Recent Developments of Electrical Drives - Part 31 ppt

In practical application, it is not fixed which one between dynamic capability and the force from maximum input current has larger value.. Although the properly designed machine can sati

Figure 3 Dynamic constraints between dynamic capability and required motional profiles.

Design strategy using dynamic constraints

In principle, dynamic capability shown in (1) should be at least larger than Force-Speed relation of required trajectory shown in (2) This relation is shown in Fig 3, where static and dynamic capability and the required motional trajectory are compared Particularly between two forces from maximum voltage and current respectively, the smaller one could be the final dynamic capability, which is based on (1) Therefore, heavy-line in Fig 3 indicates the final capability of PMLSM, which should be larger than motional profile, and this

conclusion gives effective design criteria referred as dynamic constraints Therefore, it is

reasonable that only dynamic capability at the velocity of v1, v2, vmax should be larger than the required one, which is summarized as follows

< Constraint 1; v = v1, J = Jmax, a = amax>

3

2K e

C1+√C2− C3

R2

s + (π/τ)2L2

< Constraint 2; v = v2, J = 0, a = amax>

3

2K emin



C1+√C2− C3

R2

s + (π/τ)2L2

s v2, Imax



>> mamax+ Bv2+ F l (4)

< Constraint 3; v = vmax, J = −Jmax, a = 0 >

3

2K e

C1+√C2− C3

R2

s + (π/τ)2L2

In (3), the dynamic constraints only from voltage limitation are considered, because the other constraints from maximum input current can be neglected due to the same kind

of constraints in (4) In practical application, it is not fixed which one between dynamic capability and the force from maximum input current has larger value Thereby, at velocity

of v2 in (4), both of them must be satisfied at the same time, where dynamic capability

( J = 0, a = amax) and static capability ( J = 0, a = 0) show little difference which can

be verified through (1) In constraints 3, it is sufficient to judge whether motor has an

ability to produce the force or not However, constraints 3 can be replaced by other different constraint like ∂ F e ,max /∂v >> ∂ F e(v)/∂v (at v = v2) which means that, if the slope of dynamic capability is larger than that of required motional profile at v = v2(slope < 0), constraint 3 atv = vmaxis satisfied by itself However, this constraint is so strict that a lot

of combination of design variables could fail to be selected even though they could survive through constraint 3 Therefore, it is reasonable to apply constraint 3 at design procedure, and then check the force margin in the interval ofv2< v < vmaxafter work

In addition to three basic constraints, such a relations asvmax= Vmax/K eand another

constraint, C2>> C3, should be obeyed also in all of dynamic constraints.

Meanwhile, major difference between constraints from conventional static capability and proposed dynamic capability would be noticed atv = v1andv = v2 Although the properly

designed machine can satisfy constraints given by static capability, required motional profile cannot be realized due to the dynamic constraints, especially atv = v1 (atv = v2, there

is little difference due to the zero jerk) Since discontinuous force change atv = v1 and

v = v2results purely from jerk and acceleration, high accelerating PMLSM used in short traveling displacements should be designed along the dynamic constraints

Defined design parameters in (1) will beτ, K e , R s , L s which are strongly regulated

by dynamic constraints, and used as decision criteria to the combination of the design variables judging that the dynamic constraints are fully satisfied, i.e designed machine can

be driven successfully satisfying the required motional profile Actually, sensitivity to the design parameter variance is most serious toτ and K e relatively than R s , L s which are occasionally neglected in simplified design flow Accordingly, in addition to the dynamic constraints, more generalized design consideration at the primary stage should be done focusing on the influence ofτ and K e , which makes entire design process performing more

effectively

Generalized design consideration and determination of design variables

In Fig 4, the point where the maximum output power could be generated will be near

v = Vmax/K e /2 (half to the no-load velocity) Likewise, the maximum required mechanical

power exists atv = v2, therefore a design basis should be oriented as v2≈ Vmax/K e /2 (K e2

Figure 4 Generalized design schematic diagram (K > K > K )

45 40 35 30 25 20 15 10

45 40 35 30 25 20 15 10 5

45 40 35 30 25 20 15 10 5

45 40 35 30 25 20 15 10

5 0.10 0.15 0.20

0.25 0.30

0

K e = 10

R s L s

L s

L s L 5

R s

R s

R s

(5956)

K e = 30

(11461)

K e = 20

K e = 39 (13769)

(1070)

2.0 0 4

810 0.2 0.4

0.8 1.0 1.2 1.41.6

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6

0

0 4

810

01 2

35 6 7

1 3

5 6 7 0.6

Figure 5 Admissible design combination vs K e (where Vmax = 160 V, Imax = 150 A, m = 37 kg,

B = 100 N/(m/s), F l = 50 N, amax= 20 m/s2, Vmax = 4 m/s, Jmax= 3,000 m/s3)

model in Fig 4) However, if required input current (I s = F e ,max /(1.5K e)) is considered,

K e1 model needs smaller current (I s1 ) than K e2 model (I s2), which could be also interpreted

as better efficiency In conclusion, EMF coefficient, K e[V/(m/s)], should be designed at least in the interval as follows

Another sensitive design parameter, pole pitch (τ), should be defined from the magnetic

combination (four poles and three coils) and the manufacturing feasibility One module length τ m corresponding to 4τ and 3τ c (where, τ c is coil pitch) should be multiplied with 12, which has validated itself compared with the other combinations Hence, its mini-mum and maximini-mum size are strongly restricted by the manufacturing feasibility and the cost Acceptableτ m range for relatively larger power in continuous operation is approximately from 36 mm (τ = 9 mm) to 180 mm (τ = 45 mm).

In Fig 5, distribution of design combination vs K eis shown, and if it is applied to Fig

4, K e = 20 corresponds to K e2model manifesting the best design point from a viewpoint

of size-effectiveness and usefulness in application As K eincreases, better efficiency (lower

input current) can be realized, and near the no-load speed (K e= 39), dynamic constraints strongly restrict the design combinations in the speed range ofv2≤ v ≤ vmax Particularly, the number of admissible design combination is maximum at the K e = 20, which means

the possibility to implement the machine successfully is highest at the best design point Design parameters (τ, K e , R s , L s) are electrically and magnetically composed of the design variables expressing the machine dimension, hence the design process will be done by changing the design variables and checking the validity of sets of the design variables under

Figure 6 Optimal design flowchart.

the criteria proposed by dynamic constraints Particularly, pole pitch (τ) will be sufficient to

represent the moving-directional (longitudinal) design aspects, because coil pitch and one module-length are also determined accordingly Then, the other variables including pole

pitch can be summarized as air-gap length (g0), height of magnet (h m ), height of slots (S h) (or number of turns in slots), which are flexible to the normal direction With the proposed design variables, the optimization method can be applied to the design process under the constraints such as dynamic constraints, the maximum mover length, and the maximum machine height, which are shown in Fig 6 as a flowchart

Detent force reduction

Theoretically, the detent force is the resultant one of two different reaction forces, i.e the core detent force and the teeth detent force The core detent force is the existing force between the permanent magnets and the primary core, which has a large period equal to the pole pitch Whereas, the teeth detent force between the permanent magnets and the primary teeth has a relatively small period, the greatest-common-divider (GCD) of the pole pitch and the tooth pitch (τ c , same with coil pitch)

Reduction of core detent force

Reduction of the core detent force can be done by giving the core a suitable length in order

to cancel the core detent force at both end cores each other by adjusting the phase difference between the two core detent forces, and by reforming the edge of the core to minimize the reluctance variation To begin with, making the geometric length such that the two forces

at both end cores cancel each other can be effective, which could be realized by adjusting the electrical phase difference as follows [5]

where k is integer.

The other candidate is reforming the edge of core, which is induced from avoiding a rapid reluctance change when the mover approaches or leaves the magnets

Reduction of teeth detent force

The teeth detent force, the main component to be reduced, not only occupies the total detent force up to 80%, but also is frequently produced along the motion track Feasible ways to minimize the teeth detent force based on the practical utilization are chamfering the teeth edges and skewing the magnet Firstly, chamfering the teeth edge, which is a similar idea to core chamfering, intends to make abrupt the reluctance changes minimal due to the sharp tooth edge The other one, skewing the permanent magnet which is similar in principle to rotary machines, can remove the teeth detent force outstandingly The optimized skew-angle should be determined through the following relation

Skew-angle= GC D( τ, τ c)

2

1

τ180 [Electrical degree] (8)

Equation (7) manifests the electrical 30◦in four poles and three coils combination However, this is so small one in a mechanical length In case ofτ = 45 mm, mechanical skew-length

correspondent to skew-angle (electrical 30◦) is 7.5 mm.

Investigation on reduction result

Fig 7 shows the reduction of the detent force

The peak detent force of conventional model is about 300 N But the peak value is reduced to 150 N after applying the chamfering and the skew, about 5% of the continuous thrust force The detent force pattern has many harmonics because the width of magnet is very large and many teeth affect same magnet In this case the effect of the skew is not so notable

Figure 7 Detent force reduction by proposed methods.

Figure 8 Manufactured PMLSM.

Design, manufacturing, and testing

The designed steel-cored PMLSM is manufactured and tested The picture of the manufac-tured PMLSM is presented in Fig 8 and specifications of the designed machine are listed

in Table 1

The magnetic flux distribution and air-gap flux density are shown in Figs 9 and 10 In this model, very large input current is needed to get large thrust force, so that sufficient amount of iron core should be secured to avoid magnetic saturation

The stroke of the linear motor is 1,000 mm and the maximum force/continuous force is 15,000 N/3,000 N This motor can run up to 4 m/s under the input voltage of 220 V and the maximum current of 300 A

Table 1 Design specification of sample steel-cored PMLSM

Specification Dimension General (with water cooling) Voltage/current 220 V/41 A

Stack length 200 mm Magnet height 9 mm Magnet width 41 mm Stator (NdFeB, 45 H) Pole pitch 45 mm

Slot width 22 mm Tooth height 30 mm Tooth width 38 mm Mover (coil size = 1.2 Ø) No of turns 90 per coil

Coil connection 3 parallel Chamfering 10 × 6 mm

Figure 9 Magnetic flux density distribution.

The dynamic capability of the designed PMLSM is shown in Fig 11 and the capability curve has force margin about 500 N

By using the load cell, the thrust force is measured and the input current is measured with the current probe and the oscilloscope

Fig 12 shows the measured current-thrust force curve The graph shows very good linear relation of the input current to the thrust force The continuous thrust force is generated with the input current of 58 A and the maximum thrust force with the input current of 305 A

is 15,890 N, which satisfies the objective output Over 300 A region, the linearity of the curve is broken, because it is the highest available measuring value of the current probe The thrust force constant resulting from the measured curve is 54.81 [N/A] and EMF constant is 36.54 V/(m/s) The measured results have a good agreement with calculated thrust force constant 51.53 [N/A] and EMF constant is 34.35 V/(m/s)

The measured input current is shown in Fig 13 when the motor is operated with the maximum speed The pole pitch of the machine is 90 mm and the pitch of the measured

Length mm

Bn Tesla

0

− 2

− 1

0

1

2

Figure 10 Air-gap flux density distribution.

Figure 11 Running characteristics of designed motor.

Figure 12 Current-thrust force curve.

Figure 13 Measured input current.

current wave form is 22.6 ms Therefore the moving speed can be calculated and the result

is 3.98 m/s Because the stroke is short, very large acceleration is needed to achieve the speed of 4 m/s In addition, the power capability of the testing building is not sufficient, so that the resultant speed is not over 4 m/s If long stroke or better power source is available, the machine can achieve the speed of 4 m/s

Conclusion

In this paper, steel-cored permanent magnet linear synchronous motor for large thrust force and high speed operation is designed, manufactured, and tested The machine is analyzed

by finite element method considering dynamic and static constraints The designed model

is optimized to reduce force ripples and to avoid magnetic saturation

Test machine is manufactured and the measured result of EMF constant shows good agreement with designed one Thrust force characteristic shows good linearity and the measured maximum thrust force is over 15,000 N, the objective value The measured max-imum velocity is 3.98 m/s The performances of the designed motor can guarantee the objective large thrust force and high speed

References

[1] T Sebastian, V Gangla, Analysis of induced EMF waveforms and torque ripple in a brushless permanent magnet machine, IEEE Trans Ind Appl., Vol 32, No 1, pp 195–200, 1996 [2] T Yoshimura, H.J Kim, M Watada, S Torii, D Ebihara, Analysis of the reduction of detent force in a permanent magnet linear synchronous motor, IEEE Trans Magn., Vol 31, No 6, pp 3728–3730, 1995

[3] D.L Trumpher, W.-J Kim, M.E Williams, Design and analysis framework for linear permanent-magnet machines, IEEE Trans Ind Appl., Vol 32, No 2, pp 371–379, 1996

[4] S.-Y Jung, H.-K Jung, J.-S Chun, Performance evaluation of slotless permanent magnet linear synchronous motor energized by partially excited primary current, IEEE Trans Magn., Vol 28,

No 2, pp 3757–3761, 2001

[5] N Bianchi, S Bolognani, F Tonel, “Design Criteria of a Tubular Linear IPM Motor”, Proc of IEMDC’03, 2001, pp 1–7

[6] S.-Y Jung, S.-Y Kwak, S.-K Hong, C.-G Lee, H.-K Jung, “Design Consideration of Steel-Cored PMLSM for Short Reciprocating Travel Displacements”, Proc of IEMDC’03, Vol 2, June 1–4, 2003, pp 1061–1067

[7] S.-Y Jung, J.-K Kim, H.-K Jung, C.-G Lee, S.-K Hong, Size optimization of steel-cored PMLSM aimed for rapid and smooth driving on short reciprocating trajectory using auto-tuning niching genetic algorithm, IEEE Trans Magn., Vol 40, No 2, pp 750–753, 2004

III-1.2 HIGH POLE NUMBER, PM

SYNCHRONOUS MOTOR WITH

CONCENTRATED COIL ARMATURE WINDINGS

Antonino Di Gerlando, Roberto Perini and Mario Ubaldini

Dipartimento di Elettrotecnica—Politecnico di Milano Piazza Leonardo da Vinci, 32-20133

Milano, Italy

antonino.digerlando@polimi.it, roberto.perini@polimi.it, mario.ubaldini@polimi.it

Abstract A high pole number, PM synchronous motor is presented, employing novel two-layer,

special armature windings consisting of concentrated coils wound around the stator teeth This kind

of machine is characterized by excellent e.m.f and torque waveform quality: it is well suited not only

as an inverter driven motor, but also for mains feeding, self-starting, applications In the paper, the main features of the machine are shown, together with some design, FEM, and test results

General features of the windings

In recent times, a large attention has grown toward the electrical machines equipped with concentrated coils, thanks to their great constructional and functional advantages [1–12]; nevertheless, a general approach to the concentrated winding theory seems not fully de-veloped yet In the proposed paper, a PM machine is considered, with two-layer, armature concentrated windings [13]

The features of this kind of machines are (see Figs 1 and 2):

runiformly distributed and equally shaped magnetic saliencies of the structures (stator teeth and rotor PMs);

rpractical equality among tooth pitchτtand PM pitchτm(it can beτm<τtorτm>τt, but

τm= τt);

rseries inverted connection of coils belonging to adjacent teeth of the same phase (contro-verse coils)

By adopting the representation of Fig 1 (right) to specify the winding sense of each coil around its tooth, a typical three-phase, two-layer, winding appears as shown in Fig 2 Referring to Fig 2, the following quantities and properties should be defined and con-sidered:

rcycle: space period (periphery portion at which bounds the faced structures show the same mutual disposition);

S Wiak, M Dems, K Kom˛eza (eds.), Recent Developments of Electrical Drives, 307–320.

2006 Springer.