numerical analysis on torque motor dynamics used in
TRANSCRIPT
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The 11th Asian International Conference on Fluid Machinery and Paper ID: AICFM_FP_009 The 3rd Fluid Power Technology Exhibition November 21-23, 2011, IIT Madras, Chennai, India
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Numerical Analysis on Torque Motor Dynamics used in Electrohydraulic Servovalve
A. S. Sharan1 Somashekhar S. Hiremath2 and C. S. Venkatesh3
1 Department of Mechanical Engineering, BIET, Davangere
2 Department of Mechanical Engineering, IIT Madras
3 Department of Mechanical Engineering, UBDTCE, Davangere
Davangere -577004, Karnataka state, [email protected]
Abstract
Servovalves are one of the most important electrohydraulic system components that used for controlling the flow
direction, volume flow rate, force, pressure, position, speed and acceleration. The electrohydraulic Servovalves have
two stages-first-stage includes a torque motor assembly and second-stage is spool valve. The torque motor is an
electromechanical transducer used to convert small electric current to a mechanical torque to deflect either a flapper
in case of a flapper nozzle valve and a jet pipe in case of a jet pipe servovalve. The dynamics of torque motor plays a
crucial role in creating the differential pressure across the spool valve. Hence it is essential to understand torque
motor dynamics. The torque motor generally consists of armature, armature coils, permanent magnet, and flapper or
jet pipe. The armature is pivoted in between the two permanent magnets. The working clearance (air gap) is
provided for the armature deflection is the main parameter in the dynamics. The mathematical model is available in
many text books like Merritt, Watton and Blackburn. Also some of the literatures were also available in modeling
the torque motor. In the present paper the mathematical model of torque motor proposed by many researchers were
considered to analyse the torque motor dynamics and to investigate the influence of magnetic fluids on the dynamic
characteristics. The results include variation of torque and jet pipe deflection with input current and discuss the time
and frequency response of the torque motor.
Keywords: servovalve; torque motor, air gap; flux density, magnetic fluid; torque motor dynamics.
Accepted for publication (Paper ID: AICFM_FP_009)
Corresponding author: A. S. Sharan, Department of Mechanical Engineering, BIET Email: [email protected]
Original Paper
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1. Introduction
The control of electrohydraulic systems has drawing many attentions from researchers for many years. The
electrohydraulic systems are considered for testing the performance of newly developed control techniques since
their highly nonlinear characteristics. Also, electrohydraulic components are commonly used in many engineering
applications [1–5]. Servovalves are manufactured with very narrow tolerances, thus the cost and significance of
Servovalves are higher compared to other electrohydraulic system components. Servo valves include single-,
double-, and triple stage valves; two-staged servo valves are most commonly used. In a two-staged servo valve, the
first stage transfers electric input to mechanical displacement of a pilot stage valve; the second stage is a spool valve
or other fluid control element. Commonly known pilot stage valves are nozzle–flapper valve and jet pipe valves [6].
Servovalves are used in control applications where precision and reliability has greater importance such as planes,
space vehicles, CNC tools, special test machines, motion simulators, military equipments
The electrohydraulic servovalve is a mechatronic component .A mechatronic system is a mixed and multi-domain
system, different components or parts of which fall within different domains such as mechanical, electrical,
hydraulic and control. The servovalve comprises of first stage electronic part (torque motor) and second stage
hydraulic part. The electro-magnet torque motor is used as the driving part in hydraulic servo valve. By using
torque motor the information could be transduced, generated and processed more easily than as with pure
mechanical/ fluid signals. Torque motor is an electro-mechanical transducer; it converts the input electrical energy
into the mechanical output. The versatility of torque motor makes electrohydraulic servovalve as an ideal element
for signal amplification and manipulation. For torque motors using permanent magnets, Merritt Watton and
Blackburn [7, 8& 9] developed a theory that has been widely distributed and followed by authors of books and
research papers. Arafa and Rizk made a special review on torque caused by electromagnetic forces. A nonlinear
mathematical model based on physical quantities was developed in [10]. This model includes non-linear relations
for the torque motor dynamics. From the experimental data and FEA analysis performed in [11], Fussell et al. state
that magnetic flux leakage must be considered in the lumped model for torque predictions. Li Songjing [12] has
conducted the study on 3-Dimentional magnetic field analysis of torque motor with and without magnetic fluid. The
torque increases linearly with increase in the current input. The magnetic fluid can increase the effect of the
magnetic circuit and improve the characteristics of torque when it is filled in the working clearances of the torque
motor. E Urata [13] has developed a theory for mathematical model of torque motor. The magnetic reluctance and
flux leakage in the torque motor were taken into account, which was ignored in the Merritt model. The results
obtained from the mathematical model matches closely with the experimental results. The author further explains
the affect of the torque due to unequal air gap which are induced at the time of production process. Wie Bao [14] has
worked on the magnetic fluids. Magnetic fluids can introduce a damping force to a hydraulic servo-valve Torque
Motor. According to their analysis and experimental results, magnetic fluids can be used to increase the stability of a
torque Motor and a Hydraulic servovalve. In the present work torque motor is modeled in detail for analyzing the
magnetic field and output torque. The objectives of the work is to compare the time response of the torque motor,
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by comparing the different mathematical expressions proposed by various investigators and also to reveal the
dynamic characteristics of torque motor, with and without magnetic fluid.
2. Working Principle of Torque Motor
The torque motor has an armature mounted on a torsion pivot spring and is suspended in the air gaps of a magnetic
field (Fig1). The two pole pieces, one polarized north and the other south by the permanent magnets, form the
framework around the armature and provide paths for magnetic flux flow. When current flows through the coils, the
armature becomes polarized and each end is attracted to one pole piece and repelled by the other (Fig 2). The torque
exerted on the armature is restrained by the torsion spring upon which the armature is mounted.
Fig. 1 Neutral Position of torque motor Fig. 2 Energized Position of torque motor
Fig. 1 Neutral Position of torque motor Fig. 2 Energized Position of torque motor
The rotational torque created is directly proportional to the amount of polarization or magnetic charge of the
armature - increased armature polarization creates a higher force attraction to the pole pieces. Since the amount of
polarization of the armature is proportional to the magnetic flux created by the current through the coils, torque
output of the torque motor is proportional to the coil input current. The magnetic flux created by the coils is
dependent on two factors: the number of coil wire turns and the strength of current that is applied. In other words,
the torque of the motor is dependent on the ampere-turns applied. When armature polarization is reversed by input
current polarity, the armature is attracted to the opposite pole pieces and the jet deflects to the opposite receiver.
The dynamic response of a torque motor can be analyzed both in time domain and frequency domain. Both domains
are used in the present work. The model presented by Merritt is summarized below
The voltage equations for each coil circuit are
(1)
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(2)
Subtracting equation 1 from 2 results in
(3)
It is assumed that the four air gaps constitute the dominant reluctances in the circuit, i.e. the reluctances of magnetic
materials are negligible in comparison. Based on symmetry, the reluctances of diagonally opposite air gaps are equal
and therefore given by
Fig. 3 Schematic of magnetic flux paths in Torque motor
(4&5) (4&5)
The Fundamental force equation is
(6)
Because the torques developed in the two air gaps at each end of the armature are in opposition, the net torque
developed will be proportional to the difference of the squares of the fluxes. Hence the total net torque developed on
the armature is
(7)
In order to simplify the simulation and analysis of a servo-valve torque motor, torque calculation equation is usually
liberalized to be
(8)
The dynamics equation of the armature is given
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(9)
3.0 Torque Motor with Magnetic Fluid
As a magnetic fluid shows higher saturation magnetization and larger viscosity when it is exposed to the magnetic
field inside the working gaps of the torque motor, forces will be introduced by the magnetic fluid on the armature.
There are two methods for magnetic fluids to be filled inside the gaps in accordance with different applications. If
larger damping forces due to magnetic fluids are needed, magnetic fluids should be filled as shown in Fig. 3. If only
resistances due to magnetic fluids on the armature are needed rather than damping forces, magnetic fluids can only
be filled inside the gaps without surrounding the armature. In this application, less amount of magnetic fluids are
needed. The cross section of a torque motor with magnetic fluids surrounding the end of armature is shown fig.4.
In order to investigate the torque motor dynamics in the presence of the magnetic fluid, the viscosity forces and
forces due to magnetization of the magnetic fluid studied in detail are given below.
3.1 Forces due to the viscosity of the magnetic fluids
The cross-section of an armature along the magnetic flux inside the air gaps is surrounded by magnetic fluids is
assumed to be uniformly distributed, as shown in Fig. 3, The viscosity of the magnetic fluid exerts forces of the
armature in its operation. The force on the armature due to the viscosity of magnetic fluids is shown in Fig. 4.
Fig. 3 Forces on the armature of the torque motor Fig. 4 Force due to the viscosity of magnetic fluids due to magnetic fluids
3.2 Forces due to the magnetization of magnetic fluids
When magnetic fluids are exposed to the magnetic field inside the working gaps, magnetization of magnetic fluids
works as stresses on the armature [9]. The stress on the armature developed by magnetic fluids can be written
(10) The resistance acting on the armature due to the magnetization of magnetic fluids can be calculated as
(11)
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3.3 Torque due to magnetic fluids
The torque developed on the armature due to the magnetization of magnetic fluids can be calculated as
(12)
(13)
The total load torque due to magnetic fluids
(14)
Taking into account expressions for electromagnetic forces in torque motor air gaps, where expressions for magnetic
fluxes in air gaps (obtained using the first and the second Kirchhoff’s' laws for magnetic circuits) is implemented
torque produced on armature can be calculated using (in the case of parallel coil connection):
(15)
Where Permanent Magnet Magneto-Motive force is
(16)
Linearising Eq. 15 about the null position (i = 0 and θ = 0) one can write
(17)
Where (18 &19)
d 1 2T K i K∆ θ= += += += +
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4.0 Results and discussion
Fig. 5 Variation of torque with current (Merritt) Fig. 6 Variation of Jet pipe deflection with current
The torque and the Jet pipe deflection obtained for varied current is shown in Fig. 5&6. The torque increases linearly
with increase in current. The obtained torque is a function of torque constant and spring constant of the torque
motor. The jet pipe deflection had a linear relationship with the input current. The maximum torque is 1.0 Nm and
deflection of 0.02 rad for maximum current of 1.0 mA .The stiffness of the flexural tube has a major impact on the
deflection.
Fig. 9 Variation of torque with current Fig. 10 variation of jet pipe deflection with current
The Fig 7& 8 shows the variation of torque and jet pipe deflection for varied input current. The maximum torque
obtained from Arafa proposed model is 0.2 Nm and comparatively very less compared that of the Merritt model.
This is due to the fact that the armature fully saturates at relatively high current and the total magnetic flux through it
will become constant. The torque will be proportional to the jet pipe deflection in which the stiffness of the flexure
tube will have the negative effect from magnetic torque gradient on the armature. The maximum deflection of the jet
pipe is 0.05 rad.
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Fig.11 Variation of torque with current (E.Urata) Fig. 12 variation of jet pipe deflection with current
Fig 11 &12 shows the variation of torque and Jet pipe deflection with varied input current for mathematical model
Proposed by E.urata. The initial torque is 0.18 N-m for zero current and zero deflection for zero current .The models
incorporates the effect of magnetic reluctance and flux leakage through the air gap. The jet pipe deflection is
maximum of 0.2 rad for input current of 1.0 mA.
4.1 Time response
The response of the system for a step input according Merritt model with magnetic fluid is shown in Fig 13 &14. It
can be seen that the resultant system response is oscillatory with decreasing amplitude. The transient response of the
system will die out after a time interval of 0.09 seconds. The peak amplitude was found to be 0.192 and reduced to
0.167 with introduction of magnetic fluid. The peak overshoot was reduced from 97% to 71.2% for the same time
of 0.0005 seconds.
Fig. 13 Step response of torque motor (Merritt) Fig. 14 Step response of torque motor with magnetic fluid
The response of the system for a step input according Urata model and also with magnetic fluid is shown in Fig. 15
&16. By introducing the magnetic fluid the peak amplitude was reduced from 0.109 to 0.935. The overshoot was
also reduced from 97.1% to 68.95% at the time of 0.0005 seconds. The rise time was increased from 0.00167 to
0.00183 seconds
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Fig. 15 Step response of torque motor (E.Urata) Fig. 16 Step response of torque motor with magnetic fluid
Fig. 17 Impulse response of torque motor (Merritt) Fig. 18 Impulse response of torque motor with magnetic Fluid
The response of the system for a impulse input according Merritt model and also with magnetic fluid is shown in Fig
17 &18. The amplitude was found to be decreased from 572 to 493 at time of 0.0002 seconds this is due to magnetic
fluid effect. By introducing the magnetic fluid the settling time was reduced from 0.0067 to 0.0061 seconds
The response of the system for a impulse input according reluctance induced model and also with magnetic fluid is
discussed below. The peak amplitude of the response was found to reduce from 342 to 297 at time of 0.002 seconds
is shown in fig 19& 20. This is due to introduction of magnetic fluid in the Urata model. The settling time was also
improved from 0.0068 to 0.00663 seconds. The magnitude of the vibration is also found to be much effected in the
model. The magnitude of vibration due to impulse input was found to be decreased compared to the Merritt model.
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Fig. 19 Impulse response of torque motor (E. Urata) Fig. 20 Impulse response of torque motor with magnetic fluid
4.2 Frequency response
Fig. 21 Dynamic charactertics of torque motor Fig. 22 Dynamic charactertics of torque Motor (with magnetic
fluid)
The dynamic charactertics of the torque motor with magnetic fluid are expressed in Bode plots as shown in Fig
(21&22). It is clearly evident from the figure that magnitude of the vibration has been reduced from 14 db at a
frequency of 5.96 *103 to -6.83 db at a frequency of 5.89 *103 due to the presence of magnetic fluid in the air gaps.
This shows that magnetic fluids are inducing the damping force on the motion of the armature.
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Fig. 23 Dynamic charactertics of torque motor Fig. 24 Dynamic charactertics of torque Motor (with magnetic fluid)
The Bode plot for the torque motor for the model proposed by E.Urata is as shown in Fig.23&24. It can be seen
from the figure that maximum magnitude of the figure is 12.6dB. The phase margin is equal to 200 and gain cross
over frequency is equal to 6.48×103 rad/s. By introduction of magnetic fluid in the torque motor the -6.83 at 5.89
×103 rad/s.
5. Conclusions
In the present work an attempt has been made to study the dynamics of the torque motor by considering the
mathematical models proposed by different authors. The dynamics of torque motor used in jet pipe electrohydraulic
servovalve is studied by comparing the time and frequency responses. The torque generated and deflections were
plotted for varied current input. The torque varies from 0.2 Nm to 1.0 Nm for the current of 1.0mA. The maximum
jet pipe deflection varies from 0.05 to 0.2 rad for the current of 1.0mA. The dynamic characteristics of a hydraulic
servo-valve can be improved due to the application of magnetic fluids. The resonance frequency of a hydraulic
torque motor was found to be 900Hz and the magnitude of the vibration was found to be14 db. The Magnetic fluids
can be used to increase the stability of a torque motor and a hydraulic servo-valve. The magnitude of vibration was -
6.83 db. The operating band width was also improved. But, at the same time, the amplitude of the rotation angle of
the torque motor may also be reduced slightly. Therefore care must be taken when different types of magnetic fluids
are selected for the application.
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Nomenclature
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RP Resistance of each coil, 100 ohms Ms Saturation magnetization of magnetic fluid 0.04 (T)
N Number of turns in each coil 4400
Viscosity of magnetic fluid 3.0 (Pa s)
d
dt
φ Total magnetic flux through the armature, lines
M1 permanent magnet magneto motive force 586 A
rp Internal resistance (plate resistance) of
amplifier in each coil circuit,
K1 Torque constant of the torque motor 1.21 (N m/A)
Ebb Constant voltage required for quiescent current,
K2 torque motor electromagnetic spring constant 2.42(N m/rad)
Zp Impedance in common line of coils, r Distance from armature pivot to the centre of permanent magnet pole face, 14.5⋅10-3 m
R1 Reluctance of gaps 1 and 3, amp-turn/line xp0 Length of each air gap at null, 0.45⋅10-3 m R2 Reluctance of gaps 2 and 4, amp turn/line Ap torque motor gap area 9·10-6 m2
g Length of air gap at neutral, 1 mm kr Magnetic reluctance constant 0.465 x Displacement of the armature tip from the
neutral position, m µo Permeability of free space 4п x10-7 H/m
Ag Pole face area at the gaps, 3.9 * 3 mm2 JL Jet pipe length 0.0277m µo Permeability of free space (air) B Flux density in the air 0.66 (Wb/m2) F Attractive force between magnetized parallel
surfaces separated by an air gap, K t Torque constant of the torque motor
1.0(N m/A) φ Magnetic flux in the air gap Km Mechanical torsion spring constant of
spring pipe 1.615 (Nm/rad) A Area normal to flux path, m2 Ka Magnetic spring constant 1.536 (N m/rad)
mfη
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