameter, is subject to increasing errors. Acknowledgements
R&D are carried out as a part of a state project in the sphere of scientific research ʋ8.2668.2014/Ʉ in Nizhny Novgorod State Technical University n.a. R.E. Alekseev. References [1] Gordeev BA, Maslov GV, Okhulkov SN, Osmekhin AN. On developing a magnetorheological transformer that operates in orthogonal magnetic fields. Journal of Machinery Manufacture and Reliability, vol. 43, no. 2, 2014. p. 15-21. [2] Gordeev BA, Bugaiskiy VV, Okhulkov SN, Osmekhin AN, Gorskov VP. Hydraulic fluid temperature influence on hydro pipe saddles dynamics. Vestnik mechanical engineering, no. 12, 2014. p. 22-26. [3] Gordeev BA, Erofeev VI, Sinev AV, Mugina OO. Vibration protection system with inertia and dissipation rheological fluids. Moscow: Fizmatlit; 2004. [4] Shulman ZP, Kordonskii VI. The magnetorheological effect. Minsk: Science and Technology; 1982. [5] Gordeev BA, Okhulkov SN, Plekhov AS, Titov DYu, Gorskov VP. Flow and relaxation magnetorheological fluid in the throttle channels of hydraulic support. Vestnik mechanical engineering, no. 7, 2015. p. 59-63. [6] Gordeev BA, Okhulkov SN, Plekhov AS, Zlobin PA. Application of magneto-rheological fluids in mechanical engineering. Privolzhsky Scientific Journal, no. 4, 2014. p. 29-41. [7] Gordeev BA, Kuklina IG, Osmekhin AN. Optimization of measurement of construction vibration parameters by acoustic methods. Privolzhsky Scientific Journal, no. 2, 2009. p. 13-20. [8] Gordeev BA, Kuklina IG, Golubeva KV, Gordeev AB. Ultrasonic phase vibrotransducer. Russia Patent 2 472 109, Jul. 18, 2012.
ScienceDirect Procedia Technology 24 (2016) 394 – 398
International Conference on Emerging Trends in Engineering, Science and Technology (ICETEST - 2015)
Error estimate at magnetorheological transformer calculation tests by flooding methods Gordeev B.Ⱥ.a,*, Okhulkov S.N.a, Plekhov Ⱥ.S.a a
Institute of Electric Power Engineering, NNSTU n.a. R.E. Alekseev, Nizhny Novgorod 603950, Russia
Abstract The article reviews the issues of error estimate at measuring deformations in magnetorheological transformers in which the choking channels are replaced by a cylindrical gaping between the two coaxial cylinders. The cylindrical gaping as well as the main and compensation chambers volumes are filled with magnetorheological fluid. Such construction of magnetorheological transformers is preferable for impact loads damping. At impact loads the measurement of flooding methods displacements is connected to a number of features, reviewed in this article. 2016The TheAuthors. Authors.Published PublishedbybyElsevier Elsevier Ltd. ©©2016 Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the organizing committee of ICETEST – 2015. Peer-review under responsibility of the organizing committee of ICETEST – 2015 Keywords: magnetorheological transformer; flooding method
1. Introduction The article analyses the reasons for phase measurement error, caused by sounding signal speeds and the researched object deformations ratio – damper with a magnetorheological transformer (MRT). The actions of shock loads on MRT cavitation processes are significantly increased. Therefore, improving the accuracy of measurements of deformations MRT by wave method becomes relevant.
* Corresponding author. Tel.: +0-000-000-0000 . E-mail address: [email protected]
2212-0173 © 2016 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the organizing committee of ICETEST – 2015 doi:10.1016/j.protcy.2016.05.054
B.А. Gordeev et al. / Procedia Technology 24 (2016) 394 – 398
2. Main Results The process of the damper deformations (displacements) measurement with a magnetorheological transformer by flooding methods is the following (Fig. 1) [1, 7, 8]. Longitudinal displacements radiated by an ultrasonic wave source Utt of a sounding signal are determined by the following equation U tt c 2U xx
0,
wherɟ Uxx – is the initial sounding signal displacement, ɫ
E U - the speed of sound in a rheological
environment which could be represented by gases and liquids, E – the environment elasticity module, ȡ – the environment relative density. The boundary line between the media is supposed to be influenced by ultrasonics from the radiating source and, being reflected by the surface of the researched object they are caught by the correspondent receiver. Thus the condition of continuity at the boundary line between the media is the following Z 0U t (0, t ) EU x (0, t )
P (t ) ,
EU - flood medium resistance, μ(t) – the given functional displacement. where Z 0 Considering the moving boundary impenetrable for a sounding signal, the second boundary condition at x = L + l(t) is U [ L l (ty)] l (t ) , where L – the distance from the source to a fixed boundary, l(t) – boundary displacement law.
Fig. 1. Experimental unit schematic diagram to identify MRT vibration displacements.
395
396
B.А. Gordeev et al. / Procedia Technology 24 (2016) 394 – 398
For example let’s consider the case of a boundary displacement at a steady speed V. In this case l(t) = L1 + Vt, where L1 – is the initial distance from the radiation source to the media boundary and thus the boundary displacement law is represented in the form of [7, 8] 2 L1 1V /c ], f (t ) h[ 1 V / c c(1 V / c) Thus for a harmonic source h(t )
A sin Z 0 t ,
f (t )
A sin(Z1t M ) ,
where A - amplitude, Ȧ0, Ȧ1 frequency of radiated h and reflected f(t) acoustic signals, M - constant phase advance. The constant phase advance is determined as
M
2ZL1 . c(1 V / c)
Between the frequencies of reflected and radiated acoustic signals there exists the following dependency, corresponding to a double Doppler’s effect
Z1
Z0
1V /c . 1V /c
It should be taken into consideration that the falling and reflected signals amplitudes in the environment with rheological features are not equal. However in such a case the informative features will be frequency deviations with Doppler’s effect and the phase corrugation [7, 8]. Generally at voluntary media boundary displacements, if the source is of harmonic nature, the signal received can be expressed as f (t )
A sin Z (t 2
l (t ) R (t ) ), c
(1)
where R(t) – is the function representing the phase error estimate at a given moment. At R(t) = 0 the reflected signal phase respective to the falling (input) one is a constant i.e. the expression being
f (t )
A sin Zt ,
where Ȧ – is the frequency of a reflected acoustic signal. At R(t) < 0 or R(t) > 0 the phase error estimate at a given moment is pre-conditioned by the acoustic signal travel time from the object to the receiver. So, at vibration speeds of 1 m/s rms value it corresponds to 0.3 % at 1 m distances from the researched object. To obtain the information of the law of the researched object boundary displacement the reflected signal is multiplied by the input A0 sin(Ȧt + ij), following this a low-frequency spectrum part is identified, i.e. the spectrum component is examined
f n (t )
AA0 cos(2Zl (t ) R(t ) / c M ) , 2
from which the displacement law l(t) is deducted, being calculated at a quasi-static approximation R(t) = 0. In this micro motion measurement method, the informative parameter is an index m - of frequency modulation of
B.А. Gordeev et al. / Procedia Technology 24 (2016) 394 – 398
the reflected acoustic sounding signal m
Zd :0
,
where Ȧd - the reflected acoustic signal frequency deviation, ȍ0 - the vibration frequency. Fig. 1 shows an experimental unit schematic diagram with an ultrasonic phasing tester of micro motions 1 to identify vibration displacements, determined by the sounding signal speed and the researched magnetorheological damper deformations ratio 5-6-9 [1, 7, 8]. Piezoelectric transformers – radiating unit 2 and the acoustic oscillations receiver 4 are mounted on the console 8 and customized to mechanical and electrical resonance oscillations with a frequency of 30 kHz [1, 7, 8]. As shown in Fig. 1 the magnetorheological damper 5-6-9 with a cylindrical gaping comprises: coax internal surface of a brass wall tube, piston rod external surface 5, field magnet (FM) 6, the main and compensatory chambers volume of a piston type hydromount 9 with magnetorheological fluid (MF) [3]. With the help of an ultrasonic phasing tester the micro motions of the piston rod 5 at the load of 3 have been measured. In article [1] the linear dependence between the brass piston rod speed in the cylindrical gaping with magnetorheological fluid and the magnetic induction value has been identified (Fig. 2). Fig. 2 shown on the Y-axis the relaxation speed of the magnetic fluid in m/s, on X-axis - magnetic induction in T. The brass piston rod speed decreases after being removed from the magnetic field effect in the orthogonal magnetic field of the field magnet has not been recorded.
Fig. 2. The magnetorheological fluid relaxation speed from the orthogonal magnetic field initial induction.
In article [1] the ferrite and steel piston rod speed decreases has been identified after the magnetic field effect removal in the orthogonal magnetic field of the field magnet before and after transmission through their extremes. This result is explained by a magnetorheological effect and magnetorheological fluid relaxation after the magnetic field removal and the remanent magnetic induction of the field magnet leg [4, 5]. Increase speed of the steel piston rod is determined by the magnetorheological liquid rise of temperature (over 40°ɋ) in the cylindrical gaping [1, 2]. Fig. 2 shows relaxation rates of magnetorheological fluids in a transverse (1, 2, 3) and longitudinal (4) magnetic fields, depending on the magnetic field initial induction and the piston rod material. At impact loads the piston-rods speed is rapidly changed [6], and, when it becomes coordinate to the sounding signal propagation velocity, the reflected signal spectral structure is filled with high frequency harmonics, which are absent in the real process [1, 7, 8]. The method of the reflected signal processing should comprise the absolute error of measuring the boundary
397
398
B.А. Gordeev et al. / Procedia Technology 24 (2016) 394 – 398
displacement l(t) which equals '
[l (t ) R (t ) l (t )] l (t )
R (t ) 1 .
(2)
From (2), with a relative error
G
'l (t ) , l (t )
where ǻl(t) – measurement error. So, we get the following condition of quasi-static equation applicability '
R (t ) 1 d G ,
and for the second approximation l (t ) d cG .
As a result, for į = 10-2 we get that the vibrating boundary speed should not exceed the degree of 3 m/s when measured in the air. 3. Conclusion
The results of the work show that the phase measurement error and thus of the vibration displacement are determined by the sounding signal speeds ratio of and researched object deformations ratio – magnetorheological damper. In such cases when at impact loads the rod piston displacement speed exceeds 3 m/s, the reflected signal phase identification, as the informative parameter, is subject to increasing errors. Acknowledgements
R&D are carried out as a part of a state project in the sphere of scientific research ʋ8.2668.2014/Ʉ in Nizhny Novgorod State Technical University n.a. R.E. Alekseev. References [1] Gordeev BA, Maslov GV, Okhulkov SN, Osmekhin AN. On developing a magnetorheological transformer that operates in orthogonal magnetic fields. Journal of Machinery Manufacture and Reliability, vol. 43, no. 2, 2014. p. 15-21. [2] Gordeev BA, Bugaiskiy VV, Okhulkov SN, Osmekhin AN, Gorskov VP. Hydraulic fluid temperature influence on hydro pipe saddles dynamics. Vestnik mechanical engineering, no. 12, 2014. p. 22-26. [3] Gordeev BA, Erofeev VI, Sinev AV, Mugina OO. Vibration protection system with inertia and dissipation rheological fluids. Moscow: Fizmatlit; 2004. [4] Shulman ZP, Kordonskii VI. The magnetorheological effect. Minsk: Science and Technology; 1982. [5] Gordeev BA, Okhulkov SN, Plekhov AS, Titov DYu, Gorskov VP. Flow and relaxation magnetorheological fluid in the throttle channels of hydraulic support. Vestnik mechanical engineering, no. 7, 2015. p. 59-63. [6] Gordeev BA, Okhulkov SN, Plekhov AS, Zlobin PA. Application of magneto-rheological fluids in mechanical engineering. Privolzhsky Scientific Journal, no. 4, 2014. p. 29-41. [7] Gordeev BA, Kuklina IG, Osmekhin AN. Optimization of measurement of construction vibration parameters by acoustic methods. Privolzhsky Scientific Journal, no. 2, 2009. p. 13-20. [8] Gordeev BA, Kuklina IG, Golubeva KV, Gordeev AB. Ultrasonic phase vibrotransducer. Russia Patent 2 472 109, Jul. 18, 2012.