CN100406760C - Design method for permanent magnet bias axial magnetic bearing - Google Patents

Abstract

The design method of axial magnetic bearing with permanent magnetic bias has the displacement rigidity of the magnetic bearing as main consideration, and the maximum bearing capacity, saturation magnetic induction and tankful rate as restraint conditions. Compared with available design method with optimal work point of the permanent magnet as target, the method of the present invention has the advantages of easy control of radial magnetic bearing, reasonable permanent magnet size, high accuracy, and being simple and practical. The design philosophy of the present invention may be used in design of different kinds of axial magnetic bearing with permanent magnetic bias.

Description

A kind of design method of permanent-magnetic biased axial magnetic bearing

Technical field

The present invention relates to a kind of design method of non-contact magnetically suspension bearing, particularly a kind of magnetically levitated flywheel, magnetic suspension control torque gyroscope etc. need the design method of the device of magnetic suspension bearing with permanent-magnetic biased axial magnetic bearing, and its design philosophy can be used as the design of all kinds of permanent-magnetic biased axial magnetic bearings.

Background technique

Magnetic suspension bearing divides pure electromagnetic type and permanent magnet bias to power up the hybrid magnetic suspension bearing of magnetic control system, the former uses, and electric current is big, power consumption is big, permanent magnet bias powers up the hybrid magnetic suspension bearing of magnetic control system, main bearing capacity is born in the magnetic field that permanent magnet produces, electromagnetism magnetic field provides auxiliary adjusting bearing capacity, thereby this bearing can reduce to control electric current greatly, reduces the wastage.What magnetic bearings control mode commonly used adopted is traditional pid control mode, realize that the controller parameter of this kind mode determined by bearing rigidity and damping, through facts have proved in a large number, for making magnetic bearing have excellent characteristic, should make bearing rigidity and its displacement rigidity on the same order of magnitude, so the displacement rigidity of magnetic bearing is most important for the control of magnetic bearing.The design method of existing magnetic bearing all utilizes the permanent magnet best operating point to design, purpose is to make permanent magnet volume minimum, but the magnet size that calculates by this method is often not too reasonable, and cause processing difficulties, owing to do not consider the influence of displacement rigidity, thereby existing design method exists poor accuracy, unmanageable defective to control system.

Summary of the invention

Technology of the present invention is dealt with problems and is: overcome the deficiencies in the prior art, a kind of design method of permanent-magnetic biased axial magnetic bearing is provided, this method degree of accuracy height is easy to control.

Technical solution of the present invention is: a kind of design method of permanent-magnetic biased axial magnetic bearing needs to determine: bearing support length L, width of rebate L _c, permanent magnet axial length h _Pm, interior magnetic guiding loop inside diameter D _Nn, interior magnetic guiding loop outer diameter D _Nw(be the permanent magnet outer diameter D _Pm1), outer magnetic guiding loop outer diameter D _Ww, outer magnetic guiding loop inside diameter D _Wn, the thrust disc inside diameter D _T2, the thrust disc outer diameter D _T1, the thrust disc axial length L _t, the permanent magnet outer diameter D _Pm1, conductive magnetic yoke thickness h and turn number N,

It is characterized in that: this method is based on the displacement rigidity K of magnetic bearing _x, its concrete steps are as follows:

(1) sets rotor speed n and maximum load capacity F according to the index request of the device of required magnetic suspension bearing _Max, require to set the static suspension current i according to power consumption, set gap length δ, set the displacement rigidity K of magnetic bearing according to the requirement of existing magnetic bearing controller according to existing level of processing _x, set leakage coefficient σ, set saturation magnetic induction B according to magnetic field analysis according to the magnetization characteristic of selected bearing support material _s

(2) determine the thrust disc inside diameter D according to the rotor speed n and the strength of materials _T2, consider that the air gap edge edge effect determines magnetic guiding loop inside diameter D in the axial magnetic bearing _Nn

(3) make the interior magnetic guiding loop sectional area radially of axial magnetic bearing equate, according to maximum load capacity F with outer magnetic guiding loop sectional area radially _MaxWith saturation magnetic induction B _sDetermine this sectional area A;

(4) calculate interior magnetic guiding loop outer diameter D _Nw, also be the permanent magnet outer diameter D _Pm1

(5) determine permanent magnet axial length h according to gap length δ _Pm, conductive magnetic yoke thickness h and width of rebate L _c

(6) according to displacement rigidity K _xAnd rotor gravity G determines current stiffness K _i, determine the diameter d of winding wire by current density, J and static suspension current i _c

(7) by displacement rigidity K _xCalculate the permanent magnet inside diameter D _Pm2

(8) require to determine outer magnetic guiding loop inside diameter D according to copper factor _Wn, calculate outer magnetic guiding loop outer diameter D by outer magnetic guiding loop sectional area A radially again _Ww

(9) by current stiffness K _iDetermine turn number N;

(10) by the close equal principle of magnetic circuit each several part magnetic, determine the bearing support length L.

Described gap length δ is taken as 0.15～0.35mm; Described interstice length δ ₁Greater than 2 times of gap length δ, be taken as 0.4～1mm; Described displacement rigidity span determines by controller, be taken as-0.5N/um～-2N/um; Described leakage coefficient σ is taken as 1.1～3; Described copper factor is taken as 40%～60%.

Principle of the present invention is: the present invention starts with the displacement rigidity of axial magnetic bearing and designs, and sets each parameter as requested, by the magnetic circuit analysis and the calculating of axial magnetic bearing, can obtain other physical dimension of magnetic bearing.Can determine the thrust disc inside diameter D according to the rotor speed n and the strength of materials set _T2, consider that the air gap edge edge effect can determine magnetic guiding loop inside diameter D in the axial magnetic bearing _NnFor:

D _nn＝D _t2+δ (1)

Make the interior magnetic guiding loop sectional area radially of axial magnetic bearing equate, according to maximum load capacity F with outer magnetic guiding loop sectional area radially _MaxWith saturation magnetic induction B _sDetermine this sectional area A by following formula:

$A=\frac{F_{\max }\·{\mathrm{\μ}}_0}{B_s^2}----\left(2\right)$

μ in the formula ₀=4 π * 10 ^-7H/m is the permeability of air.

Magnetic air gap length δ according between the rotor of setting can obtain permanent magnet axial length h _Pm, conductive magnetic yoke thickness h and width of rebate L _cFor:

h _pm＝K ₁·δ (3)

h＝K ₂·h _pm (4)

L _c＝K ₃·h _pm (5)

K in the formula ₁, K ₂, K ₃Be constant, rule of thumb obtain.

By (1) formula and interior magnetic guiding loop inside diameter D _NnMagnetic guiding loop outer diameter D in calculating _Nw(be the permanent magnet outer diameter D _Pm1) be:

$D_{\mathrm{nw}}=\sqrt{\frac{4\·A}{\mathrm{\π}}+D_{\mathrm{nn}}^2}---\left(6\right)$

According to displacement rigidity K _xAnd rotor gravity G can get current stiffness K _i:

$K_i=\frac{G-K_x\·x}{i}---\left(7\right)$

Rotor center was apart from the side-play amount of magnetic center when x was static suspension in the formula.

Determine the diameter d of winding wire by current density, J and static suspension current i _cFor:

$d_c=\sqrt{\frac{4\·i}{\mathrm{\π}\·J}}----\left(8\right)$

Then according to the NBS value.

By displacement rigidity K _xDetermine the permanent magnet inside diameter D according to formula (9)～(13) _Pm2:

${\mathrm{<figure-callout\; id="1"\; label="C"\; filenames="C20061011427000081.png"\; state="\{\{state\}\}">C</figure-callout>}}_1=\frac{1}{\frac{1}{R_1}+\frac{1}{R_{\mathrm{pm}}}}---\left(9\right)$

${\mathrm{<figure-callout\; id="2"\; label="C"\; filenames="C20061011427000081.png"\; state="\{\{state\}\}">C</figure-callout>}}_2=\frac{1}{{\mathrm{\&mu;}}_0\&CenterDot;A_w}+\frac{1}{{\mathrm{\&mu;}}_0\&CenterDot;A_n}---\left(10\right)$

C ₃＝(R _pm+R ₁)·δ·C ₂+R _pm·R ₁ (11)

$K_x=-\frac{2\&CenterDot;{\mathrm{<figure-callout\; id="2"\; label="F\; pm"\; filenames="C20061011427000081.png"\; state="\{\{state\}\}">F</figure-callout>}}_{\mathrm{pm}}^{}\&CenterDot;{\mathrm{<figure-callout\; id="1"\; label="R"\; filenames="C20061011427000081.png"\; state="\{\{state\}\}">R</figure-callout>}}_1^2\&CenterDot;(R_{\mathrm{pm}}+R_1)\&CenterDot;{\mathrm{<figure-callout\; id="2"\; label="C"\; filenames="C20061011427000081.png"\; state="\{\{state\}\}">C</figure-callout>}}_2}{{\mathrm{\&mu;}}_0\&CenterDot;{\mathrm{\&sigma;}}^2\&CenterDot;{\mathrm{<figure-callout\; id="3"\; label="C"\; filenames="C20061011427000081.png"\; state="\{\{state\}\}">C</figure-callout>}}_3^3}(\frac{1}{A_n}+\frac{1}{A_w})---\left(12\right)$

A in the formula _nBe interior magnetic guiding loop area, A _wBe outer magnetic guiding loop area, and A _n=A _w=A, wherein F _Pm=H _PmH _PmBe the magnetomotive force of permanent magnet, H _PmBe the coercivity of permanent magnet, generally be taken as 760kA/m～790kA/m; μ _PmBe the relative permeability of permanent magnet, generally be taken as 1.03～1.05, R ₁Be the magnetic resistance of interstice, for:

${\mathrm{<figure-callout\; id="1"\; label="R"\; filenames="C20061011427000081.png"\; state="\{\{state\}\}">R</figure-callout>}}_1=\frac{{\mathrm{\&delta;}}_1}{{\mathrm{\&mu;}}_0\&CenterDot;\mathrm{\&pi;}\&CenterDot;\frac{{\mathrm{<figure-callout\; id="2"\; label="D\; pm"\; filenames="C20061011427000081.png"\; state="\{\{state\}\}">D</figure-callout>}}_{\mathrm{pm}}^2-{\mathrm{<figure-callout\; id="2"\; label="D\; nn"\; filenames="C20061011427000081.png"\; state="\{\{state\}\}">D</figure-callout>}}_{\mathrm{nn}}^{}}{4}}----\left(13\right)$

Require to determine outer magnetic guiding loop inside diameter D according to copper factor _Wn, calculate outer magnetic guiding loop outer diameter D by outer magnetic guiding loop sectional area A radially again _WwFor:

$D_{\mathrm{ww}}=\sqrt{\frac{4\&CenterDot;A}{\mathrm{\&pi;}}+D_{\mathrm{wn}}^2}---\left(14\right)$

Consider the air gap edge edge effect, can obtain the thrust disc outer diameter D _T1For:

D _t1＝D _ww+δ (15)

By current stiffness K _iThe calculating turn number N is:

$N=\frac{{\mathrm{<figure-callout\; id="1"\; label="K"\; filenames="C20061011427000081.png"\; state="\{\{state\}\}">K</figure-callout>}}_1\&CenterDot;{\mathrm{\&mu;}}_0\&CenterDot;\mathrm{\&sigma;}\&CenterDot;{\mathrm{<figure-callout\; id="3"\; label="C"\; filenames="C20061011427000081.png"\; state="\{\{state\}\}">C</figure-callout>}}_3\&CenterDot;(\mathrm{\&delta;}\&CenterDot;{\mathrm{<figure-callout\; id="2"\; label="C"\; filenames="C20061011427000081.png"\; state="\{\{state\}\}">C</figure-callout>}}_2+C_1)}{2\&CenterDot;F_{\mathrm{pm}}\&CenterDot;{\mathrm{<figure-callout\; id="1"\; label="R"\; filenames="C20061011427000081.png"\; state="\{\{state\}\}">R</figure-callout>}}_1\&CenterDot;(\frac{1}{A_n}+\frac{1}{A_w})}---\left(16\right)$

Determine that according to the close basic principle that equates of bearing support various piece magnetic the bearing support length L is:

$L=\frac{2\&CenterDot;A}{\mathrm{\&pi;}\&CenterDot;(D_{\mathrm{wn}}+D_{\mathrm{nw}})}+L_c---\left(17\right)$

The thrust disc axial length L _tCan determine according to the close basic principle that equates of bearing support each several part magnetic equally:

$L_t=\frac{A}{\mathrm{\&pi;}\&CenterDot;\frac{{\mathrm{<figure-callout\; id="1"\; label="D\; t"\; filenames="C20061011427000081.png"\; state="\{\{state\}\}">D</figure-callout>}}_t+{\mathrm{<figure-callout\; id="2"\; label="D\; t"\; filenames="C20061011427000081.png"\; state="\{\{state\}\}">D</figure-callout>}}_t}{2}}---\left(18\right)$

So far, whole permanent-magnetic biased axial magnetic bearing design finishes.

The present invention's advantage compared with prior art is: the present invention is because employing is the design method of starting point with the axial magnetic bearing displacement rigidity, is that the design method of starting point is compared with existing axial magnetic bearing with the permanent magnet best operating point, be beneficial to control more, the structural parameter that obtain are more reasonable.

Description of drawings

Fig. 1 is the permanent-magnetic biased axial magnetic bearing structural drawing that the present invention is directed to;

Fig. 2 is a design flow diagram of the present invention;

Fig. 3 is permanent-magnetic biased axial magnetic bearing stator module pictorial diagram designed according to this invention;

Embodiment

As shown in Figure 1, design object of the present invention is a kind of magnetically levitated flywheel permanent-magnetic biased axial magnetic bearing, and 1 is conductive magnetic yoke among the figure, 2 is interstice, and 3 is permanent magnet, and 4 is coil, 5 is bearing support, and 6 are the magnetic air gap between bearing support (being also referred to as stator) and the thrust disc, and 7 is thrust disc.Set the displacement rigidity K of this axial magnetic bearing according to the requirement of existing magnetic bearing controller _xFor-0.7N/um, set gap length δ according to existing level of processing and be taken as 0.25mm, in order to make magnetic bearing electricity magnetic excitation circuit through interstice formation loop and without permanent magnet, avoid permanent magnet in the too much magnetomotive force of interstice loss simultaneously, thereby the length of interstice should be a bit larger tham 2 times of gap lengths, gets interstice δ at this ₁Be 0.6mm, setting leakage coefficient σ according to the magnetic field analysis of this magnetic bearing is 1.3, sets maximum load capacity F according to the index request of magnetically levitated flywheel _MaxBe 1230N, rotor speed n is 5000r/min, setting the static suspension current i according to the power consumption requirement of magnetically levitated flywheel is 0.2A, and the bearing support and the conductive magnetic yoke of axial magnetic bearing are selected electrical pure iron DT4 for use among this embodiment, set the saturation magnetic induction B of each magnetic conduction part material according to the magnetization curve of DT4 _sBeing 1.2T, is 40% according to the level set copper factor that rolls off the production line that has coil now.Set the thrust disc inside diameter D by the rotor speed n and the strength of materials _T2=63mm.

According to above condition, can get interior magnetic guiding loop inside diameter D by formula (1) _Nn=63.25mm.Can draw the inside and outside magnetic guiding loop of axial magnetic bearing stator sectional area A=1100mm radially by formula (2) ², establish K ₁=10, K ₂=1, K ₃=4, can obtain permanent magnet axial length h by (3)～(5) formula _Pm=2.5mm, conductive magnetic yoke thickness h=2.5mm, width of rebate L _c=10mm calculates interior magnetic guiding loop outer diameter D by formula (6) _Nw=73.9mm can get current stiffness K by formula (7) and (8) _i=374.3N/A, the diameter d of winding wire _c=0.35mm by (9)～(13) formula as can be seen, is difficult to obtain by displacement rigidity K _xThe permanent magnet inside diameter D that direct representation goes out _Pm2Representation, in order to calculate the permanent magnet inside diameter D _Pm2, adopt in the present embodiment and set the permanent magnet inside diameter D from big to small _Pm2Value, substitution displacement rigidity K _xRepresentation (12) is obtained displacement rigidity K _x, as the K that calculates _xDiffer less than 1% o'clock with setting value, think the value D of permanent magnet internal diameter this moment _Pm2Be design load.Can calculate the permanent magnet inside diameter D by this method _Pm2=66.8mm requires to determine outer magnetic guiding loop inside diameter D according to copper factor _Wn=95.9mm calculates outer magnetic guiding loop outer diameter D by outer magnetic guiding loop sectional area A radially according to formula (14) _Ww=102.8mm considers the air gap edge edge effect, can get the thrust disc outer diameter D by formula (15) _T1=103.05mm can calculate turn number N=355 by formula (16),, can get the thrust disc axial length by formula (18) and is by formula (17) calculation bearing body length L=14mm according to the close basic equal principle of bearing support each several part magnetic: L _t=4.2mm, so far, this permanent-magnetic biased axial magnetic bearing design finishes.

The content that is not described in detail in the specification of the present invention belongs to related domain professional and technical personnel's known prior art.

Claims (6)

1. the design method of a permanent-magnetic biased axial magnetic bearing is characterized in that: this method is based on the displacement rigidity K that at first determines magnetic bearing _x, its concrete steps are as follows:

(1) at first sets the displacement rigidity K of magnetic bearing _x, rotor speed n, gap length δ, interstice length δ ₁, leakage coefficient σ, maximum load capacity F _Max, static suspension current i and saturation magnetic induction B unshakable in one's determination _s

(2) determine the thrust disc inside diameter D according to the rotor speed n and the strength of materials _T2, consider that the air gap edge edge effect determines magnetic guiding loop inside diameter D in the axial magnetic bearing _Nn

(3) make the interior magnetic guiding loop sectional area radially of axial magnetic bearing equate, according to maximum load capacity F with outer magnetic guiding loop sectional area radially _MaxWith saturation magnetic induction B _sDetermine this sectional area A;

(4) calculate interior magnetic guiding loop outer diameter D _Nw, also be the permanent magnet outer diameter D _Pm1

(5) determine permanent magnet axial length h according to gap length δ _Pm, conductive magnetic yoke thickness h and width of rebate L _c

(6) according to displacement rigidity K _xAnd rotor gravity G determines current stiffness K _i, determine the diameter d of winding wire by current density, J and static suspension current i _c

(7) by displacement rigidity K _xCalculate the permanent magnet inside diameter D _Pm2

(8) require to determine outer magnetic guiding loop inside diameter D according to copper factor _Wn, calculate outer magnetic guiding loop outer diameter D by outer magnetic guiding loop sectional area A radially again _Ww, consider that the thrust disc outer diameter D is determined in the edge effect of air gap _T1

(9) by current stiffness K _iDetermine turn number N;

(10 by the close equal principle of magnetic circuit each several part magnetic, determines bearing support length L and thrust disc axial length L _t

2. the design method of a kind of permanent-magnetic biased axial magnetic bearing according to claim 1, it is characterized in that: described gap length δ is taken as 0.15～0.35mm.

3. the design method of a kind of permanent-magnetic biased axial magnetic bearing according to claim 1 is characterized in that: described interstice length δ ₁Greater than 2 times of gap length δ, be taken as 0.4～1mm.

4. the design method of a kind of permanent-magnetic biased axial magnetic bearing according to claim 1 is characterized in that: described displacement rigidity span determines by controller, be taken as-0.5N/um～-2N/um.

5. the design method of a kind of permanent-magnetic biased axial magnetic bearing according to claim 1, it is characterized in that: described leakage coefficient σ is taken as 1.1～3.

6. the design method of a kind of permanent-magnetic biased axial magnetic bearing according to claim 1, it is characterized in that: described copper factor is taken as 40%～60%.

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