Investigation on electromagnetic valve of fuel injector for

International Journal of Applied Engineering Research ISSN 0973-4562 Volume 11, Number 11 (2016) pp 7431-7438

© Research India Publications. http://www.ripublication.com

7431

Investigation on electromagnetic valve of fuel injector for accumulator fuel

equipment system

Aleksandr Aleksandrovich Kudryavtsev, Aleksandr Gavriilovich Kuznetsov,

Sergey Viktorovich Kharitonov and Dmitriy Sergeevich Vornychev

LLC TransSensor, 24, St. Geroev-Panfilovtsev 125480, Moscow, Russian Federation.

Abstract

The method of controllable electromagnetic valve design for

accumulator diesel fuel equipment system is proposed consid-

ering the need to ensure dimensions of fuel injector inner

chamber. Method is based on theoretical analysis, static and

transient calculations of electromagnetic actuator. Calculation

results were obtained with ANSYS Maxwell 16.0 software.

Electromagnetic force dependency on current and magnetic

induction field configuration were obtained for each investi-

gated valve configuration. In transient calculation, dependen-

cies on time were obtained for general parameters of actuator

such as current, moving forces and position of armature. The

use of the results obtained during the investigation enables to

choose electromagnetic valve design of the specific fuel

equipment in diesel engine. The presented results were ob-

tained during research on the development of control systems

and adaptation of sensors and actuators of fuel equipment with

perspective technical parameters with the financial support of

the Ministry of Education and Science of the Russian Federa-

tion in the form of subsidies from the federal budget (code of

the lot RFMEFI57915X0095).

Keywords: Diesel, Accumulator fuel system, Common Rail,

Fuel equipment, Electromagnetic valve actuator, Theoretical

analysis, Static calculations, Transient simulation.

FORMULATION OF INVESTIGATED PROBLEM

Nowadays, accumulator fuel equipment system such as

Common Rail became widespread. It allows control system to

get control over many injection parameters in order to ensure

economic and ecologic requirements applied to diesel en-

gines[1-3].

Efficiency of accumulator system and its possibility to obtain

required injection characteristic mainly depends on electro-

magnetic valve actuator installed in injector unit. Electromag-

netic actuator is activated by voltage pulses generated by elec-

tronic control unit.

In accumulator fuel systems electromagnetic valve and its

actuator are installed in injector unit as opposed to fuel

equipment systems which have control valve installed on out-

put of high pressure pump. Therefore dimensions of valve are

constrained by design and size of injector unit.

Control system affects injection profile through valve motion

control which is determined by forces applied to valve[4-

7].Many theoretical investigations that are reviewing work of

injector in accumulator fuel system feature motion simulation

of valve armature and fuel pressure change over time [8-11].

Design and parameters of electromagnetic actuator are con-

sidered as given initial data and thus define electromagnetic

force applied to valve[12-14].

In this paper, the problem of electromagnetic valve design for

a given chamber dimensions is reviewed. Fuel movement

through injector and fuel pressure are not taken into account at

the beginning stage of electromagnetic actuator design. Ac-

counting for fuel pressure forces is preferable at the next stage

of design process when construction and basic parameters of

actuator are set.

Point of interest in electromagnetic valve design problem is to

investigate the influence of construction parameters on actua-

tor characteristics such as force[15-18]. Dimensions of actua-

tor remain constant during investigation. It corresponds to the

problem of developing valve for existing injector unit with a

given inner chamber size. Actuator configuration, size of spe-

cific parts and applied materials could be considered as con-

struction parameters. Selection criteria of construction optimi-

zation process are force achieved by actuator and speed per-

formance.

We suppose that static electromagnetic force calculation for

different values of current in winding is worth considering

along with transient motion simulation of valve armature.

Results of such static calculation allow determining prelimi-

nary spring deformation force and analyzing different valve

constructions in terms of magnetic induction distribution in

magnetic circuit.

OBJECT OF STUDY

Electromagnetic actuator of injector valve typical to accumu-

lator diesel fuel equipment systems is considered as the object

of study in this paper. Actuator is a cylindrical electromagnet,

its constructive scheme is given on Figure 1.

Actuator consists of fixed core 1 coiled by a copper winding

2. From outside, winding is enclosed by a body 3. Core has

inner hole for spring 4. Disc armature 5 is assembled with fuel

supply valve 6.When actuator is energized, disc armature with

a valve moves until it is pressed into holder 7 which is in-

stalled at the bottom of core and made of high hardness steel.

Material of fixed core, body and disc armature is magnetic

steel “27KХ” [19].

The problem studied is to develop electromagnetic valve actu-

ator for a given injector chamber in a form of cylinder with

diameter 14 mm and height 15.2 mm.



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Figure 1: Constructive scheme of electromagnetic actuator

Theoretical analysis

Movement of armature and valve assembly is described by

Newton’s second law:

𝑚𝑑2𝑥

𝑑𝑡2= 𝐹𝑒 − 𝐹𝑠 − 𝐹𝑑 ,

(1)

where𝑚 –assembly mass;𝑑2𝑥

𝑑𝑡2 – valve acceleration;𝐹𝑒 – elec-

tromagnetic force;𝐹𝑠 – spring force;𝐹𝑑 – damping force which

is stands for energy loss, primarily because of fuel viscosity.

At current stage of research, specific construction of whole

injector is not considered so fuel pressure force is not included

in the equation (1). To calculate it one should consider hydro-

dynamic processes in injector chambers.

Generated electromagnetic force 𝐹𝑒 for specific actuator con-

struction depends on current 𝑖 in winding of electromagnet

and gap 𝑦 between core and armature (see Fig. 1), which var-

ies with armature motion: 𝐹𝑒(𝑖, 𝑥). Spring force 𝐹𝑠 = 𝐹𝑠0 + 𝑏𝑥, where 𝐹𝑠0 – preliminary spring

deformation force; b – spring stiffness.

Damping force𝐹𝑑 = 𝑐𝑑𝑥

𝑑𝑡, whereс – damping coefficient.

Balance of electromotive forces and voltages in electric circuit

of valve winding is described by Kirchhoff's second law:

𝐸𝑖 = 𝑈 – 𝑖𝑅,

where𝐸𝑖 = 𝐿𝑑𝑖

𝑑𝑡 – inducted electromotive force;𝐿 – electro-

magnet inductivity;𝑈 – voltage of control pulse, applied by

ECU to electromagnet winding;𝑅 – active resistance of wind-

ing.

Solution of equation

𝐿𝑑𝑖

𝑑𝑡 + 𝑖 =

𝑈

𝑅

(2)

for current that varies over time 𝑖(𝑡) with zero initial condi-

tions is exponent:

𝑖 = 𝑈

𝑅(1 − 𝑒−

𝑡

𝑇),

(3) where𝑈/𝑅 – steady current value; 𝑇 = 𝐿/𝑅 – time constant

of current varying processcharacterizing retardation because

of electromagnetic induction.

One of the most important constructive parameters of actuator

is winding configuration which determines values of inductiv-

ity 𝐿 and active resistance 𝑅. It is assumed that winding must

reside in given volume (see Fig.1) with following sizes: mean

diameter 𝐷 = 10.4 𝑚𝑚 , height ℎ = 8.5 𝑚𝑚 , thickness 𝑎 =1.7 𝑚𝑚. Then conductor diameter 𝑑 is defined by thickness 𝑎

and number of coil layers 𝑛1: 𝑑 = 𝑎𝑛1⁄ .Number of coil turns

in single layer 𝑛2 = ℎ/𝑑. Full quantity of coil turns in wind-

ing𝑛 = 𝑛1 ∙ 𝑛2. Wire length in winding 𝑙 = 𝜋𝐷𝑛. Let’s determine influence of coil layers number 𝑛1 on active

resistance and winding inductivity.

Active resistance of winding

𝑅 =𝜌𝑙

𝑆𝑡

,

(4) where𝜌– specific resistivity of copper; 𝑆𝑡 = 𝜋𝑑2 4⁄ – area of

wire transversal section.

Inductivity of single winding layer

𝐿1 =𝜇0 𝑆𝑤𝑛2

2

ℎ,

(5)

where𝜇0 – magnetic permeability of air; 𝑆𝑤 =𝜋𝐷2

4 – area of

winding transversal section.

For multilayered winding taking into account mutual inductiv-

ity

𝐿 = 𝐿1𝑛12.

(6) Magnetic core significantly rises inductivity of winding,

therefore full inductivity of electromagnet 𝐿𝑒 = 𝜇𝐿, where 𝜇 –

magnetic permeability of actuator magnetic circuit including

permeability of core material and air gaps.

Followed calculations within the theoretical analysis are used

for comparison of different winding configurations, thus 𝜇

value is considered the same for all reviewed configurations.

Considering winding geometry relations, equations (4) and (6)

give following expressions for active resistance and inductivi-

ty

𝑅 =4𝜌𝐷𝑎ℎ

𝑑4,

(7)

𝐿 =𝜋𝜇0𝐷2𝑎2ℎ

4𝑑4.

(8) Then, steady current value and time constant are determined

as



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𝑈

𝑅 =

𝑈𝑑4

4𝜌𝐷𝑎ℎ,

(9)

𝑇 =𝐿

𝑅 =

𝜋𝜇0𝐷𝑎

16𝜌.

(10) One should notice that received values characterize only part

of current transient process in electromagnet winding. That

part corresponds to time before armature began to move, i.e.,

when electromagnetic force is less than counteracting forces

by preliminary spring deformation and fuel pressure.

Relations (9) and (10) show that at the beginning step of cur-

rent variation process time constant does not depend on wire

diameter and layer quantity in winding. It is determined by

only mean diameter 𝐷 and winding thickness 𝑎. Steady cur-

rent value of exponential process at the beginning step is in

proportion with fourth power of wire diameter 𝑑.

Process of current variation in electromagnet winding with

slowed armature in the form of solution of equation (2) repre-

sented at the Figure 2. With wire diameter increase 𝑑2 > 𝑑1

current grows more rapidly even with the same time constants

due to rise of steady current value 𝑈 𝑅2⁄ > 𝑈 𝑅1⁄ .

Figure 2: Process of current variation in electromagnet wind-

ing with slowed armature

This kind of current variation process remains until armature

begins to move when the current reaches appropriate value 𝑖𝑏.

Fig. 2 shows that with wire diameter increase time of rest de-

creases and armature starts moving earlier.

Theoretical analysis of electromagnetic actuator operation

gives valuable qualitative results. But possibilities of such

analysis are restricted due to complexity of winding inductivi-

ty determination in transient process[20]. Numerical methods

implemented in special software are more suitable for this

kind of problem. Therefore, the following investigation of

electromagnetic actuator was performed using ANSYS Max-

well 16.0 [21].

STATIC CALCULATION OF ACTUATOR

In case of a static problem, actuator’s constructive parameters

were varied. For investigated constructions electromagnetic

force dependencies on current were obtained for constant

width of air gap𝑦 (see Fig.1).

Magnetization characteristic of material is given as the curve

representing dependency of magnetic induction 𝐵 on intensity

of magnetizing field 𝐻 (Fig. 3).

Figure 3: Magnetization characteristic of applied material for

magnetic circuit

Reviewed constructions of actuator are listed as follows. Each

actuator construction is suitable for inner chamber of given

injector. It was assumed to use an even number of winding

layers due to technological reasons.

Construction 1: Winding has two layers𝑛1 = 2. Height ℎ and

thickness 𝑎 match sizes represented on Fig.1. Diameter of

wire 𝑑 = 𝑎/2.

Construction 2:Winding has four layers 𝑛1 = 4. Height ℎ and

thickness 𝑎 of winding match sizes represented on Fig.1. Di-

ameter of wire 𝑑 = 𝑎/4.

Construction 3. Winding has only one layer 𝑛1 = 1. Height ℎ

and thickness 𝑎 match sizes represented on Fig.1. Diameter of

wire 𝑑 = 𝑎.

Construction 4. Winding has only one layer 𝑛1 = 1, but wire

diameter is the same as for the construction 1, thus winding

thickness is halved and outer diameter of fixed core increases.

Winding height matches size as on Fig.1.

Construction 5. Winding has two coil layers 𝑛1 = 2. Thick-

ness 𝑎 of winding is according to size on Fig.1. Wire diameter

𝑑 = 𝑎/2. Winding height is halved comparing to construction

1.

Construction 6. Winding has two layers 𝑛1 = 2. Height ℎ and

thickness 𝑎are the same as for Fig.1. Wire diameter 𝑑 = 𝑎/2. Mean diameter of winding 𝐷 decreased comparing with size

on Fig.1 resulting in increased thickness of outer body.

Dependencies of electromagnetic force 𝐹э on current 𝑖 for re-

viewed constructions are given on Figure 4. As it can be seen,

the number of coil turns has the highest influence on electro-

magnetic force value. Maximal force for given current is pro-

vided by construction with higher layer number (construction



7434

2). But as follows from relations (9), (10) and Fig.2 of theoret-

ical analysis, wire diameter decrease leads to decrease of

steady current value due to higher active resistance and slow

down of current growth process in winding. This effect will

became visible in transient simulation of actuator.

Figure 4 shows curves of electromagnetic force with variation

of current up to 30 A. But for small diameter of conductor

wire such current cannot be achieved with a given control

signal voltage because steady current value (see Fig.2) will be

less than required value for armature to begin movement.

Winding with single coil but with higher wire diameter (con-

struction 3) is developing low electromagnetic force for cur-

rent 30 A. But as theoretical analysis shows, current growth

will be more intense than for constructions with higher layer

number.

Curves of electromagnetic force for constructions 4, 5 and 6

lie between curves for construction 1 and 3.

Analysis of the static characteristics received shows that

curves of dependencies of electromagnetic force on current

for reviewed constructions of actuator are different.

Figure 4: Electromagnetic force dependencies on current

Results of force calculations on static problem allow estimat-

ing preliminary spring deformation force which determines

the time when armature begin to move and required current

𝑖𝑏.

Besides force dependencies it is interesting to take a look on

magnetic induction distribution in magnetic circuit material.

Visualized fields give information on how expedient material

is used for magnetic field amplification and allow proposing

another constructions of actuator.

Figure 5 shows magnetic field distribution in magnetic circuit

of actuator for constructions 1, 2 and 3 with horizontal ar-

rangement of transversal section of actuator for better layout.

It can be found that maximal values of magnetic induction

locate at inner and outer surfaces of winding. Holder 7 and

valve 6 are made of non-magnetic material and highly affect

field distribution in magnetic circuit. Air gap between core

and armature has not so great influence because of gap small-

ness. Field in actuator for construction 3 is weaker than for

constructions 1 and 2 which can be explained by small induc-

tivity of one-layered winding.

Distributions of magnetic induction for constructions 4, 5 and

6 are shown in Figure 6. Increase of core diameter in con-

struction 4 leads to weakening of magnetic field in this part of

magnetic circuit. Similarly, in construction 6 increase of outer

body thickness leads to weakening of magnetic field.

The analysis of induction distribution for all reviewed con-

structions shows that upper side of magnetic circuit almost

was not involved in amplification of magnetic field. That is

more noticeable at the figure for construction 5 with short

winding. In order to involve it, one can increase winding

height.

Figure 5: Distribution of magnetic induction for constructions

1, 2 and 3



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Figure 6: Distribution of magnetic induction for constructions

4, 5 and6

Figures with field distribution also show parts of magnetic

circuit in which magnetic permeability decreases. Such infor-

mation could be used for future construction improvement.

TRANSIENT SIMULATION OF ACTUATOR

Transient simulation of electromagnetic actuator gives the

most comprehensive information on developing actuator

work. Interrelated processes of current variation 𝑖(𝑡) and ar-

mature and valve assembly motion 𝑥(𝑡) are described by

equations (1) and (2). Simulation of six reviewed actuator

constructions was performed in ANSYS Maxwell 16.0 soft-

ware.

Control signal applied to electromagnetic actuator by ECU

has the form of pulses with different voltage levels. Signal

profile assumed for transient simulation is shown on Figure 7.

Width-modulated voltage pulses replaced by signals with con-

stant levels of “effective” voltage. Effective voltages are

equivalent to pulses of fixed voltage level with various duty

cycles from an energetic point of view. Control signal repre-

sented in Fig.7 consists of four stages differing by voltage

level and duration. Forcing stage 1 has voltage 24 V and dura-

tion 0.1 ms. Hold stages 2 and 3 have voltage 3 V and 1.5 V

and duration 0.7 and 1.2 ms respectively. Demagnetization

stage 4 has voltage of reverse polarity-24 V and duration 0.1

ms.

Followed values assumed for counteracting forces: prelimi-

nary spring deformation force 𝐹𝑠0 = 20 𝑁 , spring stiffness

𝑏 = 40 𝑁/𝑚𝑚 , damping coefficient 𝑐 = 100 𝑁 ∙ 𝑠𝑒𝑐/𝑚 .

Mass of armature and valve assembly 𝑚 = 1.5 𝑔.

Figure 7: Profile of control signal

Results of transient simulation of all constructions are shown

at Figures 8-16. Curves versus time are given for such param-

eters as voltage of control pulse 𝑈, V; current in winding 𝑖, A;

electromagnetic force 𝐹𝑒, N; spring force 𝐹𝑠, N; damping force

𝐹𝑑, N; armature and valve assembly motion 𝑥, um.

Results of transient simulation analysis for each reviewed

construction are listed as follows.

Construction 1 (Figure 8).Current in winding rises up to max-

imum value during forcing stage of control signal (Stage 1 at

Fig.7) which lasts 0.1 ms. When electromagnetic force reach-

es the value of preliminary spring deformation, force armature

and valve assembly begin to move. Then,current decreases

due to lower voltage level of next control signal stage (hold-

ing stage 2 on Fig. 7) and armature movement. Electromag-

netic force rises at first because of current growth, then as a

result of armature motion and therefore reducing of air gap

between core and armature. Assembly movement ends by

contact with holder (part 7 on Fig. 1).

Figure 8: Results of simulation for construction 1



7436

Next variation of electromagnetic force in condition of as-

sembly-holder contact occurs according to current decrease on

second holding and demagnetizing stages of control signal

(Stages 3 and 4 on Fig.7). When electromagnetic force de-

creases enough assembly starts to move in the opposite direc-

tion due to spring force. Movement ends by contact with valve

stopper.

Construction 2 (Figure 9). During the forcing stage of control

signal current grows slowly because of high inductivity of

electromagnet. After end of forcing stage current achieves so

low value that electromagnetic force doesn’t surpass prelimi-

nary spring deformation force and assembly doesn’t move.

In order to deal with this problem, duration of forcing stage

increased up to 0.5 ms for this construction. Duration of the

first holding stage became 0.3 ms, other stages retained their

lengths.


Results of simulation with modified control signal are shown

in Figure 10. Due to higher length of forcing stage current

managed to exceed the required value and therefore electro-

magnetic force surpassed over preliminary spring deformation

force. After the end of control signal forcing stage, current

and electromagnetic force decrease relatively slow. When

electromagnetic force and spring force equal each other, as-

sembly starts to move in the direction of valve stopper.


Construction 3 (Figure 11).Control signal is the same as

shown in Figure 7. Reviewed actuator construction character-

ized by rapid current variation and high movement speed. It

can be explained by low values of active resistance and induc-

tivity of winding together with small coil turns number. Elec-

tromagnetic force changes rapidly along with current. At the

demagnetizing stage of control signal, current changes so

dramatically that magnetic circuit material not only demagnet-

izes but also re-magnetizes. This leads to interesting effect:

after assembly starts to move in the opposite direction to the

valve stopper, electromagnetic force again reaches significant

value, surpasses spring force and armature returns to the hold-

er.

In this construction the current reaches such great values

which may be unacceptable due to insulation of wire break-

down and overheating of electromagnet possibility. In order to

decrease current and electromagnetic force, control signal was

modified again. Forcing stage wasn’t used, at the range of

time 0...0.8 ms low voltage level 3 V was supplied, demagnet-

izing level was reduced to-3 V.


Simulation results are shown in Figure 12.As it can be

seen,rates of change of current and electromagnetic force have

been reduced and speed performance of actuator also de-

creased. Effect of armature return vanished.


Construction 4 (Figure 13).Control signal is the same as base

(Figure 7). Use of single coil layer of base diameter 𝑑 = 𝑎/2

(see Fig.1) leads to fixed core diameter increase. As shown on

Figure 13, armature motion process in the core direction per-

forms relatively slow, but it moves faster in the opposite di-

rection.



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Construction 5 (Figure 14).Transient simulations of actuator

show that reduction of winding length doesn’t slow armature

speed and generally provides normal actuator operation. In

this case height of magnetic circuit could be decreased be-

cause magnetic induction distribution in static case shows that

top part of core is almost not involved in magnetic field

spreading process and therefore doesn’t play a role in elec-

tromagnetic force producing.


Construction 6 (Figure 15).The purpose for developing such

construction was to try in achieving uniformity of material

amount in magnetic circuit and accordingly material inductivi-

ty around the winding. Calculations in static case for construc-

tion 6 (Figure 6) show that such modification of construction

doesn’t provide uniformity of magnetic induction in magnetic

circuit around the winding. Modification caused a negative

effect also for armature motion process: decrease of electro-

magnetic force results in return motion of armature even at

holding stages of control signal. That is unacceptable due to

technical requirements for the actuator.


To provide armature holding for required time, a control sig-

nal form was modified: voltage level at second holding stage

was increased to 3 V. Figure 16 shows that it provides holding

of armature during the holding stages until demagnetizing

pulse is applied.


CONCLUSIONS

Developing of typical electromagnetic valve actuator for ac-

cumulator fuel equipment system of diesel engine was per-

formed assuming conditions of placement in given sizes of

injector inner chamber.

Theoretical analysis of electromagnetic actuator using basic

physical equations allows revealing main feature of its opera-

tion and schedule a number of possible constructions for fu-

ture research. Significant influence on actuator characteristics

performs by next following parameters: wire diameter, num-

ber of winding layers, number of coil turns in single layer.

Static and transient simulations were performed using ANSYS

Maxwell 16.0 software.

Curves of electromagnetic force dependencies on current re-

ceived as the result of static simulations are differing for every

reviewed actuator construction. These dependencies are used

for selection of preliminary spring deformation force.

In the static case, fields of magnetic induction distribution in

material of magnetic circuit were also obtained. They offer

information on involvement of magnetic circuit areas in mag-

netic field spreading and allow scheduling future modification

of actuator construction.

In transient simulation, variations over time were obtained for

the main parameters of actuator. Curves for electrical parame-

ters, forces and armature movement characterize speed per-

formance and features of reviewed actuator constructions.

Decision on specific construction of electromagnetic actuator

for a given injector according to requirements to specific ac-

cumulator fuel equipment system could be done using results

of actual investigation.

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