Tapered spiral welded structure

Abstract

A method for creating a tapered spiral welded conical structure where the overall shape of the cone is first graphically slit axially and unwrapped, and then a series of construction arcs and lines are created to form the edge lines of a strip that can then be wrapped (rolled) to form a tapered conical structure. The edges of the spirally wound strip can be welded together, and a very large conical structure can thus be achieved. Various construction options are presented from a constant width strip to strip made from straight segments. Equations are given for the formation of the strips to enable those skilled in the art of spiral welded tubing to practice the invention.

Claims

1. A tower comprising: a sheet formed as a frusto-cone having a base and a top, wherein the base has a first diameter, the top has a second diameter less than the first diameter of the base, the sheet has a first edge and a second edge coupled to one another along a spiral seam extending from the base to the top and centered about a center axis defined by the frusto-cone, the sheet has a plurality of cross-seams intersecting the spiral seam, consecutive cross-seams of the plurality of cross-seams are spaced apart from one another by progressively decreasing distances along the spiral seam in a direction from the base to the top of the frusto-cone, and each cross-seam of the plurality of cross-seams has the same length.

2. The tower of claim 1, wherein the sheet is without in-plane deformation from the base to the top of the frusto-cone.

3. The tower of claim 1, wherein the spiral seam and each cross-seam of the plurality of cross-seams include a weld.

4. The tower of claim 1, wherein the sheet has a maximum width of 2 m.

5. The tower of claim 1, wherein the first diameter of the base is greater than 4.3 m.

6. The tower of claim 1, wherein, in a planar form of the sheet, the first edge and the second edge each include respective straight sections.

7. The tower of claim 6, wherein the first edge includes a first stepped spiral, and the second edge includes a second stepped spiral parallel to the first stepped spiral.

8. The tower of claim 1, wherein the first edge and the second edge overlap one another by a predetermined amount along the spiral seam.

9. The tower of claim 1, wherein the decreasing distances between any two of the consecutive cross-seams of the plurality of cross-seams follows the relationship: $L_n=\sqrt{{\left(\pi D_b\frac{\sin \left(\alpha /2\right)}{\alpha /2}\right)}^2-S_w^2}-S_w\left(1+2n\right)\tan \left(\alpha /2\right)$ where L.sub.n is the distance between an n.sup.th cross-seam and an n.sup.th+1 cross-seam, D.sub.b is the first diameter of the base, S.sub.w is a maximum width of the sheet, and a is an angle, in radians, between equal sides of a triangle in which the equal sides each have a length equal to the cross-seam.

Description

DRAWINGS

(1) The present invention can best be understood in conjunction with the accompanying drawing, in which:

(2) FIG. 1 shows a wind turbine atop of a tapered spiral welded cone;

(3) FIG. 2a shows a cone with one wrap of a sheet to make the cone;

(4) FIG. 2b shows a cone with multiple wraps of a sheet to make the cone;

(5) FIGS. 3a-3d show the steps required to create a strip of material that can wrap in a spiral to form a cone with 3 wraps with the edges of the strip abutting each other so they can be welded together;

(6) FIGS. 4a-4c show different types of strip shapes that can be formed using the generalized method of this invention;

(7) FIG. 5a shows how multiple strips can be formed so a multi-start wrap can be created,

(8) FIG. 5b shows the strip from FIG. 3d that can be wrapped to form a cone with 4 wraps

(9) FIG. 5c shows how the strip to be wrapped to form a cone can also be segmented;

(10) FIG. 6 shows a constant width straight-sides strip (as depicted in FIG. 4a) being constructed where the segments are straight segments with triangular regions cut from between them;

(11) FIG. 7 shows a constant width arc-shape sides strip being constructed where no segments need to be cut from between regions, but the radii of curvature varies;

(12) FIG. 8 shows an involute spiral shape strip at can be formed to wrap into a conical structure;

(13) FIG. 9 shows a logarithmic spiral shape strip that can be formed to wrap into a conical structure;

(14) FIG. 10 shows a graph of the ratio of estimated tower mass versus base diameter (in) fir a standard 80 m wind turbine tower designed to support a 1.5 MW turbine;

(15) FIG. 11 shows a graph of the ratio of estimated tower mass versus base diameter (m) for a standard 100 m wind turbine tower designed to support a 2.5 MW turbine.

PREFERRED EMBODIMENT(S) OF THE INVENTION

(16) FIG. 1 shows a wind turbine 11 atop a tapered tower 10. Such towers are typically manufactured in segments from axially welded steel plate that are transported to site and assembled. This necessitates large bolted flange connections every 20 meters or so and the largest diameter that can be transported is typically 4-4.3 meters, By forming the sections on-site, diameters of 5 meters or more could be formed. Since the bending strength goes with the cube of the diameter, even a 10% increase in diameter represents a 33% increase in strength for only a 10% increase in weight if the same wall thickness structure is used. Going from a 4 meter diameter structure to a 5 meter diameter structure increases the strength by almost 100%. Hence there is a clear need to be able to make large conical towers on site so they can be used to support machines such as wind turbines shown in FIG. 1.

(17) As discussed above, however, there has not been a simple and effective way to accomplish manufacturing of a tapered tower (conical structure) that does not require in-plane deformation of the material by the machine. Machines that could form the large wide strips that would be needed to form a large tower on site would not be practical, unless perhaps installed at a steel mill to operate as the hot wide strip is made, or even economically transportable to a site for creating large towers with base diameters on the order of 5 meters.

(18) In the simplest form, FIG. 2a shows a cone 101 of height h, top diameter Dt and base diameter Db. This conical structure is formed by a single arc segment sheet 100 with a longitudinal joint 99. However, to form the conical section, the sheet must be rolled along its entire length which is not practical for a very large cone. Hence as shown in FIG. 2B a spiral wrap section 103 with spiral joint 102 is preferred to form an equivalent cone 104. The challenge is that the helix angle changes with height if a constant width strip is used, and this then necessitates changing radii of curvature of the strip. The present invention provides a generalized method for determining the geometry of any and all strips that can be wrapped onto the surface of the desired cone without requiring in-plane deformation during the wrapping process.

(19) FIGS. 3a-3d show how the present invention provides a robust method for defining the geometry of a flat strip 35 equivalent to annulus segment 100 that can be rolled to form a conical structure 101. Starting with the desired cone geometry 101, split and unwrap the cone to form a flat wedge-shaped segment 100 of an annulus with a large outside diameter edge (radius R.sub.o) and a smaller inside diameter edge (radius R.sub.i), where the larger diameter edge arc length equals the circumference of the cone base and the smaller diameter edge arc length equals the circumference of the cone top, and straight sides connecting the edges with an angle α between them; hence the parameters R.sub.o, R.sub.i, and α are defined as:

(20) $R_o=\frac{D_b\sqrt{4h^2+{\left(D_b-D_t\right)}^2}}{2\left(D_b-D_t\right)}{R}_i=\frac{D_t\sqrt{4h^2+{\left(D_b-D_t\right)}^2}}{2\left(D_b-D_t\right)}\alpha =\frac{\pi D_b}{R_o}$
Where D.sub.t is the top diameter of the desired cone, D.sub.b is the base diameter, and h is the height of the desired cone.

(21) Draw a construction curve 31, which can be continuous or segmented as may be desired, from a vertex 30a on the edge 28 on the outside arc 27 of radius R.sub.o inward to intersect a construction circle 29 whose radius is equal to and concentric with the inside arc 26 of radius R.sub.i. The angle β between the radial rays passing from the center of the annulus 30c through the start and stop points of the construction curve 31 is equal to the product of the number of desired wraps on the cone and the angle α between the straight sides 28 and 25 of the annulus segment. In FIG. 3b, the angle β is shown to be 3α, and hence the segment 35 in FIG. 3d would make 3 wraps to form a cone. Partial wraps are acceptable.

(22) FIG. 3c shows the next step in the method: copy the construction curve 31 and rotate the copy about the center 30c of the annulus segment by an angle α equal to the angle α between the straight sides 28 and 25 of the flat wedge-shaped segment; and connect the vertices of the original construction curve 31 and the copied curve 32 with arc segments 33 and 27 concentric and with equal radius to the inner and outer annuli radii respectively to form a closed section 35 which can then be wrapped to form the original cone formed by the unwrapped single segment 100.

(23) When forming a cone, the strip must be fed into the coiling system at the correct in-feed angle ϕ, also known as the helix angle. For all strips other than those formed by a logarithmic spiral, shown in FIG. 9, the in-feed angle must vary as the cone is formed. The required in-feed angle can be found on the construction by drawing a radial tine 301 from the point 30c at the center of the annulus to a point 302 on the construction curve. The angle ϕ between the line 303 tangent to the construction curve at this point 302 and radial line 301 is the helix angle of the cone when this section of the strip enters the cone.

(24) Every strip that can be formed into a cone without overlap or in-plane deformation can be found using this construction technique. The geometric properties of the strip are defined by the choice in construction curve 31. There are a number of special cases that may make construction of a strip coiling machine easier.

(25) For example, for most strips the strip in-feed angle must vary during coiling to form the cone. The exception to this is the strip formed from a logarithmic spiral 48 shown in FIG. 9. In polar coordinates this curve is defined as:

(26) $r\left(\theta \right)=e^{\theta \cot \left(\varphi \right)}r=\frac{D_t\pi }{\alpha }.fwdarw.\frac{D_b\pi }{\alpha }$
Where r(θ) is the distance from the center of the annulus 30c to points on the logarithmic spiral construction curve, and θ is the polar angle in radians to these same points measured from an arbitrary zero reference angle. The start and stop points of this curve are defined by the dimensions of the desired cone as defined by D.sub.t, D.sub.b and α. This curve, and a copy of it rotated about the origin by α, form the edges of a curved strip that can be fed into a cone at a constant helix angle ϕ. The strip will not have a constant width as shown in FIG. 4b.

(27) Flaying a non-constant width strip may make material handling more difficult for the cone forming machine, and may result in more wastage of raw materials. There are a number of solutions that result in a constant width strip.

(28) One constant width strip solution can be formed from a series of annular segments as shown in FIG. 7. Each of these annulus segments has an included angle α equal to the included angle of the original construction annulus segment 30. The difference between the inner radius r.sub.i,n and outer radius r.sub.o,n is held fixed allowing these annulus segments to be joined into a long strip with constant width S.sub.w. The inner and outer radii of the n.sup.th segment can be calculated based on the cone dimensions D.sub.t, D.sub.b and α the desired strip width S.sub.w:

(29) $r_{i,n}=\sqrt{{\left(\frac{\pi D_b}{\alpha }\right)}^2-{\left(\frac{S_w}{2\tan \left(\alpha /2\right)}\right)}^2}-S_w\left(1/2+n\right)r_{o,n}=r_{i,n}+S_w$
The initial partial annulus segment 60a is found by setting n to zero, and using this equation to determine the size and shape of the annulus segment. The section of the strip outside of the outside radius construction arc 27 must be removed so that the cone will have a flat base. The next annulus segment 60b is then found by setting n to one and appending this segment to the initial segment. Further segments 60c, 60d, are found by incrementing n by one, until the top of the cone is reached. This results in a constant width strip that can be coiled into the desired cone. The strip will have continuous and smooth edges, but will have step changes in the radius of curvature.

(30) Curved strip metal stock is generally not readily available so solutions that make use of straight strips may be preferred. One solution is a stepped spiral as shown in FIG. 4a. One way to form this shape from a straight strip is to periodically removing triangular sections of material, and rejoin the edges to form the stepped spiral. FIG. 6 shows this strip before the segments are rejoined.

(31) this solution, the triangles removed are all identical isosceles triangles with a height equal to S.sub.w, and with the angle between the equal sides equal to α, the same angle as the included angle in the original construction annulus segment 30. The distance between the n.sup.th and n.sup.th+1 cutout is given by:

(32) $L_n=\sqrt{{\left(\pi D_b\frac{\sin \left(\alpha /2\right)}{\alpha /2}\right)}^2-S_w^2}-S_w\left(1+2n\right)\tan \left(\alpha /2\right)$

(33) Using this geometry, standard strip stock could be used by a spiral welding apparatus to manufacture tapered structures. In addition to the components that comprise a classic cylinder forming machine, said apparatus must also contain a unit capable of removing triangular segments of material, and rejoining the edges, in addition to units capable of continuously changing the feed angle throughout the forming process.

(34) These are just a few examples of the strip geometry that can be used to form a cone. Each has advantages and disadvantages which impact the design of the coiling machine. The stepped spiral has the advantage of using industry standard hot rolled coil stock, but the additional cross-welding step adds to machine cost and complexity and potentially slows the rate at which cones can be formed. If custom strip shapes are formed at the steel mill, then the involute or logarithmic spirals are likely preferable. Selecting between these depends on the difficulty of building a coiling machine with either active in-feed angle control, or variable width strip handling.

(35) FIGS. 4a-4c and FIGS. 5a-5c give further examples of possible strip geometries from a linear tapered strip 42, to a constant curvature tapered strips 46, to triangular segments 47a-47c. Selection of a specific geometry should be guided by the properties of the available materials, and the details of the coiling machine, which vary depending on the cone scale and application.

(36) In some applications, it may be desirable to simultaneously coil multiple strips together to form the cone. This could increase the rate of cone production by allowing multiple welders to run in parallel, and also allows for steeper helix angles for a given strip width. FIG. 5a shows how M multiple strips 45a, 45b, and 45c can be formed by using the previously describe construction technique, but rotating the construction curve 31 by α/M rather than α. M such strips together then wrap to form the cone. In a machine to make conical structures, M narrower strips would thus be used instead of a single strip M times as wide.

(37) Some manufacturing techniques may have trouble forming a strip with step changes in the radius of curvature, so a continuous solution may be desirable. FIG. 8 shows how this shape 47 can be found by taking the previous annulus segment solution, and calculating the curve that results from making the included angle of the segments approach zero. The resulting curve is the involute to a circle centered on the origin 30c with radius equal to S.sub.w/α where α is the included angle of the annulus segment 30 measured in radians. In polar coordinates, this curve is given by:

(38) $r\left(x\right)=\frac{S_w}{\alpha }\sqrt{1+x^2}\theta \left(x\right)={\tan }^{-1}\left(x\right)-x\mathrm{from}x=\sqrt{{\left(\frac{\pi D_t}{S_w}\right)}^2-1}\mathrm{to}x=\sqrt{{\left(\frac{\pi D_b}{S_w}\right)}^2-1}$

(39) Where D.sub.t, D.sub.b, α, and S.sub.w are the previously defined geometric properties of the cone and strip. The edge of the strip is defined by the construction curve in polar coordinates r, and θ (measured in radians). The parameter x determines the distance along the involute spiral. The given bounds on x ensure that the cone starts and stops at the correct diameter. If either of the bounds on x become imaginary, then the given strip width is too large to form the desired cone without cutting or overlap.

(40) Using conical shells with large base diameters as wind turbine towers, as is made possible by the present invention, presents clear economic gains. The results yielded by a simple structural model are exposed as an illustration of this advantage as shown in FIGS. 10 and 11. For specified loads and tower heights from standard wind turbines, the minimum amount of steel is found so that the lowest limit, either material allowable stress or buckling stress, is not reached. The corresponding structure mass is readily obtained. FIGS. 10 and 11 illustrate how, according to this model, tier two different cases, the mass of a wind turbine tower varies with its base diameter.

(41) The reference (100%) is set for a base diameter of 4.3 m since it is the current maximum base diameter for standard towers due to shipping limitations. This curves show that the mass decreases significantly as the base diameter is increased until a certain point. In this region, the tower is designed with a wall thickness large enough for the local stress not to reach the steel maximum allowable stress limit. As the diameter increases, the loads are shared over a larger surface area and the stress decreases. Thus, the walls can be made thinner and the overall mass decreases. If the base diameter is larger than a certain value however, the design driving mechanism changes. The wall thickness reaches a lower limit such that the buckling stress is the lowest stress limit. Thus, the wall thickness cannot be decreased as much anymore and a larger base leads to an increased total mass unless buckling stiffeners are used.

(42) This shows there is an optimal base diameter, unless buckling stiffeners are used, which depends on each specific case. However, for this type of utility scale multi-megawatt wind turbine application, this optimum is much larger than the current 4.3 m. FIG. 11 indicate that a decrease of about 40% in the quantity of steel needed, and hence cost, can be achieved for some common utility scale wind turbines by using large diameter towers. Moreover, this potential gain can be even larger for taller towers or larger wind turbines.

(43) In addition, it could even be an enabling factor in making taller towers than would otherwise not be feasible. Taller towers could turn once marginal sites into high value wind sites and could allow other wind regimes to be reached.

(44) This analysis shows that overcoming transportation limitations and enabling a way to use large base diameter towers is a fundamental need of the wind turbine industry. Current tower manufacture techniques require heavy equipment and fixturing which cannot be made easily transportable. Spiral welding manufacture is better suited for on-site tower manufacture. Current spiral welding machines are incapable of producing the tapered towers required by the wind industry because of the required in-plane curvature. The current invention provides this much needed solution.

(45) Manufacturing a cone from the strips described above may be easier if the strip overlaps itself rather than being joined edge to edge. This also introduces buckling resistance if the helix angle is sufficiently steep as is the case in the multiple strip configurations. If overlap is desired, the strip width must be increased by the desired amount of overlap. Allowing the overlap to vary along the length of the cone may simplify the required strip geometry.

(46) Further modifications of the invention will also occur to persons skilled in the art, and all such are deemed to fall within the spirit and scope of the invention as defined by the appended claims.