A Hybrid Experimental Drive Concept of Permanent Magnet Linear Direct Actuator Servoed to a Ship's Hydraulic Rudder D. Zito, C. Bruzzese, A. Raimo, E. Santini
A. Tessarolo
Dept. of Astronautical, Electrical and Energy Engineering (DAEEE) University of Rome – Sapienza Rome, Italy
[email protected]
Dept. of Engineering and Architecture (DEA) University of Trieste Trieste, Italy
[email protected]
Abstract—The use of linear machines (LMs) is increasing in research and industry fields. All kinds of LMs are studied: synchronous, induction, flux switching. Research is leading to overcome the known drawbacks of all these machines. Anyway the use of innovative direct-drive solutions are under study to obtain more efficient energy conversion, such as for marine field. As alternative to classical systems, linear force can be used to obtain a more efficient plant. Hydraulic drives used on board ship to empower rudders, stabilizing fins, anchor winches, etc., are often characterized by low efficiencies, heavy maintenance, frequent oil leaks and large weight and size. To overcome these drawbacks, an oil-free inverter-fed alternative drives can be conceived. In this paper a concept design of full-scale permanent magnet linear synchronous motor directly coupled to a twin rudder on board ship is presented, used as a servo-motor. A complete model of the electro-mechanic-hydraulic system in Simulink environment was built. Several simulations are performed to evaluate the servo-assistance capabilities. The results show the effectiveness of the electromagnetic drive servoassistance and an increased overall efficiency of the steering gear. This research has been carried out in the framework of the Italian Defence Research National Program for the development of 'dual use' technologies. Keywords—Direct drive, efficiency, fault tolerance, forceperformance, full-electric drive, hydraulic drive, permanent magnet linear motor, rudder steering gear, servo-assistance, ship.
I
I.
INTRODUCTION
nnovative full-electric drives can be used for energy savings meeting the new challenges for the environmental sustainability. Surveying on a recent research it can be noted that the interest in linear drives is currently increasing in several fields. The sea wave energy conversion by means of linear synchronous motor exploiting the waves oscillation was the topic covered in [1]. A design of a high-force density tubular linear motor was presented in [2]. A linear induction machine prototype working as a generator was optimized and used as a piston/mover in a dual free-piston Stirling engine [3]. Linear machines are also proposed for handling applications [4] or for propulsion system by using high-temperature superconductor materials [5]. The parameter identification of linear machine was the objective of [6] and [7]. Lumped parameter networks are also used as a tools to analyze a thermal water cooling or to size linear permanent magnet machines [8], [9]. Furthermore, the interest in linear flux switching permanent magnet machines led the authors of [10] to propose a speed control strategy for a prototype of a
complementary and modular motor. The use of the thrust force permits to obtain a linear force in substitution of classical hydraulic, mechanical or pneumatic plants, increasing the reliability of the systems and the energy conversion efficiency. Then also in the area of military research is increasing the interest on oil-free linear electric drives for new and existing naval ships. The Italian Navy (Marina Militare Italiana – MMI) has commissioned a project, as a 'follow-on' of [11], with the objective to design, construct, and realize a practical application on board ship of an innovative linear electric drive after a comprehensive investigation of critical plants [12]. The new project is being developed by a consortium of university departments (DAEEE, DEA) and industry (Nidec-ASI). Hydraulic drives, such as rudders, stabilizing fins, anchor winches, etc., fed by pressurized oil feature high thrust and low speed, but are characterized by low efficiency, heavy maintenance, oil leaks, room encumbrance. In this paper a concept of a full-scale electromagnetic drive (EMD) servoed to a ship hydraulic twin rudder is shown. The hydraulic system drive (HSD) is installed on board MMI's 'Comandanti' Class Ships and for this application can not be dismounted as well as required by the MMI to obtain the permission. The EMD is based on a permanent magnet linear synchronous actuator (PMLSA) previously optimized and prototyped by DAEEE in cooperation with DEA [13]. The PMLSA is a linear double-sided moving-magnet machine with surface magnets. The actuator is based on a fault-tolerant modular design. The stator winding is fractional-slot type and each stator tooth can be dismounted for maintenance or replacement. The fault-tolerance is also granted by the modular feeding. The stator is split in 4 independent units (or module) which are fed by an inverter, so if a fault occurs in a module the inverter can be individually disconnected without service interruption. Apart fault-tolerance and modularity, other advantages with respect to the hydraulic drives are given by the EMD, such as reduction in weight and size, higher energy efficiency, scalability and better control [14], [16]. The PMLSA actuates the twin rudder by means of a prismatic rotoidal joint. It is directly coupled to the mechanical load through a torque-arm, avoiding reduction gears and the related costs and losses. In this paper the electromagnetic design and sizing of the EMD based on the load torque and room savings requirements is shown. To assess the servo-motor sizing, the double-rudder hydraulic steering gear and the EMD are modeled in Simulink environment. Many components belonging to different physic
domains (electrical, hydraulic, and mechanical) were accurately interconnected. The effectiveness of the proposed solution is shown by means of the simulations comparing the standalone HSD capabilities with the EMD capabilities. For this purpose a properly servo-assistance factor was introduced. The EMD permits to increase the efficiency of the steering gear. This improvement was also investigated by several simulations and a comparison for both small and high level of servo-assistance factor is shown. II.
PARALLEL HYDRAULIC CIRCUIT
COUNTERBALANCE VALVE 4-WAY DIRECTIONAL VALVE
THE CLASSICAL HYDRAULIC TWIN RUDDER STEERING GEAR
The plant view of the hydraulic double-rudder steering gear on board MMI's 'Comandanti'-Class ships is shown in Figs. 1-2. As well as depicted in the operation hydraulic scheme in Fig. 3, the hydraulic power unit comprises two induction motor powered fixed-flow gear-pumps. Generally only one electro-pump is working whereas the other is used for backup or doubled speed. The pump oil flow is controlled by the 4-way directional valves. The double-overcenter valves (or counterbalance) hold the rudder in the controlled position preventing any rudder slip. Two double-effect hydraulic cylinders actuates the twin rudder thanks to the pressurized oil sent into the driving chambers. The hydraulic plant rated data are resumed in Table I. Note that according to the Rules for Classification of Naval Ships [19], the actuation time is the time needed to move the rudder from an angle of +35° (on one side) to -35° (on the opposite side) with the ship at its deepest seagoing draught and at maximum cruise speed [20]. This time is 26s with one working electro-pump and 14s for two working electro-pumps. CONNECTING ROD RUDDER STOCK TILLER
TILLER
POSITION SENSOR
DOUBLE-ACTING HYDRAULIC CYLINDERS
GEAR PUMPS
Fig. 1. Hydraulic steering drive for operating the twin rudder (2V160-plant on board the “Comandanti”-Class Ship). Upper view of the original arrangement.
HYDRAULIC CYLINDERS
CONNECTING ROD
OIL TANK
Fig. 3. Hydraulic scheme of steering gear in operating conditions with one working electro-pump. The rudders are moving from 0° to +35° position. TABLE I TWIN-RUDDER PLANT 2V160 RATED DATA Rated electric power (two electro-pumps) 37kW (380V, 50Hz) Rated mechanical power (two electro-pumps) 14kW Current, RMS value (one pump) Maximum efficiency (two pumps) Hydraulic cylinder rated speed Operating torque (total for two rudders)
30A 46% 3cm/s 180kNm
Maximum pressure (pressure relief valves setting) Maximum electro-pumps pressure
170bar 240bar
Hydraulic cylinder operating pressure Flow rate
125bar 46lpm
Electro-pumps rated speed Actuation time (from +35° to -35°, one pump)
1450rpm 26s
Actuation time (from +35° to -35°, two pumps)
14s
III. THE PMLSA SERVOED TO THE HYDRAULIC STEERING GEAR
OIL TANK
HYDRAULIC POWER UNIT
GEAR-PUMPS
TILLER
Fig. 2. The steering gear plant on board “Cigala-Fulgosi” Comandanti-Class Ship is shown. The hydraulic power unit is located on the back-side (with permission of the MMI).
The PMLSA is used as a servo-motor in order to assist the hydraulic cylinders thus decreasing the effort of the hydraulic steering gear. In Fig. 4 the electric direct servo-drive concept is represented. The EMD is designed to be directly coupled to the rudder stock via a rotary-prismatic joint by using a properly sized torque-arm extension for force amplification. Another installation was investigated. In fact, the PMLSA can substitutes the connecting rod, but the preliminary design has highlighted that for encumbrance reasons this option can not be practiced. The stator design is full-modular to ensure service continuity in case of partial fault. If a fault occurs in a coil, the faulted stator tooth can be dismounted and repaired or replaced without service interruption also in loaded conditions. Fault-tolerance is also granted in case of an inverter-trip [16]. In fact the PMLSA divided by two aligned modules as in Fig. 5. Each module is fed by two electrically independent inverters, for the upper and lower sides. In case of sudden trip of one inverter, the drive can still provide 3/4 of the total rated power and thrust capability. Fig. 6 shows the control scheme which works as an open-loop force amplifier. The EMD is force-controlled, so the hydraulic force FHSD developed by the hydraulic cylinders, is measured by strain gauges placed on the lateral surfaces of the torque arms (Fig. 7).
The PMLSA is controlled in such a way to provide an amplification β of the force FHSD developed by the hydraulic cylinders:
+
r
FHSD
FEMD
L. P. FILTER
PMLSA
+
RUDDER +
+
F EMD = F HSD⋅t HSD /t EMD
(1) where 0∞ is the force gain or force-multiplication coefficient and tHSD, tEMD are the tiller lengths. The coefficient β is obtained in turn from the servo-assistance factor α ( 01 ), which represents the fraction of the overall torque applied to the rudder stocks (load torque), provided by the PMLSA:
β
α
STRAIN GAUGE MEASUREMENT
Fcyl-2 Fcyl-1
+
HYDRAULIC CYLINDER-2
+
HYDRAULIC CYLINDER-1
Fig. 6. Force control system scheme. The forces exerted by the hydraulic cylinders are measured and summed, and multiplied by β, which is in turn obtained from the desired servo-assistance factor α. The reference force is then multiplied by a reduction factor r=tHSD/tEMD, taking into account the arm extension. A saturation block limits the maximum reference force.
F EMD = F T⋅t HSD /t EMD
(2) where FT is the sum of both electromagnetic (FEMD·(tEMD/tHSD)) and hydraulic (FHSD) forces. β is computed as: =/ 1− .
PMLSA
PMLSA
MODULE-1
MODULE-2
(3)
INVERTER Tiller extension, tEMD
Note that for β=0 the servo-assistance is vanishing, whereas for β=∞ all the load is taken by the EMD. A proper low-pass filter has been also designed in Fig. 6 to prevent control instability for the highest gain values.
STRAIN GAUGE
STRAIN GAUGE
HYDRAULIC CYLINDERS
FORCE CONTROL Fig. 7. Sketch of the mechanical arrangement, with the EMD coupled to a single rudder stock. A rotary prismatic joint converts the linear motion to rotational motion. The tiller-extension (1.5m) is sized to satisfy the torque requirement. Strain gauge sensors provide the force measurements to use as inputs to the EMD control system.
IV. Fig. 4. Double-rudder drive on board a “Comandanti”-Class Ship. 3D rendering of the PMLSA-based servo-drive concept.
PMLSA MODULE-2 P/4
Ship mains
P/4 P/4 P/4
PMLSA MODULE-1
LABORATORY PROTOTYPE OF THE PMLSA
The PMLSA prototype has been realized to achieve one the objective of the project in [11] as shown in Figs. 8-9 where some mechanical details before and after assembly are depicted. The PMLSA is a double-sided moving-magnet machine with surfaces-mounted magnets. The stator winding is a fractional-slot type with twelve coils and ten magnets per side. The PMLSA was optimized for low-speed and high force operation. The optimum design was found by means a parametric Geometrical Stretching Method (GSM) used to overcome the problem of local minima whose optimization algorithms suffer [13]. Table II reports the electrical parameters measured/calculated for the prototype (with airgap width w=15cm [4]) where the 'per unit of length' (p.u.l.) phase resistance is carried out considering the coil average turn length around a single tooth.
Fig. 5. PMLSA modules supply scheme. The EMD is composed by two PMLSA -based modules which are fed by four independent inverters. Rs 23Ω
TABLE II PMLSA PROTOTYPE ELECTRICAL PARAMETERS (W=15CM) Rs (p.u.l.) Ls ψm 0.48Ω/cm
2.88H
45Wb
2⋅tan α =0.15 m/ s (5) 26 Note that the upper term of (5) is the maximum mover displacement d=2 tan(α) = 2.01m. s=
d PMLSA α tEMD
w
w
Fig. 8. Coil (A) Structural analysis of a stator tooth with stator yoke segment. (B) Wound teeth before assembly. (C) Scheme of tooth mounting on the aluminum frame. (N.B. w=width of the active air-gap or magnet width).
Prismatic rotoidal Joint
Fig. 10. Drive scheme of the rudder. The mover coupled via the mechanical joint is moving along direction d.
The torque balance of the EMD-servoed plant is: T HSDT EMD= F HSD⋅t HSD F EMD⋅t EMD =T LOAD .
(6)
The electrical parameters were carried out for the PMLSA with doubled magnet width (Fig. 12). Table III reports the parameters calculated for one PMLSA module with w'=30cm. Obviously, the stator phase inductance Ls and the magnet flux ψm are doubled. The phase resistance instead is carried out by multiplying the per-unit value by the average turn length (dashed line in Fig. 12), and it turns out to be only 1.63 times the phase resistance of the prototype, which improves a lot the PMLSA efficiency, since the losses are mainly resistive. MEASUREMENTS
THRUSTING FORCE(N)
ONE PMLSA MODULE
Fig. 9. PMLSM reduced-scale laboratory prototype. A-basement; B-bolted beams for fixing to the basement; D-vertical beam fixed to the basement; Foscilloscope; G-terminal box; H-mover; J-magnet-retention cage; L-linear bearing supports; M-horizontal screw-rod.
V.
SIZING OF THE FULL-SCALE PMLSA-BASED DRIVE
The torque requirement to refer for the design of the servomotor is 180kNm (90kNm per rudder). The rated overall load torque applied to the rudder stocks by the original HSD it is carried out by multiplying the overall force FHSD developed by the two cylinders by the arm tHSD. From experimental results, the PMLSA prototype maximum thrusting force FPMLSA is about 32kN [16], Fig. 11. By taking into account also the limited space between the two rudders, two PMLSA modules are used. So the thrusting force is doubled (64kN). To obtain more thrust, the width of the magnets has been also doubled (w'=30cm), thus achieving a maximum thrust FEMD,max=128kN. So, the torque-arm lenght tEMD has been initially sized to obtain the desired rated torque as follows: T rated t EMD = =1.4 m . (4) F EMD , max This value was lightly increased to tEMD=1.5m as safe margin and to obtain better performances. The maximum mover speed is computed considering the maximum displacement d of the PMLSA actuating the rudder from on side +35° to the other -35° in 26s, according to [19], Fig. 10. So, the speed is:
3/4 PMLSA MODULE
MOVER POSITION(mm) Fig. 11. Predicted and measured PMLSA thrust as a function of the mover position, with DC-excited stator. PMSLA's TOOTH 3cm
w=15cm
COIL
w'=30cm
Fig. 12. Single wound tooth. Since the width of the air-gap is doubled, tooth and coil widths are also doubled (w'=30cm). TABLE III MODIFIED PMLSA MODULE ELECTRICAL PARAMETERS WITH w=30CM Rs
Rs (p.u.l.)
Ls
ψm
37.4Ω
0.48Ω/cm
5.76H
90Wb
The parameters in Table III refers to a module with 8 series-connected coils in each phase, 4 in the upper side and 4 in the lower. However, the upper and lower sides can also be parallel-connected if needed. The final electric configuration chosen is shown in Fig. 13, where the upper and lower sides of the two aligned modules are all (virtually) parallel-connected.
by using a complete model. A general view of the entire model is shown in Fig. 14 and it comprises (from left): ship's main electric supply, induction motors, gear-pumps, distribution 4way directional valves, double-overcenter control valves, hydraulic pipes for cylinder parallel-connection, and the double-effect hydraulic cylinders [18]. A friction cylinder is embedded to take into account frictions between rod and case of the hydraulic cylinder. The friction force is simulated as a function of relative speed and pressure and it is assumed that is the sum of Stribeck, Coulomb, and viscous components. The rudder is modeled as a mechanical rotational inertia (16kgm2 per rudder). The non-ideality of the rudder is also modeled. A frictional inertia block takes into account the bearings and seals friction as 1.5% the rudder torque. The overall hydrodynamic forces, which is the sum of the drug and lift forces acting on the twin rudder [23], is modeled as a rotational spring with variable spring stiffness. The linear motion of the cylinders is converted to rotational motion for coupling to the rudder stock by pulley-blocks. The inverse transformation is done on the opposite side, where the twin rudder stocks are synchronized by a connecting rod. All the mechanical couplings have been modeled by proper stiffness and damping coefficients. The load losses in the pipes have been also modeled. The scheme is completed by the EMD model, which comprises a step-up transformer, a diode bridge rectifier, a braking chopper with a capacitor, a vectorcontrolled IGBT inverter, and the PMLSA model. A currentflux quadrature vector control is embedded, for motor torque maximization and stator current minimization [23]. By choosing the appropriate number of pole pairs the Simulinkembedded rotational Permanent-Magnet Synchronous Motor model can be used as a linear model. By imposing the equivalence of the back-emfs, the following conversion equation is obtained: v R= (8) r where ωR (rad/s) is the mechanical rotational speed and v (m/s) is the PMLSA linear speed. According to (8), and since the electrical rotational speed is ωe=pωR, the number of polepairs p to set into the PMLSA Simulink model is p=1/r=31.4.
PMLSA MODULE-2
PMLSA MODULE-1 Fig. 13. Armature winding connections of two PMLSA modules. Only one phase is shown. The two modules are (virtually) parallel-connected, as well as the upper and lower sides of each module.
This choice has been preferred due to the mains voltage available on board ship (380V), and taking in account the operating limits of the PMLSA given by [23]: r Rs V= F m v (7) 3 m EMD r where V is the RMS phase voltage, r=τx/2π is the length of an electric radian, τx is the pole pitch (10cm), ψm is the magnet flux linkage, and v is the mover linear speed. It should be noted that if the voltage V is taken as parameter, equation (7) represent an F-v curve family. The final EMD parameters have been carried out in consequence, Table IV. The EMD ratings are resumed in the Table V. The frequency is computed as f=v/2τx, and its very low value clarifies the quasi-DC nature of the proposed AC machine, with essentially ohmic voltage drops and losses.
TABLE IV FINAL EMD ELECTRICAL PARAMETERS. TWO PMLSA MODULES (W=30CM) Rs Ls ψm 4.67Ω
Vpk
Ipk
450V
50A
0.72H
45Wb
TABLE V RATED PERFORMANCES OF THE PMLSA P F T 33kW
128kN
192kNm
v
f
13cm/s
0.67Hz
VI. SIMULINK MODEL THE EMD SERVOED TO THE HYDRAULIC DOUBLE-RUDDER HSD Simulations of the servo-assisted double-rudder hydraulic steering gear were performed in Simulink environment (for α=0, 0.5, 0.9, with either one or two working electro-pumps),
PMLSA FORCE CONTROL
COUNTERBALANCE DOUBLE-OVERCENTER VALVES
MAINS SHIP
PIPES
PMLSA-BASED DRIVE
OIL-TANK RUDDERS ROD INDUCTION MOTORS PUMPS
4-WAY VALVES HYDRAULIC CYLINDERS
POSITION CONTROL
Fig. 14. Simulink model of the EMD-servoed double-rudder HSD steering gear. All the items are grouped in sub-blocks. Multiple physic domains (electrical, mechanical, hydraulic) are interconnected and simulated. Mains ship ratings are 380V, 50Hz, provided by an onboard 1125kVA synchronous diesel-generator.
The step-up transformer was needed to interconnect the ship voltage level (380V) to the EMD, which requires a 600V line-line input voltage for the highest load, according to (7). VII. SIMULATION OF THE DOUBLE-RUDDER HYDRAULIC STEERING GEAR WITH TWO WORKING ELECTRO-PUMPS AND α=0 In this section the results obtained from the plant simulation for α=0 with two working electro-pumps, are shown. Then EMD doesn't take load. The position task performed by the twin-rudder is steering from 0° to 35°, then reverses the motion until 0°. After 9s the twin-rudder is steering to -35°, and finally it reverses the motion to return at 0° rudder angle. The simulation time was 35s. This task is shown in Fig. 15 where the rudder angular speed, the overall power and torque applied to the steering gear, are also reported. Note that the torque rated value is 180kNm, and it's provided only by the HSD. The torque contribution of the EMD is null. Fig. 16 shows pressures and oil flow rates inside the driving and pulled chambers and the mechanical input power of the hydraulic cylinders. Note that the pressures increase with the load applied on the twin rudder. The driving chamber pressure is more high (123bar) than the pulled chamber,14bar. The flow rates remain constant due to induction-motor powered electro-pumps.
Fig. 16. Simulation of the overall plant (α=0, two working electro-pumps). Hydraulic cylinders input oil pressures, flows and powers are shown.
Fig. 17. Simulation of the overall plant (α=0, two working electro-pumps). Hydraulic cylinders output position, speed, forces, and powers.
Fig. 15. Simulation of the overall plant (α=0, two working electro-pumps). Rudder position task: at 0.5s, the reference signal steps up from 0° to 35° until t=9s, where steps down to 0°. The actual position varies slowly due to the constant-speed pumps. The motion task is reversed from t=18s. The angular speed is 4.5°/s. The mechanical load power is 14kW. The load torque is 180kNm.
Position, speed, mechanical output forces and powers of both the hydraulic cylinders are shown in Fig. 17. The overall hydraulic force is 445kN, as expected from the ratio of the rated load torque and the HSD arm, Trated/tHSD. The maximum output mechanical power is near 15kW. Fig. 18 shows the overall efficiency of the HSD (which peaks at 46% at full load), obtained by multiplying the efficiencies of all the HSD components (induction motors, gear pumps, valves and hydraulic cylinders).
Fig. 18. Simulation of the overall plant (α=0, two working electro-pumps). Per-component and overall HSD plant efficiencies.
VIII. SIMULATION OF THE DOUBLE-RUDDER HYDRAULIC STEERING GEAR WITH TWO WORKING ELECTRO-PUMPS AND α=0.9 In order to assess the validity of the sized EMD, simulations were performed for α=0.5, 0.9 with one and two working electro-pumps, but here only a salient case is shown, that is α=0.9, two working electro-pumps. The 50%-case was investigated in [24]. The task is the same for simulations in the previous section, Fig. 9. The EMD thus provides the 90% of the overall torque requested by the load. When the mover displacement is 90cm, the rated force developed by the EMD is near to 100kN, the mover speed is 12.5cm/s and the mechanical power developed by the PMLSA is close to 14kW, Fig. 19. Fig. 20 shows the three-phase voltages, currents and the instantaneous input active three-phase power of the PMLSA, which increase with the servo-assistance factor, with respect the values in Fig. 15. Fig. 21 shows the good effectiveness of the servo-assistance for α=0.9. The ratio between respectively EMD torque, input, output powers and HSD torque, input, output power is always near to 90%, with a little error due to the open-loop control.
OVERALL=180kNm EMD=164kNm
HSD=16kNm
EMD=33kW
OVERALL=45kW
HSD=12kW
OVERALL=15.6kW EMD=14kW
HSD=1.6kW
Fig. 21. Simulation of the overall plant (α=0.9, two working electro-pumps). Torque and input/output power comparisons. The maximum torque requested is 180kNm. The EMD provides 164kNm (91%) whereas the HSD provides 16kNm (9%).
IX. COMPARISON OF EFFICIENCIES Finally a comparison of efficiencies is shown for α=0, 0.5, 0.9 in Fig. 22. The case in Fig. 21-(a) is obviously the HSD in standalone operation mode. It should be noted that the EMD efficiency is always greater than the HSD efficiency which start from 0% and peaks to 36.5% as depicted in Fig. 21-(b). In the latter case, Fig. 21-(c), the HSD efficiency start from 0% and peaks to 10%. So, the overall efficiency is improved for both α=0.5, where the EMD efficiency ranges from 70% to 55%, and for α=0.9, where the EMD efficiency ranges from 70% to 43%. α=0
HSD=46%
(a)
Fig. 19. Simulation of the overall plant (α=0.9, two working electro-pumps). EMD mover displacement, speed, electromagnetic force, and mechanical power are shown.
EMD=70%
α=0.5
OVERALL=50%
HSD=36.5%
(b) EMD=70%
α=0.9
OVERALL=35% HSD=10%
(c)
Fig. 22. Simulation of the overall plant with two working electro-pumps. (a) α=0, (b) α=0.5, (c) α=0.9.
X.
Fig. 20. Simulation of the overall plant (α=0.9, two working electro-pumps). PMLSA stator phase voltages, currents, and instantaneous active three-phase power.
CONCLUSIONS
In this paper an innovative electromagnetic drive solution which improve both performance and efficiency for a ship steering gear has been shown. A model where different physic domains (electrical, hydraulic, and mechanical) were accurately interconnected was realized in Simulink environment and used to validate the sizing. Several simulations are performed to investigate capabilities of the hydraulic system drive in standalone operation mode and varying the servo-assistance factor until 90%. The results show that the HSD efficiency is 46%. But the servo-motor
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