CN101090030A - Cutting design method of symmetrical triangle rolling iron core development band of transformer - Google Patents

Abstract

This invention relates to a designing method for saving materials in cutting spread strips of ribbon-wound core of a symmetric triangle structure including: 1, setting up a math model of a ribbon-wound core section and saving materials during setting up the model: A, setting up a math model of the section of the ribbon-wound core, B, saving material during setting up the model, 2, saving material when cutting. This invention uses the algorithm of the model in cores of any round sections such as single-phase, three-phase and three-phase symmetric triangle, if the lamination factor is 0.97, the material thickness is 0.3mm and the cavetto width is 3mm, when the length of the core window of a transformer is 800mm, width is 600mm, the initial width of a core strip is 15mm and the bevel edge width is 12mm, then the usability of the material reaches over 98.6%, and the cross section area of the core is over 98.5% of a around area of the same diameter, further more, the core is divided and cut into four sections only.

Description

Symmetrical triangle energy-economic transformer rolling iron core development band cutting material-saving method for designing

Technical field

The present invention relates to the manufacturing of a kind of transformer volume iron core, especially a kind of method that is used for the rolling iron core development band cutting of three-phase symmetrical triangle round section roll-core transformer.

Background technology

Triangle round section roll-core transformer is the power transformer product of a new generation, the core structure of the stacking type that its core structure is different from the past, from before stacking type develop into present takeup type, for the manufacturing of transformer, qualitative leap to be arranged, and the quality of iron core manufacturing also is very large to the influence of transformer, therefore will have new technical method to be suggested on the iron core tailoring technology.

Transformer with the wider S11 series of the present utilization of comparative maturity day by day is an example, and its iron core mainly contains stacking type and takeup type two classes.Though promote the use of S11 takeup type transformer on a large scale, because the triangularity depressor of novel symmetrical structure and its a great difference structurally will cause and present iron core trimming algorithm and technology directly can not be applied to the triangularity depressor.For the difference of description architecture, will be example with the three-phase day font of S11 series now, illustrate it is coiled iron core equally, why the volume iron core of triangle structure transformer need have breakthrough on algorithm.Compare with regard to its structure below, three-phase day font volume iron core and the schematic cross-section of three-phase triangle volume iron core and the contrast of winding method, as shown in Figure 1, though all be to reel to form as can be seen, but because any two-phase of the volume iron core of triangular structure will constitute 60 ° angle, so any phase iron core is 60 ° of 90 ° of being different from day font as shown in the figure after coiling, so the relation of required strip width of coiling and length is complicated, cuts out being difficult for of also becoming.

At present, the transformer of production triangular structure is obviously not enough on technology and production capacity.On the one hand, the stock utilization aspect does not obtain paying attention to and solving, because the transformer of triangular structure is with respect to traditional transformer, its cutting is more irregular, and want on the original strip of the rectangle of rule can high usage the irregular strip that cuts out be a technological break-through mouth, because the solution of this technology is except bringing considerable economic benefit for the manufacturer, the more important thing is the country energy-conservation as primary strategic objective under, the proposition of its technical scheme also is that very important effect is arranged.On the one hand, the transformer kind of producing is single in addition, and Here it is because complete inadequately on technical know-how.Therefore from the essential structure feature of triangularity depressor, set up out nodal wood type core section model, the algorithmic formula and the material-saving trimming algorithm of the complete material-saving core section of one cover are proposed, concrete actual thing is theorized, systematization, the manufacturer can design the demand that diversified transformer satisfies various users according to this method for designing.

Summary of the invention

The present invention want the technical solution problem be can high usage on the original strip of the rectangle of rule the irregular strip that cuts out, and provide a kind of symmetrical triangle energy-economic transformer rolling iron core development band cutting material-saving method for designing, this methods analyst the triangle stereochemical structure novel transformer the coiling characteristics and optimize volume core section shape, thereby derive the length of the needed strip any time of reeling and the relational expression of width with the reverse thinking method, length according to a phase in the triangular structure tri-phase iron core, width, just can produce the transformer of random capacities (power) according to the resulting data of algorithm, and at the non-systematicness of strip and then the material-saving scheme when making the cutting strip.

Technical scheme of the present invention is: a kind of rolling iron core development band of transformer cutting material-saving method for designing, and its specific design step is as follows:

(1) foundation is rolled up the core section Mathematical Modeling and material-saving in modeling process

The cross section of iron core is made up of a plurality of little rectangles, and rectangle length is the width of silicon steel sheet, and the width of rectangle is the thickness of silicon steel sheet; The iron core strip that cuts out transformer at first will be known the length and the width of the every circle of iron core, and the difference of the length of the bent material of two adjacent rings equates;

(A) set up volume core section Mathematical Modeling:

The center of circle of at first setting up the cross section circle is the coordinate system of round dot, wherein: r: the radius of core section, S _h: the initial width of iron core, E _w: be the termination width of iron core;

The strip segmentation: in the bent material of this section of S → B, along with $x=\stackrel{\mathrm{wx}}{\mathrm{ox}}$ Reduce gradually, the width of bent material smoothly and lentamente increases gradually, and this section of BS is divided into same section strip, and in the process of B → O, along with $x=\stackrel{\mathrm{wx}}{\mathrm{cx}}$ Reduce gradually, the width of bent material smoothly and lentamente reduces gradually,

This section is divided into same section strip, and at the bent material of this section of O → D, along with $x=\stackrel{\mathrm{wx}}{\mathrm{ox}}$ Increase gradually, the width of bent material reduces continuously and apace;

(B) material-saving in the modeling process:

O in the core section ₁d ₁Circular arc in the section makes straight line into, and after substituting circular arc with oblique line, cutting obtains two blocks of same bent material in the square raw material of a block length, suitably selects raw-material length and width, and the material ideal utilance just reaches 100%;

Concrete grammar is: On get 1 C o ₁c ₁And c ₁d ₁Circular arc replace with straight line, choosing that wherein C is ordered will be according to E _mDifference and different, adjust according to the situation of reality, to be target near circular arc as far as possible, so that can when identical section radius, reach big as far as possible area of section;

If will keep the big as far as possible area of a circle also to require to stop width E simultaneously _WAs far as possible little, guaranteeing the maximum area of a circle, but can not be too small, otherwise can cause the waste of strip during cutting, general span is (0.08r～0.1r);

If $x=\stackrel{\mathrm{wx}}{\mathrm{ox}},$ In the bent material of this section of O → C, the width of bent material exists $0\≤x\≤\left|\stackrel{\‾}{\mathrm{OC}}\right|$ Reduce regularly by a slope of determining, in the bent material of this section of C → D, the width of the bent material of this section exists so $\left|\stackrel{\‾}{\mathrm{OC}}\right|\≤x\≤(\sqrt{{4r}^2-{E_W}^2}-\sqrt{3}{E}_W)/4$ Go up by another slope of determining and reduce regularly;

If x is a point on S → D, and $x=\stackrel{\mathrm{wx}}{\mathrm{ox}},$ Draw the width h of bent material _xUnified algorithm on S → D:

$h_x=\left\{\begin{array}{cc}2\&times;\sqrt{r^2-x^2}& (r/2<x<\sqrt{r^2-{S_h}^2/4})\\ \sqrt{3}x+\sqrt{r^2-x^2}& (0\&le;x\&le;r/2)\\ r-\frac{r-\sqrt{r^2-x^2}+\sqrt{3}x}{\left|\stackrel{\&OverBar;}{\mathrm{OC}}\right|}\&times;x& (0\&le;x\&le;|\stackrel{\&OverBar;}{\mathrm{OC}}\left|\right)\\ r-\frac{4(r-E_w)}{\sqrt{{4r}^2-{E_w}^2}-\sqrt{3}{E}_w}\&times;x& \left(\right|\stackrel{\&OverBar;}{\mathrm{OC}}|\&le;x\&le;\frac{\sqrt{{4r}^2-{E_w}^2}-\sqrt{3}{E}_w}{4})\end{array}\right.---\left(1\right)$

(2) material-saving during cutting

According to formula (1), divide

And Four parts superpose the song material by the axis, one side make the straight flange that becomes of bent material; The reduction of antisymmetry formula bent material of the same race on same original strip, the coiling branch of wherein any phase iron core

And

Four parts are carried out, and are equivalent to the initial width of cutting four classes, the most wide degree and length song material all inequality; Or cutting same kind song is expected on same original strip, and wherein, the width of original strip equals two and becomes the maximum of two width sums of 180 ° of symmetries to be with the Seed packaged band type $\{\max (h_{\mathrm{ki}}+\stackrel{\&OverBar;}{h_{\mathrm{ki}}}),K=\mathrm{1,2},,\mathrm{3,4}\},$ The value of K is represented

And

This tetrameric sequence number.

The invention has the beneficial effects as follows:

Method for designing of the present invention can be according to the actual requirements, high usage design needed type.From the practical application angle, one of its advantage, the auxiliary cutting system of iron core that method for designing according to the present invention realizes with the C language, can finish the design of high efficiency, can be fully finish processing to data by computer, if system is embedded in the networked manufacturing platform, that also will have very great significance concerning the networking manufacturing of triangle reel iron core transformer later in the future; Two of advantage is exactly the volume iron core unipolar type for example that the algorithm of formula (1) can be used for any circular section, three-phase day font or the like; From economic benefit, if the lamination coefficient gets 0.97, material thickness is got 0.3mm, and the cavetto width is 3mm, be 800mm when designed transformer core window is long, the iron core window width is 600mm, and the initial width of iron core strip is 15mm, and the value of hypotenuse width is 12mm, the utilance that calculating can draw material can reach more than 98.6%, and the cross-sectional area of volume iron core is more than 98.5% of the same diameter area of a circle, and iron core also only is divided into four sections and comes cutting, has resultant effect preferably.

Description of drawings

Fig. 1 be three-phase day font volume iron core (left side) and the three-phase triangle roll up iron core (right side) cross section and winding method schematic diagram;

Fig. 2 is the schematic diagram after the modeling of triangle round section roll-core transformer core;

Fig. 3 is a triangle round section roll-core transformer core

The song material cutting schematic diagram of part;

Fig. 4 is the song material shape schematic diagram after handling;

Fig. 5 is the schematic diagram of the different bent material of cutting on same original strip;

Fig. 6 is the schematic diagram of the bent material of cutting same kind on same original strip;

Fig. 7 is

Algorithm realization flow figure in the section;

Fig. 8 asks

The program flow diagram of charging width.

Embodiment

Below in conjunction with specific embodiment, further set forth the present invention.Should be understood that these embodiment only to be used to the present invention is described and be not used in and limit the scope of the invention.Should be understood that in addition those skilled in the art can make various changes or modifications the present invention after the content of having read the present invention's instruction, these equivalent form of values fall within the application's appended claims institute restricted portion equally.

Rolling iron core development band of transformer cutting material-saving method for designing of the present invention, its specific design step is as follows:

(1) foundation of volume core section Mathematical Modeling and the material-saving scheme of in modeling process, considering

(A) cross section of the iron core shown in Fig. 1 (right side) is made up of little rectangle one by one, and rectangle length is exactly the width of silicon steel sheet, and the width of rectangle is exactly the thickness of silicon steel sheet.When the steel silicon chip is very thin, when the number of turns is a lot, as long as cutting silicon steel sheet suitably, just can obtain width, thereby make the cross section of iron core reach the shape of expection according to certain rules with the song material of length variations, meet the requirement of manufacturing.So the iron core strip that cuts out transformer will be known the length and the width of the every circle of iron core, the difference of the length of the bent material of two adjacent rings should all equate.

Because strip must have the initial width of an iron core and the termination width of an iron core in the process of design and cutting, so its cross section can only be to be approximately a circle, because the three-phase of iron core is identical, therefore as long as analyze the cross section of a phase wherein, i.e. a semicircle among Fig. 1 (right side).In order better to address this problem a practical problem mathematicization, the coordinate system of setting up the center of circle with Fig. 1 (right side) cross section circle and be round dot as shown in Figure 2.Before deriving, provide the data that will use earlier:

R: the radius of core section, S _h: the initial width of iron core, E _w: be the termination width of iron core, the strip segmentation is considered: in the bent material of this section of S → B, along with $x=\stackrel{\mathrm{wx}}{\mathrm{ox}}$ Reduce gradually, the width of bent material smoothly and lentamente increases gradually, thus can be divided into same section strip to this section of BS, and in the process of B → O, along with $x=\stackrel{\mathrm{wx}}{\mathrm{cx}}$ Reduce gradually, the width of bent material smoothly and lentamente reduces gradually, thus also can This section is divided into same section strip.And at the bent material of this section of O → D, along with $x=\stackrel{\mathrm{wx}}{\mathrm{ox}}$ Increase gradually, the width of bent material reduces continuously and apace.

(B) the material-saving scheme of considering in the modeling process: when iron core is cut out a piece of cloth in a way with the minimum material to make two or more articles of clothing, when the width of song material reduces apace, raw-material utilance is just not high, will waste raw material in a large number like this, in order to save cost, improve the utilance of material, in the design iron core, can do following change, o in the core section ₁d ₁Circular arc in the section makes straight line into, and after substituting circular arc with oblique line, cutting can obtain two blocks of same bent material in the square raw material of a block length, as long as suitably select raw-material length and width, the material ideal utilance just can reach 100%.But at whole section o ₁d ₁Go up with straight line and substitute arc, will cause the serious distortion of cross section circle, to identical core section radius, the sectional area of iron core also will reduce greatly, and this does not meet the requirement that section radius identical in core design requires big as far as possible area of section.

To sum up, can

On get 1 C o ₁c ₁And c ₁d ₁Circular arc replace with straight line, choosing that wherein C is ordered will be according to E _mDifference and different, the designer can adjust according to the situation of reality, to be target near circular arc as far as possible, so that can reach big as far as possible area of section when identical section radius.

If will keep the big as far as possible area of a circle also to require to stop width E simultaneously _WAs far as possible little, guaranteeing the maximum area of a circle, but can not be too small, otherwise can cause the waste of strip during cutting, general span is (0.08r～0.1r).Like this, establish $x=\stackrel{\mathrm{wx}}{\mathrm{ox}},$ In the bent material of this section of O → C, the width of bent material exists $0\&le;x\&le;\left|\stackrel{\&OverBar;}{\mathrm{OC}}\right|$ Reduce regularly by a slope of determining, in the bent material of this section of C → D, the width of the bent material of this section exists so $\left|\stackrel{\&OverBar;}{\mathrm{OC}}\right|\&le;x\&le;(\sqrt{{4r}^2-{E_W}^2}-\sqrt{3}{E}_W)/4$ Go up by another slope of determining and reduce regularly.Introduction above comprehensive is a point on S → D if establish x, and $x=\stackrel{\mathrm{wx}}{\mathrm{ox}},$ So just can draw the width h of bent material _xUnified algorithm on S → D, see formula (1):

$h_x=\left\{\begin{array}{cc}2\&times;\sqrt{r^2-x^2}& (r/2<x<\sqrt{r^2-{S_h}^2/4})\\ \sqrt{3}x+\sqrt{r^2-x^2}& (0\&le;x\&le;r/2)\\ r-\frac{r-\sqrt{r^2-x^2}+\sqrt{3}x}{\left|\stackrel{\&OverBar;}{\mathrm{OC}}\right|}\&times;x& (0\&le;x\&le;|\stackrel{\&OverBar;}{\mathrm{OC}}\left|\right)\\ r-\frac{4(r-E_w)}{\sqrt{{4r}^2-{E_w}^2}-\sqrt{3}{E}_w}\&times;x& \left(\right|\stackrel{\&OverBar;}{\mathrm{OC}}|\&le;x\&le;\frac{\sqrt{{4r}^2-{E_w}^2}-\sqrt{3}{E}_w}{4})\end{array}\right.$ Formula (1)

(2) the material-saving scheme during cutting

What drawn by formula (1) is according to the anti-song material width of releasing of specification requirement and the transformation for mula of length, is to set forth according to after learning bent material length and width relational expression the material-saving scheme during cutting below.According to algorithms 1), here divide

And

Four parts are considered.Tetrameric material-saving principle is identical, here we with Section illustrates, in the circular cross-section tri-phase iron core production process of reality, in the cutting coiling

During the Duan Suoxu strip, if be not added on any measure, because the shape two sides of bent material all is an arc, cutting out track will be as shown in Figure 3, will cause the waste of material during cutting song material.A large amount of silicon steel sheets is taken as waste material and has slatterned.So the design of material-saving is necessary.In order to can be good at saving material, need do some processing.We superpose the song material in design by the axis, as shown in Figure 4.Like this, one side bent material just become straight flange, make things convenient for us in the strip of rectangle, to arrange to open material.And open the cutting bent material of the same race that the material scheme is exactly an antisymmetry formula on same original strip, because the coiling branch of wherein any phase iron core

And

Four parts are carried out, be equivalent to want the initial width of cutting four classes, the most wide degree and length song material all inequality, and according to the different bent waste materials of expecting of scheme cutting on same original strip are obviously many as shown in Figure 5, so take the scheme of the bent material of cutting same kind on same original strip as shown in Figure 6.And after taking scheme shown in Figure 6, the width of the original strip that needs establishment producer buys, this moment, the width of original strip was not the most wide degree that traditional charging width equals bent material, became the maximum of two width sums of 180 ° of symmetries to be with the Seed packaged band type but equal two $\{\max (h_{\mathrm{ki}}+\stackrel{\&OverBar;}{h_{\mathrm{ki}}}),K=\mathrm{1,2},,\mathrm{3,4}\},$ The value of K is represented

And This tetrameric sequence number.H among Fig. 7 _1i,

Represent respectively with W1

The i circle, N ₁The expansion bandwidth of-i-2 circle.

Specific implementation process of the present invention is carried out in two steps:

(1) how obtains the specific embodiments of the needed cutting data of producer's cutting transformer core by the core section model algorithm

As white portion among Fig. 4 is shape after the cutting, and the marginal portion is actual to be zigzag, just that is to say several steps several circles is arranged, what promptly control in any circle of cutting is length, width is constant, and after the Shang Yiquan cutting was intact, the width of next circle changed again.The difference of the length of the bent material of two adjacent rings should all equate, because the coiling radius of two adjacent rings only differs from a constant-the equal thickness of silicon steel sheet.So the length of the bent material of individual pen will constitute an arithmetic progression, wherein tolerance (2 π * d)/a, wherein a is for rolling up the lamination coefficient of iron core, d is the material thickness of silicon steel sheet.Known cavetto width R _h, cavetto radius X _r=(R _h* 2)/and π, the length a of inner ring _s=(L+H) * 2-8X _r+ 4R _h

According to the formula in the algorithms (1) $h_x=2\&times;\sqrt{r^2-x^2}(r/2<x<\sqrt{r^2-{S_m}^2/4})$ Can infer among Fig. 3

The cutting data of section:

$\left\{\begin{array}{c}{h}_{1i}=2\sqrt{r^2-{[\sqrt{r^2-{S_h}^2/4}-(i-1)]}^2}\\ s_{1i}=i\&times;a_s+2\mathrm{\&pi;}\&times;\frac{i(i-1)}{2}\&times;d\end{array}\right.$ Formula (2)

(i represents

The number of turns of part, h _1iExpression

The width of part i circle, S _1iExpression

Strip length during part i circle, i=1,2..., N ₁)

In like manner,

And

The cutting data as follows successively

$\left\{\begin{array}{c}{h}_{2i}=\sqrt{3}(r/2-i\&times;d)+\sqrt{r^2-{(r/2-i\&times;d)}^2}\\ s_{2i}=(i+1)a_s+2\mathrm{\&pi;}\&times;N_1(i+1)\&times;d+2\mathrm{\&pi;}\&times;\frac{i(i+1)}{i}\&times;d\end{array}\right.$ Formula (3)

(i represents

The number of turns of part, h _2iExpression

The width of part i circle, s _2iExpression

Strip length during part i circle, i=1,2..., N ₂)

$\left\{\begin{array}{c}{h}_{3i}=r-\frac{(r-\sqrt{r^2-{(i\&times;d)}^2}+\sqrt{3}\&times;i\&times;d)}{\left|\stackrel{\&OverBar;}{\mathrm{OC}}\right|}\\ s_{3i}=(i+1)a_s+2\mathrm{\&pi;}\&times;({\mathrm{<figure-callout\; id="1"\; label="N"\; filenames="A20071004058100141.png,A20071004058100151.png"\; state="\{\{state\}\}">N</figure-callout>}}_1+N_2)(i+1)\&times;d+2\mathrm{\&pi;}\&times;\frac{i(i+1)}{i}\&times;d\end{array}\right.$ Formula (4)

(i represents

The number of turns of part, h _3iExpression

The width of part i circle, s _3iExpression

Strip length during part i circle, i=1,2..., N ₃)

$\left\{\begin{array}{c}{h}_{4i}=r-\frac{4(r-E_W)}{\sqrt{{4r}^2-{E_W}^2}-\sqrt{3}{E}_W}\&times;\left(\right|\stackrel{\&OverBar;}{\mathrm{OC}}|+i\&times;d)\\ s_{4i}=(i+1)a_s+2\mathrm{\&pi;}\&times;({\mathrm{<figure-callout\; id="1"\; label="N"\; filenames="A20071004058100141.png,A20071004058100151.png"\; state="\{\{state\}\}">N</figure-callout>}}_1+N_2+N_3)(i+1)\&times;d+2\mathrm{\&pi;}\&times;\frac{i(i+1)}{i}\&times;d\end{array}\right.$ Formula (5)

(i represents

The number of turns of part, h _4iExpression

The width of part i circle, s _4iExpression Strip length during part i circle, i=1,2..., N ₄)

Above N ₁, N ₂, N ₃, N ₄Expression respectively

And

The number of turns of this three part, and ${\mathrm{<figure-callout\; id="1"\; label="N"\; filenames="A20071004058100141.png,A20071004058100151.png"\; state="\{\{state\}\}">N</figure-callout>}}_1=\sqrt{r^2-{S_h}^2/4}-r/2,$ N ₂＝r/(2×d)， $N_3=\left|\stackrel{\&OverBar;}{\mathrm{OC}}\right|/d,$ $N_4=(\frac{r}{2}-|\stackrel{\&OverBar;}{\mathrm{OC}}\left|\right)/d.$ Hypotenuse width

Value set its scope arbitrarily (0 ~ r/2) by producer.

The data of cutting strip most critical are length and width, according to formula (2) ~ formula (5), can be easy to draw with C language Do statement the length and the width of each circle, and can simulate the track schematic diagram that shows actual cutting, as Figure 12.Under the software platform of Visual C++6.0, with

Part for example illustrates, other three part can be done according to similar method, is the replacement from formula (2) to formula (5) formula.

........................

for(i＝0；i＜m_n1，i++)

{

s1[i]＝i*m_a+2*pi*i*(i-1)*m_d/2

for(t＝0；t＜1；t+＝0.001)

{

X11＝K2*(i*m_znl+2*pi*0.5*m_d*i*(i-1))；

X12＝K2*((i+1)*m_znl+2*pi*0.5*i*(i+1)*m_d)；

B1.x＝(int)(X11+(X12-X11)*t)；

B1.y＝(int)(2*K1*sqrt(m_r*m_r-(sqrt(m_r*m_r-0.25*m_Sh*m_Sh)-i*m_d)*(

sqrt(m_r*m_r-0.25*m_Sh*m_Sh)-i*m_d)))；

pDC-＞LineTo(B1)；

B＝B1；

pDC-＞MoveTo(B)；

}

}

........................

Attached: K1, K2: be convenient to show on computers the track cut out and according to concrete condition fixed scaled size m_znl: length (this of the inner ring of this segment section

The part be a _sSize), m_d: strip thickness, m_Sh: initial width, m_r: the size of section radius, the number of turns of strip in the m_n1:|SB| section, i: be used for control | the number of turns of SB| section, s1[i] length that is used for storing the i circle, (B1.x, B1.y) for showing the coordinate points of track, what B1.y stored is the width of every circle, t: the demonstration step-length of control dynamic image, B, B1 are the two-dimensional coordinate point that dynamically shows, X11, X12 are the intermediate parameters of program.(i in the read-me starts from scratch and gets).Flow chart such as Fig. 7:

How material-saving scheme during (2) according to the cutting in the summary of the invention (2) realizes that to economize material be cutting out a piece of cloth in a way with the minimum material to make two or more articles of clothing of purpose.

Can derive as shown in the formula (6) ~ formula (9) by summary of the invention (1) and formula (2) ~ formula (5):

$\stackrel{\&OverBar;}{h_{1i}}=2\sqrt{r^2-{[\sqrt{r^2-{S_h}^2/4}-(N_1-i)]}^2}---\left(6\right)$

$\stackrel{\&OverBar;}{h_{2i}}=\sqrt{3}(r/2-(N_2-i)\&times;d)+\sqrt{r^2-{(r/2-(N_2-i)\&times;d)}^2}---\left(7\right)$

$\stackrel{\&OverBar;}{h_{4i}}=r-\frac{4(r-E_W)}{\sqrt{{4r}^2-{E_W}^2}-\sqrt{3}{E}_W}\&times;\left(\right|\stackrel{\&OverBar;}{\mathrm{OC}}|+(N_4-i)\&times;d)---\left(9\right)$

Take the scheme of cutting out a piece of cloth in a way with the minimum material to make two or more articles of clothing of Fig. 6, according to the formula (6) in the summary of the invention (2) ~ formula (9), and then ought { 1≤i≤N with the realization of C language Do statement _K, K=1,2,3, during 4}, try to achieve

Charging width W as the K segment section _K(K=1,2,3,4), K represents

And

This tetrameric sequence number.Below with

Part is an example, and how concrete elaboration realizes the realization of charging width.

..............................

w＝2*(m_r*m_r-(sqr(m_r*m_r-0.25*m_Sh*m_Sh)))+2*sqr(m_r*m_r-(sqr(m_r*m_r-0.25*

m_Sh*m_Sh)-(m_n1-1)))；

for(i＝1；i＜m_n1；i++)

{

w[i]＝2*sqr(m_r*m_r-(sqr(m_r*m_r-0.25*m_Sh*m_Sh)-(i-1))+2*sqr(m_r*m_r-(sqr(m_r*m_r

-0.25*m_Sh*m_Sh)-(m_n1-i))；

if(w[i]＞w[0])

w＝w[i]

}

...............................

Attached: flow chart such as Fig. 8,

The strip total length s of each several part _1i, s _2i, s _3i, s _4i, value is respectively as { 1≤i≤N _K, K=1,2,3, the summing value during 4}.According to formula (2), formula (3), formula (4), the length and width of the strip of each circle of formula (5) can be asked, and the expansion shape of each circle unshakable in one's determination is that square is capable, therefore are easy to obtain the area of the original strip that each circle uses up, again the summation of the developed area of each circle is obtained effective materials area S, then

Be exactly the utilance of each several part is total if the utilance of knowing is right again

And

This tetrameric utilance is sued for peace again.

In sum, be the design implementation scheme of iron core development band.If come the above-mentioned embodiment of specific implementation, can generate the expansion band cutting aided design system of an energy-conservation triangle round section roll-core transformer with program language.

Claims (1)

1. symmetrical triangle energy-economic transformer rolling iron core development band cutting material-saving method for designing, the specific design step is as follows:

(1) foundation is rolled up the core section Mathematical Modeling and material-saving in modeling process

The cross section of iron core is made up of a plurality of little rectangles, and rectangle length is the width of silicon steel sheet, and the width of rectangle is the thickness of silicon steel sheet; The iron core development strip that cuts out transformer at first will be known the length and the width of the every circle of iron core, and the difference of the length of the bent material of two adjacent rings equates;

(A) set up volume core section Mathematical Modeling:

The center of circle of at first setting up the cross section circle is the coordinate system of round dot, wherein: r: the radius of core section, S _h: the initial width of iron core, E _w: be the termination width of iron core;

The strip segmentation: in the bent material of this section of S → B, along with $x=\stackrel{\mathrm{wx}}{\mathrm{ox}}$ Reduce gradually, the width of bent material smoothly and lentamente increases gradually, and this section of BS is divided into same section strip, and in the process of B → O, along with $x=\stackrel{\mathrm{wx}}{\mathrm{cx}}$ Reduce gradually, the width of bent material smoothly and lentamente reduces gradually,

This section is divided into same section strip, and at the bent material of this section of O → D, along with $x=\stackrel{\mathrm{wx}}{\mathrm{ox}}$ Increase gradually, the width of bent material reduces continuously and apace;

(B) material-saving in the modeling process:

O in the core section ₁d ₁Circular arc in the section makes straight line into, and after substituting circular arc with oblique line, cutting obtains two blocks of same bent material in the square raw material of a block length, suitably selects raw-material length and width, and the material ideal utilance just reaches 100%;

Concrete grammar is:

On get 1 C o ₁c ₁And c ₁d ₁Circular arc replace with straight line, choosing that wherein C is ordered will be according to E _mDifference and different, adjust according to the situation of reality, to be target near circular arc as far as possible, so that can when identical section radius, reach big as far as possible area of section;

If will keep the big as far as possible area of a circle also to require to stop width E simultaneously _wAs far as possible little, guaranteeing the maximum area of a circle, but can not be too small, otherwise can cause the waste of strip during cutting, general span is (0.08r～0.1r);

If $x=\stackrel{\mathrm{wx}}{\mathrm{ox}},$ In the bent material of this section of O → C, the width of bent material exists $0\&le;x\&le;\left|\stackrel{\&OverBar;}{\mathrm{OC}}\right|$ Reduce regularly by a slope of determining, in the bent material of this section of C → D, the width of the bent material of this section exists so $\left|\stackrel{\&OverBar;}{\mathrm{OC}}\right|\&le;x\&le;(\sqrt{{4r}^2-{E_W}^2}-\sqrt{3}{E}_W)/4$ Go up by another slope of determining and reduce regularly;

If x is a point on S → D, and $x=\stackrel{\mathrm{wx}}{\mathrm{ox}},$ The width hx that draws bent material unified algorithm on S → D:

$h_x=\left\{\begin{array}{cc}2\&times;\sqrt{r^2-x^2}& (r/2<x<\sqrt{r^2-{S_h}^2/4})\\ \sqrt{3}x+\sqrt{r^2-x^2}& (0\&le;x\&le;r/2)\\ r-\frac{r-\sqrt{r^2-x^2}+\sqrt{3}x}{\left|\stackrel{\&OverBar;}{\mathrm{OC}}\right|}\&times;x& (0\&le;x\&le;|\stackrel{\&OverBar;}{\mathrm{OC}}\left|\right)\\ r-\frac{4(r-E_w)}{\sqrt{4r^2-{E_w}^2}-\sqrt{3}{E}_w}\&times;x& \left(\right|\stackrel{\&OverBar;}{\mathrm{OC}}|\&le;x\&le;\frac{\sqrt{{4r}^2-{E_w}^2}-\sqrt{3}{E}_w}{4})\end{array}\right.---\left(1\right)$

(2) material-saving during cutting

According to formula (1), divide

And

Four parts superpose the song material by the axis, one side make the straight flange that becomes of bent material; The cutting of antisymmetry formula bent material of the same race on same original strip, the coiling branch of wherein any phase iron core

And

Four parts are carried out, and are equivalent to the initial width of cutting four classes, the most wide degree and length song material all inequality; Or cutting same kind song is expected on same original strip, and wherein, the width of original strip equals two and becomes the maximum of two width sums of 180 ° of symmetries to be with the Seed packaged band type $\{\max (h_{\mathrm{ki}}+\stackrel{\&OverBar;}{h_{\mathrm{ki}}}),K=\mathrm{1,2,3,4}\},$ The value of K is represented And This tetrameric sequence number.

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