METHOD OF OPTIMIZING A SYNCHRONOUS RELUCTANCE MOTOR ASSISTED BY MAGNETS

Described is a method for optimizing a synchronous reluctance motor assisted by magnets (1), comprising the arrangement of a stator (2) provided with a number (t) of slots (3), the arrangement of a rotor (4) having an outer cylindrical surface (Se) of radius (re), an inner cylindrical surface (SI) of radius (rI), a rotation axis (A) and a number (p) of pole pairs, realisation in the rotor (4) of a number (n) of slots (7) defining flow barriers (Bn) with axial extension for each pole of the motor (1), designed to house magnets (6) and definition of each barrier (Bn) with peripheral profile in the form of a circular segment with convexity facing towards the axis (A) and with concentric radii of curvature (rnA, rnB) with common centre (C) arranged along a radial axis (X). The number (n) of barriers (Bn) is greater than or equal to 3, the centre (C) is located outside the surface (Se) and each barrier (Bn) has a constant thickness (bn) along its arcuate extension defined by the difference between the radii (rnA, rnB). The thicknesses (bn) are progressively decreasing from the surface (Si) to the surface (Se) with optimal thickness (bn) of the outer barrier (Bn) equal to bn=kn−1b1, where kn−1 is a numerical coefficient relative to the n-th barrier (B) corresponding to a substantially constant magnetic permeance across the barriers (Bn) and to a response to a quadrature excitation current with minimum harmonic content.

TECHNICAL FIELD

This invention is applicable generally to the technical field of rotating electrical machines and is particularly concerned with a method of optimizing a synchronous reluctance motor assisted by magnets.

BACKGROUND ART

The use of synchronous reluctance motors assisted by magnets, which can be connected to an electricity network by means of an inverter and operationally coupled, for example, to a resistive load, has long been known in the sector of rotating electrical machines.

An electric motor typically comprises a stator having a plurality of slots equipped with electrical windings and a rotor placed inside the stator and capable of rotating about an axis of rotation due to the magnetic field produced by the stator windings.

In addition, a synchronous reluctance motor assisted by magnets can be configured with a plurality of magnets located in slots within the rotor.

It is known that, depending on the type of application envisaged, the synchronous reluctance motor assisted by magnets may include magnets made of rare earth or ferrite.

It is also known that the reluctance motors assisted by magnets typically have a high torque ripple.

Generally speaking, the use of rare earths to make magnets enables higher performance levels in terms of the magnetic field produced and, therefore, higher torque density than ferrite.

However, rare-earth based magnets have the drawback that the base material, comprising, for example, neodymium-iron-boron or samarium-cobalt, has high costs as well as a high disposal cost compared to ferrite magnets.

In this invention, the expression “torque ripple” means the percentage of the difference between the maximum torque value Tmaxand the minimum torque value Tminrelated to the average value Tmeanaccording to the following relationship:

In other words, the torque ripple is linked both to the phenomenon of the interaction between the magnetic field of the magnets and the stator slots, or cogging, but also, in an applied load situation, to the interaction between the magneto motor force and the flow harmonics through the air gap, the latter being understood as the distance between the stator and the rotor.

There is a need to determine a method of sizing the rotor barriers to overcome the drawbacks outlined above.

Technical Problem

In the light of the prior art, the technical problem which this invention is intended to solve is that of simultaneously achieving both maximum torque density and extremely low torque ripple without loss of power factor and using low-cost magnets.

DISCLOSURE OF THE INVENTION

The aim of the invention is to solve the above-mentioned problem by providing a method of optimizing a synchronous reluctance motor assisted by magnets with high efficiency characteristics and relative cost-effectiveness.

A particular aim of the invention is to make available a method of the type described above which makes it possible to use low-cost magnets and increase the electro-mechanical performance of the motor compared with conventional synchronous reluctance motors.

Another aim of the invention is to provide a method of the type described above that is versatile and easy to apply.

A further aim of the invention is to provide a method of the type described above which enables an motor to be constructed which guarantees correct operation also at high rotation speeds.

The above-mentioned aims, as well as others which will be described in more detail below, are achieved by a method of optimizing a synchronous reluctance motor assisted by magnets in accordance with claim1, which comprises the steps of arranging a stator having a certain number of total slots for the stator windings, arranging a rotor substantially in the form of a circular crown, an outer cylindrical surface of outer radius, an inner cylindrical surface of inner radius, a rotation axis and a number of pole pairs.

The method also comprises making a number of slots in the rotor defining axial flow barriers for each pole of the motor and designed to house magnets, each of the barriers being defined with a peripheral profile in the form of a circular segment with convexity facing the axis of rotation and with concentric radii of curvature with a common centre arranged along a radial axis.

In addition, the number of barriers is kept equal to or greater than 3, the common centre is placed outside the outer cylindrical surface, each of the flow barriers has a constant thickness along its arcuate extension defined by the difference between the radii of curvature, the thicknesses of the flow barriers are progressively decreasing from the inner surface to the outer surface of the rotor and with optimal thickness of the outer barrier equal to bn=kn−1b1, where kn−1is a numerical coefficient relative to the generic n-th barrier corresponding to a substantially constant magnetic permeance through the barriers and to a response to a quadrature excitation current with minimum harmonic content.

Advantageous embodiments of the invention are obtained in accordance with the dependent claims.

DETAILED DESCRIPTION OF A PREFERRED EXAMPLE EMBODIMENT

With particular reference to the drawings, a method of optimizing a synchronous reluctance motor assisted by magnets, referred to in its entirety by reference numeral1, is illustrated schematically inFIG.1.

In a known manner, the motor1is powered by a source of electrical energy and is subjected to a resistant load acting on the motor shaft or on a machine driven by the motor, such as, for example, a pump or a machine tool.

The electric motor1typically comprises a stator2provided with a number t of stator slots3for the electrical stator windings, not illustrated in the drawings, which are powered by the source of electricity to generate a variable magnetic field.

The motor1further comprises a rotor4, substantially in the form of a circular crown having an outer surface Seand an inner surface Si.

Typically, the rotor4is housed within the substantially cylindrical central slot2′ of the stator2and is separated from the inner wall of this slot by a minimum peripheral distance4′, known as the air gap, of a size sufficient to prevent sliding contact even at the maximum speed of rotation of the rotor.

A drive shaft5is rigidly attached to the central part of the rotor4to transmit the power generated by the motor to the resistant load and has an axis of rotation A.

According to an embodiment, the rotor4comprises a plurality of laminar elements, not visible in the drawings, bundled together and integral with the drive shaft5, the outer peripheral edge of which defines the outer surface Seand the inner peripheral edge of which defines the inner surface Siof the rotor4designed for coupling to the shaft5.

Hereafter, unless otherwise indicated, the electric motor1is of the reluctance type assisted by internal magnets, that is to say, with magnets6inserted in appropriate slots between the outer surface Seand the inner surface Siof the rotor4.

The internal arrangement of the rotor4and, thus, of the barriers B is determined by the optimization method according to the invention in order to optimize the performance of the reluctance motor1which is aimed at decreasing the torque ripple and increasing the power factor as well as the torque acting on the drive shaft5.

The method involves constructing the stator2with a number t of stator slots3and an internal cylindrical slot2′.

Moreover, the invention also provides for the construction of the rotor4having a number p of polar pairs, an external cylindrical surface Seof external radius re, an internal cylindrical surface Siof internal radius ri, and its positioning in the internal slot2′ of the stator2so that it can rotate around the axis of rotation A coinciding with the axis of the drive shaft5.

According to the method, a number n of rotor slots7are formed in the rotor4, defining flow barriers Bn with an axial extension for each pole of the motor and designed to house magnets6.

Thus, in the rotor4, predetermined portions of iron or solid material F and predetermined portions of hollow material are defined, defining the rotor slots7which define zones of minimum reluctance designed to guide and concentrate the magnetic flow during the operation of the motor1and which are referred to hereafter as barriers or flow barriers B.

For a correct dimensioning of the motor1and to reduce the losses in the iron, it is necessary that the total number t of stator slots3and the number n of barriers per pole Bn are linked together by the following relations as a function of the number of pole pairs p:

The relations [2] and [3] are obtained by means of experimental tests designed to demonstrate how the different combinations of the numbers t of stator slots3and the number n of barriers Bnfor each pole give a different contribution in terms of iron losses.

These experimental tests have shown that:

with reference to relation [3], when 4p(n+1)>t the losses in the rotor iron are greater than the corresponding losses in the stator iron;

With reference to relation [2], when 4p(n+1/2)<t the losses in the stator iron are greater than the corresponding losses in the rotor iron;

when t−4p(n+1/2)=4p, the best benefits are obtained in terms of both rotor iron and torque ripple losses.

After the definition of the numbers n and t, the method according to the invention comprises a step of defining each of the barriers per pole Bn with a peripheral profile in the form of a circular segment with convexity facing towards the axis of rotation A and with concentric radii of curvature rnA, rnBwith a common centre C arranged along a radial axis X, as clearly shown inFIG.2.

The greatest advantages have been obtained with a number n of barriers per pole Bngreater than or equal to 3 and with the common centre C placed outside the outer cylindrical surface Seof the rotor4.

Moreover, each of the flow barriers per pole Bn has a constant thickness bnalong its arcuate extension defined by the difference between the radii of curvature rnA, rnBof the peripheral profile of the barriers Bnand the thicknesses bnare progressively decreasing from the inner surface Sito the outer surface Seof the rotor4.

Conveniently, in the definition phase of the barriers Bn the optimal thickness bn is defined by the relation [4]:

where kn−1is a numerical coefficient relating to the generic n-th barrier corresponding to a substantially constant magnetic permeance across the barriers Bn and to a response to a quadrature excitation current with minimum harmonic content.

In particular, the above-mentioned harmonic content may be less than 4% of the fundamental and preferably not more than 2%.

In particular, b1identifies the thickness of the innermost barrier B1and close to the inner surface Siof the rotor4.

The combination of features of the above-mentioned method ensures that a magnetic permeance as constant as possible is guaranteed across the Bnbarriers so that torque ripple is minimised.

Hereafter, the expression “magnetic permeance” means the ability of a material to pass energy through it and can be expressed as the ratio between the flow through the material and the magneto motor force applied to the material. This magnitude is therefore the inverse of reluctance.

Conveniently, in order to maintain a magnetic permeance as constant as possible through the barriers Bn, it is necessary to respect the technological limits of realization of each barrier and, more precisely, of the thickness bn of the barrier B most outermost and close to the surface Seof the rotor4, represented with b3inFIG.2.

The technological limit for the construction of the external barrier means the construction of the magnet6with a smaller thickness, which may not have a thickness b below a certain construction limit set by the magnet manufacturer in order not to lose the consistency of the magnet itself.

For this reason, in spite of the thickness values b of each barrier B calculated according to the method, it is necessary to assess the feasibility of making the corresponding magnets6and, if it is not greater than the minimum feasible thickness, a correction must be made to the calculation of the outermost barrier Bn.

It has been verified experimentally that when the number n of barriers per pole Bnis determined by the relation [2] and is equal to 3, as in the examples shown in the drawings, the thickness b2of the intermediate barrier B2is obtained using a coefficient k1between 0.75 and 0.85, and therefore the thickness b2is between 0.75b1and 0.85b1, while the thickness b3of the outermost barrier B3is obtained using a coefficient k2between 0.50 and 0.60, and therefore the thickness b3is between 0.50b1and 0.60b1.

In greater detail, the method according to the invention is illustrated with reference to the schematic arrangement ofFIG.2, in which the thickness bn of the barriers per pole Bn is obtained, for each plane orthogonal to the axis of rotation A, from the initial determination of a first point G obtained from the intersection of the external surface Sewith a first radius raof the rotor forming a first angle α with respect to the radial axis X.

Subsequently, a second point D obtained from the intersection of the internal surface Siwith the radial axis X and a third point E obtained from the intersection of the internal surface Siwith a secant h forming a second angle β with the radial axis X will be determined.

Conveniently, the first angle α, the second angle β and the extension of the secant h are determined by the trigonometric relations [5], [6] and [7], respectively:

These relations can be deduced geometrically from the fact that the secant h connects the first point G with the third point E and from the fact that the radius raand the segment connecting the axis A with the third point E have the same extension, determining an isosceles triangle G-A-E.

There is also a phase for determining a circle of radius R passing through the first G and second point D with centre of curvature C located on the radial axis X.

Conveniently, the radius R is calculated using the following trigonometric formulae:

These relations can be derived from the fact that triangle G-D-C is isosceles with the sides D-C and G-C equivalent to the radius R.

Subsequently there are the stages of determining the total value of the iron or solid material F of rotor4and determining the corresponding number m of segments fmcorresponding to the projections of the solid material F on the radial axis X as a function of the number n of barriers per pole Bn.

Preferably, the total value of the iron or solid material F of the rotor4is determined as a function of the thickness lyof the stator2and of the sum of the segments fmwhich is greater than this thickness ly, as clearly illustrated inFIG.1.

It has been shown experimentally that the total value of iron or solid material F of the rotor4is determined by the relation 1.1ly<F<1.2ly, which allows for the lowest additional losses in the rotor iron4B to be obtained.

After calculating the lengths of the segments fm, there is a phase to determine the radii of curvature r1A, r1Band consequently the thickness b1of the innermost barrier B1, as well as the thicknesses bn of the other barriers Bnwhich are outermost and close to the external surface Seof the rotor4.

In fact, the radii of curvature rnA, rnBand the thickness bnof each barrier per pole Bnis determined by the following relation:

where

and where j1. . . jm−1are numerical constants relating to generic f m-th segments, obtained by simulations and experimental results to obtain a substantially sinusoidal distribution of the magnetic flow in the rotor iron.

It has been shown experimentally that when the number of slots m of segments fmis equal to 3, as in the examples shown in the drawings, and when the number n of barriers per pole Bnand the number t of total slots3of the stator windings is determined by the relation [2], the numerical constant j1is equal to 0.85 and the numerical constant j2is between 0.55 and 0.85.

Furthermore, the method according to the invention comprises determining the extension along the plane orthogonal to the axis A of the barriers per pole Bnand of the space occupied by each magnet6within each barrier Bnso as to maintain a substantially constant magnetic permeance, to optimize the magnetic flow density Bmagin the magnets of the rotor4and to avoid the risk of demagnetization of the portions of the magnets6close to the air gap4′.

The term magnetic flow density Bmagused below means the working point of the magnetic flow.

The space occupied by each magnet6in each barrier Bnis between 80% and 90% of the space of the respective barrier Bn.

These filling values allow for an empty portion8to be made within each barrier per pole Bndevoid of both magnet6and solid material F which avoids the demagnetization of the magnetic portion6contained therein.

It should be noted that the filling of this empty portion8with magnetic material does not adversely affect the electromagnetic performance of the motor1, but simply increases the production cost of the motor itself.

As better illustrated inFIG.2, each pole barrier Bncomprises a hollow portion8with an end9close to the outer surface Sihaving a rounded or arched shape for mechanical reasons related to the speed of rotation of the rotor and to the manufacturing processes for making the rotor4, as well as to the insertion in each slot7of the magnets6.

In particular, the apex of the end9of a barrier Bnis equidistant to the apex of the preceding barrier Bn−1and equal to the distance between the apex of the outermost barrier Bnand the third point E.

The barriers B may be filled with magnets6made of ferrite and with a hollow portion8suitably calculated so as to obtain a reduced risk of demagnetization near the outer surface Seof the rotor4.

Moreover, the use of ferrite makes it possible to reduce the costs of procuring the magnetic material and thus the cost of producing the rotor4compared with the use of magnets made from rare earths, even though this case is not covered by the invention.

However, the choice of material of the magnets6does not affect the optimization of motor1according to the invention in terms of power, torque and ripple.

In this way, flow densities are kept constant along the entire magnet6and consequently portions of magnets6at greater risk of demagnetization are avoided.

In addition, all the magnets6are radially magnetised in order to maximise the working point of the magnet in the motor1and thus to have a higher torque density and a better power factor over the entire operating range of motor1.

To support the advantages of a motor1optimized according to the method described above, some simulations were carried out on a synchronous reluctance machine assisted by magnets, for which two rotors were designed with different B barrier designs even though they use the same amount of magnetic material.

The two rotors can be summarised as follows:

first rotor: optimized using the method described above and therefore comprising three barriers B with constant thickness bnalong its arcuate extension defined by the difference between the radii of curvature rnA, rnBof the peripheral profile of the barriers Bnand the thicknesses bnare progressively decreasing from the inner surface Sito the outer surface Seof the rotor;

second rotor: having three curvilinear B barriers with the same thickness.

Moreover, the simulations were carried out to determine the magnetic remanence factor, or operating limit of the magnetic material, which can be expressed with the relation:

In the relation [13], the numerator value Bmagis the working point of the magnetic flow and the denominator value Br0is the remanence of the magnetic flow, that is, the residual magnetic flow after the cancellation of the external field.

In both simulations, the magnets are made of ferrite with value Br0equal to 0.35 Tesla, with a total quantity of magnetic material of 2.8 kg and the rotor is rotated at a speed of 5000 rpm.

In addition, in order to reduce the risk of irreversible demagnetization of the magnets, it was assumed that the factor Demag(%) would not fall below 20%.

The simulations have shown that the first rotor, optimized using the method according to the invention, maximises the performance obtainable both in terms of maximum power, obtaining a value of 100 kW, and nominal power, obtaining a value of 65 kW.

Moreover, for each barrier B1, B2, B3, where the thicknesses bnare progressively decreasing from the inner surface Sito the outer surface Seand thus b1>b2>b3, the values of the Demagfactor (%) are 20% for B1, 23% for B2and 30% for B3.

By way of example, it has been assumed that the thicknesses bnof the first rotor are b1=7.2 mm, b2=6 mm, that is, between 0.75b1and 0.85b1and b3=3.9 mm, that is, between 0.5b1and 0.6b1.

The simulation of the second rotor showed an increased risk of demagnetization with regard to the magnets of the internal barriers B1and B2, thus reducing the maximum power limit and obtaining a value of 87 kW, with a nominal power value of 62.6 kW.

Moreover, for each barrier B1, B2, B3, where the thicknesses bnare equal to each other and therefore b1=b2=b3, the values of the Demagfactor (%) are 20% for B1, 32% for B2and 52% for B3.

For this reason, it is considered that only the first rotor, optimized using the method according to the invention, is able to reconcile a greater resistance to demagnetization together with an optimization of the reluctance phenomenon, enabling the best performance to be achieved with the same use of magnetic material.

The optimization method according to the invention was implemented by building a synchronous reluctance machine assisted by internal magnets with a nominal power of 2.2 kW, 4 poles and a nominal torque of 14 Nm, in order to measure the efficiency and the power factor.

Experimental tests were carried out on this machine, the results of which are given below.

The motor was rotated at a speed rotation of 1500 rpm, increasing the value of torque at the shaft T (%) and obtaining the values shown in Table 1 below.

T (Nm) is the torque applied to the crankshaft and measured by means of a torque meter;

PM(kW) is the mechanical power calculated as the product of the torque T applied to the shaft and the speed of rotation;

PE(kW) is the electrical power supplied as input to the motor power supply terminals;

I (A) is the current absorbed by the motor;

ε(%) is the efficiency of the motor and calculated as the ratio between the power output of the motor and the power applied;

P.F. (°) is the power factor measured at the motor terminals.

Subsequently, a second experimental test was carried out on a synchronous reluctance machine assisted by internal magnets built according to the method described above and having a nominal power of 7.5 kW, 4 poles and a nominal speed of 1200 rpm, in order to measure the torque ripple, as shown inFIG.3.

The motor has rotor thicknesses bnequal to b1=5.8 mm, b2=4.9 mm and b3=3.5 mm, and segment values fmequal to f1=6.65 mm, f2=5.65 mm and f3=4.54 mm.

The test showed that the torque ripple calculated according to the relation [1] is 0.86% peak.

From the above, it is clear that the method of optimizing a synchronous reluctance motor assisted by magnets according to the invention achieves the intended aims and in particular makes it possible to minimise the torque ripple, increase the power factor as well as the motor torque while using low-cost magnets.

The method according to the invention is susceptible to numerous modifications and variations all within the scope of protection expressed in the attached claims.

Although the method has been described with particular reference to the accompanying drawings, the reference numbers used in the description and in the claims are used to improve the understanding of the invention and do not constitute any limitation to the claimed scope of protection.

Reference throughout the description to “an embodiment” or “the embodiment” or “certain embodiments” indicates that a particular feature, structure or element described is included in at least one embodiment according to the invention.

In addition, the particular features, structures or elements can be combined in any suitable way in one or more embodiments.

INDUSTRIAL APPLICABILITY

The invention is industrially applicable in that it can be implemented on an industrial scale by industries belonging to the sector of production of rotating electrical machines.