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

1

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, sharanas17@yahoo.co.in

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: sharanas17@yahoo.co.in

Original Paper

2

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,

3

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)

4

(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

5

(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)

6

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= += += += +

7

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.

8

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

9

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.

10

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.

11

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.

12

Nomenclature

REFRENCES

[1] Chang SO, Lee JK. “The design of a real-time simulator on the hydraulic servo system”. Int. J Korean Soc Precision Eng 2003;4(1):9–14.

[2] Cho SK, Lee H-H. “A fuzzy-logic antiswing controller for three-dimensional overhead cranes”. ISA Trans 2002; 41(2):235–43

[3] Davliakos I, Papadopoulos E. “Model-based control of a 6-dof electrohydraulic Stewart–Gough platform”. Mech Theory 2008;43(11):1385–400

[4] Zhao, C., Gao, K., Liu, X.,Wen, B.,. Control of electrohydraulic servo system for a material test system using fuzzy neural network. In: Proceedings of the world congress on intelligent control and automation (WCICA). Proceedings of the 7th world congress on intelligent control and automation, 2008;. 9351–9355.

[5] Barai RK, Nonami K. “Optimal two-degree-of-freedom fuzzy control for locomotion control of a hydraulically actuated hexapod robot”. Inform Sci 2007; 177(8):1892–915.

[6] Maskrey, R. H. and Thayer, W. J. A brief history of electrohydraulic servomechanisms. Moog Tech.Bull., 1978, 141, 110–116.

[7] Merritt, H. “Hydraulic Control Systems”, John Wiley & Sons, New York (1967.

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

13

[8] Watton, J . “Fluid Power Systems: Modeling, Simulation, Analog and Microcomputer Control”, Prentice Hall International Ltd. UK, 1989.

[9] Lee, S., J.F. Blackburn, “Contribution to Hydraulic Control-1 Steady-State Axial Forces on Control-valve Pistons”. Transactions of the ASME, 1952, pp 1005-1011 Cambridge, and Mass

[10] Arafa, H. A. and Rizk, M. “Identification and Modelling of Some Electrohydraulic Servo-Valve Non- Linearities”. Proceedings of the Institution of Mechanical Engineers, Part C: Mechanical Engi-neering Science (1987), vol. 201, no. 2, pp. 137-144.

[11] Fussell, B., Darwin, J., Prina S. “Servovalve Torque Motor Analysis, Electrical Insulation Conference/Electrical Manufacturing & Coil Winding “Expo, 1999

[12] Li Songjing, Jiang Dan, Xu Benzhou, Sheng Xiaowei. “3D Magnetic Field Analysis of Hydraulic Servovalve Torque Motor with Magnetic Fluid”. IEEE Electrical Machines and Systems; Vol 3; pp 2447 – 2450

[13] Urata. “On the Torque Generated in a Servovalve Torque Motor using Permanent Magnet”. IMechE 2007, Vol 221, pp 519-526.

[14] Wei Bao “Characteristics Analysis of Hydraulic Servo-Valve Torque Motor Using Magnetic Fluid” ASME Conference DETC2005-84704 pp. 151-158