Dynamic Characteristics of a Permanent Magnet Electromagnetic Valve Actuator
Ivan Yatchev*, Vultchan Gueorgiev*, Krastio Hinov*, Racho Ivanov* and Dimitar Dimitrov**
*Technical University of Sofia, Bulgaria
**Technical University of Varna, Bulgaria
E-mail: yatchev@tu-sofia.bg, vulchy@tu-sofia.bg, k_uk, r.ivanov@tu-sofia.bg
Abstract- The paper prents simulation of the dynamics of a
birchelectromagnetic valve actuator. The simulation is carried outaftermath
using decoupled approach where the 3D magnetic field problem
is solved parately from the electric circuit and mechanical
motion problems. Finite element method with edge elements and
ANSYS program are ud for the magnetic field analysis.
Dynamic characteristics are obtained in Matlab environment
utilizing functions derived from the field analysis. The obtained
results are compared with experiment.
I.I NTRODUCTION
牙签是什么意思In recent years, permanent magnets have been increasingly
ud in electromagnetic actuators for different applications
[1-5]. The properties of rare earth magnets give opportunities
for obtaining more suitable static and dynamic characteristics,
as well as the advantage of reduced energy consumption with
respect to the neutral actuators.
Dynamic characteristics of the actuators are subject of
permanent interest [6-18].
Different ways of dynamics modeling could be employed
but two of them have been dominating. The are coupled
models, e.g. [7-9,14] and decoupled models, e.g. [6,15-18]. In
coupled models, all the problems needed to be solved for
dynamic simulation, i.e. electromagnetic field, electric circuit
and mechanical motion problems are solved together. In
decoupled models the field is analyzed parately from the
rest of the problems.
The prent paper deals with the simulation and
experimental verification of open loop (step voltage) dynamic
behavior of a recently developed energy efficient permanent
magnet electromagnetic valve actuator. Dynamic simulation
of a similar actuator is prented in [16].
II.A CTUATOR C ONSTRUCTION
The principal construction of the studied actuator is shown in Fig. 1. The construction is developed from an existing neutral actuator. The two coils are identical and supplied in a way to create flux in the same direction. The permanent magnet is block type and magnetized in transversal direction. The total possible stroke of the mover is 1.5 mm. The overall dimensions of the actuator core are as follows: length: 38 mm; width: 22 mm; height: 27 mm
The permanent magnet is magnetized in transversal direction as shown in Fig. 1. It is NdFeB magnet with remanent flux density Br = 1.29T and coercive field Hc = 979 000 A/m. The principle of actuator operation is as follows. The two coils are connected in a way to create flux in the armature in the same direction. The permanent magnet creates flux in different directions in the two parts of the armature – from the pole ring to the side yokes. This means that when the coils are supplied in a way to create flux in Fig. 1. Principal geometry of the actuator.
2010, 12th International Conference on Optimization of Electrical and Electronic Equipment, OPTIM 2010
positive z direction, the right coil and the permanent magnet will create flux in the same direction in the right part of the armature, while in its left part the left coil and the magnet will counteract each other. Thus, if suitable balance is obtained, the flux in the left armature part and in the stopper can be minimized.
The same considerations apply when the coils are supplied in a way to create flux in left direction – the left coil and the magnet create coinciding flux in the left part of the armature and the right coil counteracts with the magnet in its right part. As the construction is magnetically non-symmetric (due to the prence of stopper) and at the left end the electromagnetic force is greater.
The working stroke of the armature is 1.5 mm.
When the armature is at left position (corresponding to air gap of 0.1 mm to the stopper) without current in the coils, the force created by the permanent magnet holds the armature in this position. When coils are supplied in a way to create flux in right direction (we will call it positive coil current), the armature moves to the right position. Without supply in the right position, a spring can be added t
o hold the armature at this position. When coils are supplied in a way to create flux in left direction (negative coil current), the electromagnetic force dominates over the spring force and the armature is moved to the left position, where, after breaking the supply, the permanent magnet holds it. In this way the actuator features much less energy consumption than any neutral actuator.
III.D YNAMICS M ODELLING
For the modeling of the actuator dynamics decoupled approach has been employed. It consists of 3D finite element modelling of the magnetic field of the actuator and solution of the electric circuit – mechanical motion problem bad on the functions obtained from the magnetic field modelling. The functions are the coil flux linkage, its derivatives with respect to the current and the displacement and the electromagnetic force. For the 3D magnetic field modelling, the finite element method and ANSYS® program [19] are ud. An example of the finite element mesh is given in Fig. 2.
The t hree-dimensional finit e element modeling is carriedsoftkitty
ou
t
famasusing edge flux formula
三人行必有我师翻译t
ion and
t
e
t
rahedral fini
t
e
element s. The studied domain consist s of t he act uat or and a
buffer zone around i, on he boundaries of which flux-
parallel boundary condit ions are impod. The t ot al number
of nodes of the mesh is about 100 000.
For both current in the coil and for the stroke minimal and
maximal values are defined. Then a grid of point s current-
stroke is generated by tting values of the current and of the
stroke to be uniformly distributed within the defined ranges.
For each poin of his grid (each poin corresponds o a
combinat ion of t he values of t he current and t he stroke) the
magne
t
ic field of
t
he ac
t
ua
t
or is analyzed and
t
he
elec romagne ic force and he flux linkage of he coil is
obt ained. Thus for bot h it ems t wo-dimensional arrays are
formed.
The res
t
of
t
he analysis is carried ou
t
in Ma
t
lab®
environment [20].
First, bicubic spline approximations of the electromagnetic
force and of the flux linkage are obtained. Using such approximations both functions and their derivatives could be
obtained at arbitrary point.
Next, the system of ordinary equations is formed and听录音
solved.
The mathematical model in this ca consists of the
equation of the electric circuit
d
U Ri
dt
Ψ
lick foot
=+, (1)
where
U is the supplied voltage;
R is the coil resistance;
i is the coil current;
Ψ is the coil flux linkage,
and the equation of the force balance (equation of motion),
which in the ca without spring is
2
2em
d x dx
m F
dt
releanotesdt
=−β, (2)
where
m is mass of the mover;
x is the stroke (displacement);
F em is the electromagnetic force;
t is time;
βis damping coefficient.
Having in mind that the flux linkage is a function of two
variables, the current and the displacement, its derivative with
respect to the time can be prented as
d di dx
dt i dt x dt
Ψ∂Ψ∂Ψ
=+
∂∂
. (3)
In order to reduce the order of the force equation, a new
unknown function is introduced – the velocity v. Thus, the
system to be solved becomes of the following form
Fig. 2. Finite element mesh.
1di U Ri dt x t
∂Ψ⎡⎤
=
−−⎢⎥∂Ψ∂⎣⎦
ν (4)
dx dt
=ν (5)
()1em d F dt m =−νβν. (6) The required functions (),em F x i , (),x i Ψ, (),x i i ∂Ψ
∂ and (),x i x
∂Ψ
∂ are obtained from the above mentioned bicubic spline approximations.
The system (4)-(6) is solved numerically using standard routines in Matlab, e.g. ode45 function.
The solution procedure is illustrated in Fig. 3.
Fig. 3. Flowchart of the solution procedure.上海艺考培训
The proper choice of the damping coefficient β can take
into account the friction at motion, aerodynamic resistance and the effect of the eddy currents, as far as switching time is concerned. Its value can be determined mainly by experiment.
IV. S IMULATION R ESULTS The dynamic characteristics are obtained for DC supply voltage of 36 V. The value of the coil resistance is 212 Ω
. The dynamics is simulated when the mover is moving in
both directions - to the right and to the left in Fig. 1 (corresponding to positive and negative current in the coil). The movement to the right is more problematic as there is no
normal working air gap at the right end of the mover. A. Positive Coil Current
The bicubic spline approximation of the electromagnetic
force is shown in Fig. 4. The stroke range is wider than the
real one.
Fig. 4. Electromagnetic force for the positive current.
The time evolutions of the current, displacement, velocity and electromagnetic force for the ca of positive coil current (i.e. movement to the right in Fig. 1) are shown in Fig. 5, Fig. 6, Fig. 7 and Fig. 8, respectively.
Fig. 5. Current versus time for the positive current.
Fig. 6. Displacement versus time for the positive current.
Fig. 7. Velocity versus time for the positive current.
Fig. 8. Electromagnetic force versus time for the positive current.
The minimum of the current is not very well outlined. This is due to the configuration of the poles in the right air gap, where there are two coaxial cylinders. The switching time – the time for reaching the armature end position – is about 15.5 ms. The motion starts about 3 ms after the voltage supply. This time is needed for increasing the current and the electromagnetic force in order to overcome the holding force by the permanent magnet.
B. Negative Coil Current
The motion for negative coil current starts at the maximal air gap of 1.6 mm and finishes at the minimal one of 0.1 mm. The dependence of the electromagnetic force on the displacement and the current is shown in Fig. 9. Here, again wider than the real range is considered for the stroke.
Fig. 9. Electromagnetic force for the negative current.
The time evolutions of the current, displacement, velocity and electromagnetic force for the ca of negative coil current (i.e. movement to the left in Fig. 1) are shown in Fig. 10, Fig.
11, Fig. 12 and Fig. 14, respectively.
Fig. 10. Current versus time for the negative current.
Fig. 11. Displacement versus time for the negative current.
Fig. 12. Velocity versus time for the negative current.
Fig. 13. Electromagnetic force versus time for the negative current.
Here, the movement starts practically immediately due to abnce of spring and not accounting for the static friction. The time for reaching the end position is less than 10 ms. The current waveform is typical for making current of a neutral electromagnet.
V.E XPERIMENTAL R ESULTS
The dynamic characteristics of a sample of the actuator have been obtained experimentally using measurements of the coil current and of the acceleration of the mover, which is subquently integrated twice.
A.Positive Coil Current
The results for the time evolution of the current and
displacement are shown in Fig. 14 and Fig. 15.
Fig. 14. Experimental current versus time for the positive current.
Fig. 15. Experimental stroke versus time for the positive current.
