CN101820240B - Spherical planning-based permanent magnetic spherical motor stator winding electrifying method - Google Patents

Abstract

The invention belongs to the technical field of permanent magnetic spherical stator current control, and relates to a spherical planning-based permanent magnetic spherical motor stator winding electrifying method, which comprises the following steps of: first establishing a static torque model of a permanent magnetic spherical motor with 54 stator windings of three layers; then planning a spherical area according to the distribution of the stator windings and dividing the spherical area into 72 spherical sub-areas for classifying detected stator position states; next marking numbers on the stator windings in each sub-area, designing electrifying rules for the stator windings in different states, and electrifying 18 of the 54 stator windings in each state; and finally resolving values of current for electrifying the 18 stator windings according to expected torque in permanent magnetic spherical motor kinetic control and the static torque model of the permanent magnetic spherical motor. Through the electrifying scheme of the invention, continuous control with relatively higher resolution can be conveniently performed on the permanent magnetic spherical motor, and all kinds of complex continuous track following can be realized.

Description

A kind of permanent magnet spherical motor stator winding electrifying method based on sphere planning

Technical field:

The invention belongs to the technical field of permanent magnet spherical motor Current Control, relate to a kind of energising strategy based on static torque model and the division of sphere subregion.

Background technology

The research and the application of space flight in modern times, military affairs, chemical industry, industrial automation and intelligent robot etc. all need realize multifreedom motion more and more.Permanent magnet spherical motor has that volume is little, in light weight, and the outstanding advantage that energy index is high can realize the motion of Three Degree Of Freedom, can be applied to joint of robot etc. and do in the precision apparatus of space multifreedom motion.

Its rotor can be realized rotation, pitching and driftage three degrees of freedom of movement, and the power-up sequence of control stator winding and energising size promptly through certain energising strategy, just can make permanent magnet spherical motor realize the synthetic of three-degree-of-freedom motion.Yet because the winding of permanent magnet spherical motor distributes and the more traditional single-degree-of-freedom motor complex of motion control, its energising strategy is also very complicated.The research of stator winding electrifying strategy becomes difficult point and the key in the research of permanent magnet spherical motor control problem.

At present, the implementation of several kinds of permanent magnet spherical motors is arranged, wherein, U.S. John Hopkins University has proposed the permanent magnet spherical motor structure that a kind of stator winding is positioned at stator sphere lower semisphere, has 16 stator winding.The present invention be directed to a kind of permanent magnet spherical motor of 3 layers of stator winding structure; 3 layers of winding of this motor stator distribute along 22.5 ° of parallel circles of north latitude on the stator sphere, equator and 22.5 ° of parallel circles of south latitude respectively for every layer; Every layer of 18 winding; The 20 ° of longitudes of being separated by between every layer of adjacent winding are so permanent magnet spherical motor involved in the present invention has 54 stator winding.Be embedded with 6 permanent magnets on the permanent magnet spherical motor rotor ball among the present invention, be the alternately distribution of N, the S utmost point along the rotor equator; Rotor magnetic pole adopts the method for parallel magnetization to magnetize.The research of electrifying method is the difficult point and the key of permanent magnet spherical motor control problem research.People such as HeFei University of Technology Wang Qun capital have proposed a kind of electrifying method of the permanent magnet spherical motor structure that proposes based on U.S. John Hopkins University.

List of references:

[1]Liang?Yan，I-Ming?Chen，Chee?Kian?Lim，Guilin?Yang，Wei?Lin，Kok-Meng?Lee.Torque?Modeling?of?Spherical?Actuators?with?Double-layer?Poles[C]，In?Proceedings?of?the?2006?IEEE/RSJ?InternationalConference?on?Intelligent?Robotics?and?Systems，2006：5447-5452.

[2] Wu Lijian, Wang Qunjing, Du Shijun, Ni Youyuan. the application [J] of magnetic field integration method in permanent magnetism stepping spherical motor field analysis. Proceedings of the CSEE, 2004,24 (9): 192-197.

Summary of the invention

The object of the present invention is to provide a kind of stator winding electrifying strategy, can make the permanent magnet spherical motor rotor in controlled range, realize the three-degree-of-freedom motion of various appointments.

For this reason, the present invention adopts following technical scheme:

A kind of permanent magnet spherical motor stator winding electrifying method based on sphere planning; Be applicable to the motor of following type: 3 layers of winding of stator distribute along 22.5 ° of parallel circles of north latitude on the stator sphere, equator and 22.5 ° of parallel circles of south latitude respectively for every layer; Every layer of 18 winding; The 20 ° of longitudes of being separated by between every layer of adjacent winding, stator coil is not installed iron core, realizes stator winding electrifying according to following steps:

The first step: according to the permanent magnet spherical motor kinetic model, the dynamics Controlling scheme of design permanent magnet spherical motor obtains the expectation torque expression formula in the kinetic control system, obtains each expectation torque value constantly in control procedure then;

Second step: the static torque model that obtains permanent magnet spherical motor with Finite Element Method or analytic method;

The 3rd step: the division of the numbering of stator winding and four types of subregions: set bulbec face and rotor sphere and be unit sphere; Definition is respectively attached to stator and epitrochanterian spherical coordinate system decides spherical coordinate system and moving spherical coordinate system; Being designated as

rotor surface upper warp and woof degree to the spherical coordinate value of certain point in above-mentioned two coordinate systems is zero point and is made as a S; According to a difference of S position, confirm corresponding energising winding and the electric current that is led to thereof, carry out sphere planning for the annular sphere zone between 22.5 ° of north latitude on the stator sphere and 22.5 ° of parallel circles of south latitude; Be divided into four types of I, II, III, IV totally 72 sub regions; Each subregion all is the zone that is similar to spherical triangle, and in plane outspread drawing, each sub regions all is similar triangles; On three angles of each subregion a stator winding is arranged respectively; Claim that three stator winding on three angles of subregion are positioned at this subregion, every type of subregion is along rotor longitude angle numbering, and every type has 18 sub regions; The analytical expression of each subregion is following

Point on the stator sphere in the I class subregion satisfies following relation:

Point on the stator sphere in the II class subregion satisfies following relation:

Point on the stator sphere in the III class subregion satisfies following relation:

Point on the stator sphere in the IV class subregion satisfies following relation:

The 4th step: the stator winding in each sub regions is carried out label.Regard the plane outspread drawing of sphere subregion as similar triangles; Then the stator winding at the place, similar angle of each similar triangles has identical regional internal label (1,2,3); Be defined on the stator sphere; Longitude angle differs 180 degree, and angle of latitude is that a pair of winding of opposite number becomes sphere diagonal angle winding, and balling-up has same regional internal label in the face of a pair of winding at angle.

The 5th step: the position to rotor is detected in real time; Confirm energising winding place subregion according to the real time position of a S; Confirm this subregion and with this subregion on the stator sphere respectively along 9 windings of positive longitudinal in 3 sub regions that 60 degree and 120 are spent; And the sphere diagonal angle winding of these 9 windings, totally 18 windings are intended the stator winding of switching on for this reason constantly.

The 6th step: according to the relative position of specific 9 windings in the fixed energising stator winding with some S; And by the second static torque model that obtain of step; Draw 3 * 9 static torque matrix, the initial point in the corresponding static torque model of some S is in static torque model; The span of longitude angle be [0,360); It is poor to get above-mentioned 9 windings and put the longitude and latitude of S in deciding spherical coordinate system; If the difference of longitude angle is less than zero; Then make the difference of longitude angle add 360; Then, above-mentioned 9 longitude and latitude differences are called static torque value wherein as the point of the coordinate position in the static torque model, above-mentioned 9 winding correspondences can be formed static torque matrix T at the static torque value of the three degree of freedom at 9 location point places of static torque model _n∈ R ^{3 * 9}, 9 column vectors in the static torque matrix are to arrange in proper order according to above-mentioned 9 windings place subregion and the label in subregion thereof;

The 7th step: go on foot the static torque matrix T that obtains with the 6th _n∈ R ^{3 * 9}Premultiplication is just decided current vector I ∈ R ^{9 * 1}Equal the expectation torque vector T ∈ R that the first step obtains ^{3 * 1}, through finding the solution the pseudo inverse matrix T of static torque matrix _n ⁺∈ R ^{9 * 3}, try to achieve and just decide current vector I ∈ R ^{9 * 1}

The 8th step: just decide current vector I and distribute: 9 components among the I/2 are distributed to 9 windings confirming in the 6th step respectively, 9 components the among-I/2 are distributed to aforementioned and 9 the corresponding sphere of windings difference diagonal angle windings respectively to what try to achieve by the 7th step.

Beneficial effect of the present invention is:

1. the present invention adopts the thought of sphere planning to divide subregion, and division methods is fairly simple, easy Analytical Expression of the subregion of division and classification, and intuitive is good, is easy to realize.

2. the present invention is based on the static torque model of permanent magnet spherical motor; This static torque model is made up of lot of data point; Have higher resolution, corresponding static torque value is all arranged when a S is positioned at the place, arbitrfary point of aforementioned sphere annular region equal resolution.Therefore, use the energising strategy that the present invention relates to, be convenient to permanent magnet spherical motor is carried out the higher continuous control of resolution, its continuous path of in the tactful scope of application of energising, realizing various complicacies is followed the tracks of.

3. according to energising strategy involved in the present invention during to the permanent magnet spherical motor stator winding electrifying, the distribution of energising stator winding is comparatively even, helps forming moment stably, and is significant for the stable control of permanent magnet spherical motor.

4. energising strategy involved in the present invention has improved the utilance of stator winding to greatest extent under the existing 3 layers of stator winding and the 3 pairs of rotor magnetic pole structures, per moment all has 18 stator winding to switch on simultaneously.Like this, each stator winding need not lead to too big electric current just can guarantee that total torque reaches the requirement of expectation torque, to accomplish the service requirement of permanent magnet spherical motor.Emulation shows that when carrying out complicated three-degree-of-freedom motion, the stator current when adopting this energising strategy is moderate, is easy on hardware, be achieved.

Description of drawings:

The three-degree-of-freedom motion sketch map of Fig. 1 rotor, (a) and (b), (c) are illustrated rotation, pitching and driftage three degree of freedom respectively.

Fig. 2 computing power moments method controller chassis figure.

Fig. 3 permanent magnet spherical motor FEM model and rotor field distribute.

Static torque spatial distribution map when Fig. 4 gas length is 2mm.

Static torque is along the distribution map of longitude angle

during Fig. 5 fixed latitude angle θ.

The relation of Fig. 6 torque value and number of ampere turns.

Fig. 7 stator winding numbering and sphere subregion sketch map.

Fig. 8 sphere subregion plane outspread drawing.

Fig. 9 subregion winding labeled graph.

Figure 10 energization area is along θ direction distribution schematic diagram.

Each track following situation in Figure 11 nutation movement.

The variation of Figure 12 nutation movement mid point S longitude and latitude in deciding spherical coordinate system.

Stator winding electrifying situation in Figure 13 nutation movement.

The space tracking of Figure 14 point S in the nutation movement of different frequency followed the tracks of.

Each step response of Figure 15.

The longitude and latitude situation of change of Figure 16 step response time point S in deciding spherical coordinate system.

Stator winding electrifying situation when Figure 17 is given as step signal.

The energising situation of all stator winding when Figure 18 is given as step signal.

Embodiment

At first introduce a kind of performing step of permanent magnet spherical motor stator winding electrifying strategy below:

The first step: according to the permanent magnet spherical motor kinetic model, the dynamics Controlling scheme of design permanent magnet spherical motor.Can obtain the expectation torque expression formula in the kinetic control system thus.According to this expression formula, can access each expectation torque value constantly in control procedure.It is 3 * 1 expectation torque vector T that the expectation torque value of certain three degree of freedom constantly can be formed dimension.

Second step: obtain the static torque model of permanent magnet spherical motor with Finite Element Method, comprise rotation, pitching and driftage three degree of freedom.In this FEM model, rotor magnetic pole adopts 6 permanent magnets, is the mode that N, the S utmost point alternately arrange and arranges along the equator of rotor sphere.Gas length location 2mm between stator winding and the rotor magnetic pole.Stator winding is not installed iron core, and therefore, magnetic saturation effect can be ignored, and electric current number of ampere turns and level of torque are directly proportional.This is the prerequisite of among the present invention current vector being carried out Solving Linear.The data precision of this static torque model is that resolution all is 1 degree on precision and latitude direction, and this data precision has determined the precision of permanent magnet spherical motor energising strategy.If improve the precision of energising strategy, can precision as required carry out interpolation to this static torque model, obtain new static torque model, to satisfy required precision.

The 3rd step: the division of the numbering of stator winding and four types of subregions.Study 3 layers of real-time energising situation of totally 54 stator winding, must number stator winding.Realize the control of permanent magnet spherical motor, will at first detect in real time the position of rotor.The radius of setting bulbec face and rotor sphere all is a unit 1, promptly ignores gas length.Definition is respectively attached to stator and epitrochanterian spherical coordinate system decides spherical coordinate system and moving spherical coordinate system.Rotor surface upper warp and woof degree is zero point and is made as a S, and the present invention confirms corresponding energising winding and the electric current that is led to thereof according to a difference of S position.The stator winding location point is distributed on the stator sphere in the annular sphere zone between 22.5 ° of the north latitude and 22.5 ° of parallel circles of south latitude; Sphere planning is carried out in this annular sphere zone; Be divided into four types of I, II, III, IV totally 72 sub regions, and provide the analytical expression of each subregion.Each subregion all is the zone of a similar spherical triangle, and a stator winding is arranged respectively on three angles, claims that three stator winding on three angles of subregion are positioned at this subregion.Every type of subregion is along rotor longitude angle numbering, and every type has 18 sub regions.In energising strategy involved in the present invention, in the time of in the some annular sphere zone of S between 22.5 ° of stator sphere north latitude and 22.5 ° of parallel circles of south latitude, when also promptly putting S and being arranged in a sub regions of above-mentioned 72 sub regions, the energising strategy is effective.

The 4th step: the stator winding in each sub regions is carried out label.The plane outspread drawing of sphere subregion can be regarded similar triangles as, and then the stator winding at the place, similar angle of these similar triangles has identical regional internal label (as 1,2,3).Provided the notion of sphere diagonal angle winding, promptly on the stator sphere, longitude angle differs 180 degree, and angle of latitude is that a pair of winding of opposite number becomes sphere diagonal angle winding.According to this notion, balling-up has same regional internal label in the face of a pair of winding at angle, and gives that two windings that are the sphere diagonal angle are logical to be waited greatly when anti-electric current, and these two windings can be to big moments such as rotor ball generations.

The 5th step: confirm energising winding place subregion according to the real time position of a S.The subregion at certain moment point S place with this subregion on the stator sphere respectively along 9 windings of positive longitudinal in 3 sub regions such as similar subregion that 60 degree and 120 are spent; And the sphere diagonal angle winding of these 9 windings, totally 18 windings are intended the stator winding of switching on for this reason constantly.

The 6th step:, and, draw 3 * 9 static torque matrix by the static torque model that second step obtained according to the relative position of specific 9 windings in the fixed energising stator winding with some S.Point S is positioned at rotor sphere upper warp and woof degree and is zero point, the initial point in the corresponding static torque model.In static torque model, the span of longitude angle be [0,360).Poor to above-mentioned 9 windings and the longitude and latitude of some S in deciding spherical coordinate system.Wherein, if the difference of longitude angle then adds 360 less than zero; The difference of angle of latitude if the words of negative need not adjust.The span of the longitude and latitude in the span that can make these 9 longitude and latitude differences like this and the static torque model conforms to.Then, above-mentioned 9 longitude and latitude differences are called static torque value wherein as the point of the coordinate position in the static torque model.Above-mentioned 9 winding correspondences can be formed static torque matrix T at the static torque value of the three degree of freedom at 9 location point places of static torque model _n∈ R ^{3 * 9}9 column vectors in the static torque matrix are to arrange in proper order according to above-mentioned 9 windings place subregion and the label in subregion thereof.

The 7th step: the static torque matrix T that the 6th step obtained _n∈ R ^{3 * 9}Premultiplication is just decided current vector I ∈ R ^{9 * 1}Equal the expectation torque vector T ∈ R that the first step obtains ^{3 * 1}So, through finding the solution the pseudo inverse matrix T of static torque matrix _n ⁺∈ R ^{9 * 3}, can be in the hope of just deciding current vector I ∈ R ^{9 * 1}Just decide the pseudo inverse matrix premultiplication expectation torque vector that current vector equals static torque matrix.

The 8th step: will by the 7th step try to achieve just decide current vector I and distribute.9 components among the I/2 are distributed to 9 windings confirming in the 6th step respectively, 9 components the among-I/2 are distributed to the sphere diagonal angle winding of aforementioned 9 windings respectively.So far, 18 electrical currents of intending the energising stator winding are all confirmed.

Permanent magnet spherical motor rotor three-degree-of-freedom motion sketch map involved in the present invention is as shown in Figure 1.

Decide cartesian coordinate system xyz and moving cartesian coordinate system dqp if adhere to respectively on the stator of permanent magnet spherical motor and the rotor, then the three-degree-of-freedom motion of relative position between two coordinate systems and permanent magnet spherical motor can be used the definition of generalized Euler angle.According to newton-Lagrangian energy method, it is following to get its kinetics equation ^[6]:

$M\left(\mathrm{\θ}\right)\stackrel{\·\·}{\mathrm{\θ}}+C(\mathrm{\θ},\stackrel{\·}{\mathrm{\θ}})\stackrel{\·}{\mathrm{\θ}}+{\mathrm{\τ}}_f=\mathrm{\τ}---\left(1\right)$

Wherein, M (θ) ∈ R ^{3 * 3}Be inertial matrix;

Be centrifugal force and coriolis force matrix; θ=(α, beta, gamma) ^TBe angle position vector;

With

Be respectively angular velocity vector and angular acceleration vector; τ _f=(τ _{F α}, τ _{F β}, τ _{F γ}) ^TBe load and moment of friction, can be counted as the destructuring uncertainty; τ=(τ _α, τ _β, τ _γ) ^TIt is the control moment vector.

The computing power moments method is a kind of control algolithm based on model, has been widely used in robot dynamics's control.The structure applications of computing power moments method is controlled in the dynamics decoupling zero of permanent magnet spherical motor, and the model that makes up through estimated value has carried out nonlinear compensation to permanent magnet spherical motor.Computing power moments method control rate is following:

$\mathrm{\τ}=\tilde{M}\left(\mathrm{\θ}\right)u+\tilde{C}(\mathrm{\θ},\stackrel{\·}{\mathrm{\θ}})\stackrel{\·}{\mathrm{\θ}}---\left(2\right)$

In the formula;

is the inertial matrix that makes up according to estimated value, be centrifugal force and the coriolis force matrix that makes up according to estimated value.U is a servo segment, representes as follows:

$u={\stackrel{\·\·}{\mathrm{\θ}}}_d+K_d\stackrel{\·}{e}+K_{p}e---\left(3\right)$

Wherein, θ _dBe given angle position vector, K _pBe proportionality coefficient matrix, K _dBe the differential coefficient matrix, they all are diagonal matrix; E=θ _d-θ is an error vector; Be the error rate vector.The control block diagram of computing power moments method is as shown in Figure 2.

When static torque model was described in logical unit positive current, stator winding was at the torque value of each location point and rotor interaction generation.Static torque model plays crucial effect to the research of spherical motor control.Find the solution static torque model can FInite Element (FInite Element that for example can adopt the present invention to provide perhaps adopts document ^[1]The FInite Element that provides, or other FInite Element), also can adopt analytic method ^[2]Inventive point of the present invention does not lie in static torque model itself; Various static torque model of the prior art; No matter be the model of setting up with analytic method or FInite Element, can use in the present invention, and; At the pseudo inverse matrix that passes through to find the solution static torque matrix subsequently, it all is identical trying to achieve the methods that step adopted such as distribution of just deciding current vector and electrical current.

The present invention analyzes the static torque of permanent magnet spherical motor with Finite Element Method.Fig. 3 (a) is the FEM model of permanent magnet spherical motor.Have 54 stator winding in the model, be divided into 3 layers, 18 every layer.Rotor has six permanent magnet poles, becomes N, the S utmost point alternately to distribute.Permanent magnet adopts the parallel magnetization mode to magnetize.Fig. 3 (b) is a rotor magnetic pole magnetic intensity vector distribution map.Can find out that by Fig. 3 (b) direction of magnetization is parallel in single permanent magnet magnetic patch, and the direction of magnetization of adjacent permanent magnet is opposite.

The internal diameter of single stator winding, external diameter and be made as R highly respectively _I, R _oAnd H, the angle of latitude between the adjacent two layers stator coil is made as φ _L, the gas length between stator winding and the rotor magnetic pole is made as δ.In FEM model of the present invention, the numerical tabular of said stator winding parameter is as shown in table 1.

Table 1 stator winding parameter

R I/mm	R o/mm	H/mm	φ L/deg	?δ/mm
					5	10	15	22.5	?2

The outer surface of rotor magnetic pole is the part of sphere, and inner surface is the part of cylinder.If the external diameter and the internal diameter of single rotor magnetic pole are respectively R _{PM_I}And R _{PM_o}, the height of rotor magnetic pole is H, residual magnetic flux density is B _r, relative permeability is μ _r, the rotor magnetic pole parameter is as shown in table 2.

Table 2 rotor magnetic pole parameter

R PM_I/mm	R PM_o/mm	H PM/mm	?B r/T	μ r
					55	80	45	?1	1.02

If θ is the longitude angle of rotor sphere;

is the angle of latitude of rotor sphere; Single stator winding suffered static torque spatial distribution map when Fig. 4 has provided the gas length that adopts FInite Element to obtain and is 2mm; Wherein, Fig. 4 (a) is static rotation torque, and Fig. 4 (b) is static pitching torque.Fig. 5 has provided the static torque grading curve of angle of latitude θ fixedly the time.Wherein, the static rotation torque grading curve during Fig. 5 (a) expression θ=15 °, the static pitching torque grading curve during Fig. 5 (b) expression θ=10 °.

As can beappreciated from fig. 5, the excursion of longitude angle θ be [0,360), unit for the degree.(being longitudinal) is the cycle variation along

angular direction for rotation and pitching torque value, and the cycle is 180 °.In fact; Static driftage torque value is similar along the distribution shape and the static pitching torque of longitude and latitude direction, and just the former lags behind 90 ° on longitude angle

direction than the latter.

Stator coil is not installed iron core, and therefore, magnetic saturation effect can be ignored, and electric current number of ampere turns and level of torque are directly proportional basically.The proportional relation of electric current number of ampere turns and level of torque when Fig. 6 has verified different air gap.Pitching and deflection torque also have same rule.

The data precision of this static torque model is that resolution all is 1 degree on precision and latitude direction, and this data precision has determined the precision of permanent magnet spherical motor energising strategy.If improve the precision of energising strategy, can precision as requested carry out interpolation to this static torque model, obtain new static torque model, to satisfy required precision.

The permanent magnet spherical motor rotor position detection is the prerequisite that it is controlled, and the precision of position probing and speed directly influence the precision and the real-time of control.Detect in each sampling instant of host computer physical location, confirm stator winding and the current value thereof that this intends energising constantly according to this position then permanent magnet spherical motor.People such as the Kok-Meng Lee of Georgia Institute of Technology have proposed a kind of contactless photoelectric sensor.This photoelectric sensor can be realized accurate position probing under the prerequisite of spherical motor not being carried out mechanical constraint, draw the angle value of its each degree of freedom, and real-time is better.

Two spheric coordinate systems are decided spherical coordinate system and moving spherical coordinate system, respectively attached on stator and the rotor.The winding numbering of setting equator, bulbec shell upper edge is followed successively by i-0, numbers along the winding of 22.5 ° of north latitude and is followed successively by i-1, and number along the winding of 22.5 ° in south latitude and be followed successively by i-2, wherein, and i=1 ..., 18.Table 4 is stator winding

value in deciding spheric coordinate system.

Table 4 stator winding

value in position fixing system

The diameter of setting son and rotor sphere all is a unit 1, promptly ignores gas length.Like this, the moving spherical coordinate system that adheres to rotor and be the unit ball coordinate system with the spherical coordinate system of deciding that stator adheres to, promptly perseverance satisfies R=1.According to general spherical coordinates definition; The coordinate figure of sphere point in spherical coordinate system is

for simplicity, below is designated as

to spherical coordinate value in above-mentioned two coordinate systems of certain point

Overlap if permanent magnet spherical motor is decided cartesian coordinate system and moving cartesian coordinate system when initial position, when this initial position, the point of decide coordinate figure in the cartesian coordinate system and being (1,0,0) is made as a S.In permanent magnet spherical motor rotor rotary movement, the position of some S can be measured through checkout gear.

Fig. 7 is coil numbering and sphere subregion sketch map.Fig. 7 (a) and Fig. 7 (b) expression stator coil coding rule.Sphere planning is carried out in annular sphere zone between 22.5 ° of north latitude on the stator sphere and 22.5 ° of parallel circles of south latitude.With this area dividing is 72 3 apex sphere face zones, and it is classified as the I class, the II class, and III class and IV class subregion, every type of subregion has 18.These subregions all are by warp, parallel and cross the sphere subregion that three spherical arc line segments of great circle minor arc of two stator winding location points surround, shown in Fig. 7 (c).Among Fig. 7 (c), some S is arranged in II class subregion.Land portions among Fig. 7 (d) is an I class subregion, and the O point is the rotor centre of sphere, and arc UV is one section warp, and VW is one section equator parallel, and WU was one section great circle minor arc of some W and some U.Respectively there is a stator winding position, three summits of subregion (like U, V, the W among Fig. 7 (d)), and in discussion of the present invention, the stator winding of claiming place, subregion summit is in this sub regions.Like this, a stator winding just is in the different several adjacent subregions.

Fig. 8 is the sphere expanded view of subregion, and each sub regions among the figure and stator winding distribute with

direction along θ.The numbering of all subregion is as shown in the figure.The 2nd II class subregion is expressed as 2, the 7 IV class subregions of II and is expressed as IV 7 among the figure, and other subregions are similar.Among Fig. 8, the circle at place, subregion summit is represented stator winding, numbers according to the rule among Fig. 7.

The thought that spherical area is planned is similar to plane planning.

coordinate system according among Fig. 8 can draw the analytical expression of each sub regions.Wherein, the point in the I class subregion satisfies following relation on the stator sphere:

Point on the stator sphere in the II class subregion satisfies following relation:

Point on the stator sphere in the III class subregion satisfies following relation:

Point on the stator sphere in the IV class subregion satisfies following relation:

In research of the present invention, have only as a some S to be between 22.5 ° of the north latitude and 22.5 ° of two parallel circles of south latitude of stator sphere, promptly to put S and be in above-mentioned four types during the sub regions in totally 72 sub regions, the energising strategy of stator winding is just effectively; As surpassing above-mentioned zone, this strategy fails of switching on.Be positioned on the equator of rotor sphere owing to put S, the scope of application of energising strategy proposed by the invention can think that also the pitching of rotor and yaw angle are not more than 22.5 ° scope.

In order each stator winding in the subregion to be distinguished and to be sorted out,, carry out label further for the stator winding in each sub regions with the research of convenient energising strategy.Fig. 9 representes the label of partial stator winding in the subregion of planar development.Subregion I 1, II 1, III 1 and IV 1 are similar triangles in plane outspread drawing, and the label (like 1,2,3 among the figure) of the winding at the place, similar angle that these four similar triangles are corresponding is identical.Label is that the winding of i (i=1,2,3) is designated as Ci in the subregion.

According to above-mentioned subregion winding index methods, stator winding I1 C1 and III 10 C1 solicit comments are in the two ends through a diameter line segment of the rotor centre of sphere well.We deserve to be called and state two windings is sphere diagonal angle winding.In fact, above-mentioned two windings are respectively stator winding 1-0 and 10-0, can find out from table 4, and two windings obviously satisfy sphere to angular dependence.Can be known that by above-mentioned analysis sphere diagonal angle winding is that the longitude on the stator sphere differs 180 degree, latitude is a pair of winding of opposite number.Usually, with winding Ii Cj (i=1 ..., 18; J=1,2,3) balling-up in the face of the winding at angle is:

$\left\{\begin{array}{c}\mathrm{III}(i+9)\mathrm{Cj},i\&le;9\\ \mathrm{III}(i+9-18)\mathrm{Cj},9<i\&le;18\end{array}\right.---\left(8\right)$

With winding II i Cj (i=1 ..., 18; J=1,2,3) balling-up in the face of the winding at angle is:

$\left\{\begin{array}{c}\mathrm{IV}(i+9)\mathrm{Cj},i\&le;9\\ \mathrm{IV}(i+9-18)\mathrm{Cj},9<i\&le;18\end{array}\right.---\left(9\right)$

With winding III i Cj (i=1 ..., 18; J=1,2,3) balling-up in the face of the winding at angle is:

$\left\{\begin{array}{c}I(i+9)\mathrm{Cj},i\&le;9\\ I(i+9-18)\mathrm{Cj},9<i\&le;18\end{array}\right.---\left(10\right)$

With winding IV i Cj (i=1 ..., 18; J=1,2,3) balling-up in the face of the winding at angle is:

$\left\{\begin{array}{c}\mathrm{II}(i+9)\mathrm{Cj},i\&le;9\\ \mathrm{II}(i+9-18)\mathrm{Cj},9<i\&le;18\end{array}\right.---\left(11\right)$

For permanent magnet spherical motor involved in the present invention, when being sphere to the logical equivalent reverse electric current of two stator winding of angular dependence, these two windings such as can produce at big torque value.

According to the analysis of front, the coordinate figure of some S in moving spherical coordinate system is (0,0).In fact; Because the reference axis on the static torque curve overlaps with

the θ reference axis on the rotor sphere, some S just in time is positioned on the origin position of static torque curve.If t ₀The pairing coordinate figure of deciding among the cartesian coordinate system xyz of moment point S is (x ₀, y ₀, z ₀), then can be in the hope of the coordinate figure in the spherical coordinate system of deciding of this coordinate figure correspondence according to the transformation relation of spheric coordinate system and cartesian coordinate system

Because the rotor sphere is a unit sphere, this transformation relation is shown in (12) formula:

Can judge t according to (4)-(7) formula ₀Which subregion moment point S is in.If this subregion is ∏ i (∏=I, II, III, IV; I=1; ...; 18); Three stator winding C1 in this subregion; C2, C3 is corresponding decides the difference that coordinate figure is respectively

establishes these three coordinate figures and

in the spherical coordinate system and is respectively

and calculates according to following rule:

During as

,

During as ,

(13) formula has guaranteed θ with (14) formula _i∈ [0,360) (i=1,2,3).Because the coordinate figure of some S in moving spherical coordinate system is always (0,0), according to the fundamental property of spherical coordinate system and relative coordinate system, at t ₀Constantly, stator winding C1, C2, the coordinate figure of C3 in moving spherical coordinate system is respectively

Owing to put the origin position that S is in static torque curve all the time, so according to t ₀Moment stator winding C1, C2, the coordinate figure of C3 in moving spherical coordinate system can draw the location point in the corresponding static torque curve of said stator winding, calls the static torque value in the static torque curve with the mode of visit array then.

The corresponding one group of static torque value (comprising pitching, driftage, rotation three degree of freedom) of each location point is made as respectively

τ ₁＝(τ _pit1，τ _yaw1，τ _spi1) ^T (15)

τ ₂＝(τ _pit2，τ _yaw2，τ _spi2) ^T (16)

τ ₃＝(τ _pit3，τ _yaw3，τ _spi3) ^T (17)

With subregion ∏ i (∏=I, II, III, IV; I=1 ..., 18) belong to one type subregion

$\left\{\begin{array}{c}\mathrm{II}(i+3),1\&le;i\&le;15\\ \mathrm{II}(i+3-18),15<i\&le;18\end{array}\right.---\left(18\right)$

Three interior stator winding are C1; C2; C3, the coordinate figure of establishing in its corresponding moving spherical coordinate system is respectively

can draw its difference correspondence according to the similar method in front static torque value:

τ ₄＝(τ _pit4，τ _yaw4，τ _spi4) ^T (19)

τ ₅＝(τ _pit5，τ _yaw5，τ _spi5) ^T (20)

τ ₆＝(τ _pit6，τ _yaw6，τ _spi6) ^T (21)

With subregion ∏ i (∏=I, II, III, IV; I=1 ..., 18) belong to another subregion of one type

$\left\{\begin{array}{c}\mathrm{II}(i+6),1\&le;i\&le;12\\ \mathrm{II}(i+6-18),12<i\&le;18\end{array}\right.---\left(22\right)$

Three interior stator winding C1; C2, the coordinate figure in the moving spherical coordinate system of C3 correspondence is made as

respectively in like manner can obtain its corresponding static torque value:

τ ₇＝(τ _pit7，τ _yaw7，τ _spi7) ^T (23)

τ ₈＝(τ _pit8，τ _yaw8，τ _spi8) ^T (24)

τ ₉＝(τ _pit9，τ _yaw9，τ _spi9) ^T (25)

So obtained the static torque matrix of 3 * 9 stator winding formed by static torque value:

T _n＝[τ ₁，τ ₂，τ ₃，τ ₄，τ ₅，τ ₆，τ ₇，τ ₈，τ ₉] (26)

Expectation torque T ∈ R ^{3 * 1}Can provide by (2) formula.Analysis by the front can know that for the winding that does not have stator core, the torque value that winding produces is directly proportional with the electric current number of ampere turns.So the expectation torque can be expressed as following formula:

T＝T _nI (27)

Wherein, I ∈ R ^{9 * 1}For aforementioned 3 ∏ (i=I, II, III, IV) 9 stator winding first decided current value in type subregion.This current value can be through asking the static torque matrix T of stator winding _nGeneralized inverse try to achieve:

I＝T _n ⁺T (28)

Wherein, T _n ⁺∈ R ^{9 * 3}Be T _nGeneralized inverse matrix.

Then, 9 electric currents that winding led to that the front is related to reduce by half, i.e. I/2.Can confirm the sphere diagonal angle winding of these 9 windings according to (8)-(11) formula.Let logical respectively its reverse current after reducing by half of the sphere diagonal angle winding of these 9 windings, the matrix that these reverse currents are formed is-I/2.Like this, at t ₀The winding of constantly switching on adds up to 18.According to the analysis of front, the torque value that these 18 windings produce just equals to expect torque value.

Figure 10 sketch map that stator winding place subregion (being designated hereinafter simply as the energising subregion) distributes along longitudinal of representing to switch on; Wherein, Figure 10 (a) expression point S is in longitude angle [0; 20) situation in the scope (this time point S be positioned at subregion I 1, II 1, III 1 or IV 1 in the middle of a sub regions), Figure 10 (b) expression point S be in longitude angle [40,60) situation in the scope (this time point S be positioned at subregion I 3, II 3, III 3 or IV 3 in the middle of sub regions); Figure 10 (c) expression point S is in longitude angle [100; 120) situation in the scope (this time point S be positioned at subregion I 6, II 6, III 6 or IV 6 in the middle of sub regions), Figure 10 (d) expression point S be in longitude angle [120,140) situation in the scope (this time point S be positioned at subregion I 7, II 7, III 7 or IV 7 in the middle of sub regions).

The present invention carries out simulating, verifying to the electrifying method of permanent magnet spherical motor.Do under the nutation movement situation in rotor of output shaft axle, actual path is shown in figure 11 for the tracking situation of desired trajectory.Wherein, Figure 11 (a), Figure 11 (b) and Figure 11 (c) represent the situation of α, β and γ axle respectively.

According to the analysis of front, this energising strategy is applicable to that a S is in and decides all situations between 22.5 ° of the north latitude and 22.5 ° of two parallel circles of south latitude in the spherical coordinate system.By the corresponding relation between Eulerian angles space and the cartesian space coordinate and (4) formula, can obtain changing at the longitude and latitude angle that above-mentioned nutation movement mid point S is deciding in the spherical coordinate system, shown in figure 12.

Can find out that by Figure 12 in above-mentioned nutation movement, the range of movement that S is ordered is in the scope of application of the energising strategy that the present invention proposes.

Figure 13 is illustrated in the above-mentioned nutation movement, the size of current that stator winding led to of permanent magnet spherical motor.Wherein, Figure 13 (a) expression stator winding 1-0, Figure 13 (b) expression stator winding 5-1, Figure 13 (c) expression stator winding 9-2, Figure 13 (d) expression stator winding 14-2, Figure 13 (e) expression stator winding 15-2, Figure 13 (f) expression stator winding 16-0.

According to the analysis of front, stator winding 5-1 and 14-2 are respectively I 5 C2 windings and III 14 C2 windings, are to be a pair of winding of sphere to angular dependence, and in galvanization, its size of current is equivalent all the time reverse.Figure 13 (b) and Figure 13 (d) have just in time verified this characteristic.Each stator winding electric current among Figure 13 is after after a while, and beginning to appear comparatively, the cycle of rule changes.This cycle is consistent with the cycle of the given signal of sine and cosine among Figure 11.For the ease of understanding nutation movement; Figure 14 has provided the track following situation of some S in the nutation movement of different frequency; Wherein, Situation when the frequency of the given signal of Figure 14 (a) expression α, β axle is 2rad/s, the situation the when frequency of the given signal of Figure 14 (b) expression α, β axle is 1rad/s.In fact, the frequency of α, the given signal of β axle has determined the hunting frequency of rotor of output shaft axle in the nutation movement, and the slope of the given signal of its γ axle has determined the rotating speed of rotor of output shaft axle rotation.In nutation movement, some S also presents the rule of periodic oscillations rotation, from Figure 14 (a) and Figure 14 (b), can find out the difference of two kinds of situation lower swing frequencies.In stable operation stage, because the given signal of γ axle is the certain ramp signal of slope, so motor rotation rotating speed remains unchanged basically.Can be found out that by Figure 14 after the time through 2 π seconds, the numerical value of the given signal of γ axle has increased by 2 π radians, promptly the permanent magnet spherical motor rotor is from circling.In the middle of second, the given signal of α, β axle has also been accomplished the variation of one-period at this 2 π.So 2 π are after second, the coordinate figure of some S in deciding spherical coordinate system equated before second with 2 π, so the stator winding electrifying electric current of confirming according to the position of a S also equated before second with 2 π.

The given signal that three Eulerian angles axles are discussed at present is the operating mode of step signal.Permanent magnet spherical motor is shown in figure 15 to the response of α, β and γ axle step signal.Deciding the longitude and latitude situation of change in the spherical coordinate system at above-mentioned step response rotor surface point S, shown in figure 16.

As can beappreciated from fig. 16, the longitude and latitude of some S in deciding spherical coordinate system changes in the scope of application of the energising strategy that is in the present invention's proposition all the time.Figure 17 is the current conditions of stator winding in the above-mentioned step response.Figure 17 (a) expression stator winding 1-1, Figure 17 (b) expression stator winding 4-0, Figure 17 (c) expression stator winding 7-0, Figure 17 (d) expression stator winding 12-2, Figure 17 (e) expression stator winding 13-0, Figure 17 (f) expression winding 16-0.

Can find out that from last figure stator winding 7-0 and 16-0, the current value among 4-0 and the 13-0 etc. are greatly to instead.This is because above-mentioned two opposing connection groups are respectively that to be sphere right to the winding of angular dependence.Figure 18 is illustrated in the electric current of all stator winding when being given as step signal.Wherein, Figure 18 (b) is the part amplification of Figure 18 (a).

As can beappreciated from fig. 18, in the incipient stage, step response is in ascent stage, and rotor of output shaft axle is being moved to appointed positions, and the electric current that needs is bigger.In the time of near rotor of output shaft axle is stabilized in assigned address gradually, the current value that needs is less.This also can find out through (4) formula.Owing to contain a large amount of Eulerian angles derivative terms, the ascent stage of expectation torque in step response is bigger, so its corresponding stator current is also bigger; When ascent stage finished, rotor stability was near a position, and the expectation torque becomes very little, and corresponding stator current is also less.

Claims (1)

1. permanent magnet spherical motor stator winding electrifying method based on sphere planning; Be applicable to the motor of following type: 3 layers of winding of stator distribute along 22.5 ° of parallel circles of north latitude on the stator sphere, equator and 22.5 ° of parallel circles of south latitude respectively for every layer; Every layer of 18 winding, the 20 ° of longitudes of being separated by between every layer of adjacent winding, stator coil is not installed iron core; It is characterized in that, realize stator winding electrifying according to following steps:

The first step: according to the permanent magnet spherical motor kinetic model, the dynamics Controlling scheme of design permanent magnet spherical motor obtains the expectation torque expression formula in the kinetic control system, obtains each expectation torque value constantly in control procedure then;

Second step: the static torque model that obtains permanent magnet spherical motor with Finite Element Method or analytic method;

The 3rd step: the division of the numbering of stator winding and four types of subregions: set bulbec face and rotor sphere and be unit sphere; Definition is respectively attached to stator and epitrochanterian spherical coordinate system decides spherical coordinate system and moving spherical coordinate system; Being designated as rotor surface upper warp and woof degree to the spherical coordinate value of certain point in above-mentioned two coordinate systems is zero point and is made as a S; According to a difference of S position, confirm corresponding energising winding and the electric current that is led to thereof, carry out sphere planning for the annular sphere zone between 22.5 ° of north latitude on the stator sphere and 22.5 ° of parallel circles of south latitude; Be divided into four types of I, II, III, IV totally 72 sub regions; Each subregion all is the zone that is similar to spherical triangle, and in plane outspread drawing, each sub regions all is similar triangles; On three angles of each subregion a stator winding is arranged respectively; Claim that three stator winding on three angles of subregion are positioned at this subregion, every type of subregion is along rotor longitude angle numbering, and every type has 18 sub regions; The analytical expression of each subregion is following

Point on the stator sphere in the I class subregion satisfies following relation:

Point on the stator sphere in the II class subregion satisfies following relation:

Point on the stator sphere in the III class subregion satisfies following relation:

Point on the stator sphere in the IV class subregion satisfies following relation:

The 4th step: the stator winding in each sub regions is carried out label: regard the plane outspread drawing of sphere subregion as similar triangles; Then the stator winding at the place, similar angle of each similar triangles has identical regional internal label (1,2,3); Be defined on the stator sphere; Longitude angle differs 180 degree, and angle of latitude is that a pair of winding of opposite number becomes sphere diagonal angle winding, and balling-up has same regional internal label in the face of a pair of winding at angle;

The 5th step: the position to rotor is detected in real time; Confirm energising winding place subregion according to the real time position of a S; Confirm this subregion and with this subregion on the stator sphere respectively along 9 windings of positive longitudinal in 3 sub regions that 60 degree and 120 are spent; And the sphere diagonal angle winding of these 9 windings, totally 18 windings are intended the stator winding of switching on for this reason constantly;

The 6th step: according to the relative position of specific 9 windings in the fixed energising stator winding with some S; And by the second static torque model that obtain of step; Draw 3 * 9 static torque matrix, the initial point in the corresponding static torque model of some S is in static torque model; The span of longitude angle be [0,360); It is poor to get above-mentioned 9 windings and put the longitude and latitude of S in deciding spherical coordinate system; If the difference of longitude angle is less than zero; Then make the difference of longitude angle add 360; Then, above-mentioned 9 longitude and latitude differences are called static torque value wherein as the point of the coordinate position in the static torque model, above-mentioned 9 winding correspondences can be formed static torque matrix T at the static torque value of the three degree of freedom at 9 location point places of static torque model _n∈ R ^{3 * 9}, 9 column vectors in the static torque matrix are to arrange in proper order according to above-mentioned 9 windings place subregion and the label in subregion thereof;

The 7th step: go on foot the static torque matrix T that obtains with the 6th _n∈ R ^{3 * 9}Premultiplication is just decided current vector I ∈ R ^{9 * 1}Equal the expectation torque vector T ∈ R that the first step obtains ^{3 * 1}, through finding the solution the pseudo inverse matrix T of static torque matrix _n ⁺∈ R ^{9 * 3}, try to achieve and just decide current vector I ∈ R ^{9 * 1}

The 8th step: just decide current vector I and distribute: 9 components among the I/2 are distributed to 9 windings confirming in the 6th step respectively, 9 components the among-I/2 are distributed to aforementioned and 9 the corresponding sphere of windings difference diagonal angle windings respectively to what try to achieve by the 7th step.

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