AU631500B2 - Improved variable pitch vertical axis wind turbine - Google Patents
Improved variable pitch vertical axis wind turbine Download PDFInfo
- Publication number
- AU631500B2 AU631500B2 AU79418/91A AU7941891A AU631500B2 AU 631500 B2 AU631500 B2 AU 631500B2 AU 79418/91 A AU79418/91 A AU 79418/91A AU 7941891 A AU7941891 A AU 7941891A AU 631500 B2 AU631500 B2 AU 631500B2
- Authority
- AU
- Australia
- Prior art keywords
- blade
- turbine
- mass
- pivotal movement
- stabiliser
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Ceased
Links
- 239000003381 stabilizer Substances 0.000 claims description 14
- 230000007246 mechanism Effects 0.000 claims description 13
- 230000003019 stabilising effect Effects 0.000 claims description 9
- 230000009471 action Effects 0.000 claims description 5
- 230000036316 preload Effects 0.000 claims description 3
- 238000005096 rolling process Methods 0.000 claims description 2
- 239000011295 pitch Substances 0.000 description 25
- 230000000694 effects Effects 0.000 description 8
- 238000013459 approach Methods 0.000 description 2
- 238000013016 damping Methods 0.000 description 2
- 230000033228 biological regulation Effects 0.000 description 1
- 230000005540 biological transmission Effects 0.000 description 1
- 230000008859 change Effects 0.000 description 1
- 238000010586 diagram Methods 0.000 description 1
- RLQJEEJISHYWON-UHFFFAOYSA-N flonicamid Chemical compound FC(F)(F)C1=CC=NC=C1C(=O)NCC#N RLQJEEJISHYWON-UHFFFAOYSA-N 0.000 description 1
- 239000012530 fluid Substances 0.000 description 1
- 230000006872 improvement Effects 0.000 description 1
- 238000009434 installation Methods 0.000 description 1
- 238000000034 method Methods 0.000 description 1
- 238000005086 pumping Methods 0.000 description 1
Classifications
-
- F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
- F03—MACHINES OR ENGINES FOR LIQUIDS; WIND, SPRING, OR WEIGHT MOTORS; PRODUCING MECHANICAL POWER OR A REACTIVE PROPULSIVE THRUST, NOT OTHERWISE PROVIDED FOR
- F03D—WIND MOTORS
- F03D3/00—Wind motors with rotation axis substantially perpendicular to the air flow entering the rotor
- F03D3/06—Rotors
- F03D3/062—Rotors characterised by their construction elements
- F03D3/066—Rotors characterised by their construction elements the wind engaging parts being movable relative to the rotor
- F03D3/067—Cyclic movements
- F03D3/068—Cyclic movements mechanically controlled by the rotor structure
-
- F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
- F03—MACHINES OR ENGINES FOR LIQUIDS; WIND, SPRING, OR WEIGHT MOTORS; PRODUCING MECHANICAL POWER OR A REACTIVE PROPULSIVE THRUST, NOT OTHERWISE PROVIDED FOR
- F03D—WIND MOTORS
- F03D7/00—Controlling wind motors
- F03D7/06—Controlling wind motors the wind motors having rotation axis substantially perpendicular to the air flow entering the rotor
-
- F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
- F05—INDEXING SCHEMES RELATING TO ENGINES OR PUMPS IN VARIOUS SUBCLASSES OF CLASSES F01-F04
- F05B—INDEXING SCHEME RELATING TO WIND, SPRING, WEIGHT, INERTIA OR LIKE MOTORS, TO MACHINES OR ENGINES FOR LIQUIDS COVERED BY SUBCLASSES F03B, F03D AND F03G
- F05B2260/00—Function
- F05B2260/70—Adjusting of angle of incidence or attack of rotating blades
- F05B2260/72—Adjusting of angle of incidence or attack of rotating blades by turning around an axis parallel to the rotor centre line
-
- Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
- Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
- Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
- Y02E10/00—Energy generation through renewable energy sources
- Y02E10/70—Wind energy
- Y02E10/74—Wind turbines with rotation axis perpendicular to the wind direction
Landscapes
- Engineering & Computer Science (AREA)
- Life Sciences & Earth Sciences (AREA)
- Sustainable Development (AREA)
- Sustainable Energy (AREA)
- Chemical & Material Sciences (AREA)
- Combustion & Propulsion (AREA)
- Mechanical Engineering (AREA)
- General Engineering & Computer Science (AREA)
- Wind Motors (AREA)
Description
'~1 Regulation 3.2
AUSTRALIA
PATENTS ACT 1990 COMPLETE SPCFCTO FOR A STANDARD PATENT
ORIGINLAL
*4 .4 4 .i 4 *0*48~ 4 4.
1*41 *44 44 44 4 *0 *9 4 9*4 Name of Applicant: BRIAN KINLOCH KIRKE Actual Inventor: BRIAN KINLOCH KIRKE Address for Service: R X( MADDERN ASSOCIATES, 345 King William Street, Adelaide, South Australia, Australia Invention title: IMPROVED VARIABLE PITCH VERTPICAL AXIS WIND
TURBINE
Details of Associated Provisional Application No PI( 133 dated 24th July 1990: The following statemnent is a full description of this, invention 1 including the best miethod of performiing it known to me, 4 44*4*9 9 4 99*4 1 91 4* 9 9 4* 4 0 *4 9 9* 04 4 4* 44 p 44 1. INTRODUCTORY STATEMENT This invention relates to a vertical axis wind turbine or "giromill" having two or more, but typically three, straight vertical blades of aerofoil section, each of which is free to pivot about a vertical axis close to its leading edge.
2. STATEMENT OF PRIOR ART.
2.1. ADVANTAGES OF VERTICAL AXIS WIND TURBINES Vertical axis wind turbines (or cross-flow wind turbines, since their axis of rotation is perpendicular to the wind flow direction) have two inherent advantages over the more common horizontal axis (or axial flow) wind a 0 turbines: aboo* They generally require no mechanism to orient themselves relative to the wind direction.
oo (ii) They permit simple transmission of power via a vertical shaft to any rotary load, such as a helical rotor pump or a generator at ground level, where installation and ,gAS servicing is easy, unlike either the conventional windelectric system in which the generator is mounted at the top of the tower, or the conventional pumping windmill which can 4 *9 only drive a reciprocating pump.
s 2.2. TURBINUS WITH AEROFOIL BLADES.
For optimum performance, the aerofoil blades of a normal propeller-shaped horizontal axis wind turbine must be of a complex tapered and twisted shape, making them difficult to construct. In contrast, the aerofoil blades of a vertical
I
axis wind turbine are untwisted and of uniform crosssection, making them relatively easy to extrude or fabricate.
2.3. DARRIEUS ROTORS OR "EGGBEATERS".
The most common form of vertical axis turbine with aerofoil blades is the Darrieus rotor or "eggbeater", which has curved blades attached at each end to the central axis of rotation. This form suffers from the disadvantage that it is not able to self-start consistently, and at best has a very low starting torque in a strong wind, making it unsuitable for stand-alone applications.
It S 2.4. GIROMILLS OR CYCLOTURBINES.
To overcome the problem of starting torque, turbines it ~have been constructc' with straight blades attached to a cam Sor other mechanical device so that each blade is forced to pivot about its own long axis in a cyclical fashion as the turbine rotates, in such a way that each blade is oriented Srelative to the wind so as to avoid stall and produce a j large torque. A vertical axis wind turbine incorporating such a system is known as a "giromill" or "cycloturbine", and although this system can achieve a high starting torque, it does so at the expense of increased complexity in two ,251* respects: The cam mechanism controlling blade pitch must be oriented relative to the wind.
(ii) To combine high starting torque with high efficiency at operating speeds the amplitude of cyclical 'Pi"=illii~b----*CII*fll i _CL pitch change of the blades must decrease as the ratio of turbine speed to windspeed increases, so a simple cam i mechanism is not sufficient.
2.5. SELF-ACTING VARIABLE PITCH.
Rather than defining the pitch angle of each blade at every point by means of mechanical devices, blades can be allowed to pivot freely within limits under the influence of aerodynamic and inertial forces. By suitable design of the blade attachments it is possible to achieve, with a i relatively simple and inexpensive device, performance comparable with that of a sophisticated giromill.
Several known designs, including those of evan~-, Herter i /O gb/oS-f@ i (International Patent F.3D 3/06, Liljegren (US Patent No. 4,430,044), Sicard (US Patent No. 4,048,947) Drees (US 1 Patent No. 4,180,367) and Kirke (Aust. Pat. App. No.
18713/88), have attempted to achieve this ideal combination of simplicity with high starting torque and high efficiency at operating speeds. No performance figures are available ,SQ: for any of these, but an examination of the principles on which they operate suggests that there is considerable room Sfor improvement.
(An early device using a crude form of the self-acting variable pitch principle was the "flapper" windmill in which the blades, which were flat rather than of aerofoil section, S were pivoted at their leading edges so they could swing progressively inwards from a tangential orientation to a radial orientation as they moved upwind, thereby generating Sa minimum of drag and attendant reverse torque, after which 4 1 they remained in a radial orientation transverse to the wind as they moved downwind, thereby acting as drag translators.
However this was a low-speed, low-efficiency device bearing only a superficial resemblance to the device described in this patent spec 'fication.) 3. PURPOSE OF THE PRESENT INVENTION m he purpose of this invention is to control the blade pitch angle of a giromill by means of a combination of aerodynamic and inertial forces in such a way as to achieve, more simply and effectively than previous designs have done, at least some of the following desirable characteristics: High torque over the complete range of operating tipspeed ratios from zero to 3 or more, to drive constant torque loads such as helical rotor pumps (ii) Efficiency comparable with fixed pitch Darrieus turbines at normal operating speeds (iii) Automatic overspeed control (iv) Quick manual shutdown.
S
Tft STrmZLS'E'4 4. PRINCIPLE ON WHICH MECHANISM OPERATES The essential feature of this mechanism is the two-way stabilising effect of a single stabilisermas4 which opposes the tendency of the blade to pitch towards zero angle of attack 3 under the action of aerodynamic force. This stabilising effect maintains zero pitch at small angles of attack, but allows the blade to pitch when the angle of attack becomes large and t approaches the stall angle.
By suitable choice of stabiliser mass and the point of action of the stabilising force, pitching can be made to occur whenever necessary to avoid stall under most conditions, while maintaining zero pitch whenever the angle of attack is well below the stall angle.
This is an advance over the known designs of Herter, in which no stabilising effect is provided at zero pitch, and Liljegren, in which a stabilising moment is provided by a complex arrangement of mass and springs.
It is also superior to that of Kirke (1988) in two important respects: It requires only one stabiliser mass per blade, making the mechanism simpler and lighter.
(ii) The outward travel of the single T shaped stabiliser mass in the present invention is inherently self-limiting. The stabiliser mass cannot move outwards beyond the point at which it contacts the blade when the blade is at its zero pitch position as shown in Figure 3. This contrasts with previous arrangements in which two stabiliser masses are used, and each i 20 must be fitted with a stop to limit outward travel. Otherwise the effect of one will tend to cancel out the effect of the other. The required stops further complicate previous arrangements.
4.2 OVERSPEED CONTROL AND MANUAL SHUTDOWN In a preferred embodiment of the present invention, governing masses are provided, which force the trailing edges of the blades outwards at a desired governing speed, resulting in a fail-safe air brake effect.
In another preferred embodiment, a "panic handle" device is provided, which can activate the air brake effect when required at lower speeds, so that the turbine idles and can be easily stopped.
DESCRIPTION OF MECHANISM The invention will now be described in greater detail with reference to the accompanying drawings in which Fig. 1 is a schematic view of a rotor having three straight blades 1i, 2 and 3, of aerofoil section, oriented vertically and
R
I,
mounted on the outer ends of radial arms 4, 5 and 6, which are attached at their inner ends to a shaft 7 which coincides with a central axis of rotation 0-0.
The embodiment shown in Fig. 1 shows three blades with one radial arm per blade, but this does not preclude the use of different numbers of blades and radial arms.
Each blade is able to pivot or "pitch" through a limited arc about a vertical axis D-D located close to its leading edge.
Fig. 2 is a plan view of the rotor shown in Fig. 1, showing a velocity vector diagram for blade 1, in which Va is the ambient wind velocity, Vb is the blade tangential velocity and V r is the vector sum of Va and Vb, i.e. the relative velocity between the blade and the surrounding air.
The angle of attack a is the angle between V r and the blade chord line C-C. Blade 1 is shown at its zero pitch position, i.e. the chord line is tangential to the path of the blade.
Blade 2 is shown pivoted so that its trailing edge is outwards, so that the chord line C-C makes an angle gamma, called the pitch angle, with the tangent. Blade 3 is shown pivoted so that its trailing edge is inwards.
Figs. 3 to 5 are plan views of one blade and the outer end of the radial arm to which is attached, showing a schematic representation of a preferred embodiment of the stabiliser mechanism.
SI
i ra Sit ''St a S i ,tt 'Ak .m 1 I Fig. 6 shows in plan view how a stationary blade, at any of a series of points on its circular path, pitches under the action of the ambient wind Va so that its trailing edge tends to move downwind.
In Fig. 3, a blade 1 is shown attached to a radial arm 4 by means of a pivot at D, which is located well forward of the "aerodynamic centre" i.e. the point A, approximately 0.25 of the distance from the leading edge to the trailing edge of the blade, through which the resultant aerodynamic force acts when the blade is unstalled.
The blade is provided with a counterweight 8 such that its centre of mass coincides with the pivot position D shown in Fig. 3.
A stabiliser mass 9 is mounted on radial arm 4 such that as the turbine rotates, the stabiliser mass moves outwards under the action of centrifugal force, and the tee piece at its outer end tends to hold the blade in its zero pitch position.
.i This tee piece may have rollers 12, 12 at its outer ends to i provide rolling rather than sliding contact with the blade.
20 For the trailing edge of the blade to move either outwards as shown in Fig. 4, or inwards as shown in Fig. 5, the stabiliser bar 9 must move inwards.
Pitch amplitude limitation, overspeed protection and emergency de-activation mechanisms may be provided by a i
L
device such as that shown attached to the trailing edge of the blade and radial arm in Fig.3.
Overspeed protection can be provided in either of two ways: 0 419 9 0 *0 9 0994s6 15' 00*9 9 90 00 09 9 9 *4*9 9 0* 99 S 9 0* 99 9 0*0* 19 I I 4 9 9 *9 A governing mass 10 is held in place by a link connected to a spring 13 so that it remains stationary relative to radial arm 4 until the desired maximum speed is reached, when centrifugal force on mass 10 overcomes the pretension in spring 13 so that mass 10 moves outwards and pushes the trailing edge of the blade outwards so that the blade acts as an air br.ake.
(Ui) A spring-loaded hinge is provided between the blade I and the counterweight 8, such that the spring preload is overcome at the desired maximum turbine speed, allowing both the counterweight and the trailing edge of the blade to swing outwards so that the blade again achieves the desired air brake effect.
Emergency de-activation is achieved for overspeed protection method by releasing the tension on spring 13 by means of quick release handle 14 so the air brake effect act8 at lower speeds.
Pitch amplitude inwards can be limited either by the governing mass 10 or by the teo piece 9 or an extension tt.ereof Pitch amplitude outwards is limited by a member 13. whose length can vary up to a preset maximum. This-member is shown as a chain in Fig. 3, but could be a telescopic link, a flexible cable or a 'piston moving in a cylinder filled with viscous fluid to provide damping, the damping factor being 9 controlled by a bypass, by a hole in the piston, or simply by clearance between the piston and the cylinder, 6. OPERATION OF THE MECHANISM As the turbine rotates in an ambient wind velocity Va (Fig. the blades move with tangential velocity Vb. The resultant relative movement V between a blade and the surrounding air generates aerodynamic lift and drag forces F 1 and Fd respectively. At low angles of attack a (up to 10-15 degrees), lift force F 1 predominates and the resultant aerodynamic force acts through the aerodynamic centre A (Fig.
a point close to 0.25 chord, i.e. one quarter of the Sdistance from the leading edge to the trailing edge of the blade.
At higher angles of attack the blade stalls, drag forces
F
d increase rapidly and the point through which the 1 a0 iv is .o r kI resultant aerodynamic force acts shifts progressively rearward towards 0.5 chord, i.e. the midpoint of the blade chord. Thus if the blade is pivoted at a point well forward of 0.25 chord, the aerodynamic forces resulting from the relative air movement Vr (Fig. will at all times produce a couple tending to pivot the blade so as to reduce the angle of attack a.
6.1 STARTING When the turbine is at rest, each blade is free to rotate through a limited arc about its own pivot, restrained only by I the friction in the pivots and the limits of travel imposed by the pivot geometry. The ambient wind will produce a coupl.e tending to rotate each blade such that its trailing edge moves downwind (Fig The blades are free to do so within limits.
For most radial arm positions, the blades will pivot into an orientation relative to the wind that will produce a large forward torque. There is no position for which a significant reverse torque is generated, so a turbine with 2 or more blades j;4 will always generate a high starting torque.
6.2 NORMAL OPERATION As the turbine starts to rotate, centrifugal force on the stabiliser mass tends to hold the blade in the zero pitch Sposition, opposing the pitching effect of the aerodynamic forces. If the moment due to aerodynamic forces is greatethan the stabilising moment due to centrifugal force the blade will pivot (within limits) so as to reduce the angle of attack.
If not, the blade will remain at zero pitch.
The magnitude of the centrifugal stabilising moment increases with the square of the blade tangential velocity Vb, Fig. 2, while the moment of the aerodynamic forces about the pivot varies with the relative air velocity V the angle of attack a, and the position of the aerodynamic centre as follows: It increases in proportion to the square of Vr.
(ii) It increases roughly linearly with the angle of attack a up to stall, (iii) Beyond stall, it will increase further with the rearward shift of the aerodynamic centre and consequent 1 5 increase in moment arm about the pivot point.
By correct selection of stabiliser bar mass it is possible to keep the blades at zero pitch for angles of attack well below stall under most conditions, thereby achieving the high efficiency obtainable at high speeds with fixed blade VAWTs, and S. (ii) to allow blades to pivot as the angle of attack approaches the stall angle, thereby averting stall and the attendant drastic drop in performance.
L
I ~iY 6.3. OVERSPEED CONTROL.
At the desired maximum operating speed, centrifugal forces overcome the pretension in the control spring 13 (Fig.3), resulting in the air brake effect described above.
6.4. MANUAL SHUTDOWN.
A quick release handle 14 (Fig.3) provides a means of releasing the control spring pretension so that the turbine ceases to function effectively and will slow down to idling speed until reset.
lit t t t L
Claims (4)
1. A self-acting variable-pitch vertical axis wind turbine or "giromill" comprising blades, each of which is counterweighted so its centre of mass is located less than one quarter of the distance from the leading to the trailing edge, and pivotally supported at its centre of mass by one or more radial support arms for pivotal movement about a vertical axis, so that inertial forces on the blade do not tend to cause pivotal movement, but aerodynamic forces tend to cause, pivotal movement in such a direction as to reduce the angle of attack, such pivotal movement in either direction being opposed whenever the turbine is in motion by the centrifugal force on a stabilising mechanism comprising a stabiliser mass which is mounted on the radial arm so that it is free to move in an outward radial direction within guides until it contacts the blade to the front and rear of the pivot point respectively in such a way that any pivotal movement of the said blade entails an inward S, movement of the said stabiliser mass against centrifugal force if the turbine is rotating.
2. A turbine according to claim 1, further comprising a system of governing masses and preloaded springs arranged so that the preload force is overcome by centrifugal force on the governing masses and the springs start to deflect beyond their preloaded deflection when a desired maximum operating speed is reached, thereby overriding the stabilising mechanism and reducing the efficiency of the turbine so that the desired maximum speed is not exceeded. S14 L (ii) To combine high starting torque with high efficiency at operating speeds the amplitude of cyclical 3
3. A mechanism according to claim 2, further comprising a means whereby the preload on the said springs may be released manually while the turbine is at rest or in motion at any speed, such that each governing mass moves outward under the action of centrifugal force and forces the trailing edge of the corresponding blade outwards so it acts as an air brake and prevents the turbine from operating at greater than idling speed.
4. A turbine according to claim 1, in which rollers are provided on the stabiliser mass where it contacts the blade on each side of the pivot point, to provide rolling contact. A self-acting variable pitch vartical axis wind turbine substantially as described herein and with reference to and illustrated in Figs 1 to 5 of the drawings. Dated this 21st day of September 1992, BRIAN KINLOCH KIRKE By his Patent Attorneys R K MADDERN ASSOCIATES i 4 4 r
Applications Claiming Priority (2)
Application Number | Priority Date | Filing Date | Title |
---|---|---|---|
AUPK1335 | 1990-07-24 | ||
AUPK133590 | 1990-07-24 |
Publications (2)
Publication Number | Publication Date |
---|---|
AU7941891A AU7941891A (en) | 1992-07-09 |
AU631500B2 true AU631500B2 (en) | 1992-11-26 |
Family
ID=3774844
Family Applications (1)
Application Number | Title | Priority Date | Filing Date |
---|---|---|---|
AU79418/91A Ceased AU631500B2 (en) | 1990-07-24 | 1991-06-28 | Improved variable pitch vertical axis wind turbine |
Country Status (1)
Country | Link |
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AU (1) | AU631500B2 (en) |
Cited By (3)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
WO2009108714A3 (en) * | 2008-02-25 | 2010-09-30 | Broadstar Developments Lp | Wind driven power generator |
WO2010108120A3 (en) * | 2009-03-20 | 2011-03-31 | Belden Ralph A | Variable area vertical axis wind turbine |
IT201900010479A1 (en) | 2019-06-28 | 2020-12-28 | Windcity Srl | PASSIVE VARIABLE GEOMETRY TURBINE |
Families Citing this family (1)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
TWI668368B (en) * | 2016-11-24 | 2019-08-11 | 伍開明 | Vertical axis wind turbine with automatic adjustment of blade angle |
Citations (2)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
AU5661886A (en) * | 1985-04-04 | 1986-10-23 | Herter Rotor G.m.b.H. | Wind energy converter |
AU1871388A (en) * | 1987-07-06 | 1989-01-12 | Brian Kinloch Kirke | Variable pitch vertical axis wind turbine |
-
1991
- 1991-06-28 AU AU79418/91A patent/AU631500B2/en not_active Ceased
Patent Citations (2)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
AU5661886A (en) * | 1985-04-04 | 1986-10-23 | Herter Rotor G.m.b.H. | Wind energy converter |
AU1871388A (en) * | 1987-07-06 | 1989-01-12 | Brian Kinloch Kirke | Variable pitch vertical axis wind turbine |
Cited By (4)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
WO2009108714A3 (en) * | 2008-02-25 | 2010-09-30 | Broadstar Developments Lp | Wind driven power generator |
WO2010108120A3 (en) * | 2009-03-20 | 2011-03-31 | Belden Ralph A | Variable area vertical axis wind turbine |
IT201900010479A1 (en) | 2019-06-28 | 2020-12-28 | Windcity Srl | PASSIVE VARIABLE GEOMETRY TURBINE |
EP3990776B1 (en) * | 2019-06-28 | 2023-06-07 | WINDCITY Srl | Passive variable geometry turbine |
Also Published As
Publication number | Publication date |
---|---|
AU7941891A (en) | 1992-07-09 |
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MK14 | Patent ceased section 143(a) (annual fees not paid) or expired |