Paper received: 21.01.2008 Paper accepted: 25.09.2008
Effects of the Variation of Torque Motor Parameters on Servovalve Performance
Dušan Gordic- Milun Babic - Nebojša Jovičic - Dobrica Milovanovic University of Kragujevac, Faculty of Mechanical Engineering in Kragujevac, Serbia
An electrohydraulic servovalve is an essential item of fluid power servomechanism where fast response, high power output and working fidelity are necessary. Based on detailed and experimentally verified mathematical model of two-stage spool position mechanical feedback electrohydraulic servovalves sensitivity analysis has been performed. The effects of variation of few torque motor electromagnetic parameters (air-gap length (thickness) at null, residual magnetic flux density (magnetic inductivity) of permanent magnet and number of turns of each coil) on dynamic performance of B.31.210.12.1000. U2V PPT servovalve have been studied. Obtained results are in accordance with servovalve engineering design practice. © 2008 Journal of Mechanical Engineering. All rights reserved. Keywords: electrohidraulics, servovalves, torque motors, sensitivity analysis
0 INTRODUCTION
Two-stage spool position feedback electrohydraulic servovalves with the torque motor as an electromechanical converter and a flapper-nozzle valve as the first stage of hydraulic amplification are the most utilised servovalves in electrohydraulic control systems for the last forty years. In spite of their relatively long period of application, all phenomena associated with their operation are not completely quantitatively and qualitatively explained. This is due to facts that a relatively complex mathematical apparatus, coming from fundamental laws of electromagnetism, fluid mechanics and general mechanics, is needed for describing their operation. Beside, these mathematical expressions include many parameters that are very difficult to precisely quantify.
In this paper authors study the influence of torque motor electromagnetic parameters on servovalve behaviour. Many authors gave contributions to the explanation of electromagnetic nature of servovalve torque motors. Still Merritt [1] explained in detail the effects of some non-linearities on the servovalve behaviour including torque motor non-linearities (magnetic hysteresis and saturation). In the paper [2], Arafa and Rizk made a special review on torque caused by electromagnetic forces. A nonlinear mathematical model based on physical quantities was developed in [3]. This model includes non-linear relations for the torque motor
dynamics. From the experimental data and FEA analysis performed in [4], Fussell et al. state that magnetic flux leakage must be considered in the lumped model for torque predictions. In [5] and [6], Urata analysed the torque motor dynamics in detail and influence of unequal air-gap length thickness in null in servo valve torque motors.
PI R 2
Fig. 1. Two-stage spool position feedback electrohydraulic servovalve (mechanical feedback) 1 - torque motor, 2 - first stage, 3 -second stage, 4 - feedback spring
1 THEORETICAL MODEL
Detailed theoretical model should be used in order to investigate the influence of torque motor electro-magnetic parameters on servovalve behaviour. It should include all physical phenomena and torque motor parameters that are
*Corr. Author's Address: University of Kragujevac, Faculty of Mechanical Engineering, Sestre Janjic 6,
34000 Kragujevac, Serbia, gordic@kg.ac.yu
expected to be of influence on behaviour of analysed servovalves.
1.1 Torque Motor
When current is made to flow through torque motor coils, armature ends become polarised. A torque is thus produced on the armature which starts to move. It is common in practice, as it was proved in [7], to use the linear expression to calculate this torque:
Te = Ki + Km0,	(1)
where values for Ki and Km are obtained experimentally.
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 Kirchhoffs' laws for magnetic circuits) are implemented torque produced on armature can be calculated using (in the case of parallel coil connection):
T =
r 'Mo ■ 4
>0
Mm + N^i xp° ;
Mm — + N (1 + kr)i
~p0
(2)
1 -
f a V
r ■ a
v V ;
+k
where permanent magnet magnetomotive force is:
l B 1
m rm -.	(3)
M m =-
Mm
Linearising Eq. 2 about the null position (i = 0 and 6 = 0) one can write:
K =
Nr MoAp Mm
Km =-
Xp20 (1 + kr )
2mOA Mm
>0
(1 + kr ))
(4)
(5)
Magnetic reluctance constant kr considers influences of permanent magnet reluctance, the non-uniformity of a magnetic field through the permanent magnet volume, reduction of the magnetic field in the permanent magnet due to influences of end poles and the leakage flux in air gaps, as it was described in [5]. Following
expressions should be used for its calculation:
R„„ 1
K =■
Rmp0 Kl
where
R„„ =-
lm J_
An Mm km
■^mp0
>0
(7)
(8)
o
	
	
o
Fig. 2. Calculation of torque caused by electromagnetic forces in the torque motor: a) neutral, b) current runs through coils
1.2 Other Parts of the Servovalve
Only final equations of the model are presented in this paper for the reference. Presented equations are related to two-stage electrohydraulic servovalves with mechanical feedback. Detailed explanation of formulae can be found in [8] AND [9].
As long as the flapper does not hit a nozzle, armature dynamics can be described with:
3
Te = J a 9+ Kd+ Tt + Fh /a + Tf ,
where:
/a = f -
(9)
(10)
The torque caused by flexure tube deformation can be written as:
B
T = f	(11)
lt
Flow force on the flapper is given by:
Fh =() - Pr ) + 8n
[^i2 (X0 -X)) (P -Pd) -Kl (X0 +X)) )Pr -Pd )] where flapper tip displacement is:
x = 61 - F,
( 13
3 A
v 3BS 1)Bt ,
(12)
(13)
-►
Fig. 3. Schematic of the servovalve with the parameters of its other parts
The torque caused by feedback spring deformation can be calculated with:
T = F/
If	f f 5
where the appropriate force is:
f	0	\y+yff| < z
Ff =
Kf [y+yff - z sgn(y+yff)]y+yff\>
where:
yff = x+fv-
(14)
(15)
(16)
<p = i
F /2 1 hf
' 2B„
Pressures in flapper-nozzle valve can be obtained using:
Pl =
a2Ps + b Pd + d2 (b2 - a2 ) a2 + b2 (a2 + b2 )2
2abd
-V(a2 + b2)(Ps - Pd) - d2
(18)
(a2 + b2 )2
a2Ps + c2Pd + d2 (c2 - a2 ) a2 + c2 (a2 + c2 )2
2acd (a2 + c2 )2
Pr =-
■\J(a2 + c2)(Ps - Pd) - d2
[(X0 - XVPl - Pd +(X0 + XWPr - Pd ]Kn0dn "
\2 ^ d^n 2 I- vd
~ =	pPd-P0 +pPd
\P 4	p

(19)
(20)
where:
a = Ko0 o
d> 2
4 \p
b = Kn0dnn(X0 - X\lp
2
c = Kn0dn^( X0 + X) —
V P
A d]n . d = y. 4
(21) (22)
(23)
(24)
Algorithm for the calculation of flow coefficients can be found in [8].
The differential equation of spool motion can be written as:
d2 n
¿P-J- = y + K y + Fc + Fa + Ff, (25)
where:
AP = Pl - Pr.	(26)
Dry friction force can be presented as:
Fcnsgn (y)'	y * 0-
F =
where:
Z- \A < Fc0
Fc 0 sgn(Z ), ¡Z| > Fc 0
y = 0,
z = APdT-F - Ff
(28)
In the case of the null lap condition for all four symmetrical and matched spool orifices of no-load servovalve, the following expression can be used for the axial component of the flow force:
K 2
Fa = 2KT f y>C0Sa(Ps + Po ) +
(29)
+(l2 - li)K^2 p(ps - p0) f & where the real value of spool valve opening is:
yi = +rs + rb)2 +(y| + rs + rb)2 -(rs + rb). (30)
Numerical data from Dong and Ueno are used for the calculation of jet angle, contraction coefficient and flow coefficient [8].
The volumetric flow through the servovalve can be mathematically formulated as:
0SV = (K,jyJPf^ - Ql)sgn(y). (31)
V P ' 2
where the internal leakage flow can be calculated from:
when y j Q,:
? • Q2 = ^
when l^-l • Qi < lyl < yti :
s j y1/2 • Qi3/2 = E^
(32-a)
and when |y| > yti :
sy1/2Qi3/2 + - -yi )Q = ^^ where
(32-b)
(32-c)
? =
0.5p
K2f2 (J \+rs + rb ) + (rs + rb)2 - rs - rf' (33)
23(pn)17 2
f 3 / 2 / 2 '
12n
v =—r , fS3 '
(34)
(35)
yti =
0.075SQj
7idsv
2 EXPERIMENTAL VERIFICATION
(36)
The presented model was numerically solved and verified with experimental results for no-load servovalve B.31.210.12.1000.U2V -manufactured by PPT- Trstenik, Serbia (Fig. 4 and Fig. 5).
3 2
.13 1
jg
" 0
>
-2 -3
	» \				1 i		= ± 25% imax		
	/iff ■w / i t								
	ni f ! ! 1 'f					i	= ± 10%		max
							i = ± 5% i max		
Cr* ""fr1 y/i									
									
									
									
						_ _ _ experiment - simulation J			
/ Ps=210 bar									
									
0 2 4 6 8 10 12 14 16 18 20
t [ms]
Fig. 4. The transient response of the servovalve (square periodic input current signal - 10 Hz frequency)
Oi
p =210 bar									
t	s -								
									
									
									
									
									
									
									
,-------					----		experiment simulation J		
									
									
-10 -8 -6 -4 -2 0 2 4 6 8 10
i [mA]
Fig. 5. The static flow characteristic of the servovalve
Parameter values of the servovalve are presented in nomenclature (in brackets). The manufacturer of permanent magnet provided values of parameters related to permanent magnet except its geometrical parameters, whereas values of constants related to permanent magnet and the
2
s
s =
torque motor were calculated according to the procedure described in [5]. The friction coefficients were estimated to match the appropriate experimental transient responses. Values for other parameters were determined with a direct measurement on the disassembled servovalve. The equilibrium distance from the flapper tip to nozzles is an exception from this rule. It was calculated according to the assemblage requirement, which demands that pressures in both nozzles should be 70 bar when the supply pressure is 140 bar and when the flapper is in the zero position.
Static and dynamic experimental analyses of the servovalve were performed on the standard servovalve testing equipment, property of PPT (static - MOOG - Plotterstand D046-030, dynamic - MOOG - Frequenzgang - Pruefstand D046032).
The model satisfactory agrees with the experiment and it can be used for the sensitivity analysis.
3 SENSITIVITY ANALYSIS
Torque motor parameters relate to its electromagnetic nature are length of each air gap at null xp0, permanent magnet cross sectional area Am, torque motor gap area Ap, magnetic flux density of permanent magnet Br m, permanent magnet length lm, number of turns of each coil N, distance from armature pivot to the centre of permanent magnet pole face r and permanent magnet permeability /
lm =11.445 mm
-i-im-=i0v9 iffl-
s
s 3
> M
O}
0 2 4 6 8 10 12 14 16 18 20 t [ms]
Fig. 6. The effect of the variation ofpermanent magnet length on servovalve performance
In order to analyse the influence of torque motor parameters on servovalve characteristics, the transient responses for step input current signal (from 0 to steady regimes determined with two input current signals i - 10% and 25% of the rated imax) were numerically modelled. Three different values for the analysed parameters were taken in numerical modelling: value of the analysed servovalve, one higher and one smaller value. Results of the modelling are shown in Fig. 6 to 12.
S3
I 3
J?2
0
0 2 4 6 8 10 12 14 16 18 20 t [ms]
Fig. 7. The effect of the variation of distance from armature pivot to the centre of permanent magnet pole face on servovalve performance
2
>
m ^ „
			X	P0	0.44	mm	\		
				X	P0 =	0.45 mm		ti	
			XP0	=0.46 mm					
				XP0 "	0.44 mm				
			---	---	f		^25%'imax) = 10%-imax J		
	:po "	■p0 =0.45 mr =0.46 mm			n	--			
0 2 4 6 8 10 12 14 16 18 20 t [ms]
Fig. 8. The effect of the variation of air-gap length at null on servovalve performance
It can be noticed on diagrams that the increase (decrease) of xp0 generates the same effects as the decrease (increase) of other analysed parameters.
Analysing the influence of torque motor geometric parameters one can conclude that
5
4
5
4
3
5
4
2
length parameters (lm, r, xp0) have greater influence on transient response then areas (Am, Ap). Variation of Am has bigger influence then variation of Ap.
It is especially important to analyse the effects of variation of xp0, Br m and N on servovalve performance. These three parameters can be easily modified when a designer wants to change the characteristics of an existing servovalve.
ö
J3 3
^ 2 O}
Am=162.41
i n-6 2
10 i m
Am=l5468-4o:6m2
-- ; -6 2 Am=146.95. 10 6 m2
1
'	- i=25%'imax
iAm=i46.95- i0-6 m2
— i = 10%-L
0 2 4 6 8 10 12 14 16 18 20 t [ms]
Fig. 9. The effect of the variation ofpermanent magnet cross sectional area at zero on servovalve performance
Ö
Ls 3
So 2
O}
				=9.9	• 10-6 n		2 i • 10	6	;
					p			m	
									
				-6	AP 2	=8.	1 • 1	0-6 m -6	2
if A		=9	• 10	m	A	9 =9p	.9 •	106	m
	h =	U •	10-6	2 m	v		25%-imax = 10%'imax		
0 2 4 6 8 10 12 14 16 18 20 t [ms]
Fig. 10. The effect of the variation of torque motor gap area on servovalve performance
The change of air-gap length at null xp0 has the greatest influence on the quality of transient response and steady values of the servovalve flow (Fig 8.). Small reduction of xp0 value (by 2 %) induce the decrease of rise time and existence (for i=10%-imax) i.e. the increase of overshoot (for
i=25%-imax) and finally higher the stationary value of servovalve flow. If the xp0 has higher value then the transient response becomes more sluggish and stationary value of servovalve flow is being reduced.
With smaller changes for the same percentage variation of parameter value, similar trend can be noticed in Fig. 11 where the value of residual magnetic flux density is changed.
> m
C^ 2
0 2 4 6 8 10 12 14 16 18 20 t [ms]
Fig. 11. The effect of the variation of residual magnetic flux density on servovalve performance
The change of number of turns of each coil N does not have influence on the quality of transient response. It only has small influence on the steady value of servovalve flow.
ö
J3 3
£ 2 O}
									
			N	=3/00		N =	5625		
		i	N =3	550					
/	N--	N =35;		/ N	=3	/00			
			=3 0	625		— i i	25 %-imax = 10%"imax J		
0 2 4 6 8 10 12 14 16 18 20 t [ms]
Fig. 12. The effect of the variation of number of turns of each coil on servovalve performance
3 CONCLUSION
Standard engineering practice considers that if servovalve designers want to redesign
5
5
4
4
3
5
5
4
4
existing or design a new servovalve they must modify some properties on physical object and then experimentally verify the results of this action. The model presented in the paper primarily gives a useful design tool, since all its parameters are physical quantities. When servovalve designers have such developed model that includes phenomena and parameters of influence and can predict their performance in a wide range of expected regimes, they can simply redesign existing servovalves without physical modification. They can numerically model all possible situations and choose results that are appropriate for their needs.
Using the detailed servovalve mathematical model authors analysed the influence of torque motor electromagnetic parameters. The analysis showed that the biggest influence on servovalve dynamic characteristics has variation of air-gap length at zero, although the influence of other parameters can not be neglected. Similar analysis can be performed for other servovalve parameters.
4 NOMENCLATURE
Am	permanent magnet cross sectional	[m2]
	area (154.68-10-6)	
Ap	torque motor gap area (9-10-6)	[m2]
Bfi	flapper bending rigidity (0.0256)	[Nm2
Bt	flexure tube rigidity (0.0302)	[Nm2
Br m	magnetic flux density of	[T]
	permanent magnet	
dn	nozzle diameter (0.28-10-3)	[m]
do	left (right) constant orifice	[m]
	diameter (0.18-10-3)	
dod	drain constant orifice diameter	[m]
	(0.4-10-3)	
ds	spool diameter (4.62-10-3)	[m]
f	spool valve area gradient	[m]
	(4.8-10-3)	
Fa	axial component of flow force on	[N]
	spool	
Fc	dry friction force on spool	[N]
Fco	initial dry friction force on spool	[N]
	(3.2-10-3)	
F 1 cn	nominal dry friction force on	[N]
	spool (2.2-10-3)	
Ff	force caused by mutual action of	[N]
	feedback spring and spool	
Fh	flow force on flapper	[N]
i	total current	[A]
imax	rate input current (10-10-3)	[A]
Ja	armature assembly moment of inertia with the respect of rotational centre (1.68-10-7)	[kgm2]
Kc	contraction coefficient of spool orifice	[-]
Kf	feedback spring stiffness (1962)	[N/m]
K	torque motor gain	[Nm/A]
kl	constant of leakage flux in air gap (0.27)	[-]
km	constant caused by the non-uniformity of magnetic field in permanent magnet (2.42)	[-]
Km	torque motor electromagnetic spring constant	[Nm]
kn	spool viscous friction coefficient (3800)	[kg/s]
Knl	flow coefficient of the left flapper-nozzle restriction	[-]
Knr	flow coefficient of the right flapper-nozzle restriction	[-]
Kn0	flow coefficient of the flapper-nozzle restrictions at zero	[-]
Kod	flow coefficient of the drain constant orifice	[-]
Ko0	flow coefficient of the left/right constant orifice an zero	[-]
kr	magnetic reluctance constant (0.465)	[-]
Kt	flow coefficient of spool orifice	[-]
kv	armature assembly viscous friction coefficient (4-10-4)	[Nms]
ii	axial length between supply and actuator ports (5.4-10-3)	[m]
l2	axial length between reservoir and actuator ports (9.2-10-3)	[m]
la	distance from the nozzle axis of symmetry to the axis of rotation of armature assembly (8.75-10-3)	[m]
if	feedback spring length (13.3-10-3)	[m]
lfl	flapper length (13-10-3)	[m]
lm	permanent magnet length (10.9-10-3)	[m]
lt	flexure tube length (8.5-10-3)	[m]
Mm	permanent magnet magnetomotive force	[A]
Ms	spool mass (3.1-10-3)	[kg]
N	number of turns of each coil (3625)	[-]
P0	atmospheric (reservoir) pressure (105)	[Pa]
Pd	drain orifice inlet pressure	[Pa]
Pl Pr Ps r
rb
Rm
R
m pO
Tt Vd
Qi
Qsv
x
Xo
xp0 y
yf yff
yi yti
z
a
ß S
n v
Mo Mm
left nozzle pressure	[Pa]
right nozzle pressure	[Pa]
supply pressure (210 • 105)	[Pa]
distance from armature pivot to	[m] the centre of permanent magnet pole face (14.5-10-3)
radius of bushing control edge	[m] (10-10-6)
permanent magnet reluctance	[H-1]
reluctance of each air gap at the	[H-1] null
radius of spool control edge	[m] (10-10-6)
torque caused by electromagnetic	[Nm] forces
torque caused by feedback spring	[Nm] deformation
torque caused by flexure tube	[Nm] deformation
drain compartment volume	[m3] (8.2-10-6)
leakage flow through spool	[m3/s] orifices
servovalve volumetric flow	[m3/s]
flapper tip displacement	[m]
distance from flapper tip to each	[m] nozzle at null (38.5-10-6)
distance from flapper tip to	[m] nozzle
length of each air gap at null	[m] (0.45-10-3)
spool displacement	[m]
feedback spring end deflection	[m]
fictive feedback spring ball	[m] displacement if there is no spool
spool orifice opening	[m]
large transition length	[m]
half the feedback spring ball	[m] clearance (2-10-6)
jet angle in spool orifice	[o]
fluid compressibility (1.9-109)	[Pa]
spool in bushing radial clearance	[m] (4-10-6)
fluid dynamic viscosity (0.012)	[Pa-s]
flapper free end inclination	[rad]
magnetic permeability of vacuum	[H/m]
permanent magnet permeability	[H/m] (5)
v d P
[1] [2]
[3]
[4]
[5]
[6]
[7]
[8]
[9]
fluid kinematic viscosity (1410-) armature deflection fluid density (871)
5 REFERENCES
[m2/s]
[rad]
[kg/m3]
Merritt, H. (1967) Hydraulic Control Systems, John Wiley & Sons, New York. Arafa, H. A. and Rizk, M. (1987) Identification and Modelling of Some Electrohydraulic Servo-Valve Non-Linearities. Proceedings of the Institution of Mechanical Engineers, Part C: Mechanical Engi-neering Science, vol. 201, no. 2, pp. 137-144.
Wang, D., Dolid, R., Donath, M., Albright, J. (1995) Development and Verification of a Two-Stage Flow Control Servovalve Model, ASME The Fluid Power and Systems Technology Division (Publication), FPST, vol. 2, pp. 121-129. Fussell, B., Darwin, Servovalve Torque Electrical Insulation
J., Prina S. (1999) Motor Analysis, Conference/Electrical
Manufacturing & Coil Winding Expo, 1999. Urata, E. (2000) Study of Magnetic Circuits for Servovalve Torque Motors, Bath Workshop on Power Transmission and Control (PTMC'00), Bath, UK, pp. 269-282. Urata, E. (2007) Influence of unequal air-gap thickness in servo valve torque motors, Proceedings of the I MECH E Part C Journal of Mechanical Engineering Science, Volume 221, Number 11, 2007, pp. 1287-1297(11). Gordic, D., Sustersic, V., Jovicic, N., Babic, M. (2004) Analysis of servovalve torque motor behaviour, Proceedings of the 29. NSS HIPNEF 2004, Vrnjacka Banja, Serbia, May, 19.-21., 2004, pp. 187-192. (in Serbian). Gordic, D., Babic, M., Jovicic, N. (2004) The modelling of a spool position feedback servovalve, International Journal of Fluid Power, vol. 5, no. 1, March 2004. Gordic, D. (2002) The Analyses of the Two-Stage Electrohydraulic Servovalves With the Spool Position Feedback, PhD thesis, University of Kragujevac, Serbia (In Serbian).
r
f
x
n